Scattering matrix formalism for polarization dependent fiber optic couplers

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.

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Quantization of an electromagnetic field in two-dimensional photonic structures based on the scattering matrix formalism (S-quantization)

Optics and Spectroscopy ◽

10.1134/s0030400x17100083 ◽

2017 ◽

Vol 123 (4) ◽

pp. 615-623 ◽

Cited By ~ 1

Author(s):

K. A. Ivanov ◽

V. V. Nikolaev ◽

A. R. Gubaydullin ◽

M. A. Kaliteevski

Keyword(s):

Electromagnetic Field ◽

Scattering Matrix ◽

Matrix Formalism ◽

Two Dimensional ◽

Photonic Structures

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Exceptional points in composite structures consisting of two dielectric diffraction gratings with Lorentzian line shape

Journal of Physics Conference Series ◽

10.1088/1742-6596/2015/1/012049 ◽

2021 ◽

Vol 2015 (1) ◽

pp. 012049

Author(s):

Nikita Golovastikov ◽

Dmitry Bykov ◽

Leonid Doskolovich

Keyword(s):

Composite Structure ◽

Composite Structures ◽

Diffraction Gratings ◽

Scattering Matrix ◽

Matrix Formalism ◽

Exceptional Points ◽

Lorentzian Line ◽

Analytical Approximations ◽

Lorentzian Profile ◽

Analytical Expressions

Abstract Using scattering matrix formalism we derive analytical expressions for the eigenmodes of a composite structure consisting of two dielectric diffraction gratings with Lorentzian profile in reflection. Analyzing these expressions we prove formation of two distinct pairs of exceptional points, provide analytical approximations for their coordinates and by rigorous simulation demonstrate eigenmodes interchange as a result of encircling said exceptional points.

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