**3.1 Method of moments**

The linear MoM presented here is based in the linear current approximation with an equivalent surface impedance model of the cylindrical conductors, with sinusoidal test and base functions [18]. The method will be explained for the particular example of a single dipole radiating in a free space, composed by plasmonic cylindrical elements made of gold.

**Figure 3** shows the geometry of the original problem, the equivalent MoM and circuit models of the nanodipole. In this figure, *L* is the length of the arms, *d* is the nanodipole gap and *a* is the dipole radius. The total length of this antenna is *Lt* = 2 *L* + *d*. In present analysis, we do not take into account the capacitance generated by the air gap (*Cgap*) of the nanodipole. In this case, our input impedance is equivalent to that *Za* presented in [20] without *Cgap*.

In the radiation problem of **Figure 3**, the gold material of the antenna is represented by the Lorentz-Drude model for complex permittivity *ε*Au = *ε*0*εr*Au:

$$
\varepsilon\_{r\text{Au}} = \varepsilon\_{\infty} - \frac{\alpha\_{p1}^2}{\alpha^2 - j\Gamma\alpha} + \frac{\alpha\_{p2}^2}{\alpha\_0^2 - \alpha^2 + j\gamma\alpha},\tag{1}
$$

*Zs* <sup>¼</sup> *TJ*0ð Þ *Ta*

*Complex permittivity of gold obtained by Lorentz-Drude model of (1) and experimental data of Johnson-*

*Wireless Optical Nanolinks with Yagi-Uda and Dipoles Plasmonic Nanoantennas*

*μ*0*ε*<sup>0</sup>

tangential to the surface of the metal, *Es* is the scattered electric field due to the induced linear current *I* on the conductor, *Ei* the incident electric field from the voltage source (**Figure 3**), and *I* is the longitudinal current in a given point of the

The integral equation for the scattered field along the length *l* of the nanodipole

*Ig R*ð Þ*dl*<sup>0</sup> þ

ð

*dI*

*dl*<sup>0</sup> <sup>∇</sup>*g R*ð Þ*dl*<sup>0</sup>

3

*ZmnIn, m* ¼ 1*,* 2*,* 3*,* …*, N*–1*,* (4)

5*,* (3)

∣ is the

*l*

being *T* ¼ *k*<sup>0</sup>

nanodipole.

**Figure 4.**

*Christy [21].*

is given by

**5**

ffiffiffiffiffiffiffiffi

*DOI: http://dx.doi.org/10.5772/intechopen.88482*

field at the conductor surface is *Es* þ *Ei*

*Es*ð Þ¼ *r*

1 *jωε*<sup>0</sup>

*Vm* <sup>¼</sup> *ZsIm*Δ*<sup>m</sup>* �<sup>X</sup>

*k*2 0 ð

2 4

*l*

where *g R*ð Þ¼ *<sup>e</sup>*�*jk*0*<sup>R</sup>=*4*π<sup>R</sup>* is the free space Green's function, and *<sup>R</sup>* <sup>¼</sup> <sup>∣</sup>*<sup>r</sup>* � *<sup>r</sup>*<sup>0</sup>

of segments in *L* � 0.5*d* with the size Δ*L* = (*L* � 0.5*d*)/*Na* (white segments in **Figure 3**), and two segments in the middle with the size Δ*L* = *d* (gray segments in **Figure 3**). Later, the current in each segment is approximated by sinusoidal basis functions. The expansion constants *In* are shown in **Figure 3** where each constant defines one triangular sinusoidal current. To calculate these constants, we use *N* � 1 rectangular pulse test functions with unitary amplitude and perform the conventional testing procedure. As a result, the following linear system of equations is obtained:

*N*�1

*n*¼1

distance between source and observation points. The numerical solution of the problem formulated by (1)–(3) is performed by linear MoM as follows. Firstly, we divide the total length *Lt* = 2 *L* + *d* in *N* = 2*Na* + 2 straight segments, where *Na* is the number

*<sup>ε</sup>rAu* <sup>p</sup> and *<sup>k</sup>*<sup>0</sup> <sup>¼</sup> *<sup>ω</sup>* ffiffiffiffiffiffiffiffiffi

<sup>2</sup>*πajωεAuJ*1ð Þ *Ta ,* (2)

p . The boundary condition for the electric

� � � *al* <sup>¼</sup> *ZsI*, where *al* is a unitary vector

where the parameters in this equation are as follows [1]: *ε*<sup>∞</sup> = 8, *<sup>ω</sup>p*<sup>1</sup> = 13.8 � <sup>10</sup>15s �1 , <sup>Γ</sup> = 1.075 � <sup>10</sup>14s �1 , *<sup>ω</sup>*<sup>0</sup> = 2π*c*/*λ*0, *<sup>c</sup>* = 3 � <sup>10</sup><sup>8</sup> m/s, *<sup>λ</sup>*<sup>0</sup> = 450 nm, *<sup>ω</sup>p*<sup>2</sup> = 45 � <sup>10</sup>14s �1 , *<sup>γ</sup>* = 9 � 1014s �1 , and *ω* is the angular frequency in rad/s. **Figure 4** presents the real and imaginary part of (1) versus wavelength (*λ*). This figure also shows the experimental data of [21]. We observe a good agreement between the results of the Lorentz-Drude model of (1) and the experimental data for *λ* > 500 nm.

The losses in metal are described by the surface impedance *Zs*. This impedance can be obtained approximately by considering cylindrical waveguide with the mode TM01. In this case, the surface impedance is given by [22].

**Figure 3.** *Geometry of nanodipole: original problem (left), MoM model (middle), and equivalent circuit model (right).*

*Wireless Optical Nanolinks with Yagi-Uda and Dipoles Plasmonic Nanoantennas DOI: http://dx.doi.org/10.5772/intechopen.88482*

#### **Figure 4.**

**3. Numerical model**

*Nanoplasmonics*

MoM [18] and FEM [19].

**3.1 Method of moments**

*<sup>ω</sup>p*<sup>1</sup> = 13.8 � <sup>10</sup>15s

*<sup>ω</sup>p*<sup>2</sup> = 45 � <sup>10</sup>14s

*λ* > 500 nm.

**Figure 3.**

**4**

�1

�1

plasmonic cylindrical elements made of gold.

is equivalent to that *Za* presented in [20] without *Cgap*.

*<sup>ε</sup><sup>r</sup>*Au <sup>¼</sup> *<sup>ε</sup>*<sup>∞</sup> � *<sup>ω</sup>*<sup>2</sup>

, <sup>Γ</sup> = 1.075 � <sup>10</sup>14s

TM01. In this case, the surface impedance is given by [22].

, *<sup>γ</sup>* = 9 � 1014s

In this section, we present the numerical methods used in the analysis of the wireless optical nanolinks described in the last section. The methods used here are

The linear MoM presented here is based in the linear current approximation with an equivalent surface impedance model of the cylindrical conductors, with sinusoidal test and base functions [18]. The method will be explained for the particular example of a single dipole radiating in a free space, composed by

**Figure 3** shows the geometry of the original problem, the equivalent MoM and circuit models of the nanodipole. In this figure, *L* is the length of the arms, *d* is the nanodipole gap and *a* is the dipole radius. The total length of this antenna is *Lt* = 2 *L* + *d*. In present analysis, we do not take into account the capacitance generated by the air gap (*Cgap*) of the nanodipole. In this case, our input impedance

In the radiation problem of **Figure 3**, the gold material of the antenna is represented by the Lorentz-Drude model for complex permittivity *ε*Au = *ε*0*εr*Au:

*p*1

�1

presents the real and imaginary part of (1) versus wavelength (*λ*). This figure also shows the experimental data of [21]. We observe a good agreement between the

The losses in metal are described by the surface impedance *Zs*. This impedance can be obtained approximately by considering cylindrical waveguide with the mode

*Geometry of nanodipole: original problem (left), MoM model (middle), and equivalent circuit model (right).*

where the parameters in this equation are as follows [1]: *ε*<sup>∞</sup> = 8,

results of the Lorentz-Drude model of (1) and the experimental data for

�1

*<sup>ω</sup>*<sup>2</sup> � *<sup>j</sup>*Γ*<sup>ω</sup>* <sup>þ</sup> *<sup>ω</sup>*<sup>2</sup>

*ω*2

*p*2

<sup>0</sup> � *<sup>ω</sup>*<sup>2</sup> <sup>þ</sup> *<sup>j</sup>γω,* (1)

, *<sup>ω</sup>*<sup>0</sup> = 2π*c*/*λ*0, *<sup>c</sup>* = 3 � <sup>10</sup><sup>8</sup> m/s, *<sup>λ</sup>*<sup>0</sup> = 450 nm,

, and *ω* is the angular frequency in rad/s. **Figure 4**

*Complex permittivity of gold obtained by Lorentz-Drude model of (1) and experimental data of Johnson-Christy [21].*

$$Z\_s = \frac{T\mathcal{J}\_0(Ta)}{2\pi a j a e\_{Au} J\_1(Ta)},\tag{2}$$

being *T* ¼ *k*<sup>0</sup> ffiffiffiffiffiffiffiffi *<sup>ε</sup>rAu* <sup>p</sup> and *<sup>k</sup>*<sup>0</sup> <sup>¼</sup> *<sup>ω</sup>* ffiffiffiffiffiffiffiffiffi *μ*0*ε*<sup>0</sup> p . The boundary condition for the electric field at the conductor surface is *Es* þ *Ei* � � � *al* <sup>¼</sup> *ZsI*, where *al* is a unitary vector tangential to the surface of the metal, *Es* is the scattered electric field due to the induced linear current *I* on the conductor, *Ei* the incident electric field from the voltage source (**Figure 3**), and *I* is the longitudinal current in a given point of the nanodipole.

The integral equation for the scattered field along the length *l* of the nanodipole is given by

$$\overline{E}\_{\mathbf{r}}(\overline{r}) = \frac{1}{j\alpha\varepsilon\_{0}} \left[ k\_{0}^{2} \int\_{l} \overline{\mathbf{J}} \mathbf{g}(\mathbf{R}) dl' + \int\_{l} \frac{dI}{dl'} \nabla \mathbf{g}(\mathbf{R}) dl' \right],\tag{3}$$

where *g R*ð Þ¼ *<sup>e</sup>*�*jk*0*<sup>R</sup>=*4*π<sup>R</sup>* is the free space Green's function, and *<sup>R</sup>* <sup>¼</sup> <sup>∣</sup>*<sup>r</sup>* � *<sup>r</sup>*<sup>0</sup> ∣ is the distance between source and observation points. The numerical solution of the problem formulated by (1)–(3) is performed by linear MoM as follows. Firstly, we divide the total length *Lt* = 2 *L* + *d* in *N* = 2*Na* + 2 straight segments, where *Na* is the number of segments in *L* � 0.5*d* with the size Δ*L* = (*L* � 0.5*d*)/*Na* (white segments in **Figure 3**), and two segments in the middle with the size Δ*L* = *d* (gray segments in **Figure 3**). Later, the current in each segment is approximated by sinusoidal basis functions. The expansion constants *In* are shown in **Figure 3** where each constant defines one triangular sinusoidal current. To calculate these constants, we use *N* � 1 rectangular pulse test functions with unitary amplitude and perform the conventional testing procedure. As a result, the following linear system of equations is obtained:

$$V\_m = Z\_s I\_m \Delta\_m - \sum\_{n=1}^{N-1} Z\_{mn} I\_n, m = 1, 2, 3, \dots, N-1,\tag{4}$$

#### **Figure 5.**

*Mesh of the problem of Figure 2 generated in COMSOL. (a) Nanolink mesh and its surroundings. (b) Enlarged Yagi-Uda antenna mesh.*

where *Zmn* is the mutual impedance between sinusoidal current elements *m* and *n*, Δ*m* = 1/2[Δ*Lm* + Δ*Lm* + 1], and *Vm* is non-zero only in the middle of the antenna (*m* = *N*/2), where *VN*/2 = *Vs*. The solution of (4) gives the current along the dipole and the input current *Is*. For *Vs* = 1 V, the input impedance is *Zin* = 1/ *Is* = (*Rr* + *RL*) + *jXin* = *Rin* + *jXin*, where *Rr*, *RL*, *Rin*, and *Xin* are the radiation resistance, loss resistance, input resistance, and input reactance, respectively. The total input power is calculated by *Pin* = 0.5Re(*VsIs*\*) = 0.5(*RL* + *Rr*)|*Is*| <sup>2</sup> = 0.5*Rin*| *Is*| <sup>2</sup> = *Pr* + *PL*, *Pr* is the radiated power, and *PL* the loss power dissipated at the antenna's surface which is calculated by

$$P\_L = 0.5 \text{Re}(Z\_s) \sum\_{n=1}^{N-1} |I\_n|^2 \Delta\_{n\nu} \tag{5}$$

resonances are in the frequency range of 100–400 THz considered. The parameters of the isolated dipole are based on [23] and those of the elements of the Yagi-Uda antenna were chosen so that the reflecting element was larger than the dipole and the smaller dipole directors. In **Table 1**, *a* = *ar* = *adT* = *ad* = *adR* and *d* = *dhr* = *dhd*. **Figure 6** shows the input impedance (*Zin*) for the Yagi-Uda antennas (**Figure 6a**) and dipole (**Figure 6b**). These input impedances were calculated by FEM with the COMSOL software, and by a linear MoM applied to cylindrical plasmonic nanoantennas [18], by coding the mathematical model in Matlab soft-

*Input impedance (Zin) of the transmitting antennas Yagi-Uda and dipole. (a) Yagi-Uda without substrate, compared to MoM, and with SiO2 substrate. (b) Dipole without substrate, compared to MoM, and with SiO2*

**Variable** *hdT ddT a hr hd hdR ddr d dTR* Values 220 20 15 700 250 220 20 100 5000

*Nanolink parameters used in simulations. All parameters are in nanometer (nm).*

*DOI: http://dx.doi.org/10.5772/intechopen.88482*

*Wireless Optical Nanolinks with Yagi-Uda and Dipoles Plasmonic Nanoantennas*

**Table 1.**

**Figure 6.**

*substrate.*

**7**

ware [24]. We observe a good agreement between these two methods.

The radiated power can be obtained by *Pr* = *Pin* � *PL*, and the resistances by *Rr* = 2*Pr*/|*Is*| <sup>2</sup> and *RL* = 2*PL*/|*Is*| 2 . The radiation efficiency is defined by *er* = *Pr*/ *Pin* = *Pr*/(*Pr* + *PL*) = *Rr*/(*Rr* + *RL*) = *Rr*/*Rin*.

#### **3.2 Finite element method**

The nanolinks of **Figure 3** were also analyzed numerically by FEM. **Figure 5a** shows the mesh of the nanolink of **Figure 2** modeled in the COMSOL, where the antennas are in a spherical domain of air, with scattering absorbing condition (PLM) applied at their ends. **Figure 5b** shows an enlarged image of the Yagi-Uda nanoantenna mesh and its surroundings.

### **4. Numerical results**

#### **4.1 Isolated antennas in transmitting mode**

In this section, the transmitting antennas Yagi-Uda and dipole (**Figure 2** without reflector and directors) are analyzed separately. For this analysis, the values of the antennas parameters are those shown in **Table 1**, where with these values the main

*Wireless Optical Nanolinks with Yagi-Uda and Dipoles Plasmonic Nanoantennas DOI: http://dx.doi.org/10.5772/intechopen.88482*


**Table 1.**

where *Zmn* is the mutual impedance between sinusoidal current elements *m* and *n*, Δ*m* = 1/2[Δ*Lm* + Δ*Lm* + 1], and *Vm* is non-zero only in the middle of the antenna (*m* = *N*/2), where *VN*/2 = *Vs*. The solution of (4) gives the current along the dipole and the input current *Is*. For *Vs* = 1 V, the input impedance is *Zin* = 1/ *Is* = (*Rr* + *RL*) + *jXin* = *Rin* + *jXin*, where *Rr*, *RL*, *Rin*, and *Xin* are the radiation resistance, loss resistance, input resistance, and input reactance, respectively. The

*Mesh of the problem of Figure 2 generated in COMSOL. (a) Nanolink mesh and its surroundings.*

<sup>2</sup> = *Pr* + *PL*, *Pr* is the radiated power, and *PL* the loss power dissipated at the

The radiated power can be obtained by *Pr* = *Pin* � *PL*, and the resistances

The nanolinks of **Figure 3** were also analyzed numerically by FEM. **Figure 5a** shows the mesh of the nanolink of **Figure 2** modeled in the COMSOL, where the antennas are in a spherical domain of air, with scattering absorbing condition (PLM) applied at their ends. **Figure 5b** shows an enlarged image of the Yagi-Uda

In this section, the transmitting antennas Yagi-Uda and dipole (**Figure 2** without reflector and directors) are analyzed separately. For this analysis, the values of the antennas parameters are those shown in **Table 1**, where with these values the main

*N* X�1 *n*¼1

j j *In* <sup>2</sup>

. The radiation efficiency is defined by *er* = *Pr*/

<sup>2</sup> = 0.5*Rin*|

Δ*n,* (5)

total input power is calculated by *Pin* = 0.5Re(*VsIs*\*) = 0.5(*RL* + *Rr*)|*Is*|

*PL* ¼ 0*:*5Reð Þ *Zs*

2

antenna's surface which is calculated by

*(b) Enlarged Yagi-Uda antenna mesh.*

<sup>2</sup> and *RL* = 2*PL*/|*Is*|

*Pin* = *Pr*/(*Pr* + *PL*) = *Rr*/(*Rr* + *RL*) = *Rr*/*Rin*.

nanoantenna mesh and its surroundings.

**4.1 Isolated antennas in transmitting mode**

**3.2 Finite element method**

**4. Numerical results**

*Is*|

**6**

**Figure 5.**

*Nanoplasmonics*

by *Rr* = 2*Pr*/|*Is*|

*Nanolink parameters used in simulations. All parameters are in nanometer (nm).*

#### **Figure 6.**

*Input impedance (Zin) of the transmitting antennas Yagi-Uda and dipole. (a) Yagi-Uda without substrate, compared to MoM, and with SiO2 substrate. (b) Dipole without substrate, compared to MoM, and with SiO2 substrate.*

resonances are in the frequency range of 100–400 THz considered. The parameters of the isolated dipole are based on [23] and those of the elements of the Yagi-Uda antenna were chosen so that the reflecting element was larger than the dipole and the smaller dipole directors. In **Table 1**, *a* = *ar* = *adT* = *ad* = *adR* and *d* = *dhr* = *dhd*.

**Figure 6** shows the input impedance (*Zin*) for the Yagi-Uda antennas (**Figure 6a**) and dipole (**Figure 6b**). These input impedances were calculated by FEM with the COMSOL software, and by a linear MoM applied to cylindrical plasmonic nanoantennas [18], by coding the mathematical model in Matlab software [24]. We observe a good agreement between these two methods.

#### *Nanoplasmonics*

Also, the input impedances of the antennas are calculated for two situations, the first with the antennas in the free space (without substrate) and the second on a SiO2 substrate with a permittivity of 2.15.

antennas in the free space. This effect of the substrate is similar to that observed in

**Figure 7** shows the results of directivity (*D*) and gain (*G*), radiation efficiency (*er*) and reflection coefficient (Γ), all in dB, versus frequency for the Yagi-Uda antennas (**Figure 7a**) and dipole (**Figure 7b**). The directivity and gain are calculated in the + *y* direction (**Figure 2**). In **Figure 7b** it is observed the conventional characteristic of the isolated dipole, where in a wide range of 150–300 THz one has

approximately *D* ≈ 1.6, *er* ≈ 0.6 e *G* ≈ 1 (*G* = *erD*). In the case of Yagi-Uda

*Wireless Optical Nanolinks with Yagi-Uda and Dipoles Plasmonic Nanoantennas*

(**Figure 7a**), there is a peak of *D* = 12, near *F* = 264 THz, but at this frequency the radiation efficiency is minimal *er* ≈ 0.1, and the gain is (*G* = 0.86). However, if greater gain and efficiency are desired rather than high directivity, the frequency near *F* ≈ 240 THz is more adequate, where the maximum gain is approximately *Gmax* ≈ 1.6. The reflection coefficient of both antennas was calculated considering a transmission line with characteristic impedance of 50 Ω connected to antennas. With this result, it is observed that the best impedance matching for both antennas occurs around the first resonant frequency, however the maximum radiation effi-

**Figure 8** shows the 3D far field gain radiation diagrams of the Yagi-Uda and dipole antennas, calculated at the frequency of 240 THz. It is observed that the maximum gain of the Yagi-Uda (*Gmax* ≈ 1.6) is approximately 60% greater than the maximum gain (*Gmax* ≈ 1) of the dipole. For the case of the Yagi-Uda antenna, the maximum gain occurs in the +*y* direction with a small lobe in

In this section, we present the results obtained in the analysis of the dipole/ dipole nanolinks (**Figure 2**, without reflector and transmitter directors), Yagi-Uda/ dipole (**Figure 2**) and Yagi-Uda/Yagi-Uda (**Figure 2**, with the receiving antenna equal to the transmitting antenna) for the frequency range of 100–400 THz. The parameters used for the receiving antennas are same as those of the transmitting

**Figure 9** shows the power transmission in dB (or power transfer function) for the three nanolinks, calculated by the ratio between the power delivered to the *ZC* load and the power delivered by the source *Vs* at the transmitting antenna terminals.

*3D far-field gain radiation diagram of (a) dipole antenna, and (b) Yagi-Uda (b), both in F = 240 THz.*

antennas, with *ZC* = 50 and 1250 Ω for each nanolink model.

The results show that the Yagi-Uda/Yagi-Uda nanolink presents a small

antennas in the microwave regime [25].

*DOI: http://dx.doi.org/10.5772/intechopen.88482*

ciency occurs at higher frequencies.

the *y* direction.

**Figure 8.**

**9**

**4.2 Nanolinks analysis**

Comparing the input impedance result between the Yagi-Uda and free-space dipole antennas, it is noted that the first two resonant frequencies are close, which shows that the directors and reflectors do not significantly affect the original resonant frequencies of the isolated dipole. The main differences between these two transmitting antennas are observed near the frequencies of 175 and 260 THz, which correspond physically to the dipole resonances of the reflector and directors, respectively. These resonances can be observed in the distributions of currents in these frequencies, which are not shown here.

**Figure 6** also shows the effect of the substrate in the input impedance and resonant properties of the antennas. It is observed that by placing the antennas on the substrate, their resonances are shifted to smaller frequencies in relation to the

**Figure 7.** *Directivity (D), gain (G), radiation efficiency (er) and reflection coefficient (Γ) of antennas (a) Yagi-Uda and (b) dipole.*

**8**

*Wireless Optical Nanolinks with Yagi-Uda and Dipoles Plasmonic Nanoantennas DOI: http://dx.doi.org/10.5772/intechopen.88482*

antennas in the free space. This effect of the substrate is similar to that observed in antennas in the microwave regime [25].

**Figure 7** shows the results of directivity (*D*) and gain (*G*), radiation efficiency (*er*) and reflection coefficient (Γ), all in dB, versus frequency for the Yagi-Uda antennas (**Figure 7a**) and dipole (**Figure 7b**). The directivity and gain are calculated in the + *y* direction (**Figure 2**). In **Figure 7b** it is observed the conventional characteristic of the isolated dipole, where in a wide range of 150–300 THz one has approximately *D* ≈ 1.6, *er* ≈ 0.6 e *G* ≈ 1 (*G* = *erD*). In the case of Yagi-Uda (**Figure 7a**), there is a peak of *D* = 12, near *F* = 264 THz, but at this frequency the radiation efficiency is minimal *er* ≈ 0.1, and the gain is (*G* = 0.86). However, if greater gain and efficiency are desired rather than high directivity, the frequency near *F* ≈ 240 THz is more adequate, where the maximum gain is approximately *Gmax* ≈ 1.6. The reflection coefficient of both antennas was calculated considering a transmission line with characteristic impedance of 50 Ω connected to antennas. With this result, it is observed that the best impedance matching for both antennas occurs around the first resonant frequency, however the maximum radiation efficiency occurs at higher frequencies.

**Figure 8** shows the 3D far field gain radiation diagrams of the Yagi-Uda and dipole antennas, calculated at the frequency of 240 THz. It is observed that the maximum gain of the Yagi-Uda (*Gmax* ≈ 1.6) is approximately 60% greater than the maximum gain (*Gmax* ≈ 1) of the dipole. For the case of the Yagi-Uda antenna, the maximum gain occurs in the +*y* direction with a small lobe in the *y* direction.

#### **4.2 Nanolinks analysis**

Also, the input impedances of the antennas are calculated for two situations, the first with the antennas in the free space (without substrate) and the second on a

Comparing the input impedance result between the Yagi-Uda and free-space dipole antennas, it is noted that the first two resonant frequencies are close, which shows that the directors and reflectors do not significantly affect the original resonant frequencies of the isolated dipole. The main differences between these two transmitting antennas are observed near the frequencies of 175 and 260 THz, which correspond physically to the dipole resonances of the reflector and directors, respectively. These resonances can be observed in the distributions of currents in

**Figure 6** also shows the effect of the substrate in the input impedance and resonant properties of the antennas. It is observed that by placing the antennas on the substrate, their resonances are shifted to smaller frequencies in relation to the

*Directivity (D), gain (G), radiation efficiency (er) and reflection coefficient (Γ) of antennas (a) Yagi-Uda and*

SiO2 substrate with a permittivity of 2.15.

*Nanoplasmonics*

these frequencies, which are not shown here.

**Figure 7.**

*(b) dipole.*

**8**

In this section, we present the results obtained in the analysis of the dipole/ dipole nanolinks (**Figure 2**, without reflector and transmitter directors), Yagi-Uda/ dipole (**Figure 2**) and Yagi-Uda/Yagi-Uda (**Figure 2**, with the receiving antenna equal to the transmitting antenna) for the frequency range of 100–400 THz. The parameters used for the receiving antennas are same as those of the transmitting antennas, with *ZC* = 50 and 1250 Ω for each nanolink model.

**Figure 9** shows the power transmission in dB (or power transfer function) for the three nanolinks, calculated by the ratio between the power delivered to the *ZC* load and the power delivered by the source *Vs* at the transmitting antenna terminals. The results show that the Yagi-Uda/Yagi-Uda nanolink presents a small

**Figure 8.** *3D far-field gain radiation diagram of (a) dipole antenna, and (b) Yagi-Uda (b), both in F = 240 THz.*

#### **Figure 9.**

*Power transmission versus frequency for the dipole/dipole nanolinks, Yagi-Uda/dipole and Yagi-Uda/Yagi-Uda, for ZC = 50 (a), e 1250 Ω (b).*

improvement in power transmission, at some frequency points, in relation to the dipole/dipole and Yagi-Uda/dipole nanolinks. In addition, it can be observed that the links can operate with good transmission power at the frequency points 170 and 240 THz, for *ZC* equal to 50 and 1250 Ω, respectively, where the power transmission are maximum.

**Figure 10** shows the magnitude and phase of the electric near field, which is defined by *E* = 20 log10(|Re (*Ex*)|), in the plane *z* = 25 nm, of the dipole/dipole nanolinks (a, b), Yagi-Uda/dipole (c, d) and Yagi-Uda/Yagi-Uda (e, f). The receiver antennas are positioned at a distance *dTR* = 5 μm from the transmitting antennas, with *F* = 170 THz and *ZC* = 50 Ω for the fields of figures (a), (c) and (e), and with *F* = 240 THz and *ZC* = 1250 Ω for the cases of figures (b), (d) and (f). In all types of nanolinks shown in this figure, the radiated wave can be visualized by propagating from the transmitting antennas to the receiving antennas, with the appropriated wavelength. It is observed the amplitude decay of the electric field with the distance and the decrease of the wavelength with the increase of the frequency.

**5. Conclusions**

**Figure 10.**

**11**

It was presented in this work, a comparative analysis of nanolinks formed by Yagi-Uda and dipole plasmonic nanoantennas, where was investigated the power transmission for Yagi-Uda/Yagi-Uda, Yagi-Uda/dipole and dipole/dipole nanolinks

*Electric near field distribution of the magnitude and phase (E = 20 log10(|Re (Ex)|)), in the plane z = 25 nm, of the dipole/dipole nanolinks (a, b), Yagi-Uda/dipole (c, d) and Yagi-Uda/Yagi-Uda (e, f). The receiver antennas are positioned at 5 μm from the transmitting antennas, with F = 170 THz and ZC = 50 Ω for figures*

*(a), (c) and (e), and with F = 240 THz and ZC = 1250 Ω for figures (b), (d) and (f).*

*Wireless Optical Nanolinks with Yagi-Uda and Dipoles Plasmonic Nanoantennas*

*DOI: http://dx.doi.org/10.5772/intechopen.88482*

*Wireless Optical Nanolinks with Yagi-Uda and Dipoles Plasmonic Nanoantennas DOI: http://dx.doi.org/10.5772/intechopen.88482*

**Figure 10.**

improvement in power transmission, at some frequency points, in relation to the dipole/dipole and Yagi-Uda/dipole nanolinks. In addition, it can be observed that the links can operate with good transmission power at the frequency points 170 and 240 THz, for *ZC* equal to 50 and 1250 Ω, respectively, where the power transmission

*Power transmission versus frequency for the dipole/dipole nanolinks, Yagi-Uda/dipole and Yagi-Uda/Yagi-*

**Figure 10** shows the magnitude and phase of the electric near field, which is defined by *E* = 20 log10(|Re (*Ex*)|), in the plane *z* = 25 nm, of the dipole/dipole nanolinks (a, b), Yagi-Uda/dipole (c, d) and Yagi-Uda/Yagi-Uda (e, f). The receiver antennas are positioned at a distance *dTR* = 5 μm from the transmitting antennas, with *F* = 170 THz and *ZC* = 50 Ω for the fields of figures (a), (c) and (e), and with *F* = 240 THz and *ZC* = 1250 Ω for the cases of figures (b), (d) and (f). In all types of nanolinks shown in this figure, the radiated wave can be visualized by propagating from the transmitting antennas to the receiving antennas, with the appropriated wavelength. It is observed the amplitude decay of the electric field with the distance

and the decrease of the wavelength with the increase of the frequency.

are maximum.

**10**

*Uda, for ZC = 50 (a), e 1250 Ω (b).*

**Figure 9.**

*Nanoplasmonics*

*Electric near field distribution of the magnitude and phase (E = 20 log10(|Re (Ex)|)), in the plane z = 25 nm, of the dipole/dipole nanolinks (a, b), Yagi-Uda/dipole (c, d) and Yagi-Uda/Yagi-Uda (e, f). The receiver antennas are positioned at 5 μm from the transmitting antennas, with F = 170 THz and ZC = 50 Ω for figures (a), (c) and (e), and with F = 240 THz and ZC = 1250 Ω for figures (b), (d) and (f).*
