Reflection Matrix Elements Research Articles

Polarized radiative transfer in dense dispersed media containing optically soft sticky particles.

This paper focuses on polarized radiative transfer in dispersed layers composed of densely packed optically soft particles while considering the effects of dependent scattering and particle agglomeration. The radiative properties of the particles for different agglomeration degrees are calculated using the Lorenz-Mie theory combined with the Percus-Yevick sticky hard sphere model, and the vector radiative transfer equation is solved by using the spectral method. The normalized Stokes reflection matrix elements of the layers for different particle sizes, particle volume fractions and layer thicknesses are discussed. The results show that the effects of multiple scattering, dependent scattering and particle agglomeration have different degrees of influence on the polarized reflection characteristics of the layers. Due to the inhibition effect of far-field interference interaction on particle scattering, the dependent scattering weakens the depolarization caused by multiple scattering. However, as the particles form agglomerations, the scattering coefficients of the particles obviously increase with the agglomeration degree, which will lead to the significant enhancement of the multiple scattering and depolarization.

What is the longitudinal magneto-optical Kerr effect?

We explore the commonly used classification scheme for the magneto-optical Kerr effect (MOKE), which essentially utilizes a dual definition based simultaneously on the Cartesian coordinate components of the magnetization vector with respect to the plane of incidence reference frame and specific elements of the reflection matrix, which describes light reflection from a ferromagnetic surface. We find that an unambiguous correspondence in between reflection matrix elements and magnetization components is valid only in special cases, while in more general cases, it leads to inconsistencies due to an intermixing of the presumed separate effects of longitudinal, transverse and polar MOKE. As an example, we investigate in this work both theoretically and experimentally a material that possesses anisotropic magneto-optical properties in accordance with its crystal symmetry. The derived equations, which specifically predict a so-far unknown polarization effect for the transverse magnetization component, are confirmed by detailed experiments on epitaxial hcp Co films. The results indicate that magneto-optical anisotropy causes significant deviations from the commonly employed MOKE data interpretation. Our work addresses the associated anomalies, provides a suitable analysis route for reliable MOKE magnetometry procedures, and proposes a revised MOKE terminology scheme.

Coherent backscattering effects for discrete random media: Numerical and theoretical results

Manifestation of the backscattering enhancement phenomenon in the reflection matrix elements of the coherent component of scattered radiation is considered. The dependence of the coherent backscattering effects on the microphysical properties of the medium scatterers are investigated. It is shown that random media of fractal-like clusters exhibit brightness and polarization opposition effects, which are like those observed for some atmosphereless Solar system bodies. Conditions for a bimodal angle dependence in the degree of linear polarization are discussed and the manifestation of the enhanced backscattering phenomenon in the intensity of scattered radiation is studied.

A new approach to computing theoretical polarization curves along the low latitude regions of a planetary disk observed at small phase angles

Linear polarization distributions computed along and around the intensity equator of a planetary disk observed at small phase angles tend to show a very pronounced artificial oscillatory behavior or wiggles. The purpose of this work is twofold: to direct attention to this rather tenacious, but not duly publicized computational problem on one hand, and to exploit some effective procedure to minimize those wiggles on the other. For these purposes, we have made extensive numerical computations of the linear polarization curves with various procedures at wavelength 365 nm employing the Venus cloud model of Hansen and Hovenier as a sample, some of which are presented in this work. Our results indicate that the use of the [0,1] part of the Gauss–Legendre quadrature points for μ, the cosine of the zenith angle of incident or emergent light, and their corresponding weights generated in the interval [−1,1] works extremely well for interpolating reflection matrix elements. Furthermore, it is shown that sufficiently well-behaved polarization distribution curves can be obtained by computing the single scattering contributions to the reflection matrix elements exactly and those due to multiple scattering approximately using a natural bicubic spline interpolation formula where the independent variable is to be switched from μ to 1−μ 2 if μ⩾0.7071 and vice versa.

Polarized neutron reflectometry with phase analysis

A novel technique, polarized neutron reflectometry with phase analysis (PNRPA), is suggested, in which not only the moduli of reflection matrix elements but also up to three phase differences are measured. It is realized in the scheme with two flippers and an analyzer, by reflection of neutrons with the spin, in succession, parallel and antiparallel to two inclined axes fixed to the sample. More detailed information about magnetic layered structures can be thus obtained. An adequate mathematical formalism is given.

Simple expressions for transmission and reflection matrix elements of a biaxial thin layer at normal incidence

The extended Jones matrix method is applied for determination of the transmission and reflection matrices for a normally incident plane wave upon an homogeneous and lossless biaxial thin layer. The elements of these matrices are expressed by simple analytical relations. By using these relations one can express analytically the polarization-dependent optical parameters to be determined by generalized ellipsometry.

Diffraction in the semiclassical description of mesoscopic devices

In pseudo-integrable systems, diffractive scattering caused by wedges and impurities can be described within the framework of the Geometric Theory of Diffraction (GDT) in a way similar to the one used in the Periodic Orbit Theory of Diffraction (POTD). We derive formulas expressing the reflection and transition matrix elements for one and many diffractive points and apply it for impurity and wedge diffraction. Diffraction can cause backscattering in situations where usual semiclassical backscattering is absent causing an erodation of ideal conductance steps. The length of diffractive periodic orbits and diffractive loops can be detected in the power spectrum of the reflection matrix elements. The tail of the power spectrum shows ~1 l 1 2 decay due to impurity scattering and ~1 l 3 2 decay due to wedge scattering. We think this is a universal sign of the presence of diffractive scattering in pseudo-integrable waveguides.

Coupling processes in the D- and E-regions at low and medium frequencies—III. The ‘coupling echo’ and the transition through ‘critical coupling’

Night-time electron density distributions are used to study ‘coupling echo’ reflections from the X = 1 level at various frequencies. Overall reflection-matrix elements R 11, R 12 (= R 21) and R 22 are calculated as functions of the variable upper height of ionospheric slabs based on the bottom of the ionosphere. At each frequency calculations are performed for various values of θ, the angle between the geomagnetic field and the vertical. Two types of coupling echoes are found. The first type, or ‘true’ coupling echoes, depend directly on the interface matrix elements, r 12 and r 21, of the elementary thin layers into which the ionosphere has been divided, near the X = 1 level. They appear in the angular range 0 < θ ≲ 2 θ c , where θ c is the angle of critical coupling, and approach a maximum near the upper limit θ ≈ 2 θ c . They are generally characterised by the three reflection-matrix elements, R 11, R 12 and R 22, being roughly equal in absolute value at the X = 1 level. For much higher angular values, θ ≳ 4 θ c , the coupling echo coefficient R 12 (= R 21) at the X = 1 level is given as the geometric mean of the direct extraordinary and ordinary reflection coefficients, R 11 and R 22, respectively, R 22 having increased markedly and R 11 showing a corresponding marked decrease. This type of coupling echo is due to a Z-coupling ‘CTR process’. The response to a vertically incident wave linearly polarised in the magnetic meridian and reflected from the X = 1 level is determined numerically, and results agreeing with the observations of Kelso et al. (1951) are obtained, although the propagation mechanism is more complicated than is generally assumed.