High-Order Finite-Difference Methods for Modeling and Simulation of High-Index-Contrast Photonic Integrated Devices

Abstract

<p> High index contrast optical waveguides have recently attracted much attention as a promising platform for ultradense photonic integrated circuits. The vector nature and fine geometry of such waveguiding structures impose new challenges for numerical modeling. By introducing the high-order finite-difference method, highly accurate and efficient modeling techniques have been developed in this thesis for simulation and design of high index contrast waveguiding structures with compact size.</p> <p> High-order mode solving techniques are first presented for modal analyses. Their advantages in accuracy have been demonstrated for high index contrast optical waveguides and bent waveguides with small bending radius.</p> <p> Later, a class of high-order propagation algorithms, including the paraxial and wide-angle beam propagation methods, reflective operator method and bidirectional beam propagation method, have been developed for modeling longitudinally slow-varying structures, single waveguide discontinuity and piecewise z-invariant structures, respectively. All the proposed propagation algorithms have been shown to provide significant improvement in accuracy and efficiency in comparison with conventional methods, especially when simulating high index contrast structures with small feature size.</p> <p> Accurate modeling of evanescent waves is critical for the simulation of strongly reflecting structures with high longitudinal index contrast. Various rational approximations to square root operators used in the bidirectional beam propagation method have been comprehensively assessed. Useful guidelines for accurate modeling of evanescent and propagating modes are provided.</p> <p> Finally, the efficient high-order bidirectional beam propagation method is introduced for the design of Bragg gratings on high index contrast and plasmonic waveguides. Good performance is achieved.</p>