Phase-adaptive basis functions for a multilevel finite element solution of the paraxial wave equation

F. Schmidt

doi:10.1117/12.185149

25 August 1994 Phase-adaptive basis functions for a multilevel finite element solution of the paraxial wave equation

F. Schmidt

Proceedings Volume 2212, Linear and Nonlinear Integrated Optics; (1994) https://doi.org/10.1117/12.185149
Event: Integrated Optoelectronics '94, 1994, Lindau, Germany

Abstract

The finite element method is a successful tool to investigate integrated optics devices, both for stationary as well as for wave propagation problems. Despite the fact that different functionals and discretizations are considered in the literature, in practice most of these approaches use piecewise linear basis functions to approximate the true solution. However, in the case of wave propagation these functions may become numerically inefficient. Therefore our proposal is to construct basis functions fitting the local situation better than the linear standard functions. We introduce new basis functions as the product of linear polynomials and local phase functions. These local phases functions are exponential functions characterized by a wave number, which in general changes in space but is assumed to be constant over a single finite element. The closer the a-priori fixed wave number resembles the true local wave number, the more efficient the simulation will be. The multilevel finite element scheme supplies a well-suited frame to determine the local wave number in an adaptive manner.

Citation Download Citation

F. Schmidt "Phase-adaptive basis functions for a multilevel finite element solution of the paraxial wave equation", Proc. SPIE 2212, Linear and Nonlinear Integrated Optics, (25 August 1994); https://doi.org/10.1117/12.185149

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