Bent waveguide analysis with a modified version of the beam propagation method

To study propagation in bent waveguides numerically the most common technique used is the Beam Propagation Method (BPM), with either the split-step procedure and Fast Fourier Transform algorithm, or a finite difference approach. Most versions are based on a first order modification of the permittivity profile for scalar or full vector wave equations. Others are based on a longitudinally variant index profile and wide angle beam propagation techniques.; New device applications are well beyond the limitations of the present numerical approaches. An example of these applications are polymer and semiconductor ring lasers, (de)multiplexing systems, and polarization converters based on bent waveguides. They will require more accurate and novel numerical approaches to solve more complex problems at smaller radii. Important issues are characteristics such as: the modal spectra, total loss and loss rates, and modal field distributions.; In this dissertation a new numerical approach for bent waveguides using BPM is discussed. The numerical version focuses on the wave equation in cylindrical coordinates for propagating the field in an arbitrarily bent structure. To bring it to a form that is useful for numerical analysis, a transformation to a local coordinate system is done and the propagation is accomplished by using the Finite Difference Beam Propagation Method (FDBPM). The finite differencing is done for the TE and TM scalar equations in 2D, and the full vector wave equations for both the {dollar}rmvec E{dollar} and {dollar}rmvec H{dollar} fields in 3D. The constraints that are imposed on the propagation schemes are discussed, such as stability and computational efficiency.; To verify the accuracy of the numerical codes, comparisons with analytical results are done for the 2D and 3D calculations. Both the field profiles of straight and curved waveguides and the loss rates for single mode waveguides are compared to analytical results in 2D. It is found that the numerical and theoretical results are in excellent agreement. Results for field profiles and propagation constants for straight 3D waveguides is also presented and confirmed with theory. Three dimensional bent waveguide calculations confirm theoretical predictions of radiation loss into the substrate and mode/polarization conversion due to the curvature.; The application of the two dimensional code to study multimode bent waveguides is done in the last chapter. Lowest order mode transmission in multimode waveguides is investigated with sine and cosine shaped S-bends. It was found that the sine-shaped S-bends are favored at low index contrasts because of the continuous transition in curvature. Also that the cosine shaped S-bends can be improved significantly if one offsets the straight waveguide portions at the transition points.