High accuracy modal analysis and beam propagation method for nano-waveguides

A mapped barycentric Chebyshev differentiation matrix (MBCDM) method is proposed for the high-accuracy modal analysis of waveguides and a new beam propagation method (BPM) based on this differentiation matrix is developed. Compared with the commonly used finite difference or finite element based modal analysis and BPM methods, MBCDM is much more accurate and efficient for the computation of guided, evanescent and leaky modes of 2D planar waveguides, 3D rectangular waveguides and circular fibers, and MBCDM-BPM is capable of simulating the propagation of all these modes. The high accuracy of MBCDM and MBCDM-BPM is particularly essential for the nanoscale waveguides with strong discontinuities, where evanescent waves play a central role and high-resolution solutions are necessary.