Use of Dirac matrices in polarization optics

Several matrix methods have been developed for studying polarization properties of light. Jones was the first to apply the matrix method to the study of polarization optics. In Jones matrix formalism the polarized wave field is represented by 2-element column matrix known as Jones Vector and the polarization device encountered by light is represented by a 2×2 matrix, known as the characteristic Jones matrix of the device. Mueller introduced a new matrix method where the wave field is represented by a 4-dimensional vector. The elements of the vector are the Stokes parameters of the beam. In Mueller matrix formalism the optical device is represented by a 4×4 real matrix known as ‘Mueller Matrix’ of the device. The use of coherency matrix also proves to the useful in the study of partially polarized light. Pauli spin matrices have been used to unify the different matrix treatments of polarization optical phenomena. The present article is an attempt to unify the analysis of polarization phenomena using Dirac matrices used by Dirac in quantum mechanics. We have however redefined the set of Dirac matrices in terms of the Kronecher product of Pauli spin matrices.     

Fresnel boundary and interface conditions for polarized radiative transfer in a multilayer medium

In many applications of the theory of radiative transfer, it is important to consider the changes in the index of refraction that occur when the physical domain being studied consists of material regions with distinct optical properties. When polarization effects are taken into account, the radiation field is described by a vector of four components known as the Stokes vector. At an interface between two different material regions, the reflected and transmitted Stokes vectors are related to the incident Stokes vector by means of reflection and transmission matrices, which are derived from the Fresnel formulas for the amplitude coefficients of reflection and transmission. Having seen that many works on polarized radiative transfer that allow for changes in the index of refraction exhibit discrepancies in their expressions for the transmission matrix, we present in this work a careful derivation of the relations between the reflected and transmitted Stokes vectors and the Stokes vector incident on an interface. We obtain a general form of a transmission factor that is required to ensure conservation of energy and we show that most of the discrepancies encountered in existing works are associated with the use of improper forms of this factor. In addition, we derive explicit and compact expressions for the Fresnel boundary and interface conditions appropriate to the study of polarized radiative transfer in a multilayer medium.     

Vector parameterization of the Lorentz group transformations and polar decomposition of Mueller matrices

It is shown that the representation of the coherence matrix (the polarization density matrix) of beams of electromagnetic waves as a biquaternion corresponding to the four-vector of a pseudo-Euclidean space whose components are the intensity and the Stokes parameters provides a possibility of introducing the group transformations of these quantities isomorphic to SO(3.1) group. These transformations are a subset of the set of Mueller polarization matrices which, generally speaking, form a semigroup. The reduction of the semigroup of Mueller matrices to the group of transformations opens the possibility to use the vector parameterization of SO(3.1) group for interpretation of the polar decomposition of Mueller matrices. In particular, in this approach, the elements of the Mueller matrices corresponding to phase elements and polarizers turn out to be most simply and naturally related to their eigenpolarizations.     

Diode-like asymmetric transmission of circularly polarized waves

Optical diode plays an important role in optical computing and information processing. In this paper, a kind of three-layered chiral metamaterial is proposed to achieve diode-like asymmetric transmission for forward and backward propagations of circularly polarized electromagnetic waves only. The metamaterial is composed of a ring–chain structure sandwiched between two identical S-shaped metallic layers with their corresponding substrates. A transparent transmission at normal incidence in one direction and a small intensity of transmission in the opposite direction are numerically demonstrated in this chiral structure. Besides, the results reveal that the bandwidth of the cross-polarization transmission of this designed structure can be tuned by varying the incident angle of circularly polarized waves.     

Reflected and transmitted powers from a planar isotropic chiral–uniaxial anisotropic chiral interface

In this paper, analysis and theoretical investigations are carried out to find the reflected and transmitted powers for a planar isotropic chiral–uniaxially anisotropic chiral interface with optical axis parallel to interface. The expressions of the reflected and transmitted powers for right-circularly polarized (RCP) and left-circularly polarized (LCP) incident waves are derived. Results of the reflected and transmitted powers for the RCP and LCP incident waves from materials with different isotropic chirality and uniaxial chirality values are presented. The effect of the uniaxial chirality on three other cases of dielectric constant combinations is also studied. The numerical results derived from the presented analytical expressions are found to be in good agreement with those obtained by computational techniques elsewhere.     

单轴各向异性手征介质平板的反射和透射特性研究

研究了光轴平行于界面的单轴各向异性手征介质平板对平面电磁波的反射和透射特性, 推导出了反射和透射系数(功率)公式; 按介电常数的正负分4种情形给出了反射和透射功率曲线; 讨论了手征参数对反射和透射特性的影响, 特别是给出了伪布儒斯特角与手征参数的变化关系曲线. 关键词： 单轴各向异性手征介质 手征参数 伪布儒斯特角 反射和透射     

Magneto-optical effects in crystals at the normal incidence

We consider the interaction of a polarized electromagnetic wave in a magnetically ordered crystal plate surrounded by an isotropic ambient at the normal incidence. The crystalline medium of the plate is specified by the general non-symmetric permittivity tensor. The results are expressed in terms of the transmission and reflection matrices which relate the electric fields of the incident wave to those of transmitted and reflected waves. Their applications are illustrated by examples of an isotropic plate magnetized normal to the interface, a cubic crystal magnetized parallel to the interface and an orthorhombic crystal magnetized along the axis normal to the interface. The effect of the reflection from the interfaces and the interference effect are included. The paper treats the reflection at an interface between an isotropic ambient and an absorbing magnetic crystal at small non-zero angles of incidence. The general reflection matrix is applied to the determination of the magneto-optical effects quadratic in magnetization.     

Differentiating characteristic microstructural features of cancerous tissues using Mueller matrix microscope

Polarized light imaging can provide rich microstructural information of samples, and has been applied to the detections of various abnormal tissues. In this paper, we report a polarized light microscope based on Mueller matrix imaging by adding the polarization state generator and analyzer (PSG and PSA) to a commercial transmission optical microscope. The maximum errors for the absolute values of Mueller matrix elements are reduced to 0.01 after calibration. This Mueller matrix microscope has been used to examine human cervical and liver cancerous tissues with fibrosis. Images of the transformed Mueller matrix parameters provide quantitative assessment on the characteristic features of the pathological tissues. Contrast mechanism of the experimental results are backed up by Monte Carlo simulations based on the sphere–cylinder birefringence model, which reveal the relationship between the pathological features in the cancerous tissues at the cellular level and the polarization parameters. Both the experimental and simulated data indicate that the microscopic transformed Mueller matrix parameters can distinguish the breaking down of birefringent normal tissues for cervical cancer, or the formation of birefringent surrounding structures accompanying the inflammatory reaction for liver cancer. With its simple structure, fast measurement and high precision, polarized light microscope based on Mueller matrix shows a good diagnosis application prospect.     

One-sided omnidirectional constant transmission between two isotropic media

In this paper, the reflection and transmission at the planar interface between an isotropic achiral medium (IAM) and an isotropic chiral medium (ICM) are theoretically studied. For one of the circularly polarized (CP) waves fullfilling the wavenumber matching condition incident from IAM with incident angle from 0 to π/2, the amplitude reflection and transmission coefficients are constant. The phenomenon is called the omnidirectional constant transmission (OCT). In the situation of CP waves incident from ICM, OCT will not occur, but the absolute values of the amplitude reflection and transmission coefficients can be constants in a range of incident angle under certain conditions. It is suggested that for OCT to occur, both the wavenumber matching condition and the mode matching condition should be satisfied.     

Transformation matrices for the Mueller-Jones formalism

The Mueller-Jones (MJ) or pure Mueller matrix formulation has been reported by using two different matrix transformations in a condensed representation. The possibility to find other transformation matrices is explored. A complete set of unitary operators (R) is found to be closely related with the MJ matrices and with the evolution of pure states on the Poincaré sphere surface. We propose an alternative deduction for the condensed representation of the MJ matrices, obtained by using the Kronecker product operation and use of R unitary matrices as a tool to combine different Mueller matrices and changes of polarized states on the Poincarè sphere surface. Finally, it is shown explicitly that the columns of the transformation matrices are the eigenvectors of the MJ matrix associated to a non-depolarizing optical system and a corollary is established as a criterion to differentiate a Mueller matrix from an MJ matrix.     

Mueller Matrix Analysis of PDL Components

A detailed Mueller-Stokes analysis of an arbitrary elliptical dichroic polarizer is presented. Explicit expressions for the Jones matrix, the Stokes parameters, and the Mueller matrix for a distributed and localized dichroic polarizer acting as a polarization-dependent loss (PDL) element are derived. Application to wavelength-dependent PDL elements is discussed. The Poincare sphere representation and the application of the Mueller matrices for the study of randomly oriented concatenated PDL elements and PDL vector measurement are addressed.     

Depolarizing differential Mueller matrices

The evolution of a polarized beam can be described by the differential formulation of Mueller calculus. The nondepolarizing differential Mueller matrices are well known. However, they only account for 7 out of the 16 independent parameters that are necessary to model a general anisotropic depolarizing medium. In this work we present the nine differential Mueller matrices for general depolarizing media, highlighting the physical implications of each of them. Group theory is applied to establish the relationship between the differential matrix and the set of transformation generators in the Minkowski space, of which Lorentz generators constitute a particular subgroup.     

Mirrors in optical schemes of ellipsometers

Expressions for Mueller matrices describing how the reflection from plane mirrors with an arbitrary orientation of the surface affects the polarization are obtained. The expressions can be useful in considering new ellipsometers’ optical schemes containing plane mirrors, as well as mirrors with a nonzero curvature of the surface.     

A phase sensitive optical rotation measurement in a scattered chiral medium using a Zeeman laser

A novel circular polarized optical heterodyne interferometer using a Zeeman laser to measure optical rotation both in nonscattered and scattered chiral medium is proposed. A pair of correlated orthogonal circular polarized light waves of different temporal frequency propagating in the chiral medium at different speed is studied. This results in phase retardation between circular polarized light waves of which the phase difference is proportional to the optical rotation angle of a linear polarized light in a chiral medium. In the mean time, two orthogonal circular polarized light waves can be treated as a circular polarized photon pair that is able to reduce the scattering effect in a scattered chiral medium. Then the optical rotation angle can be measured in the scattering medium. In addition, a common-path configuration with respect to circular polarized light waves immune the background noise. This further improves the sensitivity on optical rotation measurement based on phase difference detection.     

Imaging and multiple scattering through media containing optically active particles

This paper examines the behaviour of polarized light scattered by a medium containing small chiral spheroidal particles. We show that for single scattering the observed phenomena of optical activity may be interpreted in terms of an averaged Mueller matrix and describe how the degree of polarization is affected by such a medium. The polarization properties of multiply scattered light by chiral particles are considered through the use of Monte Carlo simulations. It is shown that the effects of chirality under multiple scattering can be interpreted as an order-preserving influence in a disordered system and that this influence can, in principle, be exploited for the purposes of imaging.     

Optical diagnosis of dengue virus infected human blood using Mueller matrix polarimetry

Currently dengue fever diagnosis methods include capture ELISAs, immunofluorescence tests, and hemagglutination assays. In this study optical diagnosis of dengue virus infection in the whole blood is presented utilizing Mueller matrix polarimetry. Mueller matrices of about 50 dengue viral infected and 25 non-dengue healthy blood samples were recorded utilizing light source from 500 to 700 nm with scanning step of 10 nm. Polar decomposition of the Mueller matrices for all the blood samples was performed that yielded polarization properties including depolarization, diattenuation, degree of polarization, retardance and optical activity, out of which, depolarization index clusters up the diseased and healthy in to different separate groups. The average depolarized light in the case of dengue infection in the whole blood at 500 nm is 18%, whereas for the healthy blood samples it is 13.5%. This suggests that depolarization index of polarized light at the wavelengths of 500, 510, 520, 530 and 540 nm, we find that in case of depolarization index values are higher for dengue viral infection as compared to normal samples. This technique can effectively be used for the characterization of the dengue virus infected at an early stage of disease.     

Imaging and multiple scattering through media containing optically active particles

Abstract

This paper examines the behaviour of polarized light scattered by a medium containing small chiral spheroidal particles. We show that for single scattering the observed phenomena of optical activity may be interpreted in terms of an averaged Mueller matrix and describe how the degree of polarization is affected by such a medium. The polarization properties of multiply scattered light by chiral particles are considered through the use of Monte Carlo simulations. It is shown that the effects of chirality under multiple scattering can be interpreted as an order-preserving influence in a disordered system and that this influence can, in principle, be exploited for the purposes of imaging.     

Polarimetric characterization of ultra-high molecular weight polyethylene (UHMWPE) for bone substitute biomaterials

In this work the UHMWPE is characterized for their optical properties with Mueller matrix polarimeter. The transmittance birefringence, retardance, polarizance, linear and circular polarization and absorbance of polarized light at different wavelengths ranging 400-800 nm are measured. The presented Mueller matrix elements along with depth resolve polarization decrease in intensity with the change in the wavelength. Linear retardance increases compared to circular through highly scattering polyethylene. High refractive index and low mean free path; and close bonding of particles of material rotates the incoming photons and circular polarization which is dominant as compared to the linear one. Therefore the average intensity increases with both the optical depth and the scattered concentration in UHMWPE, which would accordingly decrease the apparent degree of polarization.The extracted results in terms of linear and circular retardances prove that UHMWPE is compatible, strong, and compact. This research work provides an optical characterization technique for bone substitute biomaterial in the health care industry.     

Optical properties for topological insulators with metamaterials

The two fields of topological insulators and metamaterials are independent. In this Letter, we firstly investigate the Fresnel coefficients for the reflected and refracted electromagnetic waves across the interface between topological insulators and left-handed metamaterials. Then, we derive the exact analytic expressions for Kerr and Faraday rotations. By way of multiple reflections method, we demonstrate that perfect lens with left-handed metamaterials slab and topological insulators can be designed. On the other hand, the processes of reflection and refraction are investigated in the case of topological insulator and chiral metamaterial. Then, we give the reflection and transmission coefficients of topological insulator with a chiral medium slab. Lastly, the potential applications of these results are discussed.     

广义传播矩阵法分析分层各向异性材料对电磁波的反射与透射

在实验室坐标系下由Maxwell旋度方程出发构造了横向场的状态矢量和耦合矩阵,讨论了各 向异性介质中的特征波.通过引入横向场的传播矩阵,进而得到分层各向异性介质的反射系数和透射系数的解析表达式.该式可以适用于一般情况,包括分层单轴各向异性材料和回旋介质,以及半空间各向异性介质的反射和透射问题. 关键词： 广义传播矩阵 各向异性介质 反射与透射