title: Arbitrary-order interface conditions for slab structures and their applications in waveguide analysis.
abstract: We extend the continuity relations of field derivatives across an abrupt interface to arbitrary orders for transverse electric and magnetic waves in slab structures. Higher-order finite-difference formulation is then obtained by combining the systematically-obtained interface conditions with Taylor series expansion. Generalized Douglas scheme is also adopted to further enhance the convergence of truncation errors by two orders. We apply the derived finite-difference formulation, up to nine-points in this paper, to solve the guided modes in simple a slab waveguide and multiple quantum well waveguides. The results shows the truncation error is much higher, up to tenth order, as expected. Using those higher-order schemes, accurate results are obtained with much fewer sampled points, and hence with tremendously less computation time and memory.
authors.affiliation: Graduate Institute of Photonics and optoelectronics, National Taiwan University, Taipei 106-17, Taiwan.
authors.forename: Yih-Peng
authors.initials: YP
authors.lastname: Chiou
authors.forename: Cheng-Han
authors.initials: CH
authors.lastname: Du