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A detailed study on Goos-Hänchen (GH) lateral displacements of the reflected and transmitted waves propagating at the interface between an isotropic medium and a gyroelectric medium in Voigt configuration is presented. After the reflection coefficient and transmission coefficient are derived, based on the stationary phase approach, GH lateral displacements are obtained analytically. The numerical results for a specific gyroelectric medium are also given. It shows that with the existence of an applied magnetic field, the GH effect occurs not only during total reflection but also during nontotal reflection, which is not true for isotropic media. Moreover, due to the nonreciprocal property of the gyroelectric medium, the sign of the incident angle also influences the displacements. Finite-element method simulations have verified the theoretical results.

Gyroelectric medium is an electron plasma with an applied magnetic field. The characteristics of electromagnetic waves propagation in gyroelectric plasmas have been theoretically investigated in many literatures. The magnetoplasma modes in Voigt, perpendicular, and Faraday configurations have been studied by Kushwaha and Halevi [

The Goos-Hänchen (GH) effect [

In this paper, we focus on the reflection and transmission characteristics of an electromagnetic beam propagating at the interface between an isotropic medium and a gyroelectric medium in Voigt configuration. After obtaining the analytical expressions for the reflection and transmission coefficients, we get the mathematical result for the GH lateral displacement by the stationary phase approach. Based on the results, we discuss some unique phenomena.

Considering the configuration in Figure

Reflection and transmission of TM waves at an interface between a semi-infinite isotropic medium (region 1) and a gyroelectric medium in the Voigt configuration (region 2). In region 2, applied magnetic field

It is known that for gyroelectric medium in the Voigt configuration, waves can be decoupled into TE and TM modes, and only the TM mode is affected by the gyrotropy [

For Figure

According to the Maxwell equations and boundary conditions, when there is no total reflection at the boundary, the transmission and reflection coefficients for TM waves can be written as

According to (

Noting that the denominators of both coefficients are the same, the GH lateral displacements of the reflection and transmission for TM waves can be expressed as

It is interesting to note that both

When

Since the transmitted wave is evanescent in the

Here, we consider an indium antimony (InSb) with an external magnetic field as the gyroelectric medium. The isotropic medium is a vacuum. The material parameters used in the computation are ^{−3}, and

For TM waves, since

The frequency dependence of the permittivity tensor and the corresponding equivalent permittivity

Goos-Hänchen lateral displacements of TM waves transmitted and reflected from the interface of vacuum and gyroelectric medium. The frequencies are normalized to

For the plasma, when there is no applied magnetic field, since both

For TM waves, the existence of the applied magnetic field splits each region up into two, marked with subscript 1 and 2, shown in Figures _{1} and A_{2}, total reflection occurs at the interface. In regions B_{1} and B_{2}, although there is no total reflection at the interface, GH lateral displacements for both reflection and transmission are not zero, which is different from the isotropic media case.

It is also of interest to note that in regions B_{1} and B_{2} of Figure

It is important to note that the displacements with applied magnetic field are asymmetric with respect to the incident angle _{2},

We show the reflection and transmission of a Gaussian TM beam incident from the vacuum to gyroelectric medium in Figure

The reflection and transmission of a Gaussian TM beam incident from the vacuum to gyroelectric medium. The frequencies are both

This paper investigates the Goos-Hänchen lateral displacements of a TM beam propagating at the interface between an isotropic medium and a gyroelectric medium in Voigt configuration. As different from the isotropic case, there are always GH effects, not only when total reflection occurs at the boundary but also when there is no total reflection. Furthermore, due to the nonreciprocal property of the gyroelectric medium, the sign of the incident angle also influences the displacements. The results here may have potential applications in magnetic modulations and Terahertz researches.

This work is sponsored by National Natural Science Foundation of China (51107003) and Beijing Jiaotong University (2009JBM092, 2011RC049, and 2011JBM110).