scholarly journals Обобщенная нуль-эллипсометрия в схеме "поляризатор-образец-анализатор"

2022 ◽  
Vol 130 (3) ◽  
pp. 377
Author(s):  
Н.В. СопинскиЙ ◽  
Г.П. Ольховик
Keyword(s):  
Incident Light ◽  
Photometric Method ◽  
Jones Matrix ◽  
Matrix Elements ◽  
Anisotropic System ◽  
Reflected Light ◽  
Sample Orientation ◽  
Anisotropic Systems ◽  
The One ◽  
Analytical Expressions

The null-method in generalized ellipsometry with the use of the compensator-free “polarizer ‒ sample ‒ analyzer” scheme is considered for the case of s- and p-polarized incident light on an anisotropic system. Analytical expressions are given that connect the measured angular value — the analyzer azimuth at the detected radiation intensity minimum — with the (2x2) anisotropic Jones matrix elements. To determine the optical and geometric parameters of the studied anisotropic systems, it is proposed to use this value’s dependence on the sample orientation (azimuth). The method sensitivity is estimated. It was found that it is comparable to the sensitivity of the “polarizer‒compensator‒sample‒analyzer” scheme. A comparative analysis of this method and the known photometric method of generalized ellipsometry in the “polarizer-sample-analyzer” scheme based on measuring the dependence of the reflected light intensity on the sample azimuth at the fixed polarizer and analyzer positions is carried out. It is estimated that, to obtain the same sensitivity of these two methods, the one arc minute error in the proposed method corresponds to the 0.05% relative error in determining the energy reflection coefficient in the photometric method.

Stress Whitening in Polypropylene. I. Light Scattering Theory and Model Experiments

1995 ◽  
Vol 60 (11) ◽  
pp. 1875-1887 ◽  
Author(s):  
Jaroslav Holoubek ◽  
Miroslav Raab
Keyword(s):  
Refractive Index ◽  
Light Scattering ◽  
Incident Light ◽  
Polymeric Materials ◽  
Wavelength Dependence ◽  
Theoretical Background ◽  
Surrounding Matrix ◽  
Embedded Particles ◽  
The One ◽  
Stress Whitening

Theoretical background for an optical method is presented which makes it possible to distinguish unambiguously between voids and particles as light scattering sites in polymeric materials. Typical dependences of turbidity as a function of diameter of scattering elements, their volume fractions and also turbidity curves as a function of the wavelength of the incident light were calculated, based both on the Lorenz-Mie theory and the fluctuation theory. Such dependences calculated for polypropylene-containing voids on the one hand and particles, differing only slightly from the surrounding matrix in their refractive index, on the other hand, are markedly different. The most significant results are: (i) Turbidity is at least by two orders of magnitude larger for voids in comparison to embedded particles of ethylene-propylene (EPDM) rubber of the same size, concentration and at the same wavelength. (ii) The wavelength dependence of turbidity for EPDM particles and the inherent refractive index fluctuations in the polypropylene matrix is much steeper as compared to voids for all considered diameters (0.1-10 μm). Thus, the nature of stress whitening in complex polymeric materials can be determined from turbidity measurements.

scholarly journals Analytical angular solutions for the atom–diatom interaction potential in a basis set of products of two spherical harmonics: two approaches

2021 ◽  
Author(s):  
Mariusz Pawlak ◽  
Marcin Stachowiak
Keyword(s):  
Spherical Harmonics ◽  
Interaction Potential ◽  
Chem Phys ◽  
Basis Set ◽  
Matrix Elements ◽  
Trigonometric Functions ◽  
Variational Theory ◽  
Molecular Collision ◽  
The Matrix ◽  
Analytical Expressions

AbstractWe present general analytical expressions for the matrix elements of the atom–diatom interaction potential, expanded in terms of Legendre polynomials, in a basis set of products of two spherical harmonics, especially significant to the recently developed adiabatic variational theory for cold molecular collision experiments [J. Chem. Phys. 143, 074114 (2015); J. Phys. Chem. A 121, 2194 (2017)]. We used two approaches in our studies. The first involves the evaluation of the integral containing trigonometric functions with arbitrary powers. The second approach is based on the theorem of addition of spherical harmonics.

scholarly journals Electrical tuning of the polarization state of light using graphene-integrated anisotropic metasurfaces

2017 ◽  
Vol 375 (2090) ◽  
pp. 20160061 ◽  
Author(s):  
Shourya Dutta-Gupta ◽  
Nima Dabidian ◽  
Iskandar Kholmanov ◽  
Mikhail A. Belkin ◽  
Gennady Shvets
Keyword(s):  
Tilt Angle ◽  
Incident Light ◽  
Polarization State ◽  
Dynamic Control ◽  
Single Layer ◽  
Single Layer Graphene ◽  
Dynamic Polarization ◽  
Reflected Light ◽  
Electro Optic ◽  
The Way

Plasmonic metasurfaces have been employed for moulding the flow of transmitted and reflected light, thereby enabling numerous applications that benefit from their ultra-thin sub-wavelength format. Their appeal is further enhanced by the incorporation of active electro-optic elements, paving the way for dynamic control of light's properties. In this paper, we realize a dynamic polarization state generator using a graphene-integrated anisotropic metasurface (GIAM) that converts the linear polarization of the incident light into an elliptical one. This is accomplished by using an anisotropic metasurface with two principal polarization axes, one of which possesses a Fano-type resonance. A gate-controlled single-layer graphene integrated with the metasurface was employed as an electro-optic element controlling the phase and intensity of light polarized along the resonant axis of the GIAM. When the incident light is polarized at an angle to the resonant axis of the metasurface, the ellipticity of the reflected light can be dynamically controlled by the application of a gate voltage. Thus accomplished dynamic polarization control is experimentally demonstrated and characterized by measuring the Stokes polarization parameters. Large changes of the ellipticity and the tilt angle of the polarization ellipse are observed. Our measurements show that the tilt angle can be changed from positive values through zero to negative values while keeping the ellipticity constant, potentially paving the way to rapid ellipsometry and other characterization techniques requiring fast polarization shifting. This article is part of the themed issue ‘New horizons for nanophotonics’.

scholarly journals APPLICATIONS OF DENSITY MATRICES IN A TRAPPED BOSE GAS

2006 ◽  
Vol 20 (15) ◽  
pp. 2189-2221 ◽  
Author(s):  
K. CH. CHATZISAVVAS ◽  
S. E. MASSEN ◽  
CH. C. MOUSTAKIDIS ◽  
C. P. PANOS
Keyword(s):  
Quantum Information ◽  
Bose Gas ◽  
Einstein Condensation ◽  
Density Distributions ◽  
Occupation Numbers ◽  
The One ◽  
Bose Einstein ◽  
Jensen Shannon Divergence ◽  
Analytical Expressions ◽  
Short Range Correlations

An overview of the Bose–Einstein condensation of correlated atoms in a trap is presented by examining the effect of interparticle correlations to one- and two-body properties of the above systems at zero temperature in the framework of the lowest order cluster expansion. Analytical expressions for the one- and two-body properties of the Bose gas are derived using Jastrow-type correlation function. In addition numerical calculations of the natural orbitals and natural occupation numbers are also carried out. Special effort is devoted for the calculation of various quantum information properties including Shannon entropy, Onicescu informational energy, Kullback–Leibler relative entropy and the recently proposed Jensen–Shannon divergence entropy. The above quantities are calculated for the trapped Bose gases by comparing the correlated and uncorrelated cases as a function of the strength of the short-range correlations. The Gross–Piatevskii equation is solved, giving the density distributions in position and momentum space, which are employed to calculate quantum information properties of the Bose gas.

scholarly journals Semi-Analytic Evaluation of 1, 2 and 3-Electron Coulomb Integrals with Gaussian Expansion of Distance Operators W= RC1-nRD1-M, RC1-Nr12-M, R12-Nr13-M

2019 ◽  
Author(s):  
Sandor Kristyan
Keyword(s):  
Gaussian Function ◽  
Approximate Solutions ◽  
Equation System ◽  
Least Square ◽  
Position Vector ◽  
Least Square Fit ◽  
Analytic Expressions ◽  
The One ◽  
Analytical Expressions ◽  
Coulomb Integrals

The equations derived help to evaluate semi-analytically (mostly for k=1,2 or 3) the important Coulomb integrals Int rho(r1)…rho(rk) W(r1,…,rk) dr1…drk, where the one-electron density, rho(r1), is a linear combination (LC) of Gaussian functions of position vector variable r1. It is capable to describe the electron clouds in molecules, solids or any media/ensemble of materials, weight W is the distance operator indicated in the title. R stands for nucleus-electron and r for electron-electron distances. The n=m=0 case is trivial, the (n,m)=(1,0) and (0,1) cases, for which analytical expressions are well known, are widely used in the practice of computation chemistry (CC) or physics, and analytical expressions are also known for the cases n,m=0,1,2. The rest of the cases – mainly with any real (integer, non-integer, positive or negative) n and m - needs evaluation. We base this on the Gaussian expansion of |r|^-u, of which only the u=1 is the physical Coulomb potential, but the u≠1 cases are useful for (certain series based) correction for (the different) approximate solutions of Schrödinger equation, for example, in its wave-function corrections or correlation calculations. Solving the related linear equation system (LES), the expansion |r|^-u about equal SUM(k=0toL)SUM(i=1toM) Cik r^2k exp(-Aik r^2) is analyzed for |r| = r12 or RC1 with least square fit (LSF) and modified Taylor expansion. These evaluated analytic expressions for Coulomb integrals (up to Gaussian function integrand and the Gaussian expansion of |r|^-u) are useful for the manipulation with higher moments of inter-electronic distances via W, even for approximating Hamiltonian.

scholarly journals Parallel detection of Jones-matrix elements in polarization-sensitive optical coherence tomography

2019 ◽  
Vol 10 (5) ◽  
pp. 2318 ◽  
Author(s):  
Masahiro Yamanari ◽  
Sato Uematsu ◽  
Kenji Ishihara ◽  
Yasushi Ikuno
Keyword(s):  
Optical Coherence Tomography ◽  
Jones Matrix ◽  
Optical Coherence ◽  
Matrix Elements ◽  
Parallel Detection

Electron Correlation Effects on the Lattice Dynamics of Sodium and Potassium

1975 ◽  
Vol 53 (16) ◽  
pp. 1507-1512 ◽  
Author(s):  
V. K. Jindal
Keyword(s):  
Dielectric Function ◽  
Lattice Dynamics ◽  
Phonon Dispersion ◽  
Matrix Elements ◽  
Correlation Effects ◽  
Phonon Dispersion Curves ◽  
Electron Correlation Effects ◽  
Experimental Values ◽  
The One ◽  
Sodium And Potassium

The phonon dispersion curves for sodium and potassium have been calculated using the one OPW (orthogonalized plane wave) bare electron matrix elements and the dielectric function of Vashishta and Singwi. Results are compared with experimental results as well as with similar calculations using the dielectric function of Geldart and Taylor. It is found that the screening function of Vashishta and Singwi gives at least as good an agreement with experimental values as obtained from the screening function of Geldart and Taylor. The interionic potentials for these metals have also been calculated and compared with similar calculations done previously. The reason for the appreciable difference between the potentials is discussed.

A new algorithm for numerical modelling of impurity transport in the frame of statistically homogeneous sharply contrasting media

2019 ◽  
Vol 34 (6) ◽  
pp. 339-351 ◽  
Author(s):  
Petr S. Kondratenko ◽  
Leonid V. Matveev ◽  
Alexander D. Vasiliev
Keyword(s):  
Numerical Modelling ◽  
Contaminant Transport ◽  
Integral Kernel ◽  
Time Intervals ◽  
One Dimensional ◽  
Time Representation ◽  
Impurity Transport ◽  
The One ◽  
Analytical Expressions ◽  
Good Agreement

Abstract A new method is developed to calculate characteristics of contaminant transport (including non-classical regimes) in statistically homogeneous sharply contrasting media. A transport integro-differential equation in the space-time representation is formulated on the basis of the model earlier proposed by one of the authors (L. M.). Analytical expressions for transport characteristics in limiting time intervals in the one-dimensional case are derived. An interpolation form is proposed for the integral kernel of the transport equation. On a basis of this expression, an algorithm is developed for numerical modelling the contaminant transport in statistically homogeneous sharply contrasting media. Trial numerical 1D calculations are performed based on this algorithm. Good agreement was found between the numerical simulation results and the asymptotic analytical expressions.

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