Eigenmodes analysis in two-dimensional random media

Ch. M. Briskina; M. V. Ryzhkov

doi:10.1117/12.615871

15 September 2005 Eigenmodes analysis in two-dimensional random media

Ch. M. Briskina, M. V. Ryzhkov

Proceedings Volume 5924, Complex Mediums VI: Light and Complexity; 59240Y (2005) https://doi.org/10.1117/12.615871
Event: Optics and Photonics 2005, 2005, San Diego, California, United States

Abstract

Simplified method of eigenmodes simulation in random media based on numerical solution of the stationary wave equation for two-dimensional (2D) medium with a random distribution of dielectric permittivity is suggested. By means of discretization the wave equation can be reduced to the system of homogeneous linear equations that includes parameter α=(2πb/λ)², where b is the spacing between the nodes of discretization, λ - the wavelength. The values of α (and corresponding b/λ) were determined as eigenvalues of this system of linear equations. The relative field amplitudes in all discretization nodes i.e. eigenvectors were calculated with this α. 2D random medium was simulated by matrix whose elements randomly take on two different values. One of them corresponds to dielectric permittivity of the material particles, the other - to permittivity of the spaces between them. Under the assumption made, elements of such matrix represent material particles and spaces between them, quantity b - particles size. All calculations were made using MATLAB. Different variants of disordered (and ordered) media were examined. It was shown that localized modes exist only in disordered systems and in a limited range of ratio b/λ . The dependence of modes character on the value of filling ratio and dielectric permittivity is estimated. Some results for one- and three-dimensional media are represented.

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Ch. M. Briskina and M. V. Ryzhkov "Eigenmodes analysis in two-dimensional random media", Proc. SPIE 5924, Complex Mediums VI: Light and Complexity, 59240Y (15 September 2005); https://doi.org/10.1117/12.615871

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KEYWORDS

Particles

Dielectrics

Chemical elements

Numerical analysis

Computer simulations

3D modeling

Finite-difference time-domain method

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