Three-Dimensional Finite-Element Mode-Solver for Nonlinear Periodic Optical Waveguides and Its Application to Photonic Crystal Waveguides

Abstract

A 3-D finite-element mode-solver, based on a self-consistent algorithm, is newly developed for nonlinear periodic optical waveguides. The developed method makes it possible to calculate various nonlinear characteristics based on optical Kerr effect rigorously, including the nonlinear phase shift, the nonlinear refractive index distribution, and γ-value. Its validity is confirmed by analyzing a silicon-nanowire waveguide and a slot waveguide. To show the usefulness of the method, the nonlinear characteristics of photonic crystal line-defect waveguides and 1-D photonic crystal coupled resonator optical waveguides are investigated. Numerical results show that in some cases, γ-value calculated by the newly developed method and approximate linear analysis differs two-orders of magnitude. For instance, γ-value calculated by developed method is 510 000 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> W <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> for a 1-D photonic crystal coupled resonator optical waveguide, whereas γ-value calculated by conventional method is only 5000 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> W <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> . This difference indicates that, to estimate the nonlinear characteristics of 3-D waveguides precisely, the developed nonlinear guided mode solver is required.