**3. Compact tunable antenna**

#### **3.1. Introduction**

Over the past years, efforts have been made to design small antennas in the UHF band for handset applications. Because of the convergent trend, limited space is available for each antenna device. For applications like broadcast reception, the antenna should be able to cover 40% of the relative bandwidth from 470 to 702 MHz. Regarding the wavelength at the lowest part of the bandwidth (λ0=638 mm), it is obvious that small antennas are required for such applications.

To meet this requirement, the strategy is to cover the frequency range of such broadband applications using frequency tunable antennas. The basic antenna is then narrow band and the implementation of active devices introduces a frequency tunable ability. From a system point of view, it provides frequency selectable functions, which improve the signal-to-noise ratio. In [20-22], the authors show a compact tuned antenna for mobile applications. In [20,21], varactor diodes have been associated with PIFAs or meander antennas. Radiation patterns and S11 demonstrate the antenna's performances. In [23], an RF switch has been chosen rather than a varactor diode to avoid radiation influence on the device. The received measurement results show the validity of the concept.

In this section, we will consider the theoretical and physical aspects of self-inductance and investigate its effect on the resonance frequency of the MCLA (Monopole Coupled Loop Antenna) [24]. We studied them in order to explain the evolution of size reduction and the radiation pattern. We obtained a 55% reduction in the size of the antenna compared to the initial MCLA.

Finally, we associate a varactor diode with a small modified open-circuit MCLA in order to continuously control the frequency with a DC bias voltage. As a result a desirable frequency in a broadband frequency range covering 470–675 MHz is achieved. Experimental and theoretical results including *S11*, radiation patterns and gain are in good agreement.

#### **3.2. Monopole Coupled Loop Antenna (MCLA)**

In this paragraph, we propose to feed a short circuited printed half loop antenna through an electromagnetic coupling using an arc monopole line [24]. The half loop, short circuited on its both sides, has been associated to an arc monopole fed by a 50Ω SMA connector as described in Figure 22. The antenna has been printed on a dielectric substrate circuit board and mounted above a finite reflector ground plane. The theoretical antenna performances have been computed with CST Microwave Studio Software and compared to measurements. Regarding this first part of the study, we propose a physical explanation of the antenna behavior. Thereafter, parametric studies give additional information and help us to increase our knowledge of this design.

**Figure 22.** Geometry of the proposed antenna

Finally, the change of active monopole geometries has allowed us to increase the gain of the active antenna. It led to the creation of a miniature active antenna with a bandwidth of 130% around 228 MHz, the height of the active antenna is λ/80 at the lowest frequency of the bandwidth. The measured gain is-15.1 dBi at 100 MHz. We have measured a good received

Over the past years, efforts have been made to design small antennas in the UHF band for handset applications. Because of the convergent trend, limited space is available for each antenna device. For applications like broadcast reception, the antenna should be able to cover 40% of the relative bandwidth from 470 to 702 MHz. Regarding the wavelength at the lowest part of the bandwidth (λ0=638 mm), it is obvious that small antennas are required for such

To meet this requirement, the strategy is to cover the frequency range of such broadband applications using frequency tunable antennas. The basic antenna is then narrow band and the implementation of active devices introduces a frequency tunable ability. From a system point of view, it provides frequency selectable functions, which improve the signal-to-noise ratio. In [20-22], the authors show a compact tuned antenna for mobile applications. In [20,21], varactor diodes have been associated with PIFAs or meander antennas. Radiation patterns and S11 demonstrate the antenna's performances. In [23], an RF switch has been chosen rather than a varactor diode to avoid radiation influence on the device. The received measurement results

In this section, we will consider the theoretical and physical aspects of self-inductance and investigate its effect on the resonance frequency of the MCLA (Monopole Coupled Loop Antenna) [24]. We studied them in order to explain the evolution of size reduction and the radiation pattern. We obtained a 55% reduction in the size of the antenna compared to the

Finally, we associate a varactor diode with a small modified open-circuit MCLA in order to continuously control the frequency with a DC bias voltage. As a result a desirable frequency in a broadband frequency range covering 470–675 MHz is achieved. Experimental and

In this paragraph, we propose to feed a short circuited printed half loop antenna through an electromagnetic coupling using an arc monopole line [24]. The half loop, short circuited on its both sides, has been associated to an arc monopole fed by a 50Ω SMA connector as described in Figure 22. The antenna has been printed on a dielectric substrate circuit board and mounted above a finite reflector ground plane. The theoretical antenna performances have been

theoretical results including *S11*, radiation patterns and gain are in good agreement.

signal quality.

128 Progress in Compact Antennas

**3.1. Introduction**

applications.

initial MCLA.

**3. Compact tunable antenna**

show the validity of the concept.

**3.2. Monopole Coupled Loop Antenna (MCLA)**

*R* and *r* are respectively the radii of the half loop and the arc monopole lines, *w1* and *w2* are their widths. *P* is the total length of the arc monopole line and *α* is the angle between its both extremities. The radius (thus the length) of the half loop line will remain constant.

By an optimized choice of the lengths, the widths and the distance between the two lines, it is possible to achieve a broadband solution presented in Figure 23. The antenna has been printed on a Neltec NY9300 substrate (*εr*=3, *h*=0.786 mm, tanδ=0.0023) and above a limited square ground plane (300×300×4 mm3 ).

In this case, *R*=100 mm, *r*=84 mm, *w1*=0.4 mm, *w2*=0.5 mm, *X*=220 mm, *Y*=110 mm, *α*=90° and *P*=132 mm. The return loss and the input impedance of the antenna have been computed. The simulation and measurement have been performed between 200MHz and 800MHz.

The Figure 23 shows a comparison between simulation and measurement with a very good agreement. The measured return loss bandwidth is close to 70MHz (≈15.3%). With this design, we increase three times the bandwidth of the antenna proposed in [25].

On Figure 23.a, the shape of the return loss shows two resonances. The first resonance frequency depends of the λ/2 half loop radiator, whereas the second one has been created by the arc monopole considered as a quarter wavelength conventional monopole. As noticed in reference [26], the electromagnetic coupling between the two parts of the antenna affects the impedance behavior.

To increase our understanding of this antenna, we proceed to theoretical parametric studies. We investigate the dimensions of the ground plane, the length, the width of the arc monopole line, the width of the half-loop line and the distance between the two microstrip lines and we will show the influence of these parameters on the input impedance. In this section, we present just two parameters, the length of the arc monopole and the distance between the two printed lines.

impedance behavior.

between the two printed lines.

reference [26], the electromagnetic coupling between the two parts of the antenna affects the

To increase our understanding of this antenna, we proceed to theoretical parametric studies. We investigate the dimensions of the ground plane, the length, the width of the arc

section, we present just two parameters, the length of the arc monopole and the distance

*3.2.2. Distance between the two printed lines*

(—) *r*=70mm, (----) *r*=84mm, (⋅‧‧) *r*=95mm

loop remains constant.

reduce the size of the MCLA.

**3.3. MCLA loaded by self-inductance**

w2=0.5mm, Y=220mm, Z=110mm, α=90°.

0.2 0.3 0.4 0.5 0.6 0.7 0.8

α = 90°

Frequency (GHz)

3.2.2 Distance between the two printed lines

(a) (b)







0

constant.

On Figure 24(b), we can distinguish these two resonances.

α = 103.7°

α = 133°

In Figure 25, three values of the arc monopole radius *r* have been used to characterize the MCLA. *r* varies from 70 mm to 95 mm and *α* is variable to keep the same length of the arc

In Figure 25, three values of the arc monopole radius r have been used to characterize the

Figure 24. (a) Return losses of the simulated MCLA versus α (b) simulated MCLA input impedances, the

Resonant frequency of the arc monopole

Active Compact Antenna for Broadband Applications

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131

(▬) α= 133°, (-⋅-) α= 103.7°, (⋅⋅⋅) α= 90°,(----) α= 75°, () α= 64.8°.

frequency is varying between 200 and 800MHz.

18

To achieve our first purpose (size reduction of the antenna), we modify the MCLA presented in previous paragraph by loading the short circuit of the half-loop on the left side with a self

The main dimensions of the antenna are listed below: R=100mm, r=84mm, w1=0.4mm,

Figure 25. Simulated MCLA input impedances when the radius of the arc loop is varying between 70mm

() r = 70mm , (----) r = 84mm, (⋅⋅⋅) r = 95mm

**Figure 25.** Simulated MCLA input impedances when the radius of the arc loop is varying between 70mm and 95mm

The resonance frequency of the arc monopole decreases when the radius of this line increases.

A monopole coupled loop antenna (MCLA) has been proposed [24]. A better impedance bandwidth has been obtained by electromagnetic coupling effect between the two microstrip lines (arc monopole+half loop). Its bandwidth is three times wider than the conventional half loop short circuited monopole [25]. In the next paragraph, different techniques will be used to

The resonance frequency of the arc monopole decreases when the radius of this line increases. The best case is for *r*=84mm. These variations demonstrate that the coupling effect is very sensitive to the distance between the half loop and the arc monopole. The resonance of the half

and 95mm (the other parameters are constant), the frequency is varying between 200 and 800MHz.

(the other parameters are constant), the frequency is varying between 200 and 800MHz.

inductance (Figure 26). The ground plane is an infinite one [27].

The best case is for r = 84mm. These variations demonstrate that the coupling effect is very sensitive to the distance between the half loop and the arc monopole. The resonance of the half loop remains

monopole. *R*=100 mm, *w1*=0.4 mm, *w2*=0.5 mm, *P*=132 mm, *X=*220 mm and *Y*=110 mm.

R = 100 mm, w1 = 0.4 mm, w2 = 0.5 mm, P = 132 mm, X = 220 mm and Y = 110 mm.

MCLA. r varies from 70 mm to 95 mm and α is variable to keep the same length of the arc monopole.

been used to calculate the impedance bandwidth (70MHz or 15.3%). In the other case, the lower resonance frequency is too far from the highest one and it introduces a mismatching phenomenon. In Figure 24(a), for α = 103.7°, both resonance frequencies are so close that they seem to be a single one.

<sup>α</sup> = 64.8° <sup>α</sup> = 75°

#### Figure 23. (a) Simulated and measured return losses for the MCLA, (b) Simulated and measured (---) measured, (—) simulated

(---) measured, () simulated **Figure 23.** (a) Simulated and measured return losses for the MCLA, (b) Simulated and measured antenna input impe‐ dances

#### **3.2.1. Length of the arc monopole** *3.2.1. Length of the arc monopole*

antenna input impedances

In Figure 24, we present the input impedance of the MCLA versus α which is the angle between the extremities of the arc monopole. *α* varies from 64.8° to 133°. We notice that there are no modifications on the other half loop parameters. The circles on the curves represent the resonance frequencies of the arc monopole (Figure 24). The resonance of the half loop remains constant (Figure 23). The resonance mode of the arc In Figure 24, we present the input impedance of the MCLA versus α which is the angle between the extremities of the arc monopole. *α* varies from 64.8° to 133°. We notice that there are no modifications on the other half loop parameters. The circles on the curves represent the resonance frequencies of the arc monopole (Figure 24).

monopole decreases when the length of this line increases. The best case is for *α* = 90°, the resonance frequencies of the two lines are quite close and the impedance matching criterion S11 < -10 dB has been used to calculate the impedance bandwidth (70MHz or 15.3%). In the other case, the lower resonance frequency is too far from the highest one and it introduces a mismatching phenomenon. In Figure 24(a), for *α* = 103.7°, both resonance frequencies are so close that they seem to be a single one. On Figure 24(b), we can distinguish these two resonances. The resonance of the half loop remains constant (Figure 23). The resonance mode of the arc monopole decreases when the length of this line increases. The best case is for *α*=90°, the resonance frequencies of the two lines are quite close and the impedance matching criterion S11 <-10 dB has been used to calculate the impedance bandwidth (70MHz or 15.3%). In the other case, the lower resonance frequency is too far from the highest one and it introduces a mismatching phenomenon. In Figure 24(a), for *α*=103.7°, both resonance frequencies are so close that they seem to be a single one. On Figure 24(b), we can distinguish these two reso‐ nances.

the frequency is varying between 200 and 800MHz. (▬) α=133°, (- -) α=103.7°, (⋅‧‧) α=90°,(----) α=75°, (—) α=64.8°.

800MHz.

(▬) *α*= 133°, (--) *α*= 103.7°, () *α*= 90°,(----) *α*= 75°, () *α*= 64.8°. **Figure 24.** (a) Return losses of the simulated MCLA versus α (b) simulated MCLA input impedances, the frequency is varying between 200 and 800MHz.

Figure 25. Simulated MCLA input impedances when the radius of the arc loop is varying between 70mm and 95mm (the other parameters are constant), the frequency is varying between 200 and

The resonance frequency of the arc monopole decreases when the radius of this line increases. The best case is for *r* = 84mm. These variations demonstrate that the coupling

In Figure 25, three values of the arc monopole radius *r* have been used to characterize the MCLA. *r* varies from 70 mm to 95 mm and *α* is variable to keep the same length of the arc monopole. *R* = 100 mm, *w1* = 0.4 mm, *w2* = 0.5 mm, *P* = 132 mm, *X* = 220 mm and *Y* = 110 mm.

**3.2.2. Distance between the two printed lines**

() *r* = 70mm, (----) *r* = 84mm, () *r* = 95mm

Resonant frequency of the arc monopole

#### *3.2.2. Distance between the two printed lines* 3.2.2 Distance between the two printed lines

0.2 0.3 0.4 0.5 0.6 0.7 0.8

α = 90°

Frequency (GHz)

(a) (b)







0

constant.

On Figure 24(b), we can distinguish these two resonances.

α = 103.7°

α = 133°

reference [26], the electromagnetic coupling between the two parts of the antenna affects the

To increase our understanding of this antenna, we proceed to theoretical parametric studies. We investigate the dimensions of the ground plane, the length, the width of the arc monopole line, the width of the half-loop line and the distance between the two microstrip lines and we will show the influence of these parameters on the input impedance. In this section, we present just two parameters, the length of the arc monopole and the distance

(a) (b)

**Figure 23.** (a) Simulated and measured return losses for the MCLA, (b) Simulated and measured antenna input impe‐

200MHz 800MHz

In Figure 24, we present the input impedance of the MCLA versus α which is the angle between the extremities of the arc monopole. *α* varies from 64.8° to 133°. We notice that there are no modifications on the other half loop parameters. The circles on the curves

In Figure 24, we present the input impedance of the MCLA versus α which is the angle between the extremities of the arc monopole. *α* varies from 64.8° to 133°. We notice that there are no modifications on the other half loop parameters. The circles on the curves represent the

The resonance of the half loop remains constant (Figure 23). The resonance mode of the arc monopole decreases when the length of this line increases. The best case is for *α* = 90°, the resonance frequencies of the two lines are quite close and the impedance matching criterion S11 < -10 dB has been used to calculate the impedance bandwidth (70MHz or 15.3%). In the other case, the lower resonance frequency is too far from the highest one and it introduces a mismatching phenomenon. In Figure 24(a), for *α* = 103.7°, both resonance frequencies are so close that they seem to be a single one. On Figure 24(b), we can distinguish these two

The resonance of the half loop remains constant (Figure 23). The resonance mode of the arc monopole decreases when the length of this line increases. The best case is for *α*=90°, the resonance frequencies of the two lines are quite close and the impedance matching criterion S11 <-10 dB has been used to calculate the impedance bandwidth (70MHz or 15.3%). In the other case, the lower resonance frequency is too far from the highest one and it introduces a mismatching phenomenon. In Figure 24(a), for *α*=103.7°, both resonance frequencies are so close that they seem to be a single one. On Figure 24(b), we can distinguish these two reso‐

(a) (b)

Resonant frequency of the arc monopole

Figure 24. (a) Return losses of the simulated MCLA versus α (b) simulated MCLA input impedances,

**Figure 24.** (a) Return losses of the simulated MCLA versus α (b) simulated MCLA input impedances, the frequency is

In Figure 25, three values of the arc monopole radius *r* have been used to characterize the MCLA. *r* varies from 70 mm to 95 mm and *α* is variable to keep the same length of the arc monopole. *R* = 100 mm, *w1* = 0.4 mm, *w2* = 0.5 mm, *P* = 132 mm, *X* = 220 mm and *Y* = 110 mm.

Figure 25. Simulated MCLA input impedances when the radius of the arc loop is varying between 70mm and 95mm (the other parameters are constant), the frequency is varying between 200 and

The resonance frequency of the arc monopole decreases when the radius of this line increases. The best case is for *r* = 84mm. These variations demonstrate that the coupling

the frequency is varying between 200 and 800MHz.

(▬) α=133°, (- -) α=103.7°, (⋅‧‧) α=90°,(----) α=75°, (—) α=64.8°.

() *r* = 70mm, (----) *r* = 84mm, () *r* = 95mm

(▬) *α*= 133°, (--) *α*= 103.7°, () *α*= 90°,(----) *α*= 75°, () *α*= 64.8°.

**3.2.2. Distance between the two printed lines**

0.2 0.3 0.4 0.5 0.6 0.7 0.8 -25

= 90°

 = 103.7° = 133°

Frequency (GHz)

= 64.8° = 75°

represent the resonance frequencies of the arc monopole (Figure 24).

0.2 0.3 0.4 0.5 0.6 0.7 0.8 -25

Frequency (GHz)

Figure 23. (a) Simulated and measured return losses for the MCLA, (b) Simulated and measured

impedance behavior.

between the two printed lines.

antenna input impedances

*3.2.1. Length of the arc monopole*

(---) measured, (—) simulated

130 Progress in Compact Antennas

dances

nances.

resonances.



varying between 200 and 800MHz.

800MHz.

(---) measured, () simulated



**3.2.1. Length of the arc monopole**

resonance frequencies of the arc monopole (Figure 24).

In Figure 25, three values of the arc monopole radius *r* have been used to characterize the MCLA. *r* varies from 70 mm to 95 mm and *α* is variable to keep the same length of the arc monopole. *R*=100 mm, *w1*=0.4 mm, *w2*=0.5 mm, *P*=132 mm, *X=*220 mm and *Y*=110 mm. In Figure 25, three values of the arc monopole radius r have been used to characterize the MCLA. r varies from 70 mm to 95 mm and α is variable to keep the same length of the arc monopole. R = 100 mm, w1 = 0.4 mm, w2 = 0.5 mm, P = 132 mm, X = 220 mm and Y = 110 mm.

Figure 24. (a) Return losses of the simulated MCLA versus α (b) simulated MCLA input impedances, the

been used to calculate the impedance bandwidth (70MHz or 15.3%). In the other case, the lower resonance frequency is too far from the highest one and it introduces a mismatching phenomenon. In Figure 24(a), for α = 103.7°, both resonance frequencies are so close that they seem to be a single one.

<sup>α</sup> = 64.8° <sup>α</sup> = 75°

Figure 25. Simulated MCLA input impedances when the radius of the arc loop is varying between 70mm (—) *r*=70mm, (----) *r*=84mm, (⋅‧‧) *r*=95mm

and 95mm (the other parameters are constant), the frequency is varying between 200 and 800MHz. () r = 70mm , (----) r = 84mm, (⋅⋅⋅) r = 95mm **Figure 25.** Simulated MCLA input impedances when the radius of the arc loop is varying between 70mm and 95mm (the other parameters are constant), the frequency is varying between 200 and 800MHz.

The resonance frequency of the arc monopole decreases when the radius of this line increases. The best case is for r = 84mm. These variations demonstrate that the coupling effect is very sensitive to the distance between the half loop and the arc monopole. The resonance of the half loop remains The resonance frequency of the arc monopole decreases when the radius of this line increases. The best case is for *r*=84mm. These variations demonstrate that the coupling effect is very sensitive to the distance between the half loop and the arc monopole. The resonance of the half loop remains constant.

> A monopole coupled loop antenna (MCLA) has been proposed [24]. A better impedance bandwidth has been obtained by electromagnetic coupling effect between the two microstrip lines (arc monopole+half loop). Its bandwidth is three times wider than the conventional half loop short circuited monopole [25]. In the next paragraph, different techniques will be used to reduce the size of the MCLA.

#### **3.3. MCLA loaded by self-inductance**

18 To achieve our first purpose (size reduction of the antenna), we modify the MCLA presented in previous paragraph by loading the short circuit of the half-loop on the left side with a self inductance (Figure 26). The ground plane is an infinite one [27].

The main dimensions of the antenna are listed below: R=100mm, r=84mm, w1=0.4mm, w2=0.5mm, Y=220mm, Z=110mm, α=90°.

4 mm

The main dimensions of the antenna are listed below: R = 100mm, r = 84mm, w1 = 0.4mm, w2 **Figure 26.** Geometry of the proposed antenna

(equivalent to an open circuit).

= 0.5mm, Y = 220mm, Z = 110mm, α = 90°.

The inductor component used below is an ATC 0805 WL modelled with a parallel RLC device. Simulations have been performed with CST Microwave studio® where the equivalent RLC circuit model has been introduced as lumped components [27]. The inductor component used below is an ATC 0805 WL modelled with a parallel RLC device. Simulations have been performed with CST Microwave studio® where the (a) (b) (c)

225°

315°

180°

 0 (dBi) -10 -20

0°

φ=90°, (b) Eθ in XY-plane θ=90°, (c) (----) Eθ in XZ-plane and (--) Eφ in XZ-plane φ=0°

**Figure 28.** Normalized radiation patterns of the short circuited MCLA (L=0nH). (a) Eθ in YZ-plane φ=90°, (b) Eθ in XY-

For YZ-plane (Figure 28.a), we obtain a dissymmetric shape of radiation pattern due to the arc monopole influence [24]. In XY-plane, the radiation pattern is quasi-omnidirectional. Except the dissymmetry of the radiation pattern in YZ plane, we can notice that the general behavior of the antenna is very close to this provides by a monopole. The gain is equal to 1.8 dBi at 460

This analysis is completed by drawing surface currents on the radiating elements (Figure 29).

Near to the feed point and to the short circuit areas, the surface currents are maximum. It explains that the maximum radiations are obtained for the Eθ in YZ-plane when θ=90°, and for the Eθ in XZ-plane when θ=90° or 270°. In Figure 29, the surface currents become null in z

dBi at 460 MHz.

 0 (dBi) -10 -20

180°

plane θ=90°, (c) (----) Eθ in XZ-plane and (- -) Eφ in XZ-plane φ=0°

225°

315°

270°

45°

135°

90°

270°

0°

29).

MHz.

direction.

z direction.

Z

 

X

X

distribution shifts to the left.

infinite reflector plane short circuits

Y

currents distribution shifts to the left.

Y

Z

j q feed

infinite reflector plane short circuits

**Figure 29.** Schematic of surface currents distribution on radiator elements of short circuited MCLA

Y null

Figure 28. Normalized radiation patterns of the short circuited MCLA (L=0nH). (a) Eθ in YZ-plane

For YZ-plane (Figure 28.a), we obtain a dissymmetric shape of radiation pattern due to the arc monopole influence [24]. In XY-plane, the radiation pattern is quasi-omnidirectional. Except the dissymmetry of the radiation pattern in YZ plane, we can notice that the general behavior of the antenna is very close to this provides by a monopole. The gain is equal to 1.8

45°

135°

90°

270°

225°

315°

 0 (dBi) -10 -20

Active Compact Antenna for Broadband Applications

180°

45°

http://dx.doi.org/10.5772/58839

133

135°

90°

0°

This analysis is completed by drawing surface currents on the radiating elements (Figure

Near to the feed point and to the short circuit areas, the surface currents are maximum. It explains that the maximum radiations are obtained for the Eθ in YZ-plane when θ = 90°, and for the Eθ in XZ-plane when θ = 90° or 270°. In Figure 29, the surface currents become null in

Z

Y null

Figure 29. Schematic of surface currents distribution on radiator elements of short circuited MCLA

By increasing the value of the inductor, the deep null in the radiation pattern in YZ plane disappears and the antenna provides a quasi unidirectional pattern in this plane. This phenomenon could be explained in the Figure 30 where surface currents have been represented when the inductance value is 390 nH. Then, we notice that the half-loop surface currents

By increasing the value of the inductor, the deep null in the radiation pattern in YZ plane disappears and the antenna provides a quasi unidirectional pattern in this plane. This phenomenon could be explained in the Figure 30 where surface currents have been represented when the inductance value is 390 nH. Then, we notice that the half-loop surface

Z

feed

In Figure 27, we present the input impedance of the MCLA loaded versus self inductance value. The self values vary from 0nH (equivalent to short circuit) to an infinite value (equivalent to an open circuit). In Figure 27, we present the input impedance of the MCLA loaded versus self inductance value. The self values vary from 0nH (equivalent to short circuit) to an infinite value

equivalent RLC circuit model has been introduced as lumped components [27].

inductance, (b) Simulated input impedance for the proposed antenna with different values of the self inductance **Figure 27.** (a) Simulated return losses for the proposed antenna with different values of the self inductance, (b) Simu‐ lated input impedance for the proposed antenna with different values of the self inductance

Figure 27. (a) Simulated return losses for the proposed antenna with different values of the self

In Figure 27, for each inductance, we can notice two resonance frequencies. The first one, linked to the arc monopole, remains constant and very close to 450MHz, whatever the self inductor values. The second one linked to the half loop radiator associated to the self inductor decreases from 455MHz to 209MHz. We can also notice that for these resonances, the antenna becomes more and more mismatched when the inductance value increases. In the previous paragraph we have mentioned that the antenna return losses at these resonance frequencies could be matched by modifying the length of the arc monopole. In Figure 27, for each inductance, we can notice two resonance frequencies. The first one, linked to the arc monopole, remains constant and very close to 450MHz, whatever the self inductor values. The second one linked to the half loop radiator associated to the self inductor decreases from 455MHz to 209MHz. We can also notice that for these resonances, the antenna becomes more and more mismatched when the inductance value increases. In the previous paragraph we have mentioned that the antenna return losses at these resonance frequencies could be matched by modifying the length of the arc monopole.

To complete this calculation, we have computed and represented the normalized radiation patterns of the short circuited MCLA (L=0nH) (Figure 28).

φ=90°, (b) Eθ in XY-plane θ=90°, (c) (----) Eθ in XZ-plane and (--) Eφ in XZ-plane φ=0° **Figure 28.** Normalized radiation patterns of the short circuited MCLA (L=0nH). (a) Eθ in YZ-plane φ=90°, (b) Eθ in XYplane θ=90°, (c) (----) Eθ in XZ-plane and (- -) Eφ in XZ-plane φ=0°

Figure 28. Normalized radiation patterns of the short circuited MCLA (L=0nH). (a) Eθ in YZ-plane

For YZ-plane (Figure 28.a), we obtain a dissymmetric shape of radiation pattern due to the

The inductor component used below is an ATC 0805 WL modelled with a parallel RLC device. Simulations have been performed with CST Microwave studio® where the equivalent RLC

The inductor component used below is an ATC 0805 WL modelled with a parallel RLC device. Simulations have been performed with CST Microwave studio® where the

The main dimensions of the antenna are listed below: R = 100mm, r = 84mm, w1 = 0.4mm, w2

inductanceL <sup>Z</sup>

In Figure 27, we present the input impedance of the MCLA loaded versus self inductance value. The self values vary from 0nH (equivalent to short circuit) to an infinite value (equivalent to

In Figure 27, we present the input impedance of the MCLA loaded versus self inductance value. The self values vary from 0nH (equivalent to short circuit) to an infinite value

(a) (b)

Figure 27. (a) Simulated return losses for the proposed antenna with different values of the self inductance, (b) Simulated input impedance for the proposed antenna with different values of the self

In Figure 27, for each inductance, we can notice two resonance frequencies. The first one, linked to the arc monopole, remains constant and very close to 450MHz, whatever the self inductor values. The second one linked to the half loop radiator associated to the self inductor decreases from 455MHz to 209MHz. We can also notice that for these resonances, the antenna becomes more and more mismatched when the inductance value increases. In the previous paragraph we have mentioned that the antenna return losses at these resonance frequencies could be matched by modifying the length of the arc monopole.

In Figure 27, for each inductance, we can notice two resonance frequencies. The first one, linked to the arc monopole, remains constant and very close to 450MHz, whatever the self inductor values. The second one linked to the half loop radiator associated to the self inductor decreases from 455MHz to 209MHz. We can also notice that for these resonances, the antenna becomes more and more mismatched when the inductance value increases. In the previous paragraph we have mentioned that the antenna return losses at these resonance frequencies could be

To complete this calculation, we have computed and represented the normalized radiation

**Figure 27.** (a) Simulated return losses for the proposed antenna with different values of the self inductance, (b) Simu‐

 resonant frequency of the arc monopole

equivalent RLC circuit model has been introduced as lumped components [27].

circuit model has been introduced as lumped components [27].

Y

<sup>r</sup> <sup>w</sup>

short circuits feed

inductanceL <sup>Z</sup>

infinite reflector plane

R

2

<sup>a</sup> Zoom

w1

X

<sup>r</sup> <sup>w</sup>

short circuits feed

Y

Z

 

R

2

Y

X

Z

j q

Y

w1

an open circuit).

L=390nH open circuit L infinite

inductance





0

(equivalent to an open circuit).

4 mm

infinite reflector plane

**Figure 26.** Geometry of the proposed antenna

4 mm

132 Progress in Compact Antennas

Zoom

Figure 26. Geometry of the proposed antenna

= 0.5mm, Y = 220mm, Z = 110mm, α = 90°.

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 -20

L=68nH

Frequency (GHz)

matched by modifying the length of the arc monopole.

patterns of the short circuited MCLA (L=0nH) (Figure 28).

short circuit L=0nH

lated input impedance for the proposed antenna with different values of the self inductance

L=22nH

arc monopole influence [24]. In XY-plane, the radiation pattern is quasi-omnidirectional. Except the dissymmetry of the radiation pattern in YZ plane, we can notice that the general behavior of the antenna is very close to this provides by a monopole. The gain is equal to 1.8 dBi at 460 MHz. This analysis is completed by drawing surface currents on the radiating elements (Figure For YZ-plane (Figure 28.a), we obtain a dissymmetric shape of radiation pattern due to the arc monopole influence [24]. In XY-plane, the radiation pattern is quasi-omnidirectional. Except the dissymmetry of the radiation pattern in YZ plane, we can notice that the general behavior of the antenna is very close to this provides by a monopole. The gain is equal to 1.8 dBi at 460 MHz.

29). This analysis is completed by drawing surface currents on the radiating elements (Figure 29).

Near to the feed point and to the short circuit areas, the surface currents are maximum. It explains that the maximum radiations are obtained for the Eθ in YZ-plane when θ = 90°, and for the Eθ in XZ-plane when θ = 90° or 270°. In Figure 29, the surface currents become null in z direction. Y Near to the feed point and to the short circuit areas, the surface currents are maximum. It explains that the maximum radiations are obtained for the Eθ in YZ-plane when θ=90°, and for the Eθ in XZ-plane when θ=90° or 270°. In Figure 29, the surface currents become null in z direction.

represented when the inductance value is 390 nH. Then, we notice that the half-loop surface

currents distribution shifts to the left. **Figure 29.** Schematic of surface currents distribution on radiator elements of short circuited MCLA

null

Z

By increasing the value of the inductor, the deep null in the radiation pattern in YZ plane disappears and the antenna provides a quasi unidirectional pattern in this plane. This phenomenon could be explained in the Figure 30 where surface currents have been represented when the inductance value is 390 nH. Then, we notice that the half-loop surface currents distribution shifts to the left.

The inductance modifies the equivalent antenna electrical length and we can deduce that the antenna operating wavelength is lower than half a wavelength. In the extreme case, where the self inductance is infinite and equivalent to an open circuit, the open circuited MCLA operating wavelength becomes equal to a quarter wavelength.

The Figure 32 shows the theoretical and the measured return losses and input impedance with

(a) (b)

Figure 33. Normalized radiation patterns at 448 MHz

135°

225°

45°

315°

270°

90°

Eθ YZ plane Eφ XZ plane Eθ in XZ-plane Figure 33. Normalized radiation patterns at 448 MHz (- - -) measured, () simulated As expected, the radiation pattern is quasi unidirectional and the agreement between theory and experience is good. At 448 MHz, the measured and the theoretical gain are respectively 3.8dBi and

180°

While the inductor element is well-known to decrease the antenna resonance frequency, based on MCLA, a theoretical study has been performed to demonstrate the modification of radiating behavior of MCLA loaded with inductance. Thus a modified open circuit MCLA has been proposed. This antenna provides quasi unidirectional radiation pattern and size reduction (55.5%) compare to

As expected, the radiation pattern is quasi unidirectional and the agreement between theory and experience is good. At 448 MHz, the measured and the theoretical gain are respectively

While the inductor element is well-known to decrease the antenna resonance frequency, based on MCLA, a theoretical study has been performed to demonstrate the modification of radiating behavior of MCLA loaded with inductance. Thus a modified open circuit MCLA has been

In this section we present a frequency tunable antenna made with an open circuit Monopole Coupled Loop Antenna (MCLA) associated to a varactor diode [29]. The proposed antenna shows a

We investigate the capability to obtain a frequency tunable antenna with reduced size open circuit MCLA. The antenna resonance frequency is controlled with a varactor diode fed having a DC bias voltage range of [0-5]V. This low voltage requirement made this diode suitable for handset

Performances of tunable antenna have been first investigated using CST® software, substituting the diode by its equivalent circuit. The varactor component used below is a MA4ST2200 from MACOM. The equivalent circuit proposed by the vendor is a series RLC circuit with a parallel capacitance (Figure 34). Cs is the tunable capacitor. The varactor has been characterized using a vector network analyzer and then the equivalent circuit has been obtained through a de-embedding process. In order to keep an operating frequency close to 470 MHz when the DC bias voltage is equal to zero, the parameters of the modified MCLA open circuit have been optimized with the

3.8dBi and 3.9 dBi and the comparison is also good.

35,8% relative bandwidth, covering the [470-675]MHz frequency range.

22

Figure 34. Equivalent circuit model of the varactor diode

(- - -) measured, () simulated

the initial MCLA [24]. The measured gain is high (3.8dBi).

180°

3.9 dBi and the comparison is also good.

3.5 Frequency tunable MCLA

3.8dBi and 3.9 dBi and the comparison is also good.

225°

application.

315°

315°

modified open circuit MCLA.

 0 (dBi) -10 -20

180°

**Figure 33.** Normalized radiation patterns at 448 MHz

0°

270°

270°

(---) measured, (—) simulated

225°

modified open circuit MCLA.

**3.5. Frequency tunable MCLA**

corresponding diode equivalent circuit characteristics.

modified open circuit MCLA.

0 (dBi)

45°

135°

90°

0°



0.4 0.45 0.5 0.55 0.6 -35

Frequency (GHz)

and measured antenna input impedances. (---) measured, () simulated

**Figure 32.** (a) Simulated and measured return losses for the modified open circuit MCLA (b) Simulated and measured

In Figure 33, we present the measured and simulated normalized radiation patterns of the

 0 (dBi) -10 -20

0°

In Figure 33, we present the measured and simulated normalized radiation patterns of the

Figure 32. (a) Simulated and measured return losses for the modified open circuit MCLA (b) Simulated

In Figure 33, we present the measured and simulated normalized radiation patterns of the

0 (dBi)

45°

45°

135°

 0 (dBi) -10 -20

Active Compact Antenna for Broadband Applications

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135

180°

0°

135°

90°

90°

0 (dBi)

180°

225°

315°

270°

45°

135°

90°

0°


0°


315°

270°

225°

Eθ YZ plane Eφ XZ plane Eθ in XZ-plane

180°

225°

135°

315°

90°

45°

270°

As expected, the radiation pattern is quasi unidirectional and the agreement between theory and experience is good. At 448 MHz, the measured and the theoretical gain are respectively

While the inductor element is well-known to decrease the antenna resonance frequency, based on MCLA, a theoretical study has been performed to demonstrate the modification of radiating behavior of MCLA loaded with inductance. Thus a modified open circuit MCLA has been proposed. This antenna provides quasi unidirectional radiation pattern and size reduction (55.5%) compare to the initial MCLA [24]. The measured gain is high (3.8dBi).

a good agreement.



(---) measured, (—) simulated

antenna input impedances.

**Figure 30.** Schematic of surface currents distribution on elements of the MCLA loaded by a 390nH inductance

#### **3.4. Modified open-circuit MCLA**

We keep the case of the modified MCLA with an infinite self inductance [27]. We call this antenna modified open circuit MCLA. As mentioned in the previous paragraph and in [24], we could modify the arc monopole length to enhance the impedance bandwidth. As we wish that the antenna operates at 450MHz, we have optimized the arc monopole length to achieve both impedance matching and size reduction.

In Figure 31, we remind the modified open circuited MCLA design. For practical reasons, the antenna is placed perpendicularly above a limited square ground plane (300mm x 300mm x 4mm).

The main dimensions of the antenna are listed below: R=44.5mm, r=40.5mm, w1=1mm, w2=2mm, Y=100mm, Z=50mm, α=178.5°. The reduction size of the modified antenna is 55.5% compared to the initial MCLA.

**Figure 31.** Geometry of the modified open circuited MCLA

 (a) (b) 0.4 0.45 0.5 0.55 0.6 -35 -30 -25 -20 -15 -10 -5 0 Frequency (GHz) |S11| dB (---) measured, (—) simulated

The Figure 32 shows the theoretical and the measured return losses and input impedance with a good agreement.

and measured antenna input impedances. (---) measured, () simulated **Figure 32.** (a) Simulated and measured return losses for the modified open circuit MCLA (b) Simulated and measured antenna input impedances.

Figure 32. (a) Simulated and measured return losses for the modified open circuit MCLA (b) Simulated

0 (dBi)

180°

225°

315°

270°

45°

135°

90°

0°


While the inductor element is well-known to decrease the antenna resonance frequency, based on MCLA, a theoretical study has been performed to demonstrate the modification of radiating behavior of MCLA loaded with inductance. Thus a modified open circuit MCLA has been proposed. This antenna provides quasi unidirectional radiation pattern and size reduction (55.5%) compare to the initial MCLA [24]. The measured gain is high (3.8dBi).

180°

In Figure 33, we present the measured and simulated normalized radiation patterns of the modified open circuit MCLA. In Figure 33, we present the measured and simulated normalized radiation patterns of the modified open circuit MCLA.

In Figure 33, we present the measured and simulated normalized radiation patterns of the

(---) measured, (—) simulated

application.

The inductance modifies the equivalent antenna electrical length and we can deduce that the antenna operating wavelength is lower than half a wavelength. In the extreme case, where the self inductance is infinite and equivalent to an open circuit, the open circuited MCLA operating

Y

null 390nH

**Figure 30.** Schematic of surface currents distribution on elements of the MCLA loaded by a 390nH inductance

We keep the case of the modified MCLA with an infinite self inductance [27]. We call this antenna modified open circuit MCLA. As mentioned in the previous paragraph and in [24], we could modify the arc monopole length to enhance the impedance bandwidth. As we wish that the antenna operates at 450MHz, we have optimized the arc monopole length to achieve

In Figure 31, we remind the modified open circuited MCLA design. For practical reasons, the antenna is placed perpendicularly above a limited square ground plane (300mm x 300mm x

The main dimensions of the antenna are listed below: R=44.5mm, r=40.5mm, w1=1mm, w2=2mm, Y=100mm, Z=50mm, α=178.5°. The reduction size of the modified antenna is 55.5%

Y

a

r

short circuit

<sup>Z</sup> open circuit

R

w

2

feed

w1

X

Z

j q

Y

feed

Z

infinite reflector plane short circuits

Y

wavelength becomes equal to a quarter wavelength.

Z

j q

X

134 Progress in Compact Antennas

**3.4. Modified open-circuit MCLA**

compared to the initial MCLA.

4mm).

both impedance matching and size reduction.

ground plane

**Figure 31.** Geometry of the modified open circuited MCLA

Eθ YZ plane Eφ XZ plane Eθ in XZ-plane As expected, the radiation pattern is quasi unidirectional and the agreement between theory and experience is good. At 448 MHz, the measured and the theoretical gain are respectively 3.8dBi and **Figure 33.** Normalized radiation patterns at 448 MHz

modified open circuit MCLA.

180°

3.9 dBi and the comparison is also good.

Figure 33. Normalized radiation patterns at 448 MHz (- - -) measured, () simulated While the inductor element is well-known to decrease the antenna resonance frequency, based on MCLA, a theoretical study has been performed to demonstrate the modification of radiating behavior of MCLA loaded with inductance. Thus a modified open circuit MCLA has been proposed. This antenna provides quasi unidirectional radiation pattern and size reduction (55.5%) compare to the initial MCLA [24]. The measured gain is high (3.8dBi). As expected, the radiation pattern is quasi unidirectional and the agreement between theory and experience is good. At 448 MHz, the measured and the theoretical gain are respectively 3.8dBi and 3.9 dBi and the comparison is also good.

As expected, the radiation pattern is quasi unidirectional and the agreement between theory and experience is good. At 448 MHz, the measured and the theoretical gain are respectively 3.8dBi and 3.9 dBi and the comparison is also good. 3.5 Frequency tunable MCLA In this section we present a frequency tunable antenna made with an open circuit Monopole Coupled Loop Antenna (MCLA) associated to a varactor diode [29]. The proposed antenna shows a While the inductor element is well-known to decrease the antenna resonance frequency, based on MCLA, a theoretical study has been performed to demonstrate the modification of radiating behavior of MCLA loaded with inductance. Thus a modified open circuit MCLA has been

We investigate the capability to obtain a frequency tunable antenna with reduced size open circuit MCLA. The antenna resonance frequency is controlled with a varactor diode fed having a DC bias voltage range of [0-5]V. This low voltage requirement made this diode suitable for handset

Performances of tunable antenna have been first investigated using CST® software, substituting the diode by its equivalent circuit. The varactor component used below is a MA4ST2200 from MACOM. The equivalent circuit proposed by the vendor is a series RLC circuit with a parallel capacitance (Figure 34). Cs is the tunable capacitor. The varactor has been characterized using a vector network analyzer and then the equivalent circuit has been obtained through a de-embedding process. In order to keep an operating frequency close to 470 MHz when the DC bias voltage is equal to zero, the parameters of the modified MCLA open circuit have been optimized with the

22

Figure 34. Equivalent circuit model of the varactor diode

**3.5. Frequency tunable MCLA**

corresponding diode equivalent circuit characteristics.

35,8% relative bandwidth, covering the [470-675]MHz frequency range.

proposed. This antenna provides quasi unidirectional radiation pattern and size reduction (55.5%) compare to the initial MCLA [24]. The measured gain is high (3.8dBi).

obtained through a de-embedding process. In order to keep an operating frequency close to 470 MHz when the DC bias voltage is equal to zero, the parameters of the modified MCLA open circuit have been optimized with the corresponding diode equivalent circuit

A sketch of the prototype is reported in Figure 35, including the diode located on the short circuit side of the MCLA (right hand side of the drawing). The antenna has been printed on a Neltec NY9300 circuit board (εr = 3, h = 0.786 mm) and is placed perpendicularly to a square ground plane (300 mm x 300 mm x 4 mm). R and r are the radius of the half loop and the arc monopole lines respectively, w1 and w2 are their widths. α is the angle between the arc monopole extremities. The main dimensions of the antenna are listed below: R = 37.5

The bias circuit used to carry a DC control voltage to the varactor without interfering with the high frequency currents is reported in Figure 35. In order to isolate the DC voltage from RF signal a choke L = 2200 nH, a series resistance 5 kΩ and one chip capacitor (5 nF) are

DC voltage

(a) (b)

Antenna performances for different DC control voltage values obtained with CST software have been compared to measurement results. In Figure 36, good agreement between

Antenna performances for different DC control voltage values obtained with CST software have been compared to measurement results. In Figure 36, good agreement between simulated

(a) (b)


0V


0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 -25

2.5V 1.5V 2V 1V

3.5V 5V

Active Compact Antenna for Broadband Applications

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137

Frequency (GHz)

As depicted in Figure 36, the antenna covers the [470-675] MHz frequency range, which corresponds to a 35,8% relative -10dB adaptation bandwidth. For each resonance, the

As depicted in Figure 36, the antenna covers the [470-675] MHz frequency range, which corresponds to a 35,8% relative-10dB adaptation bandwidth. For each resonance, the corre‐

Normalized radiation patterns comparison for the frequency range extrema values 474MHz and 668MHz, corresponding to 0V and 5V DC order, show as well acceptable agreement. It has to be noticed that the behavior of the antenna radiation patterns in the main planes (YZ and XZ planes) is quasi unidirectional in the entire band. The cross-polarization in the XZplane becomes very low when the resonance frequency increases. The front to back

Normalized radiation patterns comparison for the frequency range extrema values 474MHz and 668MHz, corresponding to 0V and 5V DC order, show as well acceptable agreement. It has to be noticed that the behavior of the antenna radiation patterns in the main planes (YZ and XZ planes) is quasi unidirectional in the entire band. The cross-polarization in the XZplane becomes very low when the resonance frequency increases. The front to back radiation

Good agreement is obtained for simulated and measured maximum gains versus operating frequencies (Figure 37). It has to be underlined that considering the antenna electrical dimensions (λ/17 × λ/8 at 470MHz), a high gain on the whole frequency range is provided,

Good agreement is obtained for simulated and measured maximum gains versus operating frequencies (Figure 37). It has to be underlined that considering the antenna electrical dimen‐ sions (λ/17 × λ/8 at 470MHz), a high gain on the whole frequency range is provided, and

inductance of 2200nH Resistance of 5K

capacitance of 5nF

Figure 35. (a) Geometry of the open circuit MCLA (b) Photography of the antenna prototype

simulated and measured return loss for a few voltage values can be seen.

**Figure 35.** (a) Geometry of the open circuit MCLA (b) Photography of the antenna prototype

mm, r = 34.5 mm, w1 = 1 mm, w2 = 2 mm, Y = 80 mm, Z = 40 mm, α = 43.5°.

characteristics.

used.

2mm

h

<sup>X</sup> <sup>Y</sup> Z 

Figure 34. Equivalent circuit model of the varactor diode

R

short circuit

4 mm

and measured return loss for a few voltage values can be seen.

Figure 36. (a) Simulated and (b) measured return losses

sponding instantaneous bandwidth is more than 10MHz.

level decreases when the resonance frequency increases.

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 -25

1.5v 2v 2.5v 3.5v 5v

**Figure 36.** (a) Simulated and (b) measured return losses

Frequency (GHz)


0v 1v


and especially in the higher band.

especially in the higher band.

Figure 37. Simulated and measured maximum gains

(---) measured () simulated

corresponding instantaneous bandwidth is more than 10MHz.

radiation level decreases when the resonance frequency increases.

varactor diode 2 mm Zoom

Y

w1

r

feed

w2

#### **3.5. Frequency tunable MCLA**

In this section we present a frequency tunable antenna made with an open circuit Monopole Coupled Loop Antenna (MCLA) associated to a varactor diode [29]. The proposed antenna shows a 35,8% relative bandwidth, covering the [470-675]MHz frequency range.

We investigate the capability to obtain a frequency tunable antenna with reduced size open circuit MCLA. The antenna resonance frequency is controlled with a varactor diode fed having a DC bias voltage range of [0-5]V. This low voltage requirement made this diode suitable for handset application.

Performances of tunable antenna have been first investigated using CST® software, substitut‐ ing the diode by its equivalent circuit. The varactor component used below is a MA4ST2200 from MACOM. The equivalent circuit proposed by the vendor is a series RLC circuit with a parallel capacitance (Figure 34). Cs is the tunable capacitor. The varactor has been characterized using a vector network analyzer and then the equivalent circuit has been obtained through a de-embedding process. In order to keep an operating frequency close to 470 MHz when the DC bias voltage is equal to zero, the parameters of the modified MCLA open circuit have been optimized with the corresponding diode equivalent circuit characteristics.

**Figure 34.** Equivalent circuit model of the varactor diode

A sketch of the prototype is reported in Figure 35, including the diode located on the short circuit side of the MCLA (right hand side of the drawing). The antenna has been printed on a Neltec NY9300 circuit board (εr=3, h=0.786 mm) and is placed perpendicularly to a square ground plane (300 mm x 300 mm x 4 mm). R and r are the radius of the half loop and the arc monopole lines respectively, w1 and w2 are their widths. α is the angle between the arc monopole extremities. The main dimensions of the antenna are listed below: R=37.5 mm, r=34.5 mm, w1=1 mm, w2=2 mm, Y=80 mm, Z=40 mm, α=43.5°.

The bias circuit used to carry a DC control voltage to the varactor without interfering with the high frequency currents is reported in Figure 35. In order to isolate the DC voltage from RF signal a choke L=2200 nH, a series resistance 5 kΩ and one chip capacitor (5 nF) are used.

obtained through a de-embedding process. In order to keep an operating frequency close to 470 MHz when the DC bias voltage is equal to zero, the parameters of the modified MCLA open circuit have been optimized with the corresponding diode equivalent circuit

A sketch of the prototype is reported in Figure 35, including the diode located on the short circuit side of the MCLA (right hand side of the drawing). The antenna has been printed on a Neltec NY9300 circuit board (εr = 3, h = 0.786 mm) and is placed perpendicularly to a square ground plane (300 mm x 300 mm x 4 mm). R and r are the radius of the half loop and the arc monopole lines respectively, w1 and w2 are their widths. α is the angle between the arc monopole extremities. The main dimensions of the antenna are listed below: R = 37.5

mm, r = 34.5 mm, w1 = 1 mm, w2 = 2 mm, Y = 80 mm, Z = 40 mm, α = 43.5°.

characteristics.

used.

Figure 34. Equivalent circuit model of the varactor diode

Figure 35. (a) Geometry of the open circuit MCLA (b) Photography of the antenna prototype **Figure 35.** (a) Geometry of the open circuit MCLA (b) Photography of the antenna prototype

Antenna performances for different DC control voltage values obtained with CST software have been compared to measurement results. In Figure 36, good agreement between simulated and measured return loss for a few voltage values can be seen. Antenna performances for different DC control voltage values obtained with CST software have been compared to measurement results. In Figure 36, good agreement between simulated and measured return loss for a few voltage values can be seen.

As depicted in Figure 36, the antenna covers the [470-675] MHz frequency range, which **Figure 36.** (a) Simulated and (b) measured return losses

Figure 36. (a) Simulated and (b) measured return losses

Figure 37. Simulated and measured maximum gains

(---) measured () simulated

proposed. This antenna provides quasi unidirectional radiation pattern and size reduction

In this section we present a frequency tunable antenna made with an open circuit Monopole Coupled Loop Antenna (MCLA) associated to a varactor diode [29]. The proposed antenna

We investigate the capability to obtain a frequency tunable antenna with reduced size open circuit MCLA. The antenna resonance frequency is controlled with a varactor diode fed having a DC bias voltage range of [0-5]V. This low voltage requirement made this diode suitable for

Performances of tunable antenna have been first investigated using CST® software, substitut‐ ing the diode by its equivalent circuit. The varactor component used below is a MA4ST2200 from MACOM. The equivalent circuit proposed by the vendor is a series RLC circuit with a parallel capacitance (Figure 34). Cs is the tunable capacitor. The varactor has been characterized using a vector network analyzer and then the equivalent circuit has been obtained through a de-embedding process. In order to keep an operating frequency close to 470 MHz when the DC bias voltage is equal to zero, the parameters of the modified MCLA open circuit have been

A sketch of the prototype is reported in Figure 35, including the diode located on the short circuit side of the MCLA (right hand side of the drawing). The antenna has been printed on a Neltec NY9300 circuit board (εr=3, h=0.786 mm) and is placed perpendicularly to a square ground plane (300 mm x 300 mm x 4 mm). R and r are the radius of the half loop and the arc monopole lines respectively, w1 and w2 are their widths. α is the angle between the arc monopole extremities. The main dimensions of the antenna are listed below: R=37.5 mm, r=34.5

The bias circuit used to carry a DC control voltage to the varactor without interfering with the high frequency currents is reported in Figure 35. In order to isolate the DC voltage from RF signal a choke L=2200 nH, a series resistance 5 kΩ and one chip capacitor (5 nF) are used.

(55.5%) compare to the initial MCLA [24]. The measured gain is high (3.8dBi).

shows a 35,8% relative bandwidth, covering the [470-675]MHz frequency range.

optimized with the corresponding diode equivalent circuit characteristics.

**Figure 34.** Equivalent circuit model of the varactor diode

mm, w1=1 mm, w2=2 mm, Y=80 mm, Z=40 mm, α=43.5°.

**3.5. Frequency tunable MCLA**

136 Progress in Compact Antennas

handset application.

corresponds to a 35,8% relative -10dB adaptation bandwidth. For each resonance, the corresponding instantaneous bandwidth is more than 10MHz. Normalized radiation patterns comparison for the frequency range extrema values 474MHz and 668MHz, corresponding to 0V and 5V DC order, show as well acceptable agreement. It As depicted in Figure 36, the antenna covers the [470-675] MHz frequency range, which corresponds to a 35,8% relative-10dB adaptation bandwidth. For each resonance, the corre‐ sponding instantaneous bandwidth is more than 10MHz.

has to be noticed that the behavior of the antenna radiation patterns in the main planes (YZ and XZ planes) is quasi unidirectional in the entire band. The cross-polarization in the XZplane becomes very low when the resonance frequency increases. The front to back radiation level decreases when the resonance frequency increases. Good agreement is obtained for simulated and measured maximum gains versus operating frequencies (Figure 37). It has to be underlined that considering the antenna electrical dimensions (λ/17 × λ/8 at 470MHz), a high gain on the whole frequency range is provided, Normalized radiation patterns comparison for the frequency range extrema values 474MHz and 668MHz, corresponding to 0V and 5V DC order, show as well acceptable agreement. It has to be noticed that the behavior of the antenna radiation patterns in the main planes (YZ and XZ planes) is quasi unidirectional in the entire band. The cross-polarization in the XZplane becomes very low when the resonance frequency increases. The front to back radiation level decreases when the resonance frequency increases.

and especially in the higher band. Good agreement is obtained for simulated and measured maximum gains versus operating frequencies (Figure 37). It has to be underlined that considering the antenna electrical dimen‐ sions (λ/17 × λ/8 at 470MHz), a high gain on the whole frequency range is provided, and especially in the higher band.

**Author details**

nes, France

**References**

1479-1484, Dec. 1947.

462-469, July 1975.

pp. 537-539, 1971.

vol 10, issue 22, pp. 462-463, 1974.

Y. Taachouche, M. Abdallah, F. Colombel, G. Le Ray and M. Himdi\*

\*Address all correspondence to: mohamed.himdi@univ-rennes1.fr

Institute of Electronic and Telecommunication of Rennes (IETR), University of Rennes , Ren‐

Active Compact Antenna for Broadband Applications

http://dx.doi.org/10.5772/58839

139

[1] H. A. Wheeler, 'Fundamental limitations of small antennas', Proc. IRE, 35, pp.

[2] H. A. Wheeler, "Small Antennas" IEEE Trans. Antennas Propagat., vol. 23, pp.

[3] Jenshan. Lin, Itoh, T, "Active Integrated Antennas", Microwave Theory and Techni‐

[4] H.H. Meinke. "Transistorized receiving antennas" Institut fur Hochfrequenztechnik

[5] J. R. Copeland, W. J. Robertson, R. J. Verstraete, "Antennafier arrays", Antennas and

[6] F. M. Landstorfer, H. H. Meinke, "Transistorized Microwave Antenna with 1GHz Centre frequency", Microwave Conference, 2nd European, vol 1, pp.1-4, 1971.

[7] Anderson. A, Davies. W, Dawoud. M, Galanakis. D, " Note on Transistor-Fed Active-Array Antennas", Antennas and Propagation, IEEE Transactions on, vol 19, Issue 4,

[8] Ramsdale. P.A, MacLean. T. S. M, "Active Loop-Dipole Aerials", Electrical Engi‐

[9] Rangole. P.K, Saini. S.P.S, "Transistor Configurations in Integrated Transistor Anten‐

[10] Ramsdale. P.A, MacLean. T.S.M, "Active Loop-Dipole Aerials", Electrical Engineers,

[11] Rangole. P.K, Midha. S.S, "Short antenna with active inductance", Electronics Letters,

neers, Proceedings of the Institution of, vol 119, issue 4, pp 423-424, 1972.

Proceedings of the Institution of, vol 118, issue 12, pp. 1698-1710, 1971.

nas", Radio and Electronic Engineer, vol 45, issue 3, 1975.

Propagation, IEEE Transactions on, vol 12, Issue 2, pp. 227-233, Mar 1964.

ques, IEEE Transactions on, vol. 42, issue 12, pp. 2186-2194, Dec 1994.

der Technischen Hochschule, Munchen, November 1967, 99 pages.

(---) measured (—) simulated

**Figure 37.** Simulated and measured maximum gains

#### **3.6. Conclusion**

A varactor-tuned open circuit MCLA has been designed and realized. The aim of this study is to provide a simple technique to sweep the instantaneous bandwidth of the structure from 470 MHz to 675 MHz. The measured maximum gain varies between-1.5dBi to 2.8dBi. In future, this antenna can be miniaturized in order to be included in a terminal mobile. Theoretical and experimental results of S11, radiation patterns and gain have been performed and show good agreement.

#### **3.7. General conclusion**

The objectives of this chapter concern the design and the development of compact active antennas, working on a wide frequency band. We have presented innovative techniques to reduce the antenna size with a wide cover frequency rang. We have demonstrated two solutions; the first one is broadband antenna with very important size reduction and wide bandwidth. The second one is a tunable antenna.

In the first part, the capabilities offered by active antennas for miniaturization by the integra‐ tion of actives components directly on the antenna have been presented and their impact on printed antenna's performances (bandwidth, size reduction, and gain) investigated theoreti‐ cally and experimentally. Regarding the small volume dedicated for antenna in devices, a broadband miniature active antenna operating in the FM band has been presented.

In the second section, a technique of narrowband antennas miniaturization for DVB-H applications has been proposed. Some new designs of miniaturized antennas based on a coupling feeding system have been proposed and fabricated. Thus, these antennas have been associated with varactor diodes in order to achieve frequency tunable antenna.

#### **Author details**

Y. Taachouche, M. Abdallah, F. Colombel, G. Le Ray and M. Himdi\*

\*Address all correspondence to: mohamed.himdi@univ-rennes1.fr

Institute of Electronic and Telecommunication of Rennes (IETR), University of Rennes , Ren‐ nes, France

#### **References**

(---) measured (—) simulated

138 Progress in Compact Antennas

**3.6. Conclusion**

agreement.

**3.7. General conclusion**

**Figure 37.** Simulated and measured maximum gains

bandwidth. The second one is a tunable antenna.

A varactor-tuned open circuit MCLA has been designed and realized. The aim of this study is to provide a simple technique to sweep the instantaneous bandwidth of the structure from 470 MHz to 675 MHz. The measured maximum gain varies between-1.5dBi to 2.8dBi. In future, this antenna can be miniaturized in order to be included in a terminal mobile. Theoretical and experimental results of S11, radiation patterns and gain have been performed and show good

The objectives of this chapter concern the design and the development of compact active antennas, working on a wide frequency band. We have presented innovative techniques to reduce the antenna size with a wide cover frequency rang. We have demonstrated two solutions; the first one is broadband antenna with very important size reduction and wide

In the first part, the capabilities offered by active antennas for miniaturization by the integra‐ tion of actives components directly on the antenna have been presented and their impact on printed antenna's performances (bandwidth, size reduction, and gain) investigated theoreti‐ cally and experimentally. Regarding the small volume dedicated for antenna in devices, a

In the second section, a technique of narrowband antennas miniaturization for DVB-H applications has been proposed. Some new designs of miniaturized antennas based on a coupling feeding system have been proposed and fabricated. Thus, these antennas have been

broadband miniature active antenna operating in the FM band has been presented.

associated with varactor diodes in order to achieve frequency tunable antenna.


[12] Y. Qian, Tatsuo Itoh, "Progress in active integrated antennas and their applications" IEEE transactions on microwave theory and technique, Vol. 46, No. 11, Nov 1998, pp. 1891-1900.

[25] H. Lebbar, "Analyse et conception d'antennes imprimées multifilaires", phd thesis,

Active Compact Antenna for Broadband Applications

http://dx.doi.org/10.5772/58839

141

[26] Z. N. Chen and Y.W.M. Chia, 'Broadband monopole antenna with parasitic planar element', Microwave Opt. Technol. Lett., Vol.27, No. 3, pp. 209-210, Nov. 2000. [27] Abdallah, M.; Colombel, F.; Le Ray, G.; Himdi, M., "Quasi-Unidirectional Radiation Pattern of Monopole Coupled Loop Antenna," *Antennas and Wireless Propagation Let‐*

[28] Taachouche, Y.; Colombel, F.; Himdi, M., "Meandered monopole coupled loop anten‐ na," *Antennas and Propagation (EUCAP), 2012 6th European Conference on*, vol., no., pp.

[29] Abdallah, M.; Le Coq, L.; Colombel, F.; Le Ray, G.; Himdi, M., "Frequency tunable monopole coupled loop antenna with broadside radiation pattern," *Electronics Letters*,

University of Rennes 1, France, october 1994.

*ters, IEEE*, vol.8, no., pp.732,735, 2009.

vol.45, no.23, pp.1149,1151, November 2009.

3005,3008, 26-30 March 2012.


[25] H. Lebbar, "Analyse et conception d'antennes imprimées multifilaires", phd thesis, University of Rennes 1, France, october 1994.

[12] Y. Qian, Tatsuo Itoh, "Progress in active integrated antennas and their applications" IEEE transactions on microwave theory and technique, Vol. 46, No. 11, Nov 1998, pp.

[13] T.S.M MacLean and G. Marris, "Short rang active transmitting antenna with very large height reduction". IEEE. Transactions on antennas and propagation. March

[14] A.P.Anderson, M. Dawoud, "The performance of transistor fed monopoles in active antennas" IEEE transactions on antennas and propagation, Vol:21, issue:3, may 1973,

[15] V. B. Ertürk, R. G. Rojas, and P. Roblin, "Hybrid analysis/design method for active integrated antennas," IEE Proc.-Microw. Antennas Propagat., vol. 146, pp.

[16] P.S. Hall, "Analysis of radiation from active microstrip antennas" Electronics letters,

[17] H. An, B. K. J. C. Nauwelaers, A. R. Van de Capelle, R. G. Bosisio, "A novel measure‐ ment technique for amplifier-type active antennas". Microwave symposium digest,

[18] Taachouche, Y.; Colombel, F.; Himdi, M., "Influence of the transistor location on the behavior of a transistorized printed antenna," *Antennas and Propagation (EUCAP),*

[19] Y. Taachouche, F. Colombel, and M. Himdi, "Very Compact and Broadband Active Antenna for VHF Band Applications," International Journal of Antennas and Propa‐

[20] Nguyen, V.-A., Dao, M.-T., Lim, Y.T., and Park, S.-O.: 'A compact tunable internal antenna for personal communication handsets', IEEE Antennas Wire. Propag. Lett.,

[21] Komulainen, M., Berg, M., Jantunen, H., and Salonen, E.: 'Compact varactor-tuned meander line monopole antenna for DVB-H signal reception', Electron. Lett., 2007,

[22] Yoon, I.-J., Park, S.-H., and Kim, Y.-E.: 'Frequency tunable antenna for mobile TV sig‐

[23] Suzuki, H., Ohba, I., and Minemura, T.: 'Frequency tunable antennas for mobile phone for terrestrial digital TV broadcasting reception'. IEEE AP-S Int. Symp. Dig.,

[24] Abdallah, M.; Colombel, F.; Le Ray, G.; Himdi, M., "Novel Printed Monopole Cou‐ pled Loop Antenna," *Antennas and Wireless Propagation Letters, IEEE*, vol.7, no., pp.

nal reception'. IEEE AP-S Int. Symp. Dig., 2007, pp. 5861–5864

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1891-1900.

140 Progress in Compact Antennas

1975, pp. 286-287.

pp. 371-374.

131-137,1999.

2008, 7, pp. 569–572

43, (24), pp. 1324–1326

221,224, 2008.

Singapore, 2006, pp. 2329–2332.

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IEEE MTT-S international. 1994, Vol3, pp. 1473-1476.

gation, vol. 2012, Article ID 193716, 4 pages, 2012


**Chapter 6**

**Provisional chapter**

**All-Dielectric Optical Nanoantennas**

**All-Dielectric Optical Nanoantennas**

Alexandr E. Krasnok, Pavel A. Belov, Andrey E. Miroshnichenko, Arseniy Kuznetsov, Boris

Antennas are important elements of wireless information communication technologies, along with sources of electromagnetic radiations and their detectors. One can say that antennas are at the heart of modern radio and microwave frequency communications technologies. They are at the front-ends of satellites, cell-phones, laptops and other communicating devices. In radio engineering, antennas refer to devices converting electric and magnetic currents into radio propagating waves and, vice versa, radio waves to currents. Recently, the concept of

**Figure 1.** The basic principles of nanoantenna operation (exemplified by a nanodipole). Near field (a) or waveguide mode (b) transformation into freely propagating optical radiation; Panels (c, d) illustrate a reception regime. The configuration of feeding via a plasmonic waveguide is of great importance for practical applications of nanoantennas, especially for the development of

> ©2012 Krasnok et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted

© 2014 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

use, distribution, and reproduction in any medium, provided the original work is properly cited.

Andrey E. Miroshnichenko, Arseniy I. Kuznetsov,

antennas have been extended to the optical frequency domain [1–9]

wireless communication systems at the nanometer level, i.e., for future photonic chips. [8]

Alexandr E. Krasnok, Pavel A. Belov,

S. Luk'yanchuk and Yuri S. Kivshar1, 2

10.5772/58850

**1. Introduction**

Boris S. Luk'yanchuk and Yuri S. Kivshar

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

#### **All-Dielectric Optical Nanoantennas All-Dielectric Optical Nanoantennas**

Alexandr E. Krasnok, Pavel A. Belov, Andrey E. Miroshnichenko, Arseniy I. Kuznetsov, Boris S. Luk'yanchuk and Yuri S. Kivshar Alexandr E. Krasnok, Pavel A. Belov, Andrey E. Miroshnichenko, Arseniy Kuznetsov, Boris S. Luk'yanchuk and Yuri S. Kivshar1, 2

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

#### **1. Introduction**

10.5772/58850

Antennas are important elements of wireless information communication technologies, along with sources of electromagnetic radiations and their detectors. One can say that antennas are at the heart of modern radio and microwave frequency communications technologies. They are at the front-ends of satellites, cell-phones, laptops and other communicating devices. In radio engineering, antennas refer to devices converting electric and magnetic currents into radio propagating waves and, vice versa, radio waves to currents. Recently, the concept of antennas have been extended to the optical frequency domain [1–9]

**Figure 1.** The basic principles of nanoantenna operation (exemplified by a nanodipole). Near field (a) or waveguide mode (b) transformation into freely propagating optical radiation; Panels (c, d) illustrate a reception regime. The configuration of feeding via a plasmonic waveguide is of great importance for practical applications of nanoantennas, especially for the development of wireless communication systems at the nanometer level, i.e., for future photonic chips. [8]

Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2014 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

©2012 Krasnok et al., licensee InTech. This is an open access chapter distributed under the terms of the

All-Dielectric Optical Nanoantennas 145

converting incident light (optical frequency radiation) into a strongly confined field (see Fig. 1c,d), where an electromagnetic field is concentrated in a small region compared to the wavelength of light. Such fields are characterized by a spatial spectrum consisting mostly of evanescent waves. The confinement region may be of subwavelength dimension, leading to a strongly confined near field. The energy of this field contains contributions from stored and non radiated energy. However, an important particular case of nanoantennas is a device converting optical radiation into waveguide modes, and vice versa, as shown in Fig. 1c,d. In this case, the subwavelength dimension is characterized by the transverse cross section of the strongly confined field region. The longitudinal size of this region (along the waveguide axis) may be optically large, and the electromagnetic energy of the strongly confined field is referred to as expanding. The feeding configuration with a plasmonic waveguide is of great importance for practical applications of nanoantennas, especially for the development of wireless communication systems at the nanometer level, i.e., for future fully optical

Nanoantennas are the most promising area of research in the modern nanooptics due to their ability to bridge the size and impedance mismatch between nanoemitters and free space radiation, as well as manipulate light on the scale smaller than the wavelength of light. Bearing in mind the great variety of sources and detectors of strongly confined optical fields (groups of atoms and molecules, luminescent and fluorescent cells, e.g., viruses and bacteria, sometimes individual molecules, quantum dots, and quantum wires), it is safe to say that the areas of practical applications of nanoantennas in the near future will be commensurate

At present, nanoantennas are used in near-field microscopy and high-resolution biomedical sensors; their application for hyperthermal therapy of skin neoplasms is a matter of the foreseeable future. There are some other potential applications of nanoantennas (see Fig. 2) that we believe to be equally promising, including solar cells [10], molecular and biomedical sensors [11], optical communication [12], and optical tweezers [13]. The variety of applications allows us to argue that the concept of nanoantennas presents a unique example

Thus far, optical antennas have primarily been constructed from metallic materials, which support plasmonic resonances. The main types of plasmonic nanoantennas which have been realized experimentally are presented in Fig. 3. Different types of plasmonic nanoantennas

of the penetration of new physics into various spheres of human activity.

integrated circuits.

**Figure 3.** Main types of plasmonic nanoantennas. [8]

with that of their classical analogs.

**Figure 2.** Plethora of nanoantennas application in modern science. [8]

as a result of the development of a new branch of physics emerged known as nanooptics, which studies the transmission and reception of optical signals by submicron and even nanometer-sized objects.

For nanooptics it is important to efficiently detect and direct the transmitting signals for optical information between nanoelements. The sources and detectors of radiation in nanooptics are nanoelements themselves, their clusters, and even individual molecules (atoms, ions). Nanoobjects functioning as antennas must exhibit high radiation efficiency and directivity.

Nanoantennas, similar to the radiofrequency antennas, are usually divided into two types, transmitting and receiving (see Fig. 1). Figure 1a schematically shows the interaction between a nanoantenna and the near field of an quantum emitter. In this case, the nanoantenna transforms the near field into freely propagating optical radiation, i.e. it is a transmitting nanoantenna. Figure 1c illustrates the operation of a receiving nanoantenna that converts incident radiation into a strongly confined near field.

The energy is usually delivered to a microwave antenna through a waveguide. Such an antenna converts waveguide modes to freely propagating radiation. In the case of optical antennas with their sufficiently small optical size, the waveguide mode must have the subwavelength cross section attainable by using so-called plasmonic waveguides. This type of nanoantenna feeding is depicted schematically in Fig. 1b. According to the reciprocity principle, such a nanoantenna is also capable of transforming incident radiation to plasmonic waveguide modes (see Fig. 1d).

Thus, the transmitting antenna converts a strongly confined field in the optical frequency range created by a certain (weakly emitting or almost non emitting) source into optical radiation (see Fig. 1a,b). Conversely, the receiving nanoantenna is a device efficiently

converting incident light (optical frequency radiation) into a strongly confined field (see Fig. 1c,d), where an electromagnetic field is concentrated in a small region compared to the wavelength of light. Such fields are characterized by a spatial spectrum consisting mostly of evanescent waves. The confinement region may be of subwavelength dimension, leading to a strongly confined near field. The energy of this field contains contributions from stored and non radiated energy. However, an important particular case of nanoantennas is a device converting optical radiation into waveguide modes, and vice versa, as shown in Fig. 1c,d. In this case, the subwavelength dimension is characterized by the transverse cross section of the strongly confined field region. The longitudinal size of this region (along the waveguide axis) may be optically large, and the electromagnetic energy of the strongly confined field is referred to as expanding. The feeding configuration with a plasmonic waveguide is of great importance for practical applications of nanoantennas, especially for the development of wireless communication systems at the nanometer level, i.e., for future fully optical integrated circuits.

**Figure 3.** Main types of plasmonic nanoantennas. [8]

2 Progress in Compact Antennas

**Figure 2.** Plethora of nanoantennas application in modern science. [8]

incident radiation into a strongly confined near field.

nanometer-sized objects.

waveguide modes (see Fig. 1d).

and directivity.

as a result of the development of a new branch of physics emerged known as nanooptics, which studies the transmission and reception of optical signals by submicron and even

For nanooptics it is important to efficiently detect and direct the transmitting signals for optical information between nanoelements. The sources and detectors of radiation in nanooptics are nanoelements themselves, their clusters, and even individual molecules (atoms, ions). Nanoobjects functioning as antennas must exhibit high radiation efficiency

Nanoantennas, similar to the radiofrequency antennas, are usually divided into two types, transmitting and receiving (see Fig. 1). Figure 1a schematically shows the interaction between a nanoantenna and the near field of an quantum emitter. In this case, the nanoantenna transforms the near field into freely propagating optical radiation, i.e. it is a transmitting nanoantenna. Figure 1c illustrates the operation of a receiving nanoantenna that converts

The energy is usually delivered to a microwave antenna through a waveguide. Such an antenna converts waveguide modes to freely propagating radiation. In the case of optical antennas with their sufficiently small optical size, the waveguide mode must have the subwavelength cross section attainable by using so-called plasmonic waveguides. This type of nanoantenna feeding is depicted schematically in Fig. 1b. According to the reciprocity principle, such a nanoantenna is also capable of transforming incident radiation to plasmonic

Thus, the transmitting antenna converts a strongly confined field in the optical frequency range created by a certain (weakly emitting or almost non emitting) source into optical radiation (see Fig. 1a,b). Conversely, the receiving nanoantenna is a device efficiently Nanoantennas are the most promising area of research in the modern nanooptics due to their ability to bridge the size and impedance mismatch between nanoemitters and free space radiation, as well as manipulate light on the scale smaller than the wavelength of light. Bearing in mind the great variety of sources and detectors of strongly confined optical fields (groups of atoms and molecules, luminescent and fluorescent cells, e.g., viruses and bacteria, sometimes individual molecules, quantum dots, and quantum wires), it is safe to say that the areas of practical applications of nanoantennas in the near future will be commensurate with that of their classical analogs.

At present, nanoantennas are used in near-field microscopy and high-resolution biomedical sensors; their application for hyperthermal therapy of skin neoplasms is a matter of the foreseeable future. There are some other potential applications of nanoantennas (see Fig. 2) that we believe to be equally promising, including solar cells [10], molecular and biomedical sensors [11], optical communication [12], and optical tweezers [13]. The variety of applications allows us to argue that the concept of nanoantennas presents a unique example of the penetration of new physics into various spheres of human activity.

Thus far, optical antennas have primarily been constructed from metallic materials, which support plasmonic resonances. The main types of plasmonic nanoantennas which have been realized experimentally are presented in Fig. 3. Different types of plasmonic nanoantennas are designed to perform various tasks. For example dipole nanoantennas [8, 9, 14–16] demonstrate high coefficient of electric field localization, while bowtie nanoantennas [8, 9, 13, 17–24] are broadband; Yagi-Uda type nanoantennas exhibit high directivity which is very useful for optical wireless communications on an optical chip [3, 8, 9, 12, 25–35]. However, despite of a number of advantages of plasmonic nanoantennas associated with their small size and strong localization of the electric field, such nanoantennas have large dissipative losses resulting in low radiation efficiency.

10.5772/58850

All-Dielectric Optical Nanoantennas 147

**Figure 4.** Schematic representation of electric and magnetic field distribution inside a metallic split-ring resonator (a) and a

by external electromagnetic radiation and running inside the SRR produce a transverse oscillating up and down magnetic field in the center of the ring, which simulates an oscillating magnetic dipole. The major interest of these artificial systems is due to their ability to response to a magnetic component of incoming radiation and thus to have a non-unity or even negative magnetic permeability (*µ*) at optical frequencies, which does not exist in nature. This provides possibilities to design unusual material properties such as negative refraction [49–57], cloaking [58, 59], or superlensing [60]. The SRR concept works very well for gigahertz [55–57], terahertz [61, 62] and even near-infrared (few hundreds THz) [63–65] frequencies. However, for shorter wavelengths and in particular for visible spectral range this concept fails due to increasing losses and technological difficulties to fabricate smaller and smaller constituting split-ring elements [64, 66]. Several other designs based on metal nanostructures have been proposed to shift the magnetic resonance wavelength to the visible spectral range [49, 50]. However, all of them are suffering from losses inherent to metals at

An alternative approach to achieve strong magnetic response with low losses is to use nanoparticles made of high-refractive index dielectric materials [53, 67]. As it follows from the exact Mie solution of light scattering by a spherical particle, there is a particular parameter range where strong magnetic dipole resonance can be achieved. Remarkably, for the refractive indices above a certain value there is a well-established hierarchy of magnetic and electric resonances. In contrast to plasmonic particles the first resonance of dielectric nanoparticles is a magnetic dipole resonance, and takes place when the wavelength of light inside the particle equals to the diameter *λ*/*ns* 2*Rs*, where *λ* is a wavelength in a free space, *Rs* and *ns* are the radius and refractive index of spherical particle. Under this condition the polarization of the electric field is anti-parallel at opposite boundaries of the sphere, which gives rise to strong coupling to circulation displacement currents while magnetic field

Below in this section we present the experimental results demonstrating [47] that spherical silicon nanoparticles with sizes in the range from 100 nm to 200 nm have strong magnetic dipole response in the visible spectral range. The scattered ¸SmagneticT light by these ˇ nanoparticles is so strong that it can be easily seen under a dark-field optical microscope. The wavelength of this magnetic resonance can be tuned throughout the whole visible spectral

In article [47] we have chosen silicon (Si) as a material which has high refractive index in the visible spectral range (above 3.8 at 633 nm) on one side and still almost no dissipation losses on the other. Silicon nanorods have attracted considerable attention during the last few years

high-refractive index dielectric nanoparticle (b) at magnetic resonance wavelength. [47]

oscillates up and down in the middle (see Fig. 4b).

range from violet to red by just changing the nanoparticle size.

visible frequencies.

To overcome such limitations, we propose a new type of nanoantennas based on dielectric nanoparticles with a high index dielectric constant [8, 9, 36–44], for example Huygens optical elements and Yagi-Uda nanoantennas [see par.(3)]. Such all-dielectric optical nanoantennas will have low dissipative losses with enhanced magnetic response in the visible. The concept of optical magnetism based on dielectric nanoparticles is presented in the next section. The key for such novel functionalities of high index dielectric nanophotonic elements is the ability of subwavelength dielectric nanoparticles to support simultaneously both electric and magnetic resonances, which can be controlled independently. This type of nanoantennas has several unique features such as low optical losses at the nanoscale and superdirectivity. The concept of all-dielectric nanoantennas has been developed in our original papers [8, 9, 40–42, 45, 46] and also summarized below.

Furthermore all-dielectric nanoantennas allow us achieve the superdirectivity effect. Superdirectivity as a physical concept can be found in textbooks on antennas, however all so far proposed superdirective antennas are not reliably reproducible. More specifically, all previous attempts to achieve superdirectivity of antennas were based on discrete arrays of radiating dipoles with a rather cumbersome distribution of radiating currents over the array. This approach resulted in intrinsic drawbacks of known superdirective arrays ultra-narrowfrequency range, high dissipation, and extreme sensitivity to any disturbance, etc. As a result, no single superdirective antenna was demonstrated up to now. In the context of nanoantennas, which originated from radio frequency antennas a few years ago, superdirectivity has never been discussed. However, superdirectivity would be a very desirable feature in nanophotonics with numerous useful applications. Here we describe [see par.(4)] the superdirectivity effect in a very simple, elegant, and practical way for a nanoparticle with a notch. This approach is able to shape higher-harmonics of the radiation field in such a way that not only superdirectivity of this nanoantennas becomes possible but also a strong subwavelength sensitivity of the radiation pattern to the location of the emitter can be easily realized.

#### **2. Optical magnetism based on dielectric nanoparticles**

It is well known that a pair of oscillating electric charges of opposite signs, know as an oscillating electric dipole, produces electromagnetic radiation at the oscillations frequency [48]. Although, distinct ¸Smagnetic chargesT, or monopoles, have not been observed so far, ˇ magnetic dipoles are very common sources of magnetic field in nature. The field of the magnetic dipole is usually calculated as the limit of a current loop shrinking to a point. Its profile is equivalent to the one of an electric dipole considering that the electric and magnetic fields are exchanged. The most common example of a magnetic dipole radiation is an electromagnetic wave produced by an excited metal split-ring resonator (SRR), which is a basic constituting element of metamaterials (see Fig. 4a) [49–57]. The real currents excited

4 Progress in Compact Antennas

can be easily realized.

losses resulting in low radiation efficiency.

original papers [8, 9, 40–42, 45, 46] and also summarized below.

**2. Optical magnetism based on dielectric nanoparticles**

are designed to perform various tasks. For example dipole nanoantennas [8, 9, 14–16] demonstrate high coefficient of electric field localization, while bowtie nanoantennas [8, 9, 13, 17–24] are broadband; Yagi-Uda type nanoantennas exhibit high directivity which is very useful for optical wireless communications on an optical chip [3, 8, 9, 12, 25–35]. However, despite of a number of advantages of plasmonic nanoantennas associated with their small size and strong localization of the electric field, such nanoantennas have large dissipative

To overcome such limitations, we propose a new type of nanoantennas based on dielectric nanoparticles with a high index dielectric constant [8, 9, 36–44], for example Huygens optical elements and Yagi-Uda nanoantennas [see par.(3)]. Such all-dielectric optical nanoantennas will have low dissipative losses with enhanced magnetic response in the visible. The concept of optical magnetism based on dielectric nanoparticles is presented in the next section. The key for such novel functionalities of high index dielectric nanophotonic elements is the ability of subwavelength dielectric nanoparticles to support simultaneously both electric and magnetic resonances, which can be controlled independently. This type of nanoantennas has several unique features such as low optical losses at the nanoscale and superdirectivity. The concept of all-dielectric nanoantennas has been developed in our

Furthermore all-dielectric nanoantennas allow us achieve the superdirectivity effect. Superdirectivity as a physical concept can be found in textbooks on antennas, however all so far proposed superdirective antennas are not reliably reproducible. More specifically, all previous attempts to achieve superdirectivity of antennas were based on discrete arrays of radiating dipoles with a rather cumbersome distribution of radiating currents over the array. This approach resulted in intrinsic drawbacks of known superdirective arrays ultra-narrowfrequency range, high dissipation, and extreme sensitivity to any disturbance, etc. As a result, no single superdirective antenna was demonstrated up to now. In the context of nanoantennas, which originated from radio frequency antennas a few years ago, superdirectivity has never been discussed. However, superdirectivity would be a very desirable feature in nanophotonics with numerous useful applications. Here we describe [see par.(4)] the superdirectivity effect in a very simple, elegant, and practical way for a nanoparticle with a notch. This approach is able to shape higher-harmonics of the radiation field in such a way that not only superdirectivity of this nanoantennas becomes possible but also a strong subwavelength sensitivity of the radiation pattern to the location of the emitter

It is well known that a pair of oscillating electric charges of opposite signs, know as an oscillating electric dipole, produces electromagnetic radiation at the oscillations frequency [48]. Although, distinct ¸Smagnetic chargesT, or monopoles, have not been observed so far, ˇ magnetic dipoles are very common sources of magnetic field in nature. The field of the magnetic dipole is usually calculated as the limit of a current loop shrinking to a point. Its profile is equivalent to the one of an electric dipole considering that the electric and magnetic fields are exchanged. The most common example of a magnetic dipole radiation is an electromagnetic wave produced by an excited metal split-ring resonator (SRR), which is a basic constituting element of metamaterials (see Fig. 4a) [49–57]. The real currents excited

**Figure 4.** Schematic representation of electric and magnetic field distribution inside a metallic split-ring resonator (a) and a high-refractive index dielectric nanoparticle (b) at magnetic resonance wavelength. [47]

by external electromagnetic radiation and running inside the SRR produce a transverse oscillating up and down magnetic field in the center of the ring, which simulates an oscillating magnetic dipole. The major interest of these artificial systems is due to their ability to response to a magnetic component of incoming radiation and thus to have a non-unity or even negative magnetic permeability (*µ*) at optical frequencies, which does not exist in nature. This provides possibilities to design unusual material properties such as negative refraction [49–57], cloaking [58, 59], or superlensing [60]. The SRR concept works very well for gigahertz [55–57], terahertz [61, 62] and even near-infrared (few hundreds THz) [63–65] frequencies. However, for shorter wavelengths and in particular for visible spectral range this concept fails due to increasing losses and technological difficulties to fabricate smaller and smaller constituting split-ring elements [64, 66]. Several other designs based on metal nanostructures have been proposed to shift the magnetic resonance wavelength to the visible spectral range [49, 50]. However, all of them are suffering from losses inherent to metals at visible frequencies.

An alternative approach to achieve strong magnetic response with low losses is to use nanoparticles made of high-refractive index dielectric materials [53, 67]. As it follows from the exact Mie solution of light scattering by a spherical particle, there is a particular parameter range where strong magnetic dipole resonance can be achieved. Remarkably, for the refractive indices above a certain value there is a well-established hierarchy of magnetic and electric resonances. In contrast to plasmonic particles the first resonance of dielectric nanoparticles is a magnetic dipole resonance, and takes place when the wavelength of light inside the particle equals to the diameter *λ*/*ns* 2*Rs*, where *λ* is a wavelength in a free space, *Rs* and *ns* are the radius and refractive index of spherical particle. Under this condition the polarization of the electric field is anti-parallel at opposite boundaries of the sphere, which gives rise to strong coupling to circulation displacement currents while magnetic field oscillates up and down in the middle (see Fig. 4b).

Below in this section we present the experimental results demonstrating [47] that spherical silicon nanoparticles with sizes in the range from 100 nm to 200 nm have strong magnetic dipole response in the visible spectral range. The scattered ¸SmagneticT light by these ˇ nanoparticles is so strong that it can be easily seen under a dark-field optical microscope. The wavelength of this magnetic resonance can be tuned throughout the whole visible spectral range from violet to red by just changing the nanoparticle size.

In article [47] we have chosen silicon (Si) as a material which has high refractive index in the visible spectral range (above 3.8 at 633 nm) on one side and still almost no dissipation losses on the other. Silicon nanorods have attracted considerable attention during the last few years

All-Dielectric Optical Nanoantennas 149

each resonance maximum. This analysis was done for each particle size in Fig. 6 and corresponding multipole contributions were identified (see notations in the experimental and theoretical spectra). According to this analysis the first strongest resonance of these nanoparticles appearing in the longer wavelength part of the spectrum corresponds to magnetic dipole response (md). Electric field inside the particle at this resonance wavelength

**Figure 6.** Close-view dark-field microscope (i) and SEM (ii) images of the single nanoparticles selected in Fig. 5. Figures (a) to (f) correspond to nanoparticles 1 to 6 from Fig. 5 respectively. (iii) Experimental dark-field scattering spectra of the nanoparticles. (iv) Theoretical scattering and extinction spectra calculated by Mie theory for spherical silicon nanoparticles of different sizes in

free space. Corresponding nanoparticle sizes are defined from the SEM images (ii) and noted in each figure. [47]

**Figure 5.** Dark-field microscope (a) and top-view scanning electron microscope (SEM) (b) images of the same area on a silicon wafer ablated by a femtosecond laser. Microscope image is inverted in horizontal direction relative to that of the SEM. Selected nanoparticles are marked by corresponding numbers 1 to 6 in both figures. [47]

due to their ability to change their visible color with the size [68]. This effect appears due to excitation of particular modes inside the cylindrical silicon nanoresonators. Moreover, recent theoretical work predicted that spherical silicon nanoparticles with sizes of a few/several hundred nanometers should have both strong magnetic and electric dipole resonances in the visible and near-IR spectral range [69, 70]. To fabricate the silicon nanoparticles we have used the laser ablation technique, which is an efficient method to produce nanoparticles of various materials and sizes [71]. Nanoparticles produced by the ablation method can be localized on a substrate and measured separately from each other using single nanoparticle spectroscopy.

Dark-field microscopic image of a silicon sample ablated by a focused femtosecond laser beam is shown in Fig. 5a. It shines by all the colours of the rainbow from violet to red. To clarify the origin of this strong scattering we selected some nanoobjects shining with different colours on the sample (see Fig. 5a) and measured their scattering spectra by single nanoparticle dark-field spectroscopy. Then, the same sample area was characterized by scanning electron microscopy and the selected nanoobjects providing different colours have been identified (see Fig. 5b, the dark-field microscope image is inverted in horizontal direction relative to that of the SEM). The results of this comparative analysis of the same nanoobjects by dark-field optical microscopy, dark-field scattering spectroscopy, and scanning electron microscopy are presented in Fig. 6. As it can be seen from the SEM images the observed colours are provided by silicon nanoparticles of almost perfect spherical shape and varied sizes. This makes it possible to analyze scattering properties of these nanoparticles in the frames of Mie theory [72] and identify the nature of optical resonances observed in our spectral measurements. The bottom panels (iv) in Fig. 6 represent a total extinction cross-section calculated using Mie theory [72] for silicon nanoparticles of different sizes (the calculations were done in free space). In these calculations, the size of the nanoparticles in each figure was chosen to be similar to the size defined from each corresponding SEM image (ii). It can be seen that there is a clear correlation between the experimental (iii) and theoretical spectra (iv) both in the number and position of the observed resonances. This makes it obvious that Mie theory describes more or less accurately our experimental results.

One of the main advantages of the analytical Mie solution compared to other computational methods is its ability to split the observed spectra into separate contributions of different multipole modes and have a clear picture of the field distribution inside the particle at

each resonance maximum. This analysis was done for each particle size in Fig. 6 and corresponding multipole contributions were identified (see notations in the experimental and theoretical spectra). According to this analysis the first strongest resonance of these nanoparticles appearing in the longer wavelength part of the spectrum corresponds to magnetic dipole response (md). Electric field inside the particle at this resonance wavelength

6 Progress in Compact Antennas

spectroscopy.

experimental results.

**Figure 5.** Dark-field microscope (a) and top-view scanning electron microscope (SEM) (b) images of the same area on a silicon wafer ablated by a femtosecond laser. Microscope image is inverted in horizontal direction relative to that of the SEM. Selected

due to their ability to change their visible color with the size [68]. This effect appears due to excitation of particular modes inside the cylindrical silicon nanoresonators. Moreover, recent theoretical work predicted that spherical silicon nanoparticles with sizes of a few/several hundred nanometers should have both strong magnetic and electric dipole resonances in the visible and near-IR spectral range [69, 70]. To fabricate the silicon nanoparticles we have used the laser ablation technique, which is an efficient method to produce nanoparticles of various materials and sizes [71]. Nanoparticles produced by the ablation method can be localized on a substrate and measured separately from each other using single nanoparticle

Dark-field microscopic image of a silicon sample ablated by a focused femtosecond laser beam is shown in Fig. 5a. It shines by all the colours of the rainbow from violet to red. To clarify the origin of this strong scattering we selected some nanoobjects shining with different colours on the sample (see Fig. 5a) and measured their scattering spectra by single nanoparticle dark-field spectroscopy. Then, the same sample area was characterized by scanning electron microscopy and the selected nanoobjects providing different colours have been identified (see Fig. 5b, the dark-field microscope image is inverted in horizontal direction relative to that of the SEM). The results of this comparative analysis of the same nanoobjects by dark-field optical microscopy, dark-field scattering spectroscopy, and scanning electron microscopy are presented in Fig. 6. As it can be seen from the SEM images the observed colours are provided by silicon nanoparticles of almost perfect spherical shape and varied sizes. This makes it possible to analyze scattering properties of these nanoparticles in the frames of Mie theory [72] and identify the nature of optical resonances observed in our spectral measurements. The bottom panels (iv) in Fig. 6 represent a total extinction cross-section calculated using Mie theory [72] for silicon nanoparticles of different sizes (the calculations were done in free space). In these calculations, the size of the nanoparticles in each figure was chosen to be similar to the size defined from each corresponding SEM image (ii). It can be seen that there is a clear correlation between the experimental (iii) and theoretical spectra (iv) both in the number and position of the observed resonances. This makes it obvious that Mie theory describes more or less accurately our

One of the main advantages of the analytical Mie solution compared to other computational methods is its ability to split the observed spectra into separate contributions of different multipole modes and have a clear picture of the field distribution inside the particle at

nanoparticles are marked by corresponding numbers 1 to 6 in both figures. [47]

**Figure 6.** Close-view dark-field microscope (i) and SEM (ii) images of the single nanoparticles selected in Fig. 5. Figures (a) to (f) correspond to nanoparticles 1 to 6 from Fig. 5 respectively. (iii) Experimental dark-field scattering spectra of the nanoparticles. (iv) Theoretical scattering and extinction spectra calculated by Mie theory for spherical silicon nanoparticles of different sizes in free space. Corresponding nanoparticle sizes are defined from the SEM images (ii) and noted in each figure. [47]

has a ring shape while magnetic field oscillates in the particle center. Magnetic dipole resonance is the only peak observed for the smallest nanoparticles (see Fig. 6a). At increased nanoparticle size (see Fig. 6b,c) electric dipole (ed) resonance also appears at the blue part of the spectra, while magnetic dipole shifts to the red. For relatively small nanoparticles, the observed colour is mostly defined by the strongest resonance peak and changes from blue to green, yellow, and red when magnetic resonance wavelength shifts from 480 nm to 700 nm (see Fig. 6aUd). So, we can conclude that the beautiful colours observed in the ˝ dark field microscope (see Fig. 5a) correspond to magnetic dipole scattering of the silicon nanoparticles, ¸Smagnetic lightT. Further increase of the nanoparticle size leads to the shift of ˇ magnetic and electric dipole resonances further to the red and infra-red frequencies, while higher multipole modes such as magnetic and electric quadrupoles appear in the blue part of the spectra (see Fig. 6dUf). ˝

10.5772/58850

All-Dielectric Optical Nanoantennas 151

<sup>2</sup> in the plane of

2, where

**Figure 7.** (**A**) Huygens element consisting of a single silicon nanoparticle and point-like dipole source separated by a distance *Gds* = 90 nm (between dipole and sphere surface). The radius of the silicon nanoparticle is *Rs* = 70 nm. (**B**) Dielectric optical Yagi-Uda nanoantenna, consisting of the reflector of the radius *Rr* = 75 nm, and smaller director of the radii *Rd* = 70 nm. The dipole source is placed equally from the reflector and the first director surfaces at the distance G. The separation between

The mentioned above properties of dielectric nanoparticles allow us to realize optical Huygens source [80] consisting of a point-like electric dipole operating at the magnetic resonance of a dielectric nanosphere (see Fig.7A). Such a structure exhibits high directivity with vanishing backward scattering and polarization independence, being attractive for

We start our analysis by considering a radiation pattern of two ideal coupled electric and magnetic dipoles. A single point-like dipole source generates the electric far-field of the

where **p** is the electric dipole, *k* = *ω*/*c* is the wavenumber, **n** is the scattered direction, and *r* is

*α* is the scattered angle. In the plane orthogonal to the dipole (**n** · **p** = 0) the radiation pattern remains constant and angle independent, *<sup>σ</sup>*<sup>⊥</sup> <sup>∝</sup> *const*. Thus, the total radiation pattern of a single dipole emitter is a torus which radiates equally in the opposite directions. If we now place, in addition to the electric dipole, an orthogonal magnetic dipole located at the same point, the situation changes dramatically. The magnetic dipole **m** generates the electric

<sup>4</sup>*π*0*<sup>r</sup>* exp(*ikr*)[**<sup>p</sup>** <sup>−</sup> **<sup>n</sup>**(**<sup>n</sup>** · **<sup>p</sup>**)] , (1)

<sup>4</sup>*r<sup>π</sup>* exp(*ikr*)(**<sup>n</sup>** <sup>×</sup> **<sup>m</sup>**). (2)

surfaces of the neighbouring directors is also equal to G. [45]

efficient and compact designs of optical nanoantennas.

**<sup>E</sup>***<sup>p</sup>* <sup>=</sup> *<sup>k</sup>*<sup>2</sup>

**E***<sup>m</sup>* = −

the distance from the dipole source. The radiation pattern *<sup>σ</sup>* <sup>=</sup> lim*r*→<sup>∞</sup> <sup>4</sup>*πr*2|*Ep*<sup>|</sup>

*µ*<sup>0</sup> 0 *k*2

Thus, the total electric field is a sum of *two contributions* from both electric and magnetic dipoles **E**total = **E***<sup>p</sup>* + **E***m*. By assuming that the magnetic dipole is related to the electric dipole via the relation <sup>|</sup>**m**<sup>|</sup> <sup>=</sup> <sup>|</sup>**p**|/(*µ*<sup>0</sup><sup>0</sup>)1/2, which corresponds to an infinitesimally small wavefront of a plane wave often called a Huygens source [80], the radiation pattern becomes

the dipole **<sup>n</sup>** <sup>×</sup> **<sup>p</sup>** <sup>=</sup> 0 is proportional to the standard figure-eight profile, *<sup>σ</sup>*|| <sup>∝</sup> <sup>|</sup> cos *<sup>α</sup>*<sup>|</sup>

**3.1. General concept**

following form

far-field of the form

Some differences between experimental and theoretical spectra observed in Fig. 6 can be attributed to the presence of silicon substrate, which is not taken into account in our simple Mie theory solution. We should also mention that very similar results have been published almost simultaneously by a different group of authors [73] who demonstrated magnetic and electric dipole resonances of silicon particles in red and near-IR spectral range.

Recently we have also experimentally demonstrated for the first time directional light scattering by spherical silicon nanoparticles in the visible spectral range [74]. These unique scattering properties arise due to simultaneous excitation and mutual interference of magnetic and electric dipole resonances inside a single nanosphere. This phenomenon is similar to a known since long time Kerker-type scattering predicted in [75] for hypothetical magneto-dielectric nanoparticles but never observed experimentally. Directivity of the far-field radiation pattern can be controlled by changing light wavelength and the nanoparticle size. Forward-to-backward scattering ratio above 6 was experimentally obtained at visible wavelengths. Similar directional light scattering by spherical ceramic particles in GHz [76] and GaAs nanodisks in the visible [77] has also been published almost simultaneously by different groups of authors. These unique optical properties of high-refractive index dielectric nanostructures constitute the background for our approach to all-dielectric nanoantennas, which will be discussed in detail below.

## **3. Huygens optical elements and YagiUUda nanoantennas based on ˚ dielectric nanoparticles**

Recently, it was suggested [8, 9, 40–42, 45, 46] a novel type of optical nanoantennas made of all-dielectric elements. Moreover, we argue that, since the source of electromagnetic radiation is applied externally, dielectric nanoantennas can be considered as the best alternative to their metallic counterparts. First, dielectric materials exhibit low loss at the optical frequencies. Second, as was suggested earlier, nanoparticles made of high-permittivity dielectrics may support both electric and magnetic resonant modes. This feature may greatly expand the applicability of optical nanoantennas for, e.g. for detection of magnetic dipole transitions of molecules [78]. In our study we concentrate on nanoparticles made of silicon. The real part of the permittivity of the silicon in the visible spectral range is about 16 [79], while the imaginary part is up to two orders of magnitude smaller than that of nobel metals (silver and gold).

**Figure 7.** (**A**) Huygens element consisting of a single silicon nanoparticle and point-like dipole source separated by a distance *Gds* = 90 nm (between dipole and sphere surface). The radius of the silicon nanoparticle is *Rs* = 70 nm. (**B**) Dielectric optical Yagi-Uda nanoantenna, consisting of the reflector of the radius *Rr* = 75 nm, and smaller director of the radii *Rd* = 70 nm. The dipole source is placed equally from the reflector and the first director surfaces at the distance G. The separation between surfaces of the neighbouring directors is also equal to G. [45]

#### **3.1. General concept**

8 Progress in Compact Antennas

of the spectra (see Fig. 6dUf).

**dielectric nanoparticles**

and gold).

has a ring shape while magnetic field oscillates in the particle center. Magnetic dipole resonance is the only peak observed for the smallest nanoparticles (see Fig. 6a). At increased nanoparticle size (see Fig. 6b,c) electric dipole (ed) resonance also appears at the blue part of the spectra, while magnetic dipole shifts to the red. For relatively small nanoparticles, the observed colour is mostly defined by the strongest resonance peak and changes from blue to green, yellow, and red when magnetic resonance wavelength shifts from 480 nm to 700 nm (see Fig. 6aUd). So, we can conclude that the beautiful colours observed in the ˝ dark field microscope (see Fig. 5a) correspond to magnetic dipole scattering of the silicon nanoparticles, ¸Smagnetic lightT. Further increase of the nanoparticle size leads to the shift of

magnetic and electric dipole resonances further to the red and infra-red frequencies, while higher multipole modes such as magnetic and electric quadrupoles appear in the blue part

Some differences between experimental and theoretical spectra observed in Fig. 6 can be attributed to the presence of silicon substrate, which is not taken into account in our simple Mie theory solution. We should also mention that very similar results have been published almost simultaneously by a different group of authors [73] who demonstrated magnetic and

Recently we have also experimentally demonstrated for the first time directional light scattering by spherical silicon nanoparticles in the visible spectral range [74]. These unique scattering properties arise due to simultaneous excitation and mutual interference of magnetic and electric dipole resonances inside a single nanosphere. This phenomenon is similar to a known since long time Kerker-type scattering predicted in [75] for hypothetical magneto-dielectric nanoparticles but never observed experimentally. Directivity of the far-field radiation pattern can be controlled by changing light wavelength and the nanoparticle size. Forward-to-backward scattering ratio above 6 was experimentally obtained at visible wavelengths. Similar directional light scattering by spherical ceramic particles in GHz [76] and GaAs nanodisks in the visible [77] has also been published almost simultaneously by different groups of authors. These unique optical properties of high-refractive index dielectric nanostructures constitute the background for our approach

electric dipole resonances of silicon particles in red and near-IR spectral range.

to all-dielectric nanoantennas, which will be discussed in detail below.

**3. Huygens optical elements and YagiUUda nanoantennas based on ˚**

Recently, it was suggested [8, 9, 40–42, 45, 46] a novel type of optical nanoantennas made of all-dielectric elements. Moreover, we argue that, since the source of electromagnetic radiation is applied externally, dielectric nanoantennas can be considered as the best alternative to their metallic counterparts. First, dielectric materials exhibit low loss at the optical frequencies. Second, as was suggested earlier, nanoparticles made of high-permittivity dielectrics may support both electric and magnetic resonant modes. This feature may greatly expand the applicability of optical nanoantennas for, e.g. for detection of magnetic dipole transitions of molecules [78]. In our study we concentrate on nanoparticles made of silicon. The real part of the permittivity of the silicon in the visible spectral range is about 16 [79], while the imaginary part is up to two orders of magnitude smaller than that of nobel metals (silver

ˇ

˝

The mentioned above properties of dielectric nanoparticles allow us to realize optical Huygens source [80] consisting of a point-like electric dipole operating at the magnetic resonance of a dielectric nanosphere (see Fig.7A). Such a structure exhibits high directivity with vanishing backward scattering and polarization independence, being attractive for efficient and compact designs of optical nanoantennas.

We start our analysis by considering a radiation pattern of two ideal coupled electric and magnetic dipoles. A single point-like dipole source generates the electric far-field of the following form

$$\mathbf{E}\_p = \frac{k^2}{4\pi\epsilon\_0 r} \exp(ikr) \left[\mathbf{p} - \mathbf{n}(\mathbf{n} \cdot \mathbf{p})\right],\tag{1}$$

where **p** is the electric dipole, *k* = *ω*/*c* is the wavenumber, **n** is the scattered direction, and *r* is the distance from the dipole source. The radiation pattern *<sup>σ</sup>* <sup>=</sup> lim*r*→<sup>∞</sup> <sup>4</sup>*πr*2|*Ep*<sup>|</sup> <sup>2</sup> in the plane of the dipole **<sup>n</sup>** <sup>×</sup> **<sup>p</sup>** <sup>=</sup> 0 is proportional to the standard figure-eight profile, *<sup>σ</sup>*|| <sup>∝</sup> <sup>|</sup> cos *<sup>α</sup>*<sup>|</sup> 2, where *α* is the scattered angle. In the plane orthogonal to the dipole (**n** · **p** = 0) the radiation pattern remains constant and angle independent, *<sup>σ</sup>*<sup>⊥</sup> <sup>∝</sup> *const*. Thus, the total radiation pattern of a single dipole emitter is a torus which radiates equally in the opposite directions. If we now place, in addition to the electric dipole, an orthogonal magnetic dipole located at the same point, the situation changes dramatically. The magnetic dipole **m** generates the electric far-field of the form

$$\mathbf{E}\_m = -\sqrt{\frac{\mu\_0}{\epsilon\_0}} \frac{k^2}{4r\pi} \exp(ikr) \left(\mathbf{n} \times \mathbf{m}\right). \tag{2}$$

Thus, the total electric field is a sum of *two contributions* from both electric and magnetic dipoles **E**total = **E***<sup>p</sup>* + **E***m*. By assuming that the magnetic dipole is related to the electric dipole via the relation <sup>|</sup>**m**<sup>|</sup> <sup>=</sup> <sup>|</sup>**p**|/(*µ*<sup>0</sup><sup>0</sup>)1/2, which corresponds to an infinitesimally small wavefront of a plane wave often called a Huygens source [80], the radiation pattern becomes *<sup>σ</sup><sup>H</sup>* <sup>∝</sup> <sup>|</sup><sup>1</sup> <sup>+</sup> cos *<sup>α</sup>*<sup>|</sup> 2. This radiation pattern is quite different compared to that of a single electric dipole. It is *highly asymmetric* with the total suppression of the radiation in a particular direction, *α* = *π* [*σH*(*π*) = 0], and a strong enhancement in the opposite direction, *α* = 0. The complete three-dimensional radiation pattern resembles a cardioid or apple-like shape, which is also azimuthally independent. Such a radiation pattern of the Huygens source is potentially very useful for various nanoantenna applications. However, while electric dipole sources are widely used in optics, magnetic dipoles are less common.

First, we consider an electric dipole source placed in a close proximity to a dielectric sphere [see Fig. 7(a)]. As was mentioned above, it can be analytically shown that high permittivity dielectric nanoparticles exhibit strong magnetic resonance in the visible range when the wavelength inside the nanoparticle equals its diameter *λ*/*ns* ≈ 2*Rs* [81], where *nS* and *Rs* are refractive index and radius of the nanoparticle, respectively. There are many dielectric materials with high enough real part of the permittivity and very low imaginary part, indicating low dissipative losses. To name just a few, silicon (Si, <sup>1</sup> = 16), germanium (Ge, <sup>1</sup> = 20), aluminum antimonide (AlSb, <sup>1</sup> = 12), aluminum arsenide (AlAs, <sup>1</sup> = 10), and other. In our study we concentrate on the nanoparticles made of silicon, which support strong magnetic resonance in the visible range for the radius varying from 40 nm to 80 nm [69].

For such a small radius compared to the wavelength *Rs < λ*, the radiation pattern of the silicon nanoparticle in the far field at the magnetic or electric resonances will resemble that of magnetic or electric point-like dipole, respectively. Moreover, it is even possible to introduce magnetic *α<sup>m</sup>* and electric *α<sup>e</sup>* polarisabilities [69, 72, 82] based on the Mie dipole scattering coefficients *b*<sup>1</sup> and *a*1:

$$\alpha^{\varepsilon} = \frac{6\pi a\_1 i}{k^3}, \quad \alpha^m = \frac{6\pi b\_1 i}{k^3}. \tag{3}$$

10.5772/58850

All-Dielectric Optical Nanoantennas 153

**Figure 8.** Wavelength dependence of the directivity of two types of all-dielectric nanoantennas consisting of (a) single dielectric nanoparticle of radius *Rd* = 70 nm, and (b) Yagi-Uda like design for the separation distance *D* = 70 nm. Insert shows 3D

which exhibit electric polarizability only, there is an abrupt phase change from 0 to *π* in the vicinity of the localized surface plasmon resonance, which makes it difficult to tune plasmonic nanoantennas for optimal performance. The dependence of the scattering diagram on the distance between the electric dipole source and metallic nanoparticle was studied in Ref. [83]. On contrary, in the case of nanoparticles with both electric and magnetic polarisabilities, it is possible to achieve more efficient radiation from the near to far field zone, due to subtle phase manipulation. *This is exactly the case of the dielectric nanoparticles*. Any antenna is characterized by two specific properties, directivity (*D*) and radiation

Max[*p*(*θ*, *<sup>ϕ</sup>*)], *<sup>η</sup>rad* <sup>=</sup> *<sup>P</sup>*rad

where *P*rad and *P*loss are integrated radiated and absorbed powers, respectively, *θ* and *ϕ* are spherical angles of standard spherical coordinate system, and *p*(*θ*, *ϕ*) is the radiated power in the given direction *θ* and/or *ϕ*. The directivity measures the power density of the antenna radiated in the direction of its strongest emission, while Radiation Efficiency measures the electrical losses that occur throughout the antenna at a given wavelength. To calculate these quantities numerically for the structures shown in Fig. 7a, we employ CST Microwave Studio. To get reliable results, we model the electric dipole source by a Discrete Port coupled to two

In Fig. 8(a) we show the dependence of the directivity on wavelength for a single dielectric nanoparticle excited by a electric dipole source. Two inserts demonstrate 3D angular distribution of the radiated pattern *p*(*θ*, *ϕ*) corresponding to the local maxima. In this case, the system radiates predominantly to the forward direction at *λ* = 590 nm, while in another case, the radiation is predominantly in the backward direction at *λ* = 480 nm. In this case, the total electric dipole moment of the sphere and point-like source and the magnetic dipole moment of the sphere oscillate with the phase difference arg(*αm*) <sup>−</sup> arg(*αe*) = 1.3rad, resulting in the destructive interference in the forward direction. At the wavelength *λ* = 590 nm the total electric and magnetic dipole moments oscillate in phase and produce Huygens-source-like radiation pattern with the main lobe directed in the forward direction. By adding more elements to the silicon nanoparticle, we can enhance the performance of all-dielectric nanoantennas. In particular, we consider a dielectric analogue of the Yagi-Uda

*P*rad + *P*loss

, (4)

radiation pattern diagrams at particular wavelengths. [45]

efficiency (*ηrad*), defined as [80, 84]

PEC nanoparticles.

*<sup>D</sup>* <sup>=</sup> <sup>4</sup>*<sup>π</sup> P*rad

Thus, the dielectric nanoparticle excited by the electric dipole source at the magnetic resonance may result in the total far field radiation pattern which is similar to that of the Huygens source. Similar radiation patterns can be achieve in light scattering by a magnetic particle when permeability equals permittivity *µ* = , also known as Kerker's condition [75]. Our result suggests that even a dielectric nonmagnetic nanoparticle can support two induced dipoles of equal strength resulting in suppression of the radiation in the backward direction. Thus, it can be considered as the simplest and efficient optical nanoantenna with very good directivity.

In general, both polarisabilities *α<sup>m</sup>* and *α<sup>e</sup>* are nonzero in the optical region [69]. It is known that for a dipole radiation in the far field the electric and magnetic components should oscillate in phase to have nonzero energy flow. In the near field the electric and magnetic components oscillate with *π*/2 phase difference, thus, the averaged Poynting vector vanishes, and a part of energy is stored in the vicinity of the source. In the intermediate region, the phase between two components varies form *π*/2 to 0. Placing a nanoparticle close to the dipole source will change the phase difference between two components, and, thus, will affect the amount of radiation form the near field. In the case of plasmonic nanoparticles

10 Progress in Compact Antennas

2. This radiation pattern is quite different compared to that of a single electric

dipole. It is *highly asymmetric* with the total suppression of the radiation in a particular direction, *α* = *π* [*σH*(*π*) = 0], and a strong enhancement in the opposite direction, *α* = 0. The complete three-dimensional radiation pattern resembles a cardioid or apple-like shape, which is also azimuthally independent. Such a radiation pattern of the Huygens source is potentially very useful for various nanoantenna applications. However, while electric dipole

First, we consider an electric dipole source placed in a close proximity to a dielectric sphere [see Fig. 7(a)]. As was mentioned above, it can be analytically shown that high permittivity dielectric nanoparticles exhibit strong magnetic resonance in the visible range when the wavelength inside the nanoparticle equals its diameter *λ*/*ns* ≈ 2*Rs* [81], where *nS* and *Rs* are refractive index and radius of the nanoparticle, respectively. There are many dielectric materials with high enough real part of the permittivity and very low imaginary part, indicating low dissipative losses. To name just a few, silicon (Si, <sup>1</sup> = 16), germanium (Ge, <sup>1</sup> = 20), aluminum antimonide (AlSb, <sup>1</sup> = 12), aluminum arsenide (AlAs, <sup>1</sup> = 10), and other. In our study we concentrate on the nanoparticles made of silicon, which support strong magnetic resonance in the visible range for the radius varying from 40 nm to 80

For such a small radius compared to the wavelength *Rs < λ*, the radiation pattern of the silicon nanoparticle in the far field at the magnetic or electric resonances will resemble that of magnetic or electric point-like dipole, respectively. Moreover, it is even possible to introduce magnetic *α<sup>m</sup>* and electric *α<sup>e</sup>* polarisabilities [69, 72, 82] based on the Mie dipole scattering

*<sup>k</sup>*<sup>3</sup> , *<sup>α</sup><sup>m</sup>* <sup>=</sup> <sup>6</sup>*πb*1*<sup>i</sup>*

Thus, the dielectric nanoparticle excited by the electric dipole source at the magnetic resonance may result in the total far field radiation pattern which is similar to that of the Huygens source. Similar radiation patterns can be achieve in light scattering by a magnetic particle when permeability equals permittivity *µ* = , also known as Kerker's condition [75]. Our result suggests that even a dielectric nonmagnetic nanoparticle can support two induced dipoles of equal strength resulting in suppression of the radiation in the backward direction. Thus, it can be considered as the simplest and efficient optical nanoantenna with very good

In general, both polarisabilities *α<sup>m</sup>* and *α<sup>e</sup>* are nonzero in the optical region [69]. It is known that for a dipole radiation in the far field the electric and magnetic components should oscillate in phase to have nonzero energy flow. In the near field the electric and magnetic components oscillate with *π*/2 phase difference, thus, the averaged Poynting vector vanishes, and a part of energy is stored in the vicinity of the source. In the intermediate region, the phase between two components varies form *π*/2 to 0. Placing a nanoparticle close to the dipole source will change the phase difference between two components, and, thus, will affect the amount of radiation form the near field. In the case of plasmonic nanoparticles

*<sup>k</sup>*<sup>3</sup> . (3)

*<sup>α</sup><sup>e</sup>* <sup>=</sup> <sup>6</sup>*πa*1*<sup>i</sup>*

sources are widely used in optics, magnetic dipoles are less common.

*<sup>σ</sup><sup>H</sup>* <sup>∝</sup> <sup>|</sup><sup>1</sup> <sup>+</sup> cos *<sup>α</sup>*<sup>|</sup>

nm [69].

directivity.

coefficients *b*<sup>1</sup> and *a*1:

**Figure 8.** Wavelength dependence of the directivity of two types of all-dielectric nanoantennas consisting of (a) single dielectric nanoparticle of radius *Rd* = 70 nm, and (b) Yagi-Uda like design for the separation distance *D* = 70 nm. Insert shows 3D radiation pattern diagrams at particular wavelengths. [45]

which exhibit electric polarizability only, there is an abrupt phase change from 0 to *π* in the vicinity of the localized surface plasmon resonance, which makes it difficult to tune plasmonic nanoantennas for optimal performance. The dependence of the scattering diagram on the distance between the electric dipole source and metallic nanoparticle was studied in Ref. [83]. On contrary, in the case of nanoparticles with both electric and magnetic polarisabilities, it is possible to achieve more efficient radiation from the near to far field zone, due to subtle phase manipulation. *This is exactly the case of the dielectric nanoparticles*.

Any antenna is characterized by two specific properties, directivity (*D*) and radiation efficiency (*ηrad*), defined as [80, 84]

$$D = \frac{4\pi}{P\_{\rm rad}} \text{Max} [p(\theta, \varphi)], \quad \eta\_{\rm rad} = \frac{P\_{\rm rad}}{P\_{\rm rad} + P\_{\rm loss}},\tag{4}$$

where *P*rad and *P*loss are integrated radiated and absorbed powers, respectively, *θ* and *ϕ* are spherical angles of standard spherical coordinate system, and *p*(*θ*, *ϕ*) is the radiated power in the given direction *θ* and/or *ϕ*. The directivity measures the power density of the antenna radiated in the direction of its strongest emission, while Radiation Efficiency measures the electrical losses that occur throughout the antenna at a given wavelength. To calculate these quantities numerically for the structures shown in Fig. 7a, we employ CST Microwave Studio. To get reliable results, we model the electric dipole source by a Discrete Port coupled to two PEC nanoparticles.

In Fig. 8(a) we show the dependence of the directivity on wavelength for a single dielectric nanoparticle excited by a electric dipole source. Two inserts demonstrate 3D angular distribution of the radiated pattern *p*(*θ*, *ϕ*) corresponding to the local maxima. In this case, the system radiates predominantly to the forward direction at *λ* = 590 nm, while in another case, the radiation is predominantly in the backward direction at *λ* = 480 nm. In this case, the total electric dipole moment of the sphere and point-like source and the magnetic dipole moment of the sphere oscillate with the phase difference arg(*αm*) <sup>−</sup> arg(*αe*) = 1.3rad, resulting in the destructive interference in the forward direction. At the wavelength *λ* = 590 nm the total electric and magnetic dipole moments oscillate in phase and produce Huygens-source-like radiation pattern with the main lobe directed in the forward direction. By adding more elements to the silicon nanoparticle, we can enhance the performance of all-dielectric nanoantennas. In particular, we consider a dielectric analogue of the Yagi-Uda design (see Fig.7) consisting of four directors and one reflector. The radii of the directors and the reflector are chosen to achieve the maximal constructive interference in the forward direction along the array. The optimal performance of the Yagi-Uda nanoantenna should be expected when the radii of the directors correspond to the magnetic resonance, and the radius of the reflector correspond to the electric resonance at a given frequency, with the coupling between the elements taken into account. Our particular design consists of the directors with radii *Rd* = 70 nm and the reflector with the radius *Rr* = 75 nm. In Fig. 8(b) we plot the directivity of all-dielectric Yagi-Uda nanoantenna vs. wavelength with the separation distance *D* = 70 nm. Inserts demonstrate the 3D radiation patterns at particular wavelengths. We achieve a strong maximum at *λ* = 500 nm. The main lobe is extremely narrow with the beam-width about 40◦ and negligible backscattering. The maximum does not correspond exactly to either magnetic or electric resonances of a single dielectric sphere, which implies the importance of the interaction between constitutive nanoparticles.

10.5772/58850

All-Dielectric Optical Nanoantennas 155

**Figure 10.** Purcell factor of all-dielectric Yagi-Uda nanoantenna vs wavelength for various values of the separation distance

the CST Microwave Studio we calculate the total radiated in the far-field and dissipated into the particles powers and take the ratio of their sum to the total power radiated by the electric dipole in free space. Analytically, we employed the generalised multiparticle Mie solution [86] adapted for the electric dipole excitation [87]. We verified that both approaches produce similar results. In Fig. 10 we show calculated Purcell factor of the all-dielectric Yagi-Uda nanoantenna vs. wavelength for various separation distances. We observe that, by decreasing the separation between the directors, the Purcell factor becomes stronger near the magnetic dipole resonance. We can notice that a plasmonic analogue of the same nanoantenna made of Ag exhibits low Purcell factor less than one. Thus, such relatively high Purcell factor can be employed for efficient photon extraction from molecules placed near

There are exist some technological issues to reproduce an object of the nanometer size with a high accuracy. For this reason we have scaled the dimensions of the proposed optical all-dielectric Yagi-Uda nanoantenna to the microwave frequency range while keeping all the material parameters in order to study the microwave analogue of the nanoantenna experimentally. We use the design of the Yagi-Uda antenna shown in Fig. 7b. To mimic the silicon spheres in microwave frequency range, we employ MgO-TiO2 ceramic which is characterized by dielectric constant of 16 and dielectric loss factor of (1.12−1.17)10−<sup>4</sup> measured at frequency 9-12 GHz [88]. As a source, we use a half-wavelength vibrator.

We set the radius of the reflector equal to *Rr* = 5 mm. The frequencies of the electric and magnetic Mie resonances of the sphere calculated with the help of Eq. (3) are 10.2 GHz and 7 GHz, respectively. The radius of the directors is *Rd* = 4 mm. In this case, the frequencies of the electric and magnetic Mie resonances are 12.5 GHz and 9 GHz. As a source, we model a half-wavelength vibrator with the total length of *Lv* = 19.8 mm and diameter of *Dv* = 2.2 mm. The distances between the reflector, directors, and vibrator have been adjusted by numerical simulations. We achieve an effective suppression of the back and minor lobes, and the narrow major lobe (of about 40◦) of the antenna when the distance between the director's surface as well as the distance between vibrator center and the first director surface are 1.5

We study experimentally both the radiation pattern and directivity of the antenna.

mm; the distance between the surface of the reflector and vibrator centre is 1.1 mm.

Figures 11(a,b) show the photographs of the fabricated all-dielectric Yagi-Uda antenna. The reflector and directors are made of MgO-TiO2 ceramic with accuracy of ±0.05 mm. To

**3.2. Experimental verification of dielectric Yagi-Uda nanoantenna**

*D*. [45]

all-dielectric optical nanoantennas.

As the next step, we study the performance of the all-dielectric nanoantennas for different separation distances *D*, and compare it with *a plasmonic analogue* of the similar geometric design made of silver nanoparticles. According to the results summarized in Fig. 9, the radiation efficiencies of both types of nanoantennas *are nearly the same* for larger separation of directors *D* = 70 nm with the averaged value 70%. Although dissipation losses of silicon are much smaller than those of silver, the dielectric particle absorbs the EM energy by the whole spherical volume, while the metallic particles absorb mostly at the surface. As a result, there is no big difference in the overall performance of these two types of nanoantennas for relatively large distances between the elements. However, the difference becomes *very strong* for smaller separations. The radiation efficiency of the all-dielectric nanoantenna is insensitive to the separation distance [see Fig. 9 (a)]. On contrary, the radiation efficiency drops significantly for metallic nanoantennas [see Fig. 9 (b)].

Finally, we investigate the modification of the transition rate of a quantum point-like source placed in the vicinity of dielectric particles. For electric-dipole transitions and in the weak-coupling regime, the normalised spontaneous decay rate Γ/Γ0, also known as Purcell factor, can be calculated classically as the ratio of energy dissipation rates of an electric dipole *P*/*P*<sup>0</sup> [7]. Here, Γ<sup>0</sup> and *P*<sup>0</sup> correspond to transition rate of the quantum emitter and energy dissipation rate of the electric dipole in free space [85]. In the limit of the intrinsic quantum yield of the emitter close to unity, both ratios become equal to each other Γ/Γ<sup>0</sup> = *P*/*P*0, which allows us to calculate the Purcell factor in the classical regime [7]. We have calculated the Purcell factor by using both, numerical and analytical approaches. Numerically, by using

**Figure 9.** Radiation efficiencies of (a) dielectric (Si) and (b) plasmonic (Ag) Yagi-Uda optical nanoantennas of the same geometrical designs for various values of the separation distance *D*. [45]

12 Progress in Compact Antennas

design (see Fig.7) consisting of four directors and one reflector. The radii of the directors and the reflector are chosen to achieve the maximal constructive interference in the forward direction along the array. The optimal performance of the Yagi-Uda nanoantenna should be expected when the radii of the directors correspond to the magnetic resonance, and the radius of the reflector correspond to the electric resonance at a given frequency, with the coupling between the elements taken into account. Our particular design consists of the directors with radii *Rd* = 70 nm and the reflector with the radius *Rr* = 75 nm. In Fig. 8(b) we plot the directivity of all-dielectric Yagi-Uda nanoantenna vs. wavelength with the separation distance *D* = 70 nm. Inserts demonstrate the 3D radiation patterns at particular wavelengths. We achieve a strong maximum at *λ* = 500 nm. The main lobe is extremely narrow with the beam-width about 40◦ and negligible backscattering. The maximum does not correspond exactly to either magnetic or electric resonances of a single dielectric sphere, which implies

As the next step, we study the performance of the all-dielectric nanoantennas for different separation distances *D*, and compare it with *a plasmonic analogue* of the similar geometric design made of silver nanoparticles. According to the results summarized in Fig. 9, the radiation efficiencies of both types of nanoantennas *are nearly the same* for larger separation of directors *D* = 70 nm with the averaged value 70%. Although dissipation losses of silicon are much smaller than those of silver, the dielectric particle absorbs the EM energy by the whole spherical volume, while the metallic particles absorb mostly at the surface. As a result, there is no big difference in the overall performance of these two types of nanoantennas for relatively large distances between the elements. However, the difference becomes *very strong* for smaller separations. The radiation efficiency of the all-dielectric nanoantenna is insensitive to the separation distance [see Fig. 9 (a)]. On contrary, the radiation efficiency

Finally, we investigate the modification of the transition rate of a quantum point-like source placed in the vicinity of dielectric particles. For electric-dipole transitions and in the weak-coupling regime, the normalised spontaneous decay rate Γ/Γ0, also known as Purcell factor, can be calculated classically as the ratio of energy dissipation rates of an electric dipole *P*/*P*<sup>0</sup> [7]. Here, Γ<sup>0</sup> and *P*<sup>0</sup> correspond to transition rate of the quantum emitter and energy dissipation rate of the electric dipole in free space [85]. In the limit of the intrinsic quantum yield of the emitter close to unity, both ratios become equal to each other Γ/Γ<sup>0</sup> = *P*/*P*0, which allows us to calculate the Purcell factor in the classical regime [7]. We have calculated the Purcell factor by using both, numerical and analytical approaches. Numerically, by using

**Figure 9.** Radiation efficiencies of (a) dielectric (Si) and (b) plasmonic (Ag) Yagi-Uda optical nanoantennas of the same

the importance of the interaction between constitutive nanoparticles.

drops significantly for metallic nanoantennas [see Fig. 9 (b)].

geometrical designs for various values of the separation distance *D*. [45]

**Figure 10.** Purcell factor of all-dielectric Yagi-Uda nanoantenna vs wavelength for various values of the separation distance *D*. [45]

the CST Microwave Studio we calculate the total radiated in the far-field and dissipated into the particles powers and take the ratio of their sum to the total power radiated by the electric dipole in free space. Analytically, we employed the generalised multiparticle Mie solution [86] adapted for the electric dipole excitation [87]. We verified that both approaches produce similar results. In Fig. 10 we show calculated Purcell factor of the all-dielectric Yagi-Uda nanoantenna vs. wavelength for various separation distances. We observe that, by decreasing the separation between the directors, the Purcell factor becomes stronger near the magnetic dipole resonance. We can notice that a plasmonic analogue of the same nanoantenna made of Ag exhibits low Purcell factor less than one. Thus, such relatively high Purcell factor can be employed for efficient photon extraction from molecules placed near all-dielectric optical nanoantennas.

#### **3.2. Experimental verification of dielectric Yagi-Uda nanoantenna**

There are exist some technological issues to reproduce an object of the nanometer size with a high accuracy. For this reason we have scaled the dimensions of the proposed optical all-dielectric Yagi-Uda nanoantenna to the microwave frequency range while keeping all the material parameters in order to study the microwave analogue of the nanoantenna experimentally. We use the design of the Yagi-Uda antenna shown in Fig. 7b. To mimic the silicon spheres in microwave frequency range, we employ MgO-TiO2 ceramic which is characterized by dielectric constant of 16 and dielectric loss factor of (1.12−1.17)10−<sup>4</sup> measured at frequency 9-12 GHz [88]. As a source, we use a half-wavelength vibrator. We study experimentally both the radiation pattern and directivity of the antenna.

We set the radius of the reflector equal to *Rr* = 5 mm. The frequencies of the electric and magnetic Mie resonances of the sphere calculated with the help of Eq. (3) are 10.2 GHz and 7 GHz, respectively. The radius of the directors is *Rd* = 4 mm. In this case, the frequencies of the electric and magnetic Mie resonances are 12.5 GHz and 9 GHz. As a source, we model a half-wavelength vibrator with the total length of *Lv* = 19.8 mm and diameter of *Dv* = 2.2 mm. The distances between the reflector, directors, and vibrator have been adjusted by numerical simulations. We achieve an effective suppression of the back and minor lobes, and the narrow major lobe (of about 40◦) of the antenna when the distance between the director's surface as well as the distance between vibrator center and the first director surface are 1.5 mm; the distance between the surface of the reflector and vibrator centre is 1.1 mm.

Figures 11(a,b) show the photographs of the fabricated all-dielectric Yagi-Uda antenna. The reflector and directors are made of MgO-TiO2 ceramic with accuracy of ±0.05 mm. To

All-Dielectric Optical Nanoantennas 157

**Figure 13.** Radiation pattern of the antenna in (a) *E*-plane and (b) *H*-plane at the frequency 10.7 GHz. Solid lines show the

the all-dielectric Yagi-Uda antenna at microwaves, we simulate numerically the antenna's response by employing the CST Microwave Studio. We observe excellent agreement between numerical results of Fig. 12b and measured experimental data. However, we notice a small frequency shift of the measured directivity (approx. 2%) in comparison with the numerical results. This discrepancies can be explained by the effect of the antenna holders in the

The antenna radiation patterns in the far field (at the distance 3 m) are measured in an anechoic chamber by a horn antenna and rotating table. The measured radiation patterns of the antenna in *E*- and *H*-planes at the frequency 10.7 GHz are shown in Fig. 13. The measured characteristics agree very well with the numerical results. A small disagreement can be explained by the presence of the antenna holder which influence was not taken into

For optical wireless circuits on a chip, nanoantennas are required to be both highly directive and compact [12, 89–91]. In nanophotonics, directivity has been achieved for arrayed plasmonic antennas utilizing the Yagi-Uda design [37, 84, 90, 92, 93], large dielectric spheres [94], and metascreen antennas [95]. Though individual elements of these arrays are optically small, the overall size of the radiating systems is larger than the radiation wavelength *λ*. In addition, small plasmonic nanoantennas possess weak directivity close

As was discussed above, it was suggested theoretically and experimentally to employ magnetic resonances of high-index dielectric nanoparticles for enhancing the nanoantenna directivity [8, 9, 37, 40–42, 45, 46, 98]. High-permittivity nanoparticles can have nearly resonant balanced electric and magnetic dipole responses. This balance of the electric and magnetic dipoles oscillating with the same phase allows the practical realization of the Huygens source, an elementary emitting system with a cardioid pattern [37, 44, 46, 80] and with the directivity larger than 3.5. Importantly, a possibility to excite magnetic resonances leads to the improved nanoantenna directional properties without a significant increase of its

result of numerical simulations in CST; the crosses correspond to the experimental data. [46]

experiment, not included into the numerical simulation.

**4. All–dielectric superdirective optical nanoantenna**

account in our numerical simulations.

to the directivity of a point dipole [90, 96, 97].

size.

**Figure 11.** Photographs of the all-dielectric Yagi-Uda microwave antenna. (a) Detailed view of the antenna placed in a holder. (b) Antenna placed in an anechoic chamber; the coordinate *z* is directed along the vibrator axis; the coordinate *y* is directed along the antenna axis. [46]

fasten together the elements of the antenna and vibrator, we use a special holder made of a thin dielectric substrate with dielectric permittivity close to 1 [being shown in Fig. 11(a)]. Styrofoam material with the dielectric permittivity of 1 is used to fix the antenna in the azimuthal-rotation unit [see Fig. 11(b)]. To feed the vibrator, we employ a coaxial cable that is connected to an Agilent PNA E8362C vector network analyzer.

Any antenna is characterized by the total directivity (4). Sometimes it is not possible to determine the value of the total directivity experimentally due to difficulties to measure the total radiated power *P*rad. In this case, it is convenient to use directivity in the planes where electric field **E** and magnetic field **H** oscillate in the far field. For our coordinates the directivity in the evaluation plane (E-plane) and the azimuthal plane (H-plane) can be expressed as:

$$D\_{\rm E} = \left. \frac{2\pi \text{Max}[p(\theta)]}{\int\_0^{2\pi} p(\theta) d\theta} \right|\_{\theta=0}, \quad D\_H = \left. \frac{2\pi \text{Max}[p(\varphi)]}{\int\_0^{2\pi} p(\varphi) d\varphi} \right|\_{\theta=\pi/2}. \tag{5}$$

Equations (5) are multiplied by 2*π* because of the integration in the denominator is performed only for one coordinate while the second coordinate is fixed.

To extract the antenna directivity in the *E*- and *H*-planes from the experimental data, we measure the radiated power by the antenna in the frequency range from 10 GHz to 12 GHz with a step of 50 MHz. Then, by employing Eq. (5) we calculate the directivity at each frequency. The results are presented in Fig. 12a. To estimate the performance of

**Figure 12.** (a) Experimentally measured and (b) numerically calculated antenna's directivity in both *E*- and *H*-planes. [46]

**Figure 13.** Radiation pattern of the antenna in (a) *E*-plane and (b) *H*-plane at the frequency 10.7 GHz. Solid lines show the result of numerical simulations in CST; the crosses correspond to the experimental data. [46]

the all-dielectric Yagi-Uda antenna at microwaves, we simulate numerically the antenna's response by employing the CST Microwave Studio. We observe excellent agreement between numerical results of Fig. 12b and measured experimental data. However, we notice a small frequency shift of the measured directivity (approx. 2%) in comparison with the numerical results. This discrepancies can be explained by the effect of the antenna holders in the experiment, not included into the numerical simulation.

The antenna radiation patterns in the far field (at the distance 3 m) are measured in an anechoic chamber by a horn antenna and rotating table. The measured radiation patterns of the antenna in *E*- and *H*-planes at the frequency 10.7 GHz are shown in Fig. 13. The measured characteristics agree very well with the numerical results. A small disagreement can be explained by the presence of the antenna holder which influence was not taken into account in our numerical simulations.

#### **4. All–dielectric superdirective optical nanoantenna**

14 Progress in Compact Antennas

along the antenna axis. [46]

expressed as:

**Figure 11.** Photographs of the all-dielectric Yagi-Uda microwave antenna. (a) Detailed view of the antenna placed in a holder. (b) Antenna placed in an anechoic chamber; the coordinate *z* is directed along the vibrator axis; the coordinate *y* is directed

fasten together the elements of the antenna and vibrator, we use a special holder made of a thin dielectric substrate with dielectric permittivity close to 1 [being shown in Fig. 11(a)]. Styrofoam material with the dielectric permittivity of 1 is used to fix the antenna in the azimuthal-rotation unit [see Fig. 11(b)]. To feed the vibrator, we employ a coaxial cable that

Any antenna is characterized by the total directivity (4). Sometimes it is not possible to determine the value of the total directivity experimentally due to difficulties to measure the total radiated power *P*rad. In this case, it is convenient to use directivity in the planes where electric field **E** and magnetic field **H** oscillate in the far field. For our coordinates the directivity in the evaluation plane (E-plane) and the azimuthal plane (H-plane) can be

Equations (5) are multiplied by 2*π* because of the integration in the denominator is

To extract the antenna directivity in the *E*- and *H*-planes from the experimental data, we measure the radiated power by the antenna in the frequency range from 10 GHz to 12 GHz with a step of 50 MHz. Then, by employing Eq. (5) we calculate the directivity at each frequency. The results are presented in Fig. 12a. To estimate the performance of

**Figure 12.** (a) Experimentally measured and (b) numerically calculated antenna's directivity in both *E*- and *H*-planes. [46]

, *DH* <sup>=</sup> <sup>2</sup>*π*Max[*p*(*ϕ*)] <sup>2</sup>*<sup>π</sup>* <sup>0</sup> *p*(*ϕ*)*dϕ*

 *θ*=*π*/2

. (5)

 *ϕ*=0

performed only for one coordinate while the second coordinate is fixed.

is connected to an Agilent PNA E8362C vector network analyzer.

*DE* <sup>=</sup> <sup>2</sup>*π*Max[*p*(*θ*)] <sup>2</sup>*<sup>π</sup>* <sup>0</sup> *p*(*θ*)*dθ*

> For optical wireless circuits on a chip, nanoantennas are required to be both highly directive and compact [12, 89–91]. In nanophotonics, directivity has been achieved for arrayed plasmonic antennas utilizing the Yagi-Uda design [37, 84, 90, 92, 93], large dielectric spheres [94], and metascreen antennas [95]. Though individual elements of these arrays are optically small, the overall size of the radiating systems is larger than the radiation wavelength *λ*. In addition, small plasmonic nanoantennas possess weak directivity close to the directivity of a point dipole [90, 96, 97].

> As was discussed above, it was suggested theoretically and experimentally to employ magnetic resonances of high-index dielectric nanoparticles for enhancing the nanoantenna directivity [8, 9, 37, 40–42, 45, 46, 98]. High-permittivity nanoparticles can have nearly resonant balanced electric and magnetic dipole responses. This balance of the electric and magnetic dipoles oscillating with the same phase allows the practical realization of the Huygens source, an elementary emitting system with a cardioid pattern [37, 44, 46, 80] and with the directivity larger than 3.5. Importantly, a possibility to excite magnetic resonances leads to the improved nanoantenna directional properties without a significant increase of its size.

Superdirectivity has been already discussed for radio-frequency antennas, and it is defined as directivity of an electrically small radiating system that significantly exceeds (at least in 3 times) directivity of an electric dipole [80, 99, 100]. In that sense, the Huygens source is not superdirective. In the antenna literature, superdirectivity is claimed to be achievable only in antenna arrays by the price of ultimately narrow frequency range and by employing very precise phase shifters (see, e.g., Ref. [80, 99, 100]). Therefore, superdirective antennas, though very desirable for many applications such as space communications and radioastronomy, were never demonstrated and implemented for practical applications.

10.5772/58850

All-Dielectric Optical Nanoantennas 159

1 (6)

<sup>S</sup>*<sup>n</sup>* <sup>=</sup> Dmax*λ*<sup>2</sup> 4*π*2R2 s

value of 5.9 is demonstrated experimentally for the microwave frequency range.

**4.1. Concept of all–dielectric superdirective optical nanoantennas**

a red arrow.

Practically, the value S*<sup>n</sup>* = 4 . . . 5 is sufficient for superdirectivity of a sphere. In this work, maximum of 6.5 for S*<sup>n</sup>* is predicted theoretically for the optical frequency range, and the

*Here we demonstrate a possibility to create a superdirective nanoantenna without hypothetic metamaterials and plasmonic arrays.* We consider a silicon nanoparticle, taking into account the frequency dispersion of the dielectric permittivity [79]. The radius of the silicon sphere is equal in our example to Rs = 90 nm. For a simple sphere under rather homogeneous (e.g. plane-wave) excitation, only electric and magnetic dipoles can be resonantly excited while the contribution of higher-order multipoles is negligible in the visible [37]. Making a notch in the sphere breaks the symmetry and increases the contribution of higher-order multipoles into scattering even if the sphere is still excited homogeneously. Further, placing a nanoemitter (e.g. a quantum dot) inside the notch, as shown in Fig. 14 we create the conditions for the resonant excitation of multipoles: the field exciting the resonator is now spatially very non-uniform as well as the field of a set of multipoles. In principle, the notched particle operating as a nanoantenna can be performed by different semiconductor materials and have various shapes – spherical, ellipsoidal, cubic, conical, as well as the notch. However, in this work, the particle is a silicon sphere and the notch has the shape of a hemisphere with a radius Rn *<* Rs. The emitter is modeled as a point-like dipole and it is shown in Fig. 14 by

It is important to mention that our approach is seemingly close to the idea of references [101, 102] where a small notch on a surface of a semiconductor microlaser was used to achieve higher emission directivity by modifying the field distribution inside the resonator [103]. An important difference between those earlier studies and our work is that the design discussed earlier is not optically small and the directive emission is not related to superdirectivity. In our case, the nanoparticle is much smaller than the wavelength, and our design allows superdirectivity. For the same reason our nanoantenna is not dielectric [104, 105] or Luneburg [106, 107] lenses. For example, immersion lenses [108–111] are the smallest from known dielectric lenses, characterized by the large size 1-2 *µ*m in optical frequency range. The working methodology of such lenses is to collect a radiation by large geometric aperture S, while S*<sup>n</sup>* 1. *Our approach demonstrates that the subwavelength system, with small geometric aperture, can have high directing power because of an increase of the effective aperture.* Moreover, there are articles (see. references [85, 112]) where the transition rates of atoms inside and outside big dielectric spheres with low dielectric constant (approximately 2), were studied. First, we consider a particle without a notch but excited inhomogeneously by an emitter point. To study the problem numerically, we employed the simulation software CST Microwave Studio. Image Fig. 15A shows the dependence of the maximum directivity Dmax on the position of the source in the case of a sphere Rs = 90 nm without a notch, at the

Superdirectivity was predicted theoretically for an antenna system [95] where some phase shifts were required between radiating elements to achieve complex shapes of the elements of a radiating system which operates as an antenna array. In this paper, we employ the properties of subwavelength particles excited by an inhomogeneous field with higher-order magnetic multipoles. We consider a subwavelength dielectric nanoantenna (with the size of 0.4 wavelength) with a notch resonator excited by a point-like emitter located in the notch. The notch transforms the energy of the generated magneto-dipole Mie resonance into high-order multipole moments, where the magnetic multipoles dominate. This system is resonantly scattering i.e. it is very different from dielectric lenses and usual dielectric cavities which are large compared to the wavelength. Another important feature of the notched resonator is its huge sensitivity of the radiation direction to a spatial position of the emitter. This property leads to a strong beam steering effect and subwavelength sensitivity of the radiation direction to the source location. The proposed design of superdirective nanoantennas may also be useful for collecting single-source radiation, monitoring quantum objects states, and nanoscale microscopy. In order to achieve superdirectivity, we should generate subwavelength spatial oscillations of the radiating currents [80, 99, 100]. Then, near fields of the antenna become strongly inhomogeneous, and the near-field zone expands farther than that of a point dipole. The effective antenna aperture can be defined as <sup>S</sup> = Dmax*λ*2/(4*π*), where the maximum of directivity Dmax = <sup>4</sup>*π*Pmax/Ptot, *<sup>λ</sup>* is the wavelength in free space in our case, Pmax and Ptot are respectively the maximum power in the direction of the radiation pattern and the total radiation power. By normalizing the effective aperture S by the geometric aperture for a spherical antenna S0 = *π*R<sup>2</sup> s, we obtain the definition of superdirectivity [80, 99]:

**Figure 14.** (**A**) Geometry of an all-dielectric superdirective nanoantenna excited by a point-like dipole. (**B**) Concept of the beam steering effect at the nanoscale.

$$\mathbf{S}\_{\rm ll} = \frac{\mathbf{D}\_{\rm max} \lambda^2}{4\pi^2 \mathbf{R}\_{\rm S}^2} \gg 1 \tag{6}$$

Practically, the value S*<sup>n</sup>* = 4 . . . 5 is sufficient for superdirectivity of a sphere. In this work, maximum of 6.5 for S*<sup>n</sup>* is predicted theoretically for the optical frequency range, and the value of 5.9 is demonstrated experimentally for the microwave frequency range.

#### **4.1. Concept of all–dielectric superdirective optical nanoantennas**

16 Progress in Compact Antennas

Superdirectivity has been already discussed for radio-frequency antennas, and it is defined as directivity of an electrically small radiating system that significantly exceeds (at least in 3 times) directivity of an electric dipole [80, 99, 100]. In that sense, the Huygens source is not superdirective. In the antenna literature, superdirectivity is claimed to be achievable only in antenna arrays by the price of ultimately narrow frequency range and by employing very precise phase shifters (see, e.g., Ref. [80, 99, 100]). Therefore, superdirective antennas, though very desirable for many applications such as space communications and radioastronomy,

Superdirectivity was predicted theoretically for an antenna system [95] where some phase shifts were required between radiating elements to achieve complex shapes of the elements of a radiating system which operates as an antenna array. In this paper, we employ the properties of subwavelength particles excited by an inhomogeneous field with higher-order magnetic multipoles. We consider a subwavelength dielectric nanoantenna (with the size of 0.4 wavelength) with a notch resonator excited by a point-like emitter located in the notch. The notch transforms the energy of the generated magneto-dipole Mie resonance into high-order multipole moments, where the magnetic multipoles dominate. This system is resonantly scattering i.e. it is very different from dielectric lenses and usual dielectric cavities which are large compared to the wavelength. Another important feature of the notched resonator is its huge sensitivity of the radiation direction to a spatial position of the emitter. This property leads to a strong beam steering effect and subwavelength sensitivity of the radiation direction to the source location. The proposed design of superdirective nanoantennas may also be useful for collecting single-source radiation, monitoring quantum objects states, and nanoscale microscopy. In order to achieve superdirectivity, we should generate subwavelength spatial oscillations of the radiating currents [80, 99, 100]. Then, near fields of the antenna become strongly inhomogeneous, and the near-field zone expands farther than that of a point dipole. The effective antenna aperture can be defined as <sup>S</sup> = Dmax*λ*2/(4*π*), where the maximum of directivity Dmax = <sup>4</sup>*π*Pmax/Ptot, *<sup>λ</sup>* is the wavelength in free space in our case, Pmax and Ptot are respectively the maximum power in the direction of the radiation pattern and the total radiation power. By normalizing the

effective aperture S by the geometric aperture for a spherical antenna S0 = *π*R<sup>2</sup>

**Figure 14.** (**A**) Geometry of an all-dielectric superdirective nanoantenna excited by a point-like dipole. (**B**) Concept of the

the definition of superdirectivity [80, 99]:

beam steering effect at the nanoscale.

s, we obtain

were never demonstrated and implemented for practical applications.

*Here we demonstrate a possibility to create a superdirective nanoantenna without hypothetic metamaterials and plasmonic arrays.* We consider a silicon nanoparticle, taking into account the frequency dispersion of the dielectric permittivity [79]. The radius of the silicon sphere is equal in our example to Rs = 90 nm. For a simple sphere under rather homogeneous (e.g. plane-wave) excitation, only electric and magnetic dipoles can be resonantly excited while the contribution of higher-order multipoles is negligible in the visible [37]. Making a notch in the sphere breaks the symmetry and increases the contribution of higher-order multipoles into scattering even if the sphere is still excited homogeneously. Further, placing a nanoemitter (e.g. a quantum dot) inside the notch, as shown in Fig. 14 we create the conditions for the resonant excitation of multipoles: the field exciting the resonator is now spatially very non-uniform as well as the field of a set of multipoles. In principle, the notched particle operating as a nanoantenna can be performed by different semiconductor materials and have various shapes – spherical, ellipsoidal, cubic, conical, as well as the notch. However, in this work, the particle is a silicon sphere and the notch has the shape of a hemisphere with a radius Rn *<* Rs. The emitter is modeled as a point-like dipole and it is shown in Fig. 14 by a red arrow.

It is important to mention that our approach is seemingly close to the idea of references [101, 102] where a small notch on a surface of a semiconductor microlaser was used to achieve higher emission directivity by modifying the field distribution inside the resonator [103]. An important difference between those earlier studies and our work is that the design discussed earlier is not optically small and the directive emission is not related to superdirectivity. In our case, the nanoparticle is much smaller than the wavelength, and our design allows superdirectivity. For the same reason our nanoantenna is not dielectric [104, 105] or Luneburg [106, 107] lenses. For example, immersion lenses [108–111] are the smallest from known dielectric lenses, characterized by the large size 1-2 *µ*m in optical frequency range. The working methodology of such lenses is to collect a radiation by large geometric aperture S, while S*<sup>n</sup>* 1. *Our approach demonstrates that the subwavelength system, with small geometric aperture, can have high directing power because of an increase of the effective aperture.* Moreover, there are articles (see. references [85, 112]) where the transition rates of atoms inside and outside big dielectric spheres with low dielectric constant (approximately 2), were studied.

First, we consider a particle without a notch but excited inhomogeneously by an emitter point. To study the problem numerically, we employed the simulation software CST Microwave Studio. Image Fig. 15A shows the dependence of the maximum directivity Dmax on the position of the source in the case of a sphere Rs = 90 nm without a notch, at the wavelength *λ* = 455 nm (blue curve with crosses). This dependence has the maximum (Dmax = 7.1) when the emitter is placed inside the particle at the distance 20 nm from its surface. The analysis shows that in this case the electric field distribution inside a particle corresponds to the noticeable excitation of higher-order multipole modes not achievable with the homogeneous excitation.

10.5772/58850

All-Dielectric Optical Nanoantennas 161

**Figure 16.** Distribution of (**A**) absolute values and (**B**) phases of the electric field (**C** and **D** for magnetic field, respectively) of the all-dielectric superdirective nanoantenna with source in the center of notch, at the wavelength *λ* = 455 nm. (**E**) Dependence of the radiation pattern of all-dielectric superdirective nanoantenna on the number of taken into account multipoles. Dipole like

simulated internal field, producing the polarization currents in the nanoparticle, into multipole moments following to [116]. The expansion is a series of vector spherical harmonics with the coefficients *aE*(*l*, *m*) and *aM*(*l*, *m*), which characterize the electrical and

> *lm*div **<sup>r</sup>** <sup>×</sup> **<sup>j</sup>** *c*

where *ρ* = 1/(4*π*)div(E) and **j** = *c*/(4*π*)(rot(H) + *ik*E) are densities of the *total* electrical charges and currents that can be easily expressed through the internal electric E and magnetic H fields of the sphere, *Ylm* are the spherical harmonics of the orders (*l >* 0 and 0 ≥ |*m*| ≤ *l*), *k* = 2*π*/*λ*, *jl*(*kr*) are the *l*-order spherical Bessel function and *c* is the speed of light. Coefficients *aE*(*l*, *m*) and *aM*(*l*, *m*) determine the electric and magnetic mutipole moments,

The multipole coefficients determine not only the mode structure of the internal field but also the angular distribution of the radiation. In particular, in the far field zone electric and

[*rjl*(*kr*)] + *ik*

*<sup>c</sup>* (**<sup>r</sup>** · **<sup>j</sup>**)*jl*(*kr*)

 *d*3*x*,

*jl*(*kr*)*d*3*x*, (7)

source located along the *z* axis.

magnetic multipole moments [116]:

*aE*(*l*, *<sup>m</sup>*) = <sup>4</sup>*πk*<sup>2</sup> *i*

*aM*(*l*, *<sup>m</sup>*) = <sup>4</sup>*πk*<sup>2</sup> *i*

*l*(*l* + 1)

*l*(*l* + 1)

namely dipole at *l* = 1, quadrupole at *l* = 2, octupole at *l* = 3 etc.

 *Y*∗ *lm ρ ∂ ∂r*

 *Y*∗

Furthermore, the amplitudes of high-order multipoles are significantly enhanced with a small notch around the emitter, as it is shown in Fig. 14. This geometry transforms it into a resonator with high-order multipole moments. In this example the center of the notch is on the nanosphere's surface. The optimal radius of the notch (for maximal directivity) is Rn = 40 nm. In Fig. 15A the extrapolation red curve with circles, corresponding to simulation results, shows the maximal directivity versus the location of the emitter at the wavelength 455 nm. The Fig. 15B shows the directivity versus *λ* with and without a notch, it exhibits a maximum of 10 for the directivity at 455 nm. The inset shows the three-dimensional radiation pattern of the structure at *λ* =455 nm. This pattern has an angular width (at the level of 3 dB) of the main lobe equal to 40◦. This value of directivity corresponds to the normalized effective aperture S*<sup>n</sup>* = 6.5.

Figures Fig. 16A and B show the distribution of the absolute values and phases of the internal electric field in the vicinity of the nanoantenna. Electric and magnetic fields inside the particle are strongly inhomogeneous at *λ* =455 nm i.e. in the regime of the maximal directivity. In this regime, the internal area where the electric field oscillates with approximately the same phase turns out to be maximal. This area is located near the back side of the spherical particle, as can be seen in figure Fig. 16B,D. In other words, the effective near zone of the nanoantenna is maximal in the superdirective regime.

Usually, high directivity of plasmonic nanoantennas is achieved by the excitation of higher *electrical* multipole moments in plasmonic nanoparticles [83, 113, 114] or for core-shell resonators consisting of a plasmonic material and a hypothetic metamaterial which would demonstrate the extreme material properties in the nanoscale [115]. Although, the values of directivity achieved for such nanoantennas do not allow superdirectivity, these studies stress the importance of higher multipoles for the antenna directivity.

Next, we demonstrate how to find multipole modes excited in the all-dielectric superdirective nanoantenna which are responsible for its enhanced directivity. We expand the exactly

**Figure 15.** (**A**) Maximum of directivity depending on the position of the emitter (*λ* = 455 nm) in the case of a sphere with and without notch. Vertical dashed line marks the particle radius centered at the coordinate system. (**B**) Directivity dependence on the radiation wavelength. The inset shows three-dimensional radiation pattern of the structure (Rs = 90 nm and Rn = 40 nm).

18 Progress in Compact Antennas

the homogeneous excitation.

effective aperture S*<sup>n</sup>* = 6.5.

nanoantenna is maximal in the superdirective regime.

the importance of higher multipoles for the antenna directivity.

wavelength *λ* = 455 nm (blue curve with crosses). This dependence has the maximum (Dmax = 7.1) when the emitter is placed inside the particle at the distance 20 nm from its surface. The analysis shows that in this case the electric field distribution inside a particle corresponds to the noticeable excitation of higher-order multipole modes not achievable with

Furthermore, the amplitudes of high-order multipoles are significantly enhanced with a small notch around the emitter, as it is shown in Fig. 14. This geometry transforms it into a resonator with high-order multipole moments. In this example the center of the notch is on the nanosphere's surface. The optimal radius of the notch (for maximal directivity) is Rn = 40 nm. In Fig. 15A the extrapolation red curve with circles, corresponding to simulation results, shows the maximal directivity versus the location of the emitter at the wavelength 455 nm. The Fig. 15B shows the directivity versus *λ* with and without a notch, it exhibits a maximum of 10 for the directivity at 455 nm. The inset shows the three-dimensional radiation pattern of the structure at *λ* =455 nm. This pattern has an angular width (at the level of 3 dB) of the main lobe equal to 40◦. This value of directivity corresponds to the normalized

Figures Fig. 16A and B show the distribution of the absolute values and phases of the internal electric field in the vicinity of the nanoantenna. Electric and magnetic fields inside the particle are strongly inhomogeneous at *λ* =455 nm i.e. in the regime of the maximal directivity. In this regime, the internal area where the electric field oscillates with approximately the same phase turns out to be maximal. This area is located near the back side of the spherical particle, as can be seen in figure Fig. 16B,D. In other words, the effective near zone of the

Usually, high directivity of plasmonic nanoantennas is achieved by the excitation of higher *electrical* multipole moments in plasmonic nanoparticles [83, 113, 114] or for core-shell resonators consisting of a plasmonic material and a hypothetic metamaterial which would demonstrate the extreme material properties in the nanoscale [115]. Although, the values of directivity achieved for such nanoantennas do not allow superdirectivity, these studies stress

Next, we demonstrate how to find multipole modes excited in the all-dielectric superdirective nanoantenna which are responsible for its enhanced directivity. We expand the exactly

**Figure 15.** (**A**) Maximum of directivity depending on the position of the emitter (*λ* = 455 nm) in the case of a sphere with and without notch. Vertical dashed line marks the particle radius centered at the coordinate system. (**B**) Directivity dependence on the radiation wavelength. The inset shows three-dimensional radiation pattern of the structure (Rs = 90 nm and Rn = 40 nm).

**Figure 16.** Distribution of (**A**) absolute values and (**B**) phases of the electric field (**C** and **D** for magnetic field, respectively) of the all-dielectric superdirective nanoantenna with source in the center of notch, at the wavelength *λ* = 455 nm. (**E**) Dependence of the radiation pattern of all-dielectric superdirective nanoantenna on the number of taken into account multipoles. Dipole like source located along the *z* axis.

simulated internal field, producing the polarization currents in the nanoparticle, into multipole moments following to [116]. The expansion is a series of vector spherical harmonics with the coefficients *aE*(*l*, *m*) and *aM*(*l*, *m*), which characterize the electrical and magnetic multipole moments [116]:

$$a\_E(l,m) = \frac{4\pi k^2}{i\sqrt{l(l+1)}} \int Y\_{lm}^\* \left[\rho \frac{\partial}{\partial r} [r j\_l(kr)] + \frac{ik}{c} (\mathbf{r} \cdot \mathbf{j}) j\_l(kr) \right] d^3 \mathbf{x},$$

$$a\_M(l,m) = \frac{4\pi k^2}{i\sqrt{l(l+1)}} \int Y\_{lm}^\* \text{div} \left(\frac{\mathbf{r} \times \mathbf{j}}{c}\right) j\_l(kr) d^3 \mathbf{x},\tag{7}$$

where *ρ* = 1/(4*π*)div(E) and **j** = *c*/(4*π*)(rot(H) + *ik*E) are densities of the *total* electrical charges and currents that can be easily expressed through the internal electric E and magnetic H fields of the sphere, *Ylm* are the spherical harmonics of the orders (*l >* 0 and 0 ≥ |*m*| ≤ *l*), *k* = 2*π*/*λ*, *jl*(*kr*) are the *l*-order spherical Bessel function and *c* is the speed of light. Coefficients *aE*(*l*, *m*) and *aM*(*l*, *m*) determine the electric and magnetic mutipole moments, namely dipole at *l* = 1, quadrupole at *l* = 2, octupole at *l* = 3 etc.

The multipole coefficients determine not only the mode structure of the internal field but also the angular distribution of the radiation. In particular, in the far field zone electric and magnetic fields of *<sup>l</sup>*-order multipole depend on the distance *<sup>r</sup>* as [116] <sup>∼</sup> (−1)*i*+<sup>1</sup> exp(*ikr*) *kr* and expression for the angular distribution of the radiation power can be written as follows:

$$\frac{\mathrm{d}P(\theta,\boldsymbol{\theta})}{\mathrm{d}\Omega} = \frac{c}{8\pi k^2} \left| \sum\_{l,m} (-i)^{l+1} [a\_E(l,m)\mathbf{X}\_{lm} \times \mathbf{n} + a\_M(l,m)\mathbf{X}\_{lm}] \right|^2,$$

$$\mathbf{X}\_{lm}(\theta,\boldsymbol{\theta}) = \frac{1}{\sqrt{l(l+1)}} \begin{bmatrix} A\_{l,m}^- Y\_{l,m+1} + A\_{l,m}^+ Y\_{l,m-1} \\ -i A\_{l,m}^- Y\_{l,m+1} + i A\_{l,m}^+ Y\_{l,m-1} \\ m Y\_{l,m} \end{bmatrix},\tag{8}$$

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All-Dielectric Optical Nanoantennas 163

We have performed the transformation of multipole coefficients into an angular distribution of radiation in accordance to (8) by using distribution of the electric and magnetic fields Fig. 16A-D and determined the relative contribution of each order *l*. Fig. 16E shows how the directivity grows versus the spectrum of multipoles with equivalent amplitudes. The right panel of Fig. 16E nearly corresponds to the inset in Fig. 15 that fits to the results shown in

Generally, the superdirectivity effect is accompanied by a significant increase of the effective near field zone of the antenna compared to the one of a point dipole for which the near zone radius is equal to *λ*/2*π*. In the optical frequency range this effect is especially important,

Usually, the superdirectivity regime corresponds to a strong increase of dissipative losses [80]. Radiation efficiency of the nanoantenna is determined by *η*rad = Prad/Pin, where Pin is the accepted input power of the nanoantenna. However, the multipole moments excited in our nanoantenna are mainly of magnetic type that leads to a strong increase of the near magnetic field that dominates over the electric one. Since the dielectric material does not dissipate the magnetic energy, the effect of superdirectivity does not lead to a so large increase of losses in our nanoantenna as it would be in the case of dominating electric multipoles. However, since the electric near field is nonzero the losses are not negligible. At wavelengths 440-460 nm (blue light) the directivity achieves 10 but the radiation efficiency is less than 0.1 (see [Fig. 18)]. This is because silicon has very high losses in this range [79]. Peak of directivity is shifted to longer wavelengths with the increase of the nanoantenna size. For the design parameters corresponding to the operation wavelength 630 nm (red light) the calculated value of radiation efficiency is as high as 0.5, with nearly same directivity close to 10. In the infrared range, there are high dielectric permittivity materials with even lower losses. In principle, the proposed superdirectivity effect is not achieved by price of increased losses, and this is an important advantage compared to known superdirective radio-frequency antenna arrays [80] and compared to their possible optical analogues –

Here we examine the response of the nanoantenna to subwavelength displacements of the emitter. Displacement in the plane perpendicular to the axial symmetry of antenna (i.e. along

**Figure 18.** Dependence of directivity (**A**) and radiation efficiency (**B**) on the size of nanoantenna. Here, the blue solid lines corresponds to the geometry – Rs = 90 nm, Rn = 40 nm, the green dashed curves – Rs = 120 nm, Rn = 55 nm and red point curves – Rs = 150 nm, Rn = 65 nm. Growth of the nanoantenna efficiency due to the reduction of dissipative losses in silicon

considering the crucial role of the near fields at the nanoscale.

arrays of plasmonic nanoantennas.

with increasing of wavelength.

**4.2. Steering of light at the nanoscale**

Fig. 16E.

where *A*± *<sup>l</sup>*,*<sup>m</sup>* = (1/2) (*<sup>l</sup>* <sup>±</sup> *<sup>m</sup>*)(*<sup>l</sup>* <sup>∓</sup> *<sup>m</sup>* <sup>+</sup> <sup>1</sup>), d<sup>Ω</sup> <sup>=</sup> sin(*θ*)d*θ*d*<sup>ϕ</sup>* is the solid angle element in spherical coordinates and **n** - unit vector of the observation point. All coefficients *aE*(*l*, *m*) and *aM*(*l*, *m*) give the same contribution to the radiation, if they have the same values. Since higher-order multipoles for optically small systems have usually negligibly small amplitudes compared to *aE*(1, *m*) and *aM*(1, *m*), they are, as a rule, not considered.

The amplitudes of multipole moments, are found by using the expressions (7) for electric and magnetic fields distribution Fig. 16A-D are shown in Fig. 17, where we observe strong excitation of *aE*(1, 0), *aM*(1, 1), *aM*(1, −1), *aM*(2, 2), *aM*(2, −2), *aM*(3, 3), *aM*(3, −3), *aM*(4, 2), *aM*(4, −2), *aM*(4, 4) and *aM*(4, −4). These multipole moments determine the angular pattern of the antenna. All other ones give a negligible contribution. Absolute values of all magnetic moments are larger than those of the electric moments in the corresponding multipole orders, and the effective spectrum of magnetic multipoles is also broader than the one of the electric moments. Thus, the operation of the antenna is mainly determined by the magnetic multipole response. Absolute values of multipole coefficients *aM*(*l*, ±|*m*|) of the same order *l* are practically equivalent. However, the phase of some coefficients are different. Therefore, the modes with +|*m*| and −|*m*| form a strong anisotropy of the forward–backward directions that results in the unidirectional radiation.

**Figure 17.** Absolute values and phases of (**A**) electric and (**B**) magnetic multipole moments that provide the main contribution of the radiation of all-dielectric superdirective optical nanoantenna at the wavelength 455 nm. Multipole coefficients providing the largest contribution to the antenna direction are highlighted by red circles.

We have performed the transformation of multipole coefficients into an angular distribution of radiation in accordance to (8) by using distribution of the electric and magnetic fields Fig. 16A-D and determined the relative contribution of each order *l*. Fig. 16E shows how the directivity grows versus the spectrum of multipoles with equivalent amplitudes. The right panel of Fig. 16E nearly corresponds to the inset in Fig. 15 that fits to the results shown in Fig. 16E.

Generally, the superdirectivity effect is accompanied by a significant increase of the effective near field zone of the antenna compared to the one of a point dipole for which the near zone radius is equal to *λ*/2*π*. In the optical frequency range this effect is especially important, considering the crucial role of the near fields at the nanoscale.

Usually, the superdirectivity regime corresponds to a strong increase of dissipative losses [80]. Radiation efficiency of the nanoantenna is determined by *η*rad = Prad/Pin, where Pin is the accepted input power of the nanoantenna. However, the multipole moments excited in our nanoantenna are mainly of magnetic type that leads to a strong increase of the near magnetic field that dominates over the electric one. Since the dielectric material does not dissipate the magnetic energy, the effect of superdirectivity does not lead to a so large increase of losses in our nanoantenna as it would be in the case of dominating electric multipoles. However, since the electric near field is nonzero the losses are not negligible. At wavelengths 440-460 nm (blue light) the directivity achieves 10 but the radiation efficiency is less than 0.1 (see [Fig. 18)]. This is because silicon has very high losses in this range [79]. Peak of directivity is shifted to longer wavelengths with the increase of the nanoantenna size. For the design parameters corresponding to the operation wavelength 630 nm (red light) the calculated value of radiation efficiency is as high as 0.5, with nearly same directivity close to 10. In the infrared range, there are high dielectric permittivity materials with even lower losses. In principle, the proposed superdirectivity effect is not achieved by price of increased losses, and this is an important advantage compared to known superdirective radio-frequency antenna arrays [80] and compared to their possible optical analogues – arrays of plasmonic nanoantennas.

#### **4.2. Steering of light at the nanoscale**

20 Progress in Compact Antennas

where *A*±

d*P*(*θ*, *ϕ*)

*<sup>l</sup>*,*<sup>m</sup>* = (1/2)

<sup>d</sup><sup>Ω</sup> <sup>=</sup> *<sup>c</sup>*

**<sup>X</sup>***lm*(*θ*, *<sup>ϕ</sup>*) = <sup>1</sup>

that results in the unidirectional radiation.

the largest contribution to the antenna direction are highlighted by red circles.

8*πk*<sup>2</sup>

 ∑ *l*,*m*

> 

compared to *aE*(1, *m*) and *aM*(1, *m*), they are, as a rule, not considered.

*A*−

−*iA*<sup>−</sup>

*l*(*l* + 1)

magnetic fields of *<sup>l</sup>*-order multipole depend on the distance *<sup>r</sup>* as [116] <sup>∼</sup> (−1)*i*+<sup>1</sup> exp(*ikr*)

expression for the angular distribution of the radiation power can be written as follows:

(−*i*)*l*+1[*aE*(*l*, *<sup>m</sup>*)**X***lm* <sup>×</sup> **<sup>n</sup>** <sup>+</sup> *aM*(*l*, *<sup>m</sup>*)**X***lm*]

(*<sup>l</sup>* <sup>±</sup> *<sup>m</sup>*)(*<sup>l</sup>* <sup>∓</sup> *<sup>m</sup>* <sup>+</sup> <sup>1</sup>), d<sup>Ω</sup> <sup>=</sup> sin(*θ*)d*θ*d*<sup>ϕ</sup>* is the solid angle element in

*<sup>l</sup>*,*mYl*,*m*−<sup>1</sup>

*<sup>l</sup>*,*mYl*,*m*−<sup>1</sup>

*<sup>l</sup>*,*mYl*,*m*+<sup>1</sup> <sup>+</sup> *<sup>A</sup>*<sup>+</sup>

spherical coordinates and **n** - unit vector of the observation point. All coefficients *aE*(*l*, *m*) and *aM*(*l*, *m*) give the same contribution to the radiation, if they have the same values. Since higher-order multipoles for optically small systems have usually negligibly small amplitudes

The amplitudes of multipole moments, are found by using the expressions (7) for electric and magnetic fields distribution Fig. 16A-D are shown in Fig. 17, where we observe strong excitation of *aE*(1, 0), *aM*(1, 1), *aM*(1, −1), *aM*(2, 2), *aM*(2, −2), *aM*(3, 3), *aM*(3, −3), *aM*(4, 2), *aM*(4, −2), *aM*(4, 4) and *aM*(4, −4). These multipole moments determine the angular pattern of the antenna. All other ones give a negligible contribution. Absolute values of all magnetic moments are larger than those of the electric moments in the corresponding multipole orders, and the effective spectrum of magnetic multipoles is also broader than the one of the electric moments. Thus, the operation of the antenna is mainly determined by the magnetic multipole response. Absolute values of multipole coefficients *aM*(*l*, ±|*m*|) of the same order *l* are practically equivalent. However, the phase of some coefficients are different. Therefore, the modes with +|*m*| and −|*m*| form a strong anisotropy of the forward–backward directions

**Figure 17.** Absolute values and phases of (**A**) electric and (**B**) magnetic multipole moments that provide the main contribution of the radiation of all-dielectric superdirective optical nanoantenna at the wavelength 455 nm. Multipole coefficients providing

*<sup>l</sup>*,*mYl*,*m*+<sup>1</sup> <sup>+</sup> *iA*<sup>+</sup>

*mYl*,*<sup>m</sup>*

*kr* and

  2 ,

, (8)

Here we examine the response of the nanoantenna to subwavelength displacements of the emitter. Displacement in the plane perpendicular to the axial symmetry of antenna (i.e. along

**Figure 18.** Dependence of directivity (**A**) and radiation efficiency (**B**) on the size of nanoantenna. Here, the blue solid lines corresponds to the geometry – Rs = 90 nm, Rn = 40 nm, the green dashed curves – Rs = 120 nm, Rn = 55 nm and red point curves – Rs = 150 nm, Rn = 65 nm. Growth of the nanoantenna efficiency due to the reduction of dissipative losses in silicon with increasing of wavelength.

All-Dielectric Optical Nanoantennas 165

**Figure 21.** Photographs of (**A**) top view and (**B**) perspective view of a notched all-dielectric microwave antenna. Image of (**C**) the experimental setup for measuring of power patterns. Experimental (i) and numerical (ii) radiation patterns of the antenna in both *E*- and *H*-planes at the frequency 16.8 GHz. The crosses and circles correspond to the experimental data. Experimental

To interpret the beam steering effect, we can consider the result of field expansion to electric and magnetic multipoles, as shown in Fig.20. In the case of asymmetrical location (the 20 nm left offset) of the source in the notch absolute values of *aM*(*l*, ±|*m*|) are different. This means that the mode *aM*(*l*, +|*m*|) is excited more strongly than *aM*(*l*, −|*m*|), or vice versa, that depends on direction of displacement. The effect of superdirectivity remains even with an offset of the source until to the edge of the notch. Small displacements of the source along

Instead of the movement of a single quantum dot one we can have the emission of two or more quantum dots located near the edges of the notch. In this case, the dynamics of their spontaneous decay will be well displayed in the angular distribution of the radiation. This

Beam steering effect described above is similar to the effect of beam rotation in hyperlens [117–119], where the displacement of a point-like source leads to a change of the angular distribution of the radiation power. However, in our case, the nanoantenna has subwavelength dimensions and therefore it can be neither classified as a hyperlens nor as a micro-spherical dielectric nanoscope [104, 105], moreover it is not an analogue of solid immersion micro-lenses [108–111], which are characterized by the size 1-5 *µm* in the same frequency range. These lens has a subwavelength resolving power due to the large geometric aperture but the value of normalized effective aperture is S*<sup>n</sup>* 1. Our study demonstrates that the sub-wavelength system, with *small compared to the wavelength* geometric aperture can have both high directing and resolving power *because of a strong increase of the effective aperture*

We have confirmed both predicted effects studying the similar problem for the microwave range. Therefore, we have scaled up the nanoantenna as above to low frequencies. Instead

can be useful for quantum information processing and for biomedical applications.

**4.3. Experimental verification of superdirective optical nanoantenna**

(iii) and numerical (iv) demonstration of beam steering effect, displacement of dipole is equal 0.5 mm.

*x* and *z* do not lead to the rotation of the pattern.

*compared to the geometrical one*.

**Figure 19.** The rotation effect of the main beam radiation pattern, with subwavelength displacement of emitter inside the notch. (**A**) The radiation patterns of the antenna with the source in center (solid line) and the rotation of the beam radiation pattern for the 20 nm left/right offset (dashed lines). (**B**) Dependence of the rotation angle on the source offset.

the *y* axis) leads to the rotation of the beam *without damaging the superdirectivity*. Fig.19A shows the radiation patterns of the antenna with the source in center (solid line) and the rotation of the beam for the 20 nm left/right offset (dashed lines). Shifting of the source in the right side leads to the rotation of pattern to the left, and vice versa. The angle of the beam rotation is equal to 20 degrees, that is essential and available to experimental observations. The result depends on the geometry of the notch. For a hemispherical notch, the dependence of the rotation angle on the displacement is presented in Fig.19B.

**Figure 20.** Absolute values and phases of (**A**) electric and (**B**) magnetic multipole moments that provide the main contribution to the radiation of all-dielectric superdirective optical nanoantenna in case of asymmetrical location of source at the wavelength 455 nm. Coefficients that give the largest contribution to the antenna directivity are highlighted by red circles.

22 Progress in Compact Antennas

**Figure 19.** The rotation effect of the main beam radiation pattern, with subwavelength displacement of emitter inside the notch. (**A**) The radiation patterns of the antenna with the source in center (solid line) and the rotation of the beam radiation

the *y* axis) leads to the rotation of the beam *without damaging the superdirectivity*. Fig.19A shows the radiation patterns of the antenna with the source in center (solid line) and the rotation of the beam for the 20 nm left/right offset (dashed lines). Shifting of the source in the right side leads to the rotation of pattern to the left, and vice versa. The angle of the beam rotation is equal to 20 degrees, that is essential and available to experimental observations. The result depends on the geometry of the notch. For a hemispherical notch, the dependence

**Figure 20.** Absolute values and phases of (**A**) electric and (**B**) magnetic multipole moments that provide the main contribution to the radiation of all-dielectric superdirective optical nanoantenna in case of asymmetrical location of source at the wavelength

455 nm. Coefficients that give the largest contribution to the antenna directivity are highlighted by red circles.

pattern for the 20 nm left/right offset (dashed lines). (**B**) Dependence of the rotation angle on the source offset.

of the rotation angle on the displacement is presented in Fig.19B.

**Figure 21.** Photographs of (**A**) top view and (**B**) perspective view of a notched all-dielectric microwave antenna. Image of (**C**) the experimental setup for measuring of power patterns. Experimental (i) and numerical (ii) radiation patterns of the antenna in both *E*- and *H*-planes at the frequency 16.8 GHz. The crosses and circles correspond to the experimental data. Experimental (iii) and numerical (iv) demonstration of beam steering effect, displacement of dipole is equal 0.5 mm.

To interpret the beam steering effect, we can consider the result of field expansion to electric and magnetic multipoles, as shown in Fig.20. In the case of asymmetrical location (the 20 nm left offset) of the source in the notch absolute values of *aM*(*l*, ±|*m*|) are different. This means that the mode *aM*(*l*, +|*m*|) is excited more strongly than *aM*(*l*, −|*m*|), or vice versa, that depends on direction of displacement. The effect of superdirectivity remains even with an offset of the source until to the edge of the notch. Small displacements of the source along *x* and *z* do not lead to the rotation of the pattern.

Instead of the movement of a single quantum dot one we can have the emission of two or more quantum dots located near the edges of the notch. In this case, the dynamics of their spontaneous decay will be well displayed in the angular distribution of the radiation. This can be useful for quantum information processing and for biomedical applications.

Beam steering effect described above is similar to the effect of beam rotation in hyperlens [117–119], where the displacement of a point-like source leads to a change of the angular distribution of the radiation power. However, in our case, the nanoantenna has subwavelength dimensions and therefore it can be neither classified as a hyperlens nor as a micro-spherical dielectric nanoscope [104, 105], moreover it is not an analogue of solid immersion micro-lenses [108–111], which are characterized by the size 1-5 *µm* in the same frequency range. These lens has a subwavelength resolving power due to the large geometric aperture but the value of normalized effective aperture is S*<sup>n</sup>* 1. Our study demonstrates that the sub-wavelength system, with *small compared to the wavelength* geometric aperture can have both high directing and resolving power *because of a strong increase of the effective aperture compared to the geometrical one*.

#### **4.3. Experimental verification of superdirective optical nanoantenna**

We have confirmed both predicted effects studying the similar problem for the microwave range. Therefore, we have scaled up the nanoantenna as above to low frequencies. Instead of Si we employ MgO-TiO2 ceramic [46] characterized at microwaves by a dispersion-less dielectric constant 16 and dielectric loss factor of 1.12·10−4. We have used the sphere of radius Rs = 5 mm and applied a small wire dipole [80] excited by a coaxial cable as shown in Fig. 21A,B. The size of the hemispherical notch is approximately equal to Rn = 2 mm. Antenna properties have been studied in an anechoic chamber Fig. 21C.

10.5772/58850

All-Dielectric Optical Nanoantennas 167

perfect spherical nanoparticles and helium ion beam milling to structure their surface with sub-5nm resolution [120]. This novel approach can become a suitable candidate for realizing

In this chapter, we propose a new type of highly efficient Yagi-Uda nanoantenna and introduced a novel concept of superdirective nanoantennas based on silicon nanoparticles. In addition to the electric response, this silicon nanoantennas exhibit very strong magnetic resonances at the nanoscale. Both types of nanoantennas are studied analytically, numerically and experimentally. For superdirective nanoantennas we also predict the effect of the beam steering at the nanoscale characterized by a subwavelength sensitivity of the beam radiation

Dielectric nanoparticles with high refractive index offer new possibilities for achieving wave interference. Indeed, the coexistence of both electric and magnetic resonances results in a unidirectional scattering. This property makes subwavelength dielectric nanoparticles the smallest and most efficient nanoantennas. Moreover, unidirectionality can be swapped for

The unique optical properties and low losses make dielectric nanoparticles perfect candidates for a design of high-performance nanoantennas, low-loss metamaterials, and other novel all-dielectric nanophotonic devices. The key to such novel functionalities of high-index dielectric nanophotonic elements is the ability of subwavelength dielectric nanoparticles to support simultaneously both electric and magnetic resonances, which can be controlled

Alexandr E. Krasnok1, Pavel A. Belov1, Andrey E. Miroshnichenko2, Arseniy I. Kuznetsov3,

2 Nonlinear Physics Centre, Research School of Physics and Engineering, Australian National

3 Data Storage Institute, A\*STAR (Agency for Science, Technology and Research), Singapore

[1] Palash Bharadwaj, Bradley Deutsch, and Lukas Novotny. Optical antennas. *Advances*

[2] Lukas Novotny and Niek van Hulst. Antennas for light. *Nat. Photon.*, 5:83–90, 2011.

[3] Alberto G. Curto, Giorgio Volpe, Tim H. Taminiau, Mark P. Kreuzer, Romain Quidant, and Niek F. van Hulst. Unidirectional emission of a quantum dot coupled to a

all-dielectric superdirective nanoantennas.

direction to the source position.

different wavelengths [74, 76].

**Author details**

**References**

independently for particles of non spherical forms [77, 121].

University, Canberra, Australian Capital Territory, Australia

*in Optics and Photonics*, 1:438–483, 2009.

nanoantenna. *Science*, 329:930–933, 2010.

Boris S. Luk'yanchuk3 and Yuri S. Kivshar1,2

1 ITMO University, St. Petersburg, Russia

**Conclusion**

The results of the experimental investigations and numerical simulations of the pattern in both *E*- and *H*-planes are summarized in Figs. 21i,ii. Radiation patterns in both planes are narrow beams with a lobe angle about 35◦. Experimentally obtained coefficients of the directivity in both *E*- and *H*-planes are equal to 5.9 and 8.4, respectively (theoretical predictions for them were respectively equal 6.8 and 8.1). Our experimental data are in a good agreement with the numerical results except a small difference for the E plane, that can be explained by the imperfect symmetry of the emitter. Note, that the observed directivity is close to that of an all-dielectric Yagi-Uda antenna with maximum size of 2*λ* [46]. The maximum size of our experimental antenna is closed to *λ*/2.5. Thus, our experiment clearly demonstrates the superdirective effect.

**Figure 22.** Level of the return losses of superdirective dielectric antenna. Blue area shows the operating frequency range.

Experimental and numerical demonstration of the beam steering effect are presented in Figs. 21iii,iv. For the chosen geometry of antenna, displacement of source by 0.5 mm leads to a beam rotation of about 10◦. Note that the ratio of *λ* = 18.7 mm to value of the source displacement 0.5 mm is equal to 37. Therefore the beam steering effect observed at subwavelength source displacement.

Finally, we consider the question of dielectric superdirective antenna matching with coaxial cable. Despite that length of the wire dipole is close to *λ*/10, dielectric superdirective antenna is well matched with the coaxial cable in the operating frequency range. Fig.22 shows the level of return loss for this case. The antenna matching is explained by the strong coupling of the wire dipole with the excited modes of notched dielectric particle and is not related to the dissipative losses in the superdirectivity regime. For this reason, we have not used additional matching devices (e.g. "balun").

Though the concept of the superdirectivity of high-refractive index dielectric particles with notch has now only been proven in GHz spectral range there is a hope that it can be transferred into the visible and near-IR spectrum in the nearest future. Recently we have experimentally demonstrated that it is possible to engineer resonant modes of spherical nanoresonators using a combined approach of laser-induced transfer to generate almost

perfect spherical nanoparticles and helium ion beam milling to structure their surface with sub-5nm resolution [120]. This novel approach can become a suitable candidate for realizing all-dielectric superdirective nanoantennas.

#### **Conclusion**

24 Progress in Compact Antennas

demonstrates the superdirective effect.

at subwavelength source displacement.

additional matching devices (e.g. "balun").

of Si we employ MgO-TiO2 ceramic [46] characterized at microwaves by a dispersion-less dielectric constant 16 and dielectric loss factor of 1.12·10−4. We have used the sphere of radius Rs = 5 mm and applied a small wire dipole [80] excited by a coaxial cable as shown in Fig. 21A,B. The size of the hemispherical notch is approximately equal to Rn = 2 mm.

The results of the experimental investigations and numerical simulations of the pattern in both *E*- and *H*-planes are summarized in Figs. 21i,ii. Radiation patterns in both planes are narrow beams with a lobe angle about 35◦. Experimentally obtained coefficients of the directivity in both *E*- and *H*-planes are equal to 5.9 and 8.4, respectively (theoretical predictions for them were respectively equal 6.8 and 8.1). Our experimental data are in a good agreement with the numerical results except a small difference for the E plane, that can be explained by the imperfect symmetry of the emitter. Note, that the observed directivity is close to that of an all-dielectric Yagi-Uda antenna with maximum size of 2*λ* [46]. The maximum size of our experimental antenna is closed to *λ*/2.5. Thus, our experiment clearly

**Figure 22.** Level of the return losses of superdirective dielectric antenna. Blue area shows the operating frequency range. Experimental and numerical demonstration of the beam steering effect are presented in Figs. 21iii,iv. For the chosen geometry of antenna, displacement of source by 0.5 mm leads to a beam rotation of about 10◦. Note that the ratio of *λ* = 18.7 mm to value of the source displacement 0.5 mm is equal to 37. Therefore the beam steering effect observed

Finally, we consider the question of dielectric superdirective antenna matching with coaxial cable. Despite that length of the wire dipole is close to *λ*/10, dielectric superdirective antenna is well matched with the coaxial cable in the operating frequency range. Fig.22 shows the level of return loss for this case. The antenna matching is explained by the strong coupling of the wire dipole with the excited modes of notched dielectric particle and is not related to the dissipative losses in the superdirectivity regime. For this reason, we have not used

Though the concept of the superdirectivity of high-refractive index dielectric particles with notch has now only been proven in GHz spectral range there is a hope that it can be transferred into the visible and near-IR spectrum in the nearest future. Recently we have experimentally demonstrated that it is possible to engineer resonant modes of spherical nanoresonators using a combined approach of laser-induced transfer to generate almost

Antenna properties have been studied in an anechoic chamber Fig. 21C.

In this chapter, we propose a new type of highly efficient Yagi-Uda nanoantenna and introduced a novel concept of superdirective nanoantennas based on silicon nanoparticles. In addition to the electric response, this silicon nanoantennas exhibit very strong magnetic resonances at the nanoscale. Both types of nanoantennas are studied analytically, numerically and experimentally. For superdirective nanoantennas we also predict the effect of the beam steering at the nanoscale characterized by a subwavelength sensitivity of the beam radiation direction to the source position.

Dielectric nanoparticles with high refractive index offer new possibilities for achieving wave interference. Indeed, the coexistence of both electric and magnetic resonances results in a unidirectional scattering. This property makes subwavelength dielectric nanoparticles the smallest and most efficient nanoantennas. Moreover, unidirectionality can be swapped for different wavelengths [74, 76].

The unique optical properties and low losses make dielectric nanoparticles perfect candidates for a design of high-performance nanoantennas, low-loss metamaterials, and other novel all-dielectric nanophotonic devices. The key to such novel functionalities of high-index dielectric nanophotonic elements is the ability of subwavelength dielectric nanoparticles to support simultaneously both electric and magnetic resonances, which can be controlled independently for particles of non spherical forms [77, 121].

#### **Author details**

Alexandr E. Krasnok1, Pavel A. Belov1, Andrey E. Miroshnichenko2, Arseniy I. Kuznetsov3, Boris S. Luk'yanchuk3 and Yuri S. Kivshar1,2

1 ITMO University, St. Petersburg, Russia

2 Nonlinear Physics Centre, Research School of Physics and Engineering, Australian National University, Canberra, Australian Capital Territory, Australia

3 Data Storage Institute, A\*STAR (Agency for Science, Technology and Research), Singapore

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**Chapter 7**

**Building Partial Discharge Signal Wireless Probes**

In the recent years compact ultra-wideband (UWB) antennas have received a great attention [1-3] due to the allocation of various frequency bands to UWB systems by Federal Communi‐ cations Committee (FCC) [4]. One of the most interesting aspects of these antennas is their aptitude of detecting electromagnetic (EM) transients with frequency content up to the very high frequency (VHF) range. EM transient phenomena with the above mentioned frequency content are those encountered, for example, in partial discharge (PD) detection. This diagnostic method is now widely used to identify defects taking place in the insulation systems. Wireless systems offer the possibility to achieve the whole shape of PD signals radiated from the source

Modern diagnostic procedures require clear PD patterns for the identification of defects generating PD because different defects can affect differently the insulation reliability, [5-7]. Different pulsating sources can be simultaneously active during a PD measurement session and mixed PD patterns can be recorded. Thus, an effective separation of mixed PD patterns into sub-patterns each one pertinent to a specific noise or PD source typology, is a fundamental task to avoid wrong defect identification, [8-9]. One of the possible approaches in signal separation is based on the assumption that the same defect generates similar waveforms and features derived from signals grouped by similarity can be adopted to identify the defect or noise source. Thus, the dynamic characteristics of the antenna probe must be designed/

Both the time and the frequency domain can be used for separation purposes. Recently, the use of the Auto-Correlation Function (ACF) has been proposed for its ability to synthesize both the time and frequency domain features as well as to be less affected by superimposed highfrequency noise, random truncation of the pulse-tail (frequency leakage) and different trigger

> © 2014 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

of the PD defects with less distortion due to the electric transmission path.

evaluated in order to fit the above mentioned requirements.

Fabio Viola and Pietro Romano

http://dx.doi.org/10.5772/58840

**1. Introduction**

activation, [10].

Additional information is available at the end of the chapter
