Comparison of the continuous, semi-discrete and fully-discrete transparent boundary conditions (TBC) for the parabolic wave equation 1. Theory

For the simulation of the propagation of optical waves in open wave guiding structures of integrated optics the parabolic approximation of the scalar wave equation is commonly used. This approach is commonly termed the beam propagation method (BPM). It is of paramount importance to have well-performing transparent boundary conditions applied on the boundaries of the finite computational window, to enable the superfluous portion of the propagating wave to radiate away from the wave guiding structure. Three different formulations (continuous, semi-discrete and fully-discrete) of the non-local transparent boundary conditions are described and compared here

Iterative full-vectorial "finite differences - variational principle" approach for the determination of the modal spectrum of photonic waveguides

There are several methods to determine numerically modal spectrum of photonic waveguides. The problem itself can be formulated using appropriate discretisation scheme as a well-known algebraic problem of eigenvalues and eigenvectors. The difficulty consists in the large matrix dimensions which requires special approach to the determination of the eigenvalues and eigenvectors of the sparse matrices and complicates effective calculation due to immense demands on the computer memory. Recently proposed iterative method [1] modified for the use in full vectorial formulation can be efficiently employed. The feasibility of the method together with some improvements will be presented

Note on the habits of some Mexican reptiles

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