Wavelet-collocation finite-difference analysis of 3D optical ring resonator

Planar optical waveguides typically have very large physical dimensions compared to the wavelength of the transmitted signals, thus resulting in an excessive memory requirement to analyze with conventional space discrete methods. We have applied a wavelet based high-order finite-difference method, and investigated the possible reduction in the required computational resources as well as the accuracy of the method. The proposed scheme based on the 2nd, 4th and 10th-order Deslauriers-Dubuc functions have the accuracy approximately comparable to the 4th, 6th and 10th high-order finite-difference schemes, respectively.