Numerical techniques for wide angle propagation and beam propagation design of multimode devices

Most photonic device and circuit analyses have traditionally relied on experience and trial-and-error for engineering; a method that is time-consuming, inaccurate, and often unable to produce designs that satisfy engineering requirements and system performance as the complexity of photonic circuits increases. In this thesis, a tool for efficient simulations of arbitrary shaped, wide-angled waveguiding structures using computational numerical schemes has been developed.;The simulation algorithm used employs the beam propagation method (BPM) based on solutions of the unidirectional Helmholtz equation in paraxial approximation. An analytical and numerical study of the accuracy of the beam propagation method that includes approximate treatments of wide-angle propagation based on Pade rational functions is presented. The investigation has identified the error terms associated with a sequence of higher-order operators. The range of application of different approximant operators and algorithmic schemes is studied through examination of 2D waveguide structures. Guidelines are developed for the choice of numerical parameters needed to achieve a specified error constraint with minimum CPU time cost. We have also examined a phenomenon that the Pade-based wide-angle technique applied to step-index waveguides displays an inherent error which ultimately limits its accuracy, independent of the Pade order. An alternate numerical scheme has been developed to alleviate this problem.;In addition, it is shown that a poor choice of reference wavenumber used in the paraxial approximation of the equation prohibits accurate results with Pade approximants of any order. Thus, for simulations of smoothly curved bends with a large angular spread, the error will be significantly reduced when the reference wavenumber is allowed to be varied along the structure such that it is equal to the local angle, instead of using the fixed value.;Using the developed simulation algorithm, a design study of highly multimode-input and integrated-optic devices is presented. We have modeled the operation of a passive, polymeric N x N star coupler. Its performance has been analyzed, and scaling parameters describing settling length and power fluctuations of the device output established. In addition, the design process allowed a comparison to be made of two different simulation methods--ray tracing and beam propagation. We show that the results obtained with either of these methods agree well with actual measurements on a fabricated device.