**Spin Photodetector: Conversion of Light Polarization Information into Electric Voltage Using Inverse Spin Hall Effect**

Kazuya Ando and Eiji Saitoh *Institute for Materials Research, Tohoku University Japan* 

### **1. Introduction**

16 Will-be-set-by-IN-TECH

404 Photodetectors

U. Leonhardt, *Measuring the Quantum State of Light*, (Cambridge University Press, Cambridge,

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Recent developments in optical and material science have led to remarkable industrial applications, such as optical data recording and optical communication. The scope of the conventional optical technology can be extended by exploring simple and effective methods for detecting light circular polarization; light circular polarization carries single-photon information, making it essential in future optical technology, including quantum cryptography and quantum communication.

Light circular polarization is coupled with electron spins in semiconductors (Meier, 1984). When circularly polarized light is absorbed in a semiconductor crystal, the angular momentum of the light is transferred to the semiconductor, inducing spin-polarized carriers though the optical selection rules for interband transitions [see Fig. 1(a)]. This process allows conversion of light circular polarization into electron-spin polarization, enabling the integration of light-polarization information into spintronic technologies.

If one can convert electron spin information into an electric signal, light circular polarization information can be measured through the above process. Recently, in the field of spintronics, a powerful technique for detecting electron spin information has been established, which utilizes the inverse spin Hall effect (ISHE) (Saitoh, 2006; Valenzuela, 2006; Kimura, 2007). The ISHE converts a spin current, a flow of electron spins in a solid, into an electric field through the spin-orbit interaction, enabling the transcription of electron-spin information into an electric voltage. This suggests that light-polarization information can be converted into an electric signal by combining the optical selection rules and the ISHE.

This chapter describes the conversion of light circular polarization information into an electric voltage in a Pt/GaAs structure though the optical generation of spin-polarized carriers and the ISHE: the photoinduced ISHE (Ando, 2010).

### **2. Optical excitation of spin-polarized carriers in semiconductors**

When circularly polarized light is absorbed in a semiconductor, the angular momentum of the light is transferred to the material, which polarizes carrier spins in the semiconductor

Spin Photodetector: Conversion of

spin-orbit split-off band (SO).

for spin up (

where 

**j**c**j**↑**j**↓:

Since charge

**3. Spin current and inverse spin Hall effect** 

= ↑) and spin down (

materials, a spin current is expressed as **j**s (

↑↓ =N/2.

conductivity is spin-independent:

is the electrical conductivity for spin up (

potential. A current density for spin channel

Light Polarization Information into Electric Voltage Using Inverse Spin Hall Effect 407

Table 1. Wave functions for the conduction band (CB), heavy hole (HH), light hole (LH), and

A spin current is a flow of electron spins in a solid. One of the driving forces for a spin current is a gradient of the difference in the spin-dependent electrochemical potential

= ↓). Here,

**j**

<sup>c</sup> <sup>1</sup> . *<sup>e</sup>* 

This flow is schematically illustrated in Fig. 2(a). This flow carries electron charge while the

<sup>s</sup> <sup>1</sup> , *<sup>e</sup>* 

carries electron spins without a charge current. This is a spin current. In nonmagnetic

<sup>c</sup> · . *<sup>d</sup>*

*dt*   

is a conserved quantity, the continuity equation of charge is described as

N/2*e*)↑

, *<sup>e</sup>* 

 = 

is expressed as

c *e*, where

(1)

<sup>↓</sup>), since the electrical

= ↑) and spin down (

**j** (2)

**j** (3)

**j** (4)

Here, a charge current, a flow of electron charge, is the sum of the current for

flow of spins is cancelled. In contrast, the opposite flow of **j**↑ and **j**↓, **j**s**j**↑**j**↓, or

c is the chemical

= ↓) channel.

= ↑ and ↓ as

through the spin-orbit interaction (Meier, 1984). This optical generation of spin-polarized carriers has been a powerful technique for exploring spin physics in direct band gap semiconductors, such as GaAs. In GaAs, the valence band maximum and the conduction band minimum are at with an energy gap *E*g = 1.43 eV at room temperature. The valence band (*p* symmetry) splits into fourfold degenerate *P*3/2 and twofold degenerate *P*1/2 states, which lie = 0.34 eV below *P*3/2 at , whereas the conduction band (*s* symmetry) is twofold degenerate *S*1/2 as schematically shown in Fig. 1(a). In the fourfold degenerate *P*3/2 state, holes can occupy states with values of angular momentum *mj* = 1/2,3/2, corresponding to light hole (LH) and heavy hole (HH) sates, respectively (see Fig. 1(a)). Let *J*, *mj* be the Bloch states according to the total angular momentum *J* and its projection onto the positive *z* axis *mj*. The band wave functions can be expressed as listed in Table 1, where *S*,*X*,*Y*, and *Z* are the wave functions with the symmetry of *s*, *px*, *py*, and *px* orbitals. The interband transitions satisfy the selection rule *mj* = 1, reflecting absorption of the photon's original angular momentum. The probability of a transition involving a LH or HH state is weighted by the square of the corresponding matrix element connecting it to the appropriate electron state, so that the relative intensity of the optical transition between the heavy and the light hole subbands and the conduction band induced by circularly polarized light illumination is 3. Thus absorption of photons with angular momentum +1 produces three spin-down (*mj* = 1/2) electrons for every one spin-up (*mj* = 1/2) electron, resulting in an electron population with a spin polarization of 50% in a bulk material, where the HH and LH states are degenerate. The relative transition rates are summarized in Fig. 1(b). Therefore, because of the difference in the relative intensity, a spin-polarized carriers can be generated by the illumination of circularly polarized light. Note that the resulting electron spin is oriented parallel or anti-parallel to the propagation direction of the incident photon.

Fig. 1. (a) Optical generation of spin-polarized carriers in semiconductors. (b) Interband transitions for right and left circularly polarized light illumination.


Table 1. Wave functions for the conduction band (CB), heavy hole (HH), light hole (LH), and spin-orbit split-off band (SO).

#### **3. Spin current and inverse spin Hall effect**

406 Photodetectors

through the spin-orbit interaction (Meier, 1984). This optical generation of spin-polarized carriers has been a powerful technique for exploring spin physics in direct band gap semiconductors, such as GaAs. In GaAs, the valence band maximum and the conduction band minimum are at with an energy gap *E*g = 1.43 eV at room temperature. The valence band (*p* symmetry) splits into fourfold degenerate *P*3/2 and twofold degenerate *P*1/2 states, which lie = 0.34 eV below *P*3/2 at , whereas the conduction band (*s* symmetry) is twofold degenerate *S*1/2 as schematically shown in Fig. 1(a). In the fourfold degenerate *P*3/2 state, holes can occupy states with values of angular momentum *mj* = 1/2,3/2, corresponding to light hole (LH) and heavy hole (HH) sates, respectively (see Fig. 1(a)). Let *J*, *mj* be the Bloch states according to the total angular momentum *J* and its projection onto the positive *z* axis *mj*. The band wave functions can be expressed as listed in Table 1, where *S*,*X*,*Y*, and *Z* are the wave functions with the symmetry of *s*, *px*, *py*, and *px* orbitals. The interband transitions satisfy the selection rule *mj* = 1, reflecting absorption of the photon's original angular momentum. The probability of a transition involving a LH or HH state is weighted by the square of the corresponding matrix element connecting it to the appropriate electron state, so that the relative intensity of the optical transition between the heavy and the light hole subbands and the conduction band induced by circularly polarized light illumination is 3. Thus absorption of photons with angular momentum +1 produces three spin-down (*mj* = 1/2) electrons for every one spin-up (*mj* = 1/2) electron, resulting in an electron population with a spin polarization of 50% in a bulk material, where the HH and LH states are degenerate. The relative transition rates are summarized in Fig. 1(b). Therefore, because of the difference in the relative intensity, a spin-polarized carriers can be generated by the illumination of circularly polarized light. Note that the resulting electron spin is oriented parallel or anti-parallel to the propagation

Fig. 1. (a) Optical generation of spin-polarized carriers in semiconductors. (b) Interband

transitions for right and left circularly polarized light illumination.

direction of the incident photon.

A spin current is a flow of electron spins in a solid. One of the driving forces for a spin current is a gradient of the difference in the spin-dependent electrochemical potential for spin up ( = ↑) and spin down ( = ↓). Here, = c *e*, where c is the chemical potential. A current density for spin channelis expressed as

$$\mathbf{j}\_{\sigma} = \frac{\sigma\_{\sigma}}{e} \nabla \mu\_{\sigma},\tag{1}$$

where is the electrical conductivity for spin up ( = ↑) and spin down ( = ↓) channel. Here, a charge current, a flow of electron charge, is the sum of the current for = ↑ and ↓ as **j**c**j**↑**j**↓:

$$\mathbf{j}\_c = \frac{1}{\varepsilon} \nabla \left( \sigma\_\uparrow \mu\_\uparrow + \sigma\_\downarrow \mu\_\downarrow \right). \tag{2}$$

This flow is schematically illustrated in Fig. 2(a). This flow carries electron charge while the flow of spins is cancelled. In contrast, the opposite flow of **j**↑ and **j**↓, **j**s**j**↑**j**↓, or

$$\mathbf{j}\_s = \frac{1}{\mathcal{e}} \nabla \left( \sigma\_\uparrow \mu\_\uparrow - \sigma\_\downarrow \mu\_\downarrow \right), \tag{3}$$

carries electron spins without a charge current. This is a spin current. In nonmagnetic materials, a spin current is expressed as **j**s (N/2*e*)↑<sup>↓</sup>), since the electrical conductivity is spin-independent: ↑↓ =N/2.

Since charge is a conserved quantity, the continuity equation of charge is described as

$$\frac{d}{dt}\rho = -\nabla \cdot \mathbf{j}\_c.\tag{4}$$

Spin Photodetector: Conversion of

dipole moment **P**' as

induced.

Eq. (8).

Light Polarization Information into Electric Voltage Using Inverse Spin Hall Effect 409

Fig. 4. (a) A schematic illustration of the magnetic-field **H** generation from a charge current **j**c according to Ampere's law. (b) A schematic illustration of the electric-field **E** generation from a hypothetical magnetic-monopole current **j**m according to the electromagnetic duality and Ampere's law. (c) A schematic illustration of the electric-field **E** generation from a pair

A spin current can be detected electrically using the inverse spin Hall effect (ISHE), conversion of a spin current into an electric field [see Fig. 3(a)]. The ISHE has the same symmetry as that of the relativistic transformation of magnetic moment into electric polarization, which is derived from the Lorentz transformation, as follows. Consider a magnet with the magnetic moment **M** moving at a constant velocity **v** along the *z* axis with respect to an observer [see Fig. 3(b)]. This motion of the magnet is a flow of angular momentum, meaning an existence of a "spin current". In the observer's coordinate system, the Lorentz transformation converts a part of this magnetic moment **M** into an electric

> <sup>0</sup> <sup>2</sup> <sup>1</sup> ( ),

**P v M** (8)

1 ( /) *v c* 

where *c* and 0 are the light velocity and the electric constant, respectively. This indicates that electric polarization perpendicular to the direction of the magnetic-moment velocity is

This electric-polarization generation can also be regarded as the spin-current version of Ampere's law as follows. As shown in Fig. 4(a), when a charge current **j**c flows, a circular magnetic field **H** is induced around the charge current, according to Ampere's law: rot**H** = **j**c. If a hypothetical magnetic monopole flows, a circular electric field **E** is expected to be induced around the monopole current **j**m according to rot**E** = **j**m [see Fig. 4(b)], from the electromagnetic duality. Although this monopole has never been observed in reality, a spin current can be regarded as a pair of the hypothetical monopole currents flowing in the opposite directions along the spin current spatial direction. Therefore, a spin current may generate an electric field and this field is the superposition of the two electric fields induced by this pair of the monopole current, as shown in Fig. 4(c). This spin-currentinduced electric field is identical to the field induced by the dipole moment described by

In this way, electromagnetism and relativity predict that a spin current generates an electric field. According to Eq. (8), however, this electric field is too weak in a vacuum to be detected

of hypothetical magnetic-monopole currents, **j**m and **j**m, or a spin current.

Fig. 2. (a) A schematic illustration of a charge current. (b) A schematic illustration of a spin current.

In contrast, spins are not conserved; a spin current decays typically in a length scale of nm to m. Therefore, the continuity equation of spins are written as

$$\frac{d}{dt}M\_x = -\nabla \cdot \mathbf{j}\_s + \mathcal{T}\_{x'} \tag{5}$$

where *M*z is the *z* component of magnetization. *z* is defined as the quantization axis. Here, *<sup>z</sup> en n en n* ( )/ ( )/ represents spin relaxation. *n* is the equilibrium carrier density with spin and ' is the scattering time of an electron from spin state from to '. Note that the detailed balance principle imposes that *N*↑/↑↓ = *N*↓/↓↑, so that in equilibrium no net spin scattering takes place, where *N* denotes the spin dependent density of states at the Fermi energy. This indicates that, in general, in a ferromagnet, ↑↓ and ↓↑ are not the same. In the equilibrium condition, d/d*t*=d*M*z/d*t* = 0, using the continuity equations, one finds the spin-diffusion equations:

$$\nabla^2(\sigma\_\uparrow \mu\_\uparrow + \sigma\_\downarrow \mu\_\downarrow) = 0,\tag{6}$$

$$\nabla^2(\mu\_\uparrow - \mu\_\downarrow) = \frac{1}{\mathcal{X}^2}(\mu\_\uparrow - \mu\_\downarrow)\_\prime \tag{7}$$

where *D* sf is the spin diffusion length. *D* = *D*↑*D*↓(*N*↑ + *N*↓)/(*N*↑*D*↑ + *N*↓*D*↓) is the diffusion constant. The spin relaxation time sf is given by 1/sf = 1/↑↓ + 1/↓↑. By solving the diffusion equations, one can obtain the spatial variation of spin currents generated by ↑↓. A spin current generated by ↑<sup>↓</sup> decays as e/*<sup>x</sup>*. Thus a spin current play a key role only in a system with the scale of .

Fig. 3. (a) A schematic illustration of the inverse spin Hall effect. (b) Conversion of magnetic moment **M** into electric polarization **P**'.

Fig. 2. (a) A schematic illustration of a charge current. (b) A schematic illustration of a spin

In contrast, spins are not conserved; a spin current decays typically in a length scale of nm to

where *M*z is the *z* component of magnetization. *z* is defined as the quantization axis. Here,

 

<sup>1</sup> ( )

2

the diffusion equations, one can obtain the spatial variation of spin currents generated by

Fig. 3. (a) A schematic illustration of the inverse spin Hall effect. (b) Conversion of magnetic

 ( ),

is the spin diffusion length. *D* = *D*↑*D*↓(*N*↑ + *N*↓)/(*N*↑*D*↑ + *N*↓*D*↓) is the

sf is given by 1/

*<sup>d</sup> <sup>M</sup> dt*

z sz · ,

' is the scattering time of an electron from spin state from

↑↓ = *N*↓/

**j** (5)

is the equilibrium carrier

↓↑, so that in equilibrium

 to '.

↓↑ are not the

↓↑. By solving

/d*t*=d*M*z/d*t* = 0, using the continuity equations, one

) 0, (6)

(7)

sf = 1/↑↓ + 1/

<sup>↓</sup> decays as e/*<sup>x</sup>*. Thus a spin current play a key

denotes the spin dependent density of states at

↑↓ and 

m. Therefore, the continuity equation of spins are written as

represents spin relaxation. *n*

the Fermi energy. This indicates that, in general, in a ferromagnet,

2 (

> ↑

> > .

Note that the detailed balance principle imposes that *N*↑/

*<sup>z</sup> en n en n* ( )/ ( )/ 

> and

same. In the equilibrium condition, d

<sup>2</sup>

diffusion constant. The spin relaxation time

↓. A spin current generated by

role only in a system with the scale of

moment **M** into electric polarization **P**'.

finds the spin-diffusion equations:

no net spin scattering takes place, where *N*

density with spin

where *D* sf 

↑

current.

Fig. 4. (a) A schematic illustration of the magnetic-field **H** generation from a charge current **j**c according to Ampere's law. (b) A schematic illustration of the electric-field **E** generation from a hypothetical magnetic-monopole current **j**m according to the electromagnetic duality and Ampere's law. (c) A schematic illustration of the electric-field **E** generation from a pair of hypothetical magnetic-monopole currents, **j**m and **j**m, or a spin current.

A spin current can be detected electrically using the inverse spin Hall effect (ISHE), conversion of a spin current into an electric field [see Fig. 3(a)]. The ISHE has the same symmetry as that of the relativistic transformation of magnetic moment into electric polarization, which is derived from the Lorentz transformation, as follows. Consider a magnet with the magnetic moment **M** moving at a constant velocity **v** along the *z* axis with respect to an observer [see Fig. 3(b)]. This motion of the magnet is a flow of angular momentum, meaning an existence of a "spin current". In the observer's coordinate system, the Lorentz transformation converts a part of this magnetic moment **M** into an electric dipole moment **P**' as

$$\mathbf{P'} = -\frac{1}{\sqrt{1 - \left(\mathbf{v} \,/\, c\right)^2}} (\epsilon\_0 \mathbf{v} \times \mathbf{M})\_\prime \tag{8}$$

where *c* and 0 are the light velocity and the electric constant, respectively. This indicates that electric polarization perpendicular to the direction of the magnetic-moment velocity is induced.

This electric-polarization generation can also be regarded as the spin-current version of Ampere's law as follows. As shown in Fig. 4(a), when a charge current **j**c flows, a circular magnetic field **H** is induced around the charge current, according to Ampere's law: rot**H** = **j**c. If a hypothetical magnetic monopole flows, a circular electric field **E** is expected to be induced around the monopole current **j**m according to rot**E** = **j**m [see Fig. 4(b)], from the electromagnetic duality. Although this monopole has never been observed in reality, a spin current can be regarded as a pair of the hypothetical monopole currents flowing in the opposite directions along the spin current spatial direction. Therefore, a spin current may generate an electric field and this field is the superposition of the two electric fields induced by this pair of the monopole current, as shown in Fig. 4(c). This spin-currentinduced electric field is identical to the field induced by the dipole moment described by Eq. (8).

In this way, electromagnetism and relativity predict that a spin current generates an electric field. According to Eq. (8), however, this electric field is too weak in a vacuum to be detected

Spin Photodetector: Conversion of

In-plane light illumination angle

component of **j**s ×

intensity GaAs

of R L GaAs <sup>t</sup> ( )/ *VV I* .

in Fig. 5(b), where the in-plane angle

ISHE. The relation of the ISHE, **E**ISHE **j**s ×

photoinduced ISHE is proportional to |**j**s ×

Light Polarization Information into Electric Voltage Using Inverse Spin Hall Effect 411

Cu/GaAs system, where the Pt layer is replaced by Cu with very weak ISHE, supporting

Fig. 5. (a) A schematic illustration of the Pt/GaAs hybrid structure and the photoinduced

Fig. 6. (a) Ellipticity *A* of the illuminated light dependence of *V*R *V*L. (b) *A* dependence of the ellipticity *A*GaAs of the light injected into the GaAs layer. (c) *A* dependence of the

circular polarization GaAs *P*circ of the light injected into the GaAs layer. (e) GaAs *P*circ dependence

*<sup>t</sup> I* of the light injected into the GaAs layer. (d) *A* dependence of the degree of


dependence of *V*R*V*L for the Pt/GaAs sample is shown

[see Fig. 5(a)]. This electromotive force was found to be disappeared in a

dependence of *V*R−*V*<sup>L</sup>

, since 

is defined in Fig. 5(a). Figure 5(b) shows that *V*R*V*<sup>L</sup>

. Notable is that this variation is

and **j**s are directed along the


, as expected for the photoinduced

, indicates that the electric voltage due to the

varies systematically by changing the illumination angle

that ISHE is responsible for the observed electric voltage.

ISHE in the Pt/GaAs system. (b) In-plane illumination angle

measured for the Pt/GaAs hybrid structure.

well reproduced using a function proportional to cos

light propagation direction and the *z* axis, respectively. Here, |**j**s ×

in reality. In a solid with strong spin-orbit interaction, in contrast, a similar but strong conversion between spin currents and electric fields appears, which is the ISHE.

In a solid, existence of a spin current can be modelled as that two electrons with opposite spins travel in opposite directions along the spin-current spatial direction **j**s, as shown in Fig. 3(a). Here, denotes the spin polarization vector of the spin current. The spin-orbit interaction bends these two electrons in the same direction and induces an electromotive force **E**ISHE transverse to **j**s and , which is the ISHE. The relation among **j**s, **E**ISHE, and is therefore given by (Saitoh, 2006)

$$\mathbf{E}\_{\rm ISHE} = D\_{\rm ISHE} \mathbf{J}\_s \times \boldsymbol{\sigma}\_\prime \tag{9}$$

where *D*ISHE is the ISHE efficiency. This equation is similar to Eq. (8) but this effect may be enhanced by the strong spin-orbit interaction in solids.

The ISHE was recently observed using a spin-pumping method operated by ferromagnetic resonance (FMR) and by a non-local method in metallic nanostructures (Saitoh, 2006; Valenzuela, 2006; Kimura, 2007). Since the ISHE enables the electric detection of a spin current, it will be useful for exploring spin currents in condensed matter.

#### **4. Photoinduced inverse spin Hall effect: Experiment**

The combination of the optical generation of spin-polarized carriers and the ISHE enables direct conversion of light-polarization information into electric voltage in a Pt/GaAs interface (Ando, 2010). Figure 5(a) shows a schematic illustration of the Pt/GaAs sample. Here, the thickness of the Pt layer is 5 nm. The Pt layer was sputtered on a Si-doped GaAs substrate with a doping concentration of *N*D = 4.7 × 1018 cm3. The surface of the GaAs layer was cleaned by chemical etching immediately before the sputtering. Two electrodes are attached to the ends of the Pt layer as shown in Fig. 5(a). During the measurement, circularly polarized light with a wavelength of = 670 nm and a power of *I*i = 10 mW was illuminated to the Pt/GaAs sample as shown in Fig. 5(a). In the GaAs layer, electrons with a spin polarization along the light propagation direction are excited to the conduction band by the circularly polarized light due to the optical selection rule. Here, note that hole spin polarization plays a minor role in this setup, since it relaxes in ~ 100 fs, which is much faster than the relaxation time of ~ 35 ps for electron spin polarization (Hilton, 2002; Kimel, 2001). This spin polarization of electrons then travels into the Pt layer across the interface as a pure spin current. The injected spin current is converted into an electric voltage by the ISHE in the Pt layer due to the strong spin-orbit interaction in Pt (Ando, 2008). Here, note that the angle of the light illumination to the normal axis of the film plane is set at 0 = 65° to obtain the photoinduced ISHE signal, since the electric voltage due to the photoinduced ISHE is proportional to *j*ssin0 because of the relation **E**ISHE **j**s × , where the spin polarization is directed along the light propagation direction. The difference in the generated voltage between illumination with right circularly polarized (RCP) and left circularly polarized (LCP) light, *V*R*V*L, was measured by a polarization-lock-in technique using a photoelastic modulator operated at 50 kHz. The difference in the intensities between RCP and LCP light incident on the sample was confirmed to be vanishingly small. All the measurements were performed at room temperature at zero applied bias across the junction.

in reality. In a solid with strong spin-orbit interaction, in contrast, a similar but strong

In a solid, existence of a spin current can be modelled as that two electrons with opposite spins travel in opposite directions along the spin-current spatial direction **j**s, as shown in

interaction bends these two electrons in the same direction and induces an electromotive

ISHE ISHE s **E J** *D*

where *D*ISHE is the ISHE efficiency. This equation is similar to Eq. (8) but this effect may be

The ISHE was recently observed using a spin-pumping method operated by ferromagnetic resonance (FMR) and by a non-local method in metallic nanostructures (Saitoh, 2006; Valenzuela, 2006; Kimura, 2007). Since the ISHE enables the electric detection of a spin

The combination of the optical generation of spin-polarized carriers and the ISHE enables direct conversion of light-polarization information into electric voltage in a Pt/GaAs interface (Ando, 2010). Figure 5(a) shows a schematic illustration of the Pt/GaAs sample. Here, the thickness of the Pt layer is 5 nm. The Pt layer was sputtered on a Si-doped GaAs substrate with a doping concentration of *N*D = 4.7 × 1018 cm3. The surface of the GaAs layer was cleaned by chemical etching immediately before the sputtering. Two electrodes are attached to the ends of the Pt layer as shown in Fig. 5(a). During the measurement,

along the light propagation direction are excited to the conduction band

illuminated to the Pt/GaAs sample as shown in Fig. 5(a). In the GaAs layer, electrons with a

by the circularly polarized light due to the optical selection rule. Here, note that hole spin polarization plays a minor role in this setup, since it relaxes in ~ 100 fs, which is much faster than the relaxation time of ~ 35 ps for electron spin polarization (Hilton, 2002; Kimel, 2001). This spin polarization of electrons then travels into the Pt layer across the interface as a pure spin current. The injected spin current is converted into an electric voltage by the ISHE in the Pt layer due to the strong spin-orbit interaction in Pt (Ando, 2008). Here, note that the

the photoinduced ISHE signal, since the electric voltage due to the photoinduced ISHE is

directed along the light propagation direction. The difference in the generated voltage between illumination with right circularly polarized (RCP) and left circularly polarized (LCP) light, *V*R*V*L, was measured by a polarization-lock-in technique using a photoelastic modulator operated at 50 kHz. The difference in the intensities between RCP and LCP light incident on the sample was confirmed to be vanishingly small. All the measurements were

denotes the spin polarization vector of the spin current. The spin-orbit

, which is the ISHE. The relation among **j**s, **E**ISHE, and

, (9)

= 670 nm and a power of *I*i = 10 mW was

, where the spin polarization

0 = 65° to obtain

is

is

conversion between spin currents and electric fields appears, which is the ISHE.

current, it will be useful for exploring spin currents in condensed matter.

angle of the light illumination to the normal axis of the film plane is set at

performed at room temperature at zero applied bias across the junction.

0 because of the relation **E**ISHE **j**s ×

**4. Photoinduced inverse spin Hall effect: Experiment** 

enhanced by the strong spin-orbit interaction in solids.

circularly polarized light with a wavelength of

Fig. 3(a). Here,

spin polarization

proportional to *j*ssin

force **E**ISHE transverse to **j**s and

therefore given by (Saitoh, 2006)

In-plane light illumination angle dependence of *V*R*V*L for the Pt/GaAs sample is shown in Fig. 5(b), where the in-plane angle is defined in Fig. 5(a). Figure 5(b) shows that *V*R*V*<sup>L</sup> varies systematically by changing the illumination angle . Notable is that this variation is well reproduced using a function proportional to cos, as expected for the photoinduced ISHE. The relation of the ISHE, **E**ISHE **j**s × , indicates that the electric voltage due to the photoinduced ISHE is proportional to |**j**s × |*<sup>x</sup>* cos, since and **j**s are directed along the light propagation direction and the *z* axis, respectively. Here, |**j**s × |*x* denotes the *x* component of **j**s × [see Fig. 5(a)]. This electromotive force was found to be disappeared in a Cu/GaAs system, where the Pt layer is replaced by Cu with very weak ISHE, supporting that ISHE is responsible for the observed electric voltage.

Fig. 5. (a) A schematic illustration of the Pt/GaAs hybrid structure and the photoinduced ISHE in the Pt/GaAs system. (b) In-plane illumination angle dependence of *V*R−*V*<sup>L</sup> measured for the Pt/GaAs hybrid structure.

Fig. 6. (a) Ellipticity *A* of the illuminated light dependence of *V*R *V*L. (b) *A* dependence of the ellipticity *A*GaAs of the light injected into the GaAs layer. (c) *A* dependence of the intensity GaAs *<sup>t</sup> I* of the light injected into the GaAs layer. (d) *A* dependence of the degree of circular polarization GaAs *P*circ of the light injected into the GaAs layer. (e) GaAs *P*circ dependence of R L GaAs <sup>t</sup> ( )/ *VV I* .

Spin Photodetector: Conversion of

 

GaAs <sup>s</sup> <sup>p</sup> *A* ( [ ]/ [ ]) 

written as,

where *I*+ and *I*-

t s

structure.

GaA

GaAs

Here, <sup>s</sup> <sup>p</sup>

s s p p

calculate R L GaAs

is the wavelength of the light.

6(e). As shown in Fig. 6(e), R L GaAs

i

*<sup>t</sup> I* of the light injected into the GaAs layer obtained from

Light Polarization Information into Electric Voltage Using Inverse Spin Hall Effect 413

polarization *P*circ, the difference in the numbers between RCP and LCP photons, can be

circ 2

circular polarization GaAs *P*circ of the light injected into the GaAs layer is shown in Fig. 6(d), which is obtained from the ellipticity shown in Fig. 6(b) using Eq. (13). Here, notable is that the degree of circular polarization GaAs *P*circ of the light injected into the GaAs layer is proportional to the electron spin polarization generated by the circularly polarized light. The propagation of the circularly polarized light also changes the intensity of the light as

<sup>i</sup> *I TI T I* . Figure 6(c) shows the light ellipticity *A* dependence of the intensity

2 GaAs s p

*<sup>A</sup> IT T I*

t i 2 2

photoinduced ISHE is expected to be proportional to the intensity of the absorbed light, or the number of spin-polarized carriers generated by the circularly polarized light, one should

polarization. This is consistent with the prediction of the photoinduced ISHE. Thus both the light illumination angle and light ellipticity dependence of the electric voltage support that the electric voltage is induced by the ISHE driven by photoinduced spin-polarized carriers.

Table 2. The parameters used in the calculation. *n*0, *n*1, and *n*2 are the complex refractive

of the illumination to the normal axis of the film plane. *d*1 is the thickness of the Pt layer and

polarized light for different *A*. The GaAs *P*circ dependence of R L GaAs

indices for air, Pt, and GaAs, respectively (Adachi, 1993; Ordal, 1983).

Table 3. The transmittance *T*s(p) and the transmission coefficient

<sup>1</sup> . 1 1

<sup>t</sup> ( )/ *VV I* to compare the electric voltage induced by the circularly

<sup>t</sup> ( )/ *VV I* is proportional to GaAs *P*circ , or the electron spin

*A A* 

i i <sup>i</sup> *III* is the illuminated light intensity. Since the electric voltage due to the

*II A <sup>P</sup> II A*

 

*A* . From the value of the ellipticity *A*, the degree of circular

<sup>2</sup> , <sup>1</sup>

are the intensities of the RCP and LCP light, respectively. The degree of

(13)

(14)

<sup>t</sup> ( )/ *VV I* is shown in Fig.

0 is the incident angle

s(p) for the Pt/GaAs hybrid

The observed electric voltage signal depends strongly on the ellipticity of the illuminated light polarization. Here, the ellipticity *A* is defined as the ratio of the minor to major radiuses of the elliptically polarized light. Figure 6(a) shows the illuminated-light ellipticity *A* dependence of *V*R*V*L. As shown in Fig. 6(a), the *V*R*V*L signal increases with the ellipticity *A* of the illuminated light. This supports that this signal is induced by the photoinduced ISHE, since the angular momentum component of a photon along the light propagation direction is zero (maximized) when *A* = 0 (1).

#### **5. Photoinduced inverse spin Hall effect: Theory**

The *A* dependence of *V*R*V*L shown in Fig. 6(a) demonstrates that the electric voltage observed in the Pt/GaAs junction is induced by the circularly polarized light illumination. However, the variation of the electric voltage with respect to *A* is not straightforward to understand; the *V*R*V*L signal is not linear to *A*. In the following, we discuss in detail on the experimental result by calculating the polarization of the light injected into the GaAs layer.

The propagation of light in a multilayer film is characterized by the optical admittance *Y*s(p) = *C*s(p)/*B*s(p), where s(p) denotes s(p) polarized light. *B*s(p) and *C*s(p) are expressed as

$$
\begin{pmatrix} \mathcal{B}^{s(\mathfrak{p})} \\ \mathcal{C}^{s(\mathfrak{p})} \end{pmatrix} = \begin{pmatrix} \cos \delta & \left( i \sin \delta \right) / \eta\_1^{s(\mathfrak{p})} \\ i \eta\_1^{s(\mathfrak{p})} \sin \delta & \cos \delta \end{pmatrix} \begin{pmatrix} 1 \\ \eta\_2^{s(\mathfrak{p})} \end{pmatrix} \tag{10}
$$

where 11 1 2 cos / , *n d* <sup>p</sup> 1/2 0 0 ( , / ) / cos *r r n <sup>r</sup>* and <sup>s</sup> 1/2 0 0 ( / ) cos *r r n <sup>r</sup>* (*r* = 0, 1, 2). Here, *n*0, *n*1, and *n*2 are the complex refractive indices for air, Pt, and GaAs, respectively. *d*1 is the thickness of the Pt layer and *<sup>r</sup>* is the incident angle of the light defined as shown in Fig. 7. Using *B*s(p) and *C*s(p), the transmittance s(p) s(p) s(p) *T II* <sup>t</sup> / <sup>i</sup> and the transmission coefficient s(p) s(p) s(p) *E E* <sup>t</sup> / <sup>i</sup> are obtained as

$$T^{s(\mathbf{p})} = \frac{4\eta\_0^{s(\mathbf{p})} \Re[\eta\_2^{s(\mathbf{p})}]}{(\eta\_0^{s(\mathbf{p})} \mathcal{B}^{s(\mathbf{p})} + \mathcal{C}^{s(\mathbf{p})})(\eta\_0^{s(\mathbf{p})} \mathcal{B}^{s(\mathbf{p})} + \mathcal{C}^{s(\mathbf{p})})} \, \tag{11}$$

$$
\tau^s = \frac{2\eta\_0^s}{\eta\_0^s B^s + \mathcal{C}^s}, \quad \tau^\mathbb{P} = \frac{2\eta\_0^\mathbb{P}}{\eta\_0^\mathbb{P} B^\mathbb{P} + \mathcal{C}^\mathbb{P}} \frac{\cos \theta\_0}{\cos \theta\_2} \,\tag{12}
$$

where s(p) i(t) *<sup>I</sup>* and s(p) i(t) *E* are the illuminated (transmitted) light intensity and the amplitude of the electric field of s(p) polarized light [see Fig. 7], respectively. Here, s(p) <sup>2</sup> [ ] is the real part of s(p) <sup>2</sup> . Using Eqs. (11) and (12) with the parameters shown in Table 2, the transmittance *T*s(p) and the transmission coefficient s(p) for the Pt/GaAs system are obtained as shown in Table 3. The calculated transmission coefficients s(p) show that the transmission of the s and p polarized light is different. This indicates that the ellipticity of the illuminated to the sample is changed during the propagation of the film. The relation between the ellipticity *A*GaAs of the light injected into the GaAs layer and the ellipticity *A* of the illuminated light is shown in Fig. 6(b). Here, *A*GaAs is obtained using

The observed electric voltage signal depends strongly on the ellipticity of the illuminated light polarization. Here, the ellipticity *A* is defined as the ratio of the minor to major radiuses of the elliptically polarized light. Figure 6(a) shows the illuminated-light ellipticity *A* dependence of *V*R*V*L. As shown in Fig. 6(a), the *V*R*V*L signal increases with the ellipticity *A* of the illuminated light. This supports that this signal is induced by the photoinduced ISHE, since the angular momentum component of a photon along the light

The *A* dependence of *V*R*V*L shown in Fig. 6(a) demonstrates that the electric voltage observed in the Pt/GaAs junction is induced by the circularly polarized light illumination. However, the variation of the electric voltage with respect to *A* is not straightforward to understand; the *V*R*V*L signal is not linear to *A*. In the following, we discuss in detail on the experimental result by calculating the polarization of the light injected into the GaAs layer. The propagation of light in a multilayer film is characterized by the optical admittance *Y*s(p)

= *C*s(p)/*B*s(p), where s(p) denotes s(p) polarized light. *B*s(p) and *C*s(p) are expressed as

*B i*

*C i*

*n d* <sup>p</sup> 1/2

as shown in Table 3. The calculated transmission coefficients

where 11 1 

where s(p)

part of s(p) 

i(t) *<sup>I</sup>* and s(p)

 2 cos / , 

 

transmission coefficient s(p) s(p) s(p) *E E* <sup>t</sup> / <sup>i</sup> 

respectively. *d*1 is the thickness of the Pt layer and

*T*

transmittance *T*s(p) and the transmission coefficient

s(p) s(p)

*r r n <sup>r</sup>* 

are obtained as

s(p) s(p) s(p) 0 2

the electric field of s(p) polarized light [see Fig. 7], respectively. Here, s(p)

0 0

 

<sup>s</sup> <sup>p</sup> <sup>s</sup> <sup>0</sup> <sup>p</sup> 0 0 ss s p p p 0 0 2 <sup>2</sup> <sup>2</sup> cos , , *B C B C* cos

of the s and p polarized light is different. This indicates that the ellipticity of the illuminated to the sample is changed during the propagation of the film. The relation between the ellipticity *A*GaAs of the light injected into the GaAs layer and the ellipticity *A* of the illuminated light is shown in Fig. 6(b). Here, *A*GaAs is obtained using

s(p) s(p) s(p) 1 2 cos ( sin ) / <sup>1</sup> ,

0 0 ( , / ) / cos

1, 2). Here, *n*0, *n*1, and *n*2 are the complex refractive indices for air, Pt, and GaAs,

as shown in Fig. 7. Using *B*s(p) and *C*s(p), the transmittance s(p) s(p) s(p) *T II* <sup>t</sup> / <sup>i</sup> and the

 

sin cos

1

(12)

and <sup>s</sup> 1/2

0 0 ( / ) cos

<sup>2</sup> [ ] 

s(p) show that the transmission

s(p) for the Pt/GaAs system are obtained

 

*r r n <sup>r</sup>* 

*<sup>r</sup>* is the incident angle of the light defined

(10)

(*r* = 0,

(11)

is the real

 

 

s(p) s(p) s(p) s(p) s(p) s(p) \*

i(t) *E* are the illuminated (transmitted) light intensity and the amplitude of

<sup>2</sup> . Using Eqs. (11) and (12) with the parameters shown in Table 2, the

 

4 [] , ( )( )

*BC BC*

 

propagation direction is zero (maximized) when *A* = 0 (1).

**5. Photoinduced inverse spin Hall effect: Theory** 

GaAs <sup>s</sup> <sup>p</sup> *A* ( [ ]/ [ ]) *A* . From the value of the ellipticity *A*, the degree of circular polarization *P*circ, the difference in the numbers between RCP and LCP photons, can be written as,

$$P\_{\rm circ} \equiv \frac{I^+ - I^-}{I^+ + I^-} = \frac{2A}{1 + A^2} \,\prime \tag{13}$$

where *I*+ and *I* are the intensities of the RCP and LCP light, respectively. The degree of circular polarization GaAs *P*circ of the light injected into the GaAs layer is shown in Fig. 6(d), which is obtained from the ellipticity shown in Fig. 6(b) using Eq. (13). Here, notable is that the degree of circular polarization GaAs *P*circ of the light injected into the GaAs layer is proportional to the electron spin polarization generated by the circularly polarized light. The propagation of the circularly polarized light also changes the intensity of the light as s s p p t s i GaA <sup>i</sup> *I TI T I* . Figure 6(c) shows the light ellipticity *A* dependence of the intensity GaAs *<sup>t</sup> I* of the light injected into the GaAs layer obtained from

$$I\_{\rm t}^{\rm GaAs} = \left( T^s \frac{A^2}{1 + A^2} + T^\mathbb{P} \frac{1}{1 + A^2} \right) I\_{\rm i.} \tag{14}$$

Here, <sup>s</sup> <sup>p</sup> i i <sup>i</sup> *III* is the illuminated light intensity. Since the electric voltage due to the photoinduced ISHE is expected to be proportional to the intensity of the absorbed light, or the number of spin-polarized carriers generated by the circularly polarized light, one should calculate R L GaAs <sup>t</sup> ( )/ *VV I* to compare the electric voltage induced by the circularly polarized light for different *A*. The GaAs *P*circ dependence of R L GaAs <sup>t</sup> ( )/ *VV I* is shown in Fig. 6(e). As shown in Fig. 6(e), R L GaAs <sup>t</sup> ( )/ *VV I* is proportional to GaAs *P*circ , or the electron spin polarization. This is consistent with the prediction of the photoinduced ISHE. Thus both the light illumination angle and light ellipticity dependence of the electric voltage support that the electric voltage is induced by the ISHE driven by photoinduced spin-polarized carriers.


Table 2. The parameters used in the calculation. *n*0, *n*1, and *n*2 are the complex refractive indices for air, Pt, and GaAs, respectively (Adachi, 1993; Ordal, 1983). 0 is the incident angle of the illumination to the normal axis of the film plane. *d*1 is the thickness of the Pt layer and is the wavelength of the light.


Table 3. The transmittance *T*s(p) and the transmission coefficient s(p) for the Pt/GaAs hybrid structure.

Spin Photodetector: Conversion of

Here, R L GaAs GaAs

 

where 2 02 0 *Q Q Qn n* sin ( / )sin 

we used GaAs s <sup>p</sup> *A* (/)

because of Eq. (9), we obtain

and thus

of GaAs

outside the sample.

**6. Conclusion** 

technology.

**7. Acknowledgment** 

**8. References** 

Kurebayashi for valuable discussions.

*Letters* Vol. 101: 036601.

Adachi, S. (1993). *Properties of Aluminium Gallium Arsenide*, Inspec.

into electric voltage, *Applied Physics Letters* Vol. 96: 082502.

polarized holes in GaAs, *Physical Review Letters* Vol. 89: 146601.

Light Polarization Information into Electric Voltage Using Inverse Spin Hall Effect 415

*p <sup>n</sup> V V Q IP n* 

2 0 i circ *VV Q* ( cos tan ) , 

0 0

t circ *QV V I P* ( )/( ) is the proportionality constant as seen from Fig. 6(e) and

 

t i *I I* and GaAs *P P* circ circ due to the presence of the top Pt layer and oblique illumination, the output signal *V*R*V*L is proportional to the degree of circular polarization *P*circ of the illuminated light outside the sample. This indicates that the photoinduced ISHE can be used as a spin photodetector: the direct conversion of circular polarization information into electric voltage. This function is demonstrated experimentally in Fig. 8, in which *V*R*V*L is proportional to the degree of circular polarization of the illuminated light

The photoinduced inverse spin Hall effect provides a simple way for detecting light circular polarization through a spin current. This phenomenon enables the direct conversion of light-polarization information into electric voltage in a Pt/GaAs junction. This technique will be useful both in spintronics and photonics, promising significant advances in optical

The authors thank to M. Morikawa, T. Trypiniotis, Y. Fujikawa, C. H. W. Barnes, and H.

Ando, K., Takahashi, S., Harii, K., Sasage, K., Ieda, J., Maekawa, S. & Saitoh, E. (2008).

Ando, K., Morikawa, M., Trypiniotis, T., Fujikawa, Y., Barnes, C. H. W. & Saitoh, E. (2010).

Hilton, D. J. & Tang, C. L. (2002). Optical orientation and femtosecond relaxation of spin-

Electric manipulation of spin relaxation using the spin Hall effect, *Physical Review* 

Photoinduced inverse spin Hall effect Conversion of light-polarization information

i circ

*I P* (18)

(17)

2

cos . cos

*A* . Since the proportionality constant *Q* is proportional to sin

 

. Equation (18) shows that, in spite of the inequalities

 

<sup>s</sup> R L 2 2

RL s p

Fig. 7. The definition of 0, 1, and 2.

The photoinduced ISHE allows direct conversion of the circular-polarization information *P*circ of the illuminated light into an electric voltage. The relation between *V*R*V*L and the circular-polarization information *P*circ of the illuminated light can be argued from the linear dependence of R L GaAs <sup>t</sup> ( )/ *VV I* on GaAs *P*circ shown in Fig. 6(e). For simplicity, we assume that the imaginary parts of *n*2 and s(p) are negligibly small: 2 2 *n n* [ ] and s(p) s(p) [ ] [see Tables 2 and 3]. From Eqs. (11), (12), (13), and (14), one obtains

$$I\_{\rm t}^{\rm GaAs} = \left( (\tau^s)^2 \frac{A^2}{1+A^2} + (\tau^p)^2 \frac{1}{1+A^2} \right) \frac{n\_2 \cos \theta\_2}{n\_0 \cos \theta\_0} I\_{\rm i\,\prime} \tag{15}$$

$$P\_{\rm circ}^{\rm GaAs} = \frac{2\pi^s \pi^p A}{\left(\pi^p\right)^2 + \left(\pi^s\right)^2 A^2},\tag{16}$$

Fig. 8. The degree of circular polarization of the illuminated light ellipticity *A* of the illuminated light *P*circ dependence of *V*R *V*L.

and thus

414 Photodetectors

The photoinduced ISHE allows direct conversion of the circular-polarization information *P*circ of the illuminated light into an electric voltage. The relation between *V*R*V*L and the circular-polarization information *P*circ of the illuminated light can be argued from the linear

2

GaAs s 2 p 2 2 2 t i 2 2

 

> <sup>s</sup> <sup>p</sup> GaAs circ p 2 s2 2 <sup>2</sup> , () ()

Fig. 8. The degree of circular polarization of the illuminated light ellipticity *A* of the

*<sup>A</sup> <sup>P</sup>*

*A n I I*

 

1 cos () () , 1 1 cos

*A A n*

 

 

[see Tables 2 and 3]. From Eqs. (11), (12), (13), and (14), one obtains

<sup>t</sup> ( )/ *VV I* on GaAs *P*circ shown in Fig. 6(e). For simplicity, we assume

*A*

s(p) are negligibly small: 2 2 *n n* [ ] and s(p) s(p)

0 0

(15)

 [ ]

(16)

Fig. 7. The definition of

dependence of R L GaAs

that the imaginary parts of *n*2 and

illuminated light *P*circ dependence of *V*R *V*L.

0, 1, and 2.

$$V^{\mathbb{R}} - V^{\mathbb{L}} = \left( Q \frac{\tau^s \tau^p n\_2 \cos \theta\_2}{n\_0 \cos \theta\_0} I\_{\mathbf{i}} \right) P\_{\text{circ}}.\tag{17}$$

Here, R L GaAs GaAs t circ *QV V I P* ( )/( ) is the proportionality constant as seen from Fig. 6(e) and we used GaAs s <sup>p</sup> *A* (/) *A* . Since the proportionality constant *Q* is proportional to sin2 because of Eq. (9), we obtain

$$V^{\mathbb{R}} - V^{\mathbb{L}} = (Q' \tau^s \tau^p \cos \theta\_2 \tan \theta\_0 I\_i) P\_{\text{circ}} \tag{18}$$

where 2 02 0 *Q Q Qn n* sin ( / )sin . Equation (18) shows that, in spite of the inequalities of GaAs t i *I I* and GaAs *P P* circ circ due to the presence of the top Pt layer and oblique illumination, the output signal *V*R*V*L is proportional to the degree of circular polarization *P*circ of the illuminated light outside the sample. This indicates that the photoinduced ISHE can be used as a spin photodetector: the direct conversion of circular polarization information into electric voltage. This function is demonstrated experimentally in Fig. 8, in which *V*R*V*L is proportional to the degree of circular polarization of the illuminated light outside the sample.

### **6. Conclusion**

The photoinduced inverse spin Hall effect provides a simple way for detecting light circular polarization through a spin current. This phenomenon enables the direct conversion of light-polarization information into electric voltage in a Pt/GaAs junction. This technique will be useful both in spintronics and photonics, promising significant advances in optical technology.

### **7. Acknowledgment**

The authors thank to M. Morikawa, T. Trypiniotis, Y. Fujikawa, C. H. W. Barnes, and H. Kurebayashi for valuable discussions.

### **8. References**

Adachi, S. (1993). *Properties of Aluminium Gallium Arsenide*, Inspec.


**19** 

*Bulgaria* 

**Shape of the Coherent Population Trapping** 

There has been permanent interest in investigations of new magnetic sensors and their various applications (Edelstein, 2007). Last years there is a rapid progress in development of magneto-optical sensors because of their sensitivity and potential for miniaturization. Magnetometers, based on magneto-optical sensors have high sensitivity - comparable to, or even surpassing this of the SQUIDs (Superconducting Quantum Interference Devices) (Kominis et al., 2003; Dang et al., 2010; Savukov, 2010; Knappe, 2010). Microfabrication of components using the techniques of Micro-Electro-Mechanical Systems (MEMS) developed for atomic clocks (Knappe, 2004) gives the opportunity for building small, low consuming, low cost and non-cryogenic (as SQUIDs) sensors (Griffith et al., 2010). Coherent optical effects can be applied for magnetic field detection and offer perspectives for development of high-precision optical magnetometers (Cox et al., 2011; Kitching et al., 2011). These magnetometers are appropriate for geomagnetic, space, nuclear and biological magnetic field measurements (cardio and brain magnetic field imaging), environmental monitoring, magnetic microscopy, investigations of fundamental physics, etc. Coherent magneto-optical resonances have many applications not only in magnetometry, but in high-resolution spectroscopy, lasing without inversion, laser cooling, ultraslow group velocity propagation

Magneto-optical resonances can be prepared and registered in different ways (Budker&Romalis, 2007 and references therein). Most frequently Coherent–Population-Trapping (CPT) is observed when two hyperfine levels of the ground state of alkali atoms are coupled by two laser fields to a common excited level. When the frequency difference between the laser fields equals the frequency difference between the two ground states, the atoms are prepared in a non-absorbing state, which can be registered as a fluorescence quenching and transparency enhancement in spectral interval narrower than the natural

In degenerate two-level systems coherent states can be created by means of Hanle effect configuration (Alzetta et al., 1976). In this case the coherent non-absorbing state is prepared on two Zeeman sublevels of one hyperfine level by monochromatic laser field (the so called single frequency CPT). Hanle configuration is important for performing significantly

width of the observed optical transition (Arimondo, 1996).

simplified experiments and to build practical devices as well.

**1. Introduction** 

of light, etc. (Gao, 2009).

**Resonances Registered in Fluorescence** 

Sanka Gateva and Georgi Todorov

*Institute of Electronics, Bulgarian Academy of Sciences* 

