scholarly journals Квантование электромагнитного поля в трехмерных фотонных структурах на основе формализма матрицы рассеяния (S-квантование)

2018 ◽  
Vol 52 (9) ◽  
pp. 1023
Author(s):  
К.А. Иванов ◽  
А.Р. Губайдуллин ◽  
М.А. Калитеевский
Keyword(s):  
Dielectric Constant ◽  
Three Dimensional ◽  
Scattering Matrix ◽  
Real Space ◽  
Matrix Formalism ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
The Fourier Transform ◽  
Computational Resources ◽  
The Waves

AbstractA technique for quantization of the electromagnetic field in photonic nanostructures with three-dimensional modulation of the dielectric constant is developed on the basis of the scattering matrix formalism ( S quantization in the three-dimensional case). Quantization is based on equating the eigenvalues of the scattering matrix to unity, which is equivalent to equating each other the sets of Fourier expansions for the fields of the waves incident on the structure and propagating away from the structure. The spatial distribution of electromagnetic fields of the modes in a photonic nanostructure is calculated on the basis of the R and T matrices describing the reflection and transmission of the Fourier components by the structure. To calculate the reflection and transmission coefficients of individual real-space and Fourier-space components, the structure is divided into parallel layers within which the dielectric constant varies as a function of two-dimensional coordinates. Using the Fourier transform, Maxwell’s equations are written in the form of a matrix connecting the Fourier components of the electric field at the boundaries of neighboring layers. Based on the calculated reflection and transmission vectors for all polarizations and Fourier components, the scattering matrix for the entire structure is formed and quantization is carried out by equating the eigenvalues of the scattering matrix to unity. The developed method makes it possible to obtain the spatial profiles of eigenmodes without solving a system of nonlinear integro-differential equations and significantly reduces the computational resources required for calculating the probability of spontaneous emission in three-dimensional systems.

scholarly journals Estimation of S-parameters and dielectric permittivity of quartz ceramics samples in millimeter waveband

Doklady BGUIR ◽  
2021 ◽  
Vol 19 (7) ◽  
pp. 65-71
Author(s):  
N. A. Pevneva ◽  
D. A. Kondrashov ◽  
A. L. Gurskii ◽  
A. V. Gusinsky
Keyword(s):  
Dielectric Constant ◽  
Dielectric Permittivity ◽  
Ceramic Materials ◽  
Reflection And Transmission Coefficients ◽  
Frequency Range ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Higher Order Modes ◽  
S Parameters ◽  
The Fourier Transform

A modified Nicholson – Ross – Weir method was used to determine complex parameters and dielectric permittivity of ceramic materials in the range 78.33–118.1 GHz. The measuring equipment is a meter of complex reflection and transmission coefficients, a waveguide measuring canal with a special measuring cell, consisting of two irregular waveguides and a waveguide chamber between them, which provides insignificant influence of higher-order modes. The dependences of the amplitude and phase of the reflection and transmission coefficients on frequency were obtained experimentally for fluoroplastic and three ceramic samples in the frequency range 78.33–118.1 GHz. The obtained S-parameters are processed according to an algorithm that includes their averaging based on the Fourier transform in order to obtain the values of the dielectric permittivity. Fluoroplastic was used as a reference material with a known dielectric constant. The dielectric constant of fluoroplastic has a stable value of 2.1 in the above mentioned frequency range. The dielectric constant of sample No. 1 varies from 3.6 to 2.5 at the boundaries of the range, sample No. 2 – from 3.7 to 2.1, sample No. 3 – from 2.9 to 1.5. The experimental data are in satisfactory agreement with the literature data for other frequencies taking into account the limits set by the measurement uncertainty.

scholarly journals Homogenization of very rough three-dimensional interfaces for the poroelasticity theory with Biot's model

2019 ◽  
Author(s):  
Nguyen Thi Kieu ◽  
Pham Chi Vinh ◽  
Do Xuan Tung
Keyword(s):  
Incident Angle ◽  
Three Dimensional ◽  
Homogenization Method ◽  
Reflection And Transmission Coefficients ◽  
Biot Theory ◽  
Rough Interface ◽  
Matrix Formulation ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
The Matrix

In this paper, we carry out the homogenization of a very rough three-dimensional interface separating  two dissimilar generally anisotropic poroelastic solids modeled by the Biot theory. The very rough interface is assumed to be a cylindrical surface that rapidly oscillates between two parallel planes, and the motion is time-harmonic. Using the homogenization method with the matrix formulation of the poroelasicity theory, the explicit  homogenized equations have been derived. Since the obtained  homogenized equations are totally explicit, they are very convenient for solving various practical problems. As an example proving this, the reflection and transmission of SH waves at a very rough interface of tooth-comb type is considered. The closed-form analytical expressions of the reflection and transmission coefficients have been  derived. Based on them, the effect of the incident angle and some material parameters  on the reflection and transmission coefficients are examined numerically.

Reflection and Transmission Coefficients for Two- and Three-Dimensional Quantum Wires

1997 ◽  
Vol 11 (23) ◽  
pp. 2777-2790 ◽  
Author(s):  
M. Razavy
Keyword(s):  
Reflection Coefficient ◽  
Quantum Wires ◽  
Three Dimensional ◽  
Variable Cross Section ◽  
Wave Number ◽  
Variable Cross ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Matrix Differential Equations ◽  
Matrix Differential

The problem of a quantum wire connected smoothly on both sides to leads of variable cross section is studied. A method for solving this problem in terms of a set of nonlinear first order matrix differential equations for the variable reflection amplitude is discussed. The reflection coefficient obtained in this way is directly related to the conductivity, and is calculated as a function of the energy of the ballistic electrons. This formulation can be applied to three-dimensional as well as two dimensional quantum wires. For two specific cases the reflection coefficient is obtained as a function of the wave number of the incident electron, and the contribution of quantum tunneling to the transmission in each case is demonstrated. Also a model with a dissipative force is introduced and its effect on the transmission of the electrons is investigated.

The Transition Matrix Formalism for the Scattering of an Alluvium on an Elastic Half-Space

2007 ◽  
Author(s):  
Wen-I Liao ◽  
Tsung-Jen Teng ◽  
Shiang-Jung Wang
Keyword(s):  
Half Space ◽  
Transition Matrix ◽  
Plane Waves ◽  
Three Dimensional ◽  
Scattering Matrix ◽  
Elastic Half Space ◽  
Basis Functions ◽  
Matrix Formalism ◽  
T Matrix ◽  
Singular Wave

This paper develops the transition matrix formalism for scattering from an three-dimensional alluvium on an elastic half-space. Betti’s third identity is employed to establish orthogonality conditions among basis functions that are Lamb’s singular wave functions. The total displacements and associated tractions exterior and interior to the surface are expanded in a Rayleigh series. The boundary conditions are applied and the T-matrix is derived. A linear transformation is utilized to construct a set of orthogonal basis functions. The transformed T-matrix is related to the scattering matrix and it is shown that the scattering matrix is symmetric and unitary and that the T-matrix is symmetric. Typical numerical results obtained by incident plane waves for verification are presented.

Thin-Film Optical Constants Determined from Infrared Reflectance and Transmittance Measurements

1989 ◽  
Vol 43 (6) ◽  
pp. 1027-1032 ◽  
Author(s):  
Thierry Buffeteau ◽  
Bernard Desbat
Keyword(s):  
Thin Films ◽  
Optical Constants ◽  
Grazing Incidence ◽  
Infrared Region ◽  
Matrix Formalism ◽  
Experimental Conditions ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Multilayered Systems

A general method based upon reflectance and transmittance measurements in the infrared region has been developed for the determination of the optical constants n( v) and k( v) of thin films deposited on any substrate (transparent or not). The corresponding computer program, written in FORTRAN 77, involves three main parts: (1) a matrix formalism to compute reflection and transmission coefficients of multilayered systems; (2) an iterative Newton-Raphson method to estimate the optical constants by comparison of the calculated and experimental values; and (3) a fast Kramers-Krönig transform to improve the accuracy of calculating the refractive index. The first part of this program can be used independently to simulate reflection and transmission spectra of any multilayered system using various experimental conditions. Two practical examples are given for illustration. Simulation of reflection spectra at grazing incidence for thin films deposited on a metal surface and determination of the optical constants for thin CaF2 layers deposited on a silicon substrate are presented.

Cavity-Opening Tensor Method and its Applications to Reflection and Transmission of Ultrasonic Wave by Defects

1996 ◽  
Vol 63 (3) ◽  
pp. 836-842
Author(s):  
Yonglin Xu
Keyword(s):  
Three Dimensional ◽  
Boundary Integral ◽  
Ultrasonic Waves ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Single Defect ◽  
Interaction Factors ◽  
Cavity Opening ◽  
Conventional Numerical Method ◽  
Scattered Fields

The reflection and transmission of ultrasonic waves by an array of planar defects are investigated using the cavity-opening tensor (COT) method, whereby each defect or flaw can be simulated as a three-dimensional tensor in terms of the displacement distribution over the surface of the defect. The closed-form expressions of reflection and transmission coefficients represented by one set of COTs are derived, and the interaction factors of COTs are computed using the boundary integral equation with the approximate integral only on the single defect surface. Moreover, the analytical expressions of scattered fields at a distance from the defects are given by the representation of COT. As compared with the conventional numerical method, the COT method greatly simplifies the calculations, and also makes it possible to more efficiently characterize defects with more complicated distributions.

Homogenization of very rough two-dimensional interfaces separating two dissimilar poroelastic solids with time-harmonic motions

2018 ◽  
Vol 24 (5) ◽  
pp. 1349-1367
Author(s):  
PC Vinh ◽  
DX Tung ◽  
NT Kieu
Keyword(s):  
Three Dimensional ◽  
Homogenization Method ◽  
Reflection And Transmission Coefficients ◽  
Two Dimensional ◽  
Matrix Formulation ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Time Harmonic ◽  
The Matrix ◽  
Homogenization Approach

The homogenization of a very rough three-dimensional interface separating two dissimilar isotropic poroelastic solids with time-harmonic motions was considered by Gilbert and Ou (Acoustic wave propagation in a composite of two different poroelastic materials with a very rough periodic interface: A homogenization approach. Int J Multiscale Comput Eng 2003; 1(4): 431–440). The homogenized equations have been derived; however, they are still in implicit form. In this paper, the homogenization of a very rough two-dimensional interface separating two dissimilar generally anisotropic poroelastic solids with time-harmonic motions is investigated. The main aim of the investigation is to derive homogenized equations in explicit form. By employing the homogenization method, along with the matrix formulation of the poroelasticity theory, the explicit homogenized equations have been derived. Since these equations are totally explicit, they are very useful in solving practical problems. As an example proving this, the reflection and transmission of SH waves at a very rough interface of the tooth-comb type is considered. The closed-form analytical expressions of the reflection and transmission coefficients are obtained. Based on these expressions, the dependence of the reflection and transmission coefficients on some parameters is examined numerically.

Complex Dielectric Constant as a Function of Frequency for a Liquid Hydrocarbon Fuel in the Microwave Region

1994 ◽  
Vol 347 ◽  
Author(s):  
Donald A. Wiegand ◽  
Frank Murray
Keyword(s):  
Dielectric Constant ◽  
Power Loss ◽  
Liquid Fuel ◽  
Hydrocarbon Fuel ◽  
Liquid Hydrocarbon ◽  
Complex Dielectric Constant ◽  
Interference Effects ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
The Difference

ABSTRACTThe incident, reflected and transmitted powers were measured and the reflection and transmission coefficients calculated for a liquid fuel. Two sizes of double ridge waveguide were used to cover the frequency ranges 2.5 to 7.5 and 7.5 to 18 GHz and corrections were made for waveguide losses. Strong interference effects were observed and the real part of the dielectric constant, ε', was obtained primarily from the separation of interference maxima and minima while the loss tangent, ε“/ε', was obtained by curve fitting to the normalized power loss. The final values of ε′ and ε“/ε′ were determined at each frequency by minimizing the difference between the experimental and theoretical values of the reflection coefficient and the normalized power loss. With increasing frequency ε' decreases and then becomes constant while ε“/ε' decreases throughout the frequency range within experimental accuracy.

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