Dr. Vadym Zayets

The transverse Magneto-optical (MO) MO effect is comparable to and often greater than the conventional longitudinal MO effect. The transverse MO effect can be used in a variety of applications where only conventional MO effect is used at present. It could be a powerful tool in different applications, but it should be used wisely.

For the first time the origin and the properties of the transverse non-reciprocal magneto-optical effect were described here (download from this site here).

Conventional longitudinal MO effect

The magneto-optical (MO) effect is important for a variety of applications. The effect is utilized to read data in a MO disk driver, to switch an optical beam in optical switches and to modulate light intensity in spacial light modulators. It is a powerful scientific tool to determine the local magnetization of a material, to study the bandgap structure and spin-orbit interaction in a solid. A unique feature of the MO effect is non-reciprocity. The optical properties of non-reciprocal devices are different for two opposite directions of light propagation. The non-reciprocal effect can occur only in a MO material and the important optical non-reciprocal devices such as an optical isolator and an optical circulator can only be fabricated by utilizing the MO materials.

MO effect was discovered by Faraday in 1845. The MO effect is known to occur in a configuration when light propagates along a magnetic field. When the magnetic field is applied to a material, the electrons with spin directed along and opposite to the magnetic field have different energies. Since the electrons of one spin direction interact with light either of left or right circular polarization, light of the left and right circular polarizations experiences different refraction and absorption. When light is transmitted through a MO material, there is a difference of refractive indexes (Faraday effect) and optical absorption (magnetic circular dichroism (MCD effect)) for left and right circularly polarized light. When light is reflected from a MO material, the reflectivity of the right and left circular polarized light is different (polar and longitudinal Kerr effects). All above-mentioned effects have the same origin and the similar properties and will be referred as longitudinal MO effects.

Transverse MO effect?

The transverse MO effect occurs in the case when light propagates perpendicularly to the magnetic field.

It should be no MO effect in the case of the magnetic field applied perpendicularly to the light propagation direction. Since an electromagnetic wave is transverse, its polarization should be in a plane, which is perpendicular to the light propagation direction. The polarization rotation is possible only around an axis, which is out of this plane. It implies that in the case of transverse magnetization, the polarization rotation around axis parallel to the magnetic field is impossible and the interaction of photons with electrons of opposite spins does not depend on the polarization of light.  Therefore, in this geometry the probability to excite electrons with opposite spins is equal for left and right circularly polarized light and light should not be sensitive to the energy difference of electrons with opposite spins. It should be no MO effect in this case. It is true in the case of free-space propagation. Light only experiences birefringence, which is proportional to the square intensity of the magnetic field. It is called the Cotton–Mouton effect (in the case of gases it is called the Voigt effect). It is a reciprocal effect and may be simply considered as a magnetically-induced anisotropy.

I have found that there is one special case when the non-reciprocal transverse MO effect exists. Light can experience the transverse MO effect only when it propagates in the vicinity of a boundary between two materials and the optical field at least in one material is evanescent. This MO effect is linearly proportional to the applied magnetic field.

 

At present, there are overwhelming experimental evidences for existence of transverse MO effect. There are several reasons why the origin of the transverse MO effect has not been found earlier. The first reason is that the transverse MO effect occurs when the light propagates along an interface. It does not occur in a bulk. The second reason is that in order to assume existence of transverse MO effect, it should be accepted that the polarization of the light could rotate around an axis, which is perpendicular to the light propagation direction. It was an unacceptable assumption. The third reason is following. The transverse MO effect is pure electro-dynamical effect. It can be always correctly calculated by solving Maxwell's equations with correct permittivity tensor. Therefore, all following experiments were well described by solution of Maxwell's equations. For long time it was a good excuse for not understanding origin of the transverse MO effect. 

 

Content

1. Experimental observation of the transverse MO effect

The transverse MO effect is not new and have been experimentally measured, calculated and used in different applications for many years. I will show most-known applications, where the transverse MO effect is utilized

2. Properties of the transverse MO effect.

Here I would like to emphasise the difference in properties between conventional longitudinal MO effect and transverse MO effect

3. Origin of the transverse MO effect

Main part

4. Transverse ellipticity.

Understanding the transverse ellipticity is crucially important. Only light, which polarization is transverse elliptical, may experience the transverse MO effect. The magnitude of the transverse MO effect is linearly proportional to the transverse ellipticity of light.

5. Two contributions to transverse MO effect

Existence of two contribution of opposite sign is unique feature of the transverse MO effect. Understanding them is important to achieve large magnitude of the effect.

6. Magnetization-dependent optical loss

The calculations of the transverse MO effect using general facts and principals

7.Calculations of transverse MO effect in the case of multilayer structure

Rigourous calculation of the transverse MO effect in the case of multilayer structure. The simple scalar dispersion is derived, which describes waveguide modes, surface plasmons and Kerr effect even in the case of large number of layers.

8. Optical excitation of spin-polarized electrons utilizing transverse MO

Method to excite spin-polarized electrons in a solid utilizing transverse MO effect

9. Plasmons

Properties of plasmons in transition metals are described.

10. Enhancement of Transverse MO

Giant enhancement of transverse MO effect is described in the case of plasmons in a multilayer structure.