Several Efficient Numerical Methods In The Optical Waveguide

Some numerical methods such as, Pade rational approximation method,Marching and bidirectional beam propagation method which are used to solveHelmhotlz equation are compared in this paper. And a new bidirectional beampropagation method is applied in the waveguide grating.Bidirectional beam propagation method is developed by one-way method. Paderational approximation method is used to compute initial value operator in the processof marching. Propagating mode can be accurately computed by normal Pade rationalapproximation method, but not for evanescent mode and reflectivity. To get a moreaccurate result and eliminate error, a rotating branch-cut Pade rational approximationmethod is introduced. In the process of marching, Chebyshev collocation method isused to compute Dirichlet-to-Nuemann operator. The numerical result is very accurateand the number of operations of this method is smaller than other methods so that thismethod is more efficient. At last, a appropriate PML condition is constructed to get amore accurate numerical result.