# MOKE

MOKE
관련코스 현대광학
소분류 물리
선행 키워드
연관 키워드

MOKE is named after John Kerr who reported it in 1875. It is similar to Faraday rotation, but it describes changes in polarization of light when it is reflected at a magnetized material. In general, magnetic experiments using magnetic thin films are used and the films with substrates are generally opaque. Also, it is less damaging for the samples than Faraday rotation. So MOKE which uses reflection is more appropriate than Faraday rotation which uses transmission. Magneto-optical Kerr effect is also different from electro-optical Kerr effect. In MOKE microscopy, there are 3 measurement types depending on the direction between the magnetization of sample and incident direction. If magnetization is perpendicular to the thin film, it is called Polar MOKE. If magnetization is parallel to thin film surface, it is called Longitudinal MOKE when magnetization is parallel to plane of incidence, and Transverse MOKE in perpendicular case. Rotation of polarization can be described by permittivity tensor.

$\mathbf{D}=\overset{\leftrightarrow}{\epsilon}\mathbf{E}$
$\mathbf{D}=\epsilon(\mathbf{E}+iQ\mathbf{m}\times\mathbf{E})$

Q is the magneto-optical constant. The Lorentz movement vLor generated by second term rotate the polarization vector of the reflected light by an angle θk. Since the angle θk is very small, it could be approximated as following:

$\theta_{k}\approx\tan\theta_{k}=\frac{K}{N}.$

N is the reflected amplitude and K is the projection of Lorentz velocity in the polarization plane.

#### Fresnel equation

When a beam incidents to the magnetic medium on the dielectric medium, the reflection of the beam can be expressed using Fresnel equation:

$\begin{bmatrix} E_{rs} \\ E_{rp} \end{bmatrix}= \begin{bmatrix}r_{ss} & r_{sp} \\ r_{ps} & r_{pp}\end{bmatrix} \begin{bmatrix} E_{is} \\ E_{ip} \end{bmatrix}$

Here Fresnel coefficients can be written as:

$r_{ss}=\frac{\mu_{2}N_{1}\cos\theta_{1}-\mu_{1}N_{2}\cos\theta_{2}}{\mu_{2}N_{1}\cos\theta_{1}+\mu_{1}N_{2}\cos\theta_{2}}$
$r_{sp}=\frac{i\mu_{1}\mu_{2}N_1N_2\cos\theta_{1}Q(m_{x}\sin\theta_{2}+m_{z}\cos\theta_{2})}{(\mu_{1}N_{2}\cos\theta_{1}+\mu_{2}N_{1}\cos\theta_{2})(\mu_{2}N_{1}\cos\theta_{1}+\mu_{1}N_{2}\cos\theta_{2})\cos\theta_{2}}$
$r_{ps}=\frac{-i\mu_{1}\mu_{2}N_1N_2\cos\theta_{1}Q(m_{x}\sin\theta_{2}-m_{z}\cos\theta_{2})}{(\mu_{1}N_{2}\cos\theta_{1}+\mu_{2}N_{1}\cos\theta_{2})(\mu_{2}N_{1}\cos\theta_{1}+\mu_{1}N_{2}\cos\theta_{2})\cos\theta_{2}}$
$r_{ss}=\frac{\mu_{2}N_{1}\cos\theta_{1}-\mu_{2}N_{1}\cos\theta_{2}}{\mu_{1}N_{2}\cos\theta_{1}+\mu_{2}N_{1}\cos\theta_{2}} + \frac{2i\mu_{1}\mu_{2}N_{1}N_{2}\cos\theta_{1}QM_{y}\sin\theta_{2}} {\mu_{1}N_{2}\cos\theta_{1}+\mu_{2}N_{1}\cos\theta_{2}}$