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ISSN Печать: 0040-2508
ISSN Онлайн: 1943-6009
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Determination of the Allowed Frequencies of Electromagnetic Wave Propagation in 2D Photonic Crystal by the Coupled Waves Method (CWM)
Краткое описание
The paper demonstrates that at imposition of periodic boundary conditions and using the coupled waves method (CWM) which is applied previously for the analysis of diffraction of electromagnetic waves in plane 1D, grating it is possible to quickly define if the given frequency of the electromagnetic wave is allowed for propagation in a 2D photonic crystal. The problem is reduced to the problem of higher algebra on the eigen values and the eigen vectors of the kind A+X = ρA−X and to verification if the module of ρ is equal to one. If |ρ| = 1 , the given frequency is allowed. At a calculation the dimension of vector X is equal to the doubled number of the used coupled waves (2N) and is determined by the required accuracy of analysis. High accuracy of determination of the allowed frequencies of branches of band structure is secured at N ≥ 30, which determines the band gap of the photonic crystal. Due to the fact that standard photonic crystals possess symmetrical spatial dependence of the dielectric constant the use of symmetry depending upon its type permits to pass on to the dimension of X vector N±1 or N without the loss in accuracy of the analysis with simultaneous diminishing of calculation time by approximately 8 times.