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In this research we propose an accelerated plane wave expansion method (PWEM) for calculation of slab photonic crystal (slab PC) modes. In this method instead of creating artificial periodicity in the direction of slab normal and solving the problem as a full 3D one, which is done in standard PWEM, we consider constant coefficients in 2D PWEM as functions of slab normal component. Then we eliminate electric and magnetic fields in Maxwell’s equations in favour of electric and magnetic vector potentials to obtain equations that contain Laplace operator. Using the Green’s functioned for Laplace operator we then changes the problem from differential to integral form. Replacing the integral operators with their matrix representations and doing some matrix algebra we finally obtain a matrix which slab PC modes can be extracted from its eigenvalues. Advantages of this method over the common approach are its less computational complexity, faster creation of the eigenvalue problem, and faster convergence of eigenvalues as the matrix dimensions increase.
Efficient Analysis of Photonic Crystal Slabs
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