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9 June 2006 Simplified method of numerical simulation of eigenmodes in random media
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Proceedings Volume 6054, International Conference on Lasers, Applications, and Technologies 2005: Advanced Lasers and Systems; 60540X (2006) https://doi.org/10.1117/12.660941
Event: International Conference on Lasers, Applications, and Technologies 2005, 2005, St. Petersburg, Russian Federation
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 a (and corresponding b/λ) for every mode were determined from condition of zero value of the system determinant. The relative field amplitudes in all discretization nodes were calculated with this a. 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 spacings between them. Under the assumption made, elements of such matrix represent material particles and spacings between them correspondingly, 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 with sufficiently large filling ratio and in a limited range of ratio b/λ .
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Ch. M. Briskina and M. V. Ryzhkov "Simplified method of numerical simulation of eigenmodes in random media", Proc. SPIE 6054, International Conference on Lasers, Applications, and Technologies 2005: Advanced Lasers and Systems, 60540X (9 June 2006); https://doi.org/10.1117/12.660941
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