Elsevier

Physics Letters A

Volume 384, Issue 27, 28 September 2020, 126699
Physics Letters A

Coupling effects between dichroism and birefringence of anisotropic media

https://doi.org/10.1016/j.physleta.2020.126699Get rights and content

Highlights

  • The types of coupling effects are identified. The conditions for calculating diattenuation from the measured Mueller matrix are derived.

  • It is found that for the medium with birefringence and dichroism simultaneously the symmetry property is broken even for deterministic media.

  • The conditions under which a measured Mueller matrix can be expressed as a sum of several component matrices in terms of Lorentz generators are given.

Abstract

The basic polarization properties of media are their dichroism and birefringence. In this work we report the possible consequences of the coupling effects between dichroism and birefringence of anisotropic media. Our analysis is based on a solution of the differential equation of the Stokes four-dimensional vector. It is shown that there exist three types of coupling effects between the components of the dichroism vector and birefringence vector of the medium. The conditions under which the polarization properties of a continuous medium can be calculated are identified. These results are helpful for any study involved an interpretation of the measured Mueller matrix of continuous anisotropic medium.

Introduction

The dichroism of medium will induce polarization selective attenuation and the birefringence will result in a retardation of one of the orthogonal polarization light field component with respect to the other. Both birefringence and dichroism are two elementary types of polarization properties of anisotropic media. It is then usually believed that their influences on the incident polarized light field are independent.

In addition, in the analysis of the polarization properties of an optically anisotropic medium, it is usually assumed that the directions of the birefringence three-vector and the dichroism three-vector in the Stokes space are parallel, which greatly simplifies the forms of both the Jones matrix and the Mueller matrix of the medium [1], [2]. Furthermore, it is believed that in terms of the differential Mueller matrix components, each basic polarization property of the medium can be represented by a matrix of the specific form [3], [4], [5], [6], [7], [8].

In the investigation of the polarization effects in single mode (SM) fibers [9], [10], [11], Brown recognized that, in terms of Stokes vector, the matrix part of the Stokes four-dimensional vector equation of motion is of the Lorentz symmetry [10]. One consequence of this fact is that the Stokes vector at any point within the medium can be expressed in terms of the Lorentz group generators [12]. However, this important finding has not been exploited in the interpretation of the measured Mueller matrices (for example).

Note that one of the main achievements in the interpretation of the measured Mueller matrices of continuous medium with several types of polarization properties simultaneously is that first to calculate the corresponding differential Mueller matrices and then to express the differential Mueller matrices in terms of the Lorentz group generators [13]. It is then desirable to know if it is possible to express the measured macroscopic Mueller matrices directly in terms of the Lorentz group generators.

In this work, to our knowledge, for the first time the possible consequences of coupling effects between the dichroism and birefringence on interpretation of measured Mueller matrices of anisotropic media are clearly discussed. This consideration was stimulated by the results obtained by Brown [11].

Section snippets

Theory

Starting from the coupling of the two orthogonal transverse components of the electric field vector by arbitrary perturbation of the medium, it has been shown that the Mueller matrix of the anisotropic medium at any point z into the medium can be expressed as [11]:Mˆ(d0,d;β;z)=([(RpNp)2cosh(Ipz)+(IpNp)2cos(Rpz)]Iˆ+[(1Np)2(cosh(Ipz)cos(Rpz))]{((βBˆ))2+((dDˆ))2+[(β×d)Λˆ]}+[(1Np)2(Ipsinh(Ipz))+Rpsin(Rpz)]{(βBˆ)(dDˆ)}+[(1Np)2(Ipsin(Rpz))Rpsinh(Ipz)]{(dBˆ)+(βDˆ)})exp(Ipz), where β(z){β1

Conclusions

In this work, based on the solution of the differential equation of the Stokes vector of a light beam propagating through an anisotropic medium, the types of the coupling effects are identified. The conditions under which the diattenuation of the medium can be calculated from the measured Mueller matrix are derived. We found that, for the medium with birefringence and dichroism simultaneously as functions of the thickness of the medium the symmetry property is broken even for deterministic

Declaration of Competing Interest

The authors declare no conflicts of interest.

Acknowledgements

This research was supported by the Fundamental Research Funds for the Central Universities (30920010003), the Natural Science Foundation of China (NSFC) (61275198, 60978069) and the Key Special Projects of “Major Scientific Instruments and Equipment Development” of the National Key Research and Development Plan, Ministry of Science and Technology, P. R. China (2017YFF0107100).

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