Equivalent network analysis of dielectric channel waveguides

Abstract

The rectangular dielectric waveguides, their arrays, optical strip waveguides, and Bragg channel waveguides are analyzed. Analysis of these waveguides is important in integrated optics using semiconductor substrate in particular. For the analysis of the rectangular dielectric waveguides, their arrays, and optical strip waveguides, an alternative representation for the equivalent network approach is suggested. A simple fourier integral formulation is used with the normal-mode transmission-direction chosen perpendicular to the substrate surface. Along the transmission direction, the whole structure is divided into three separable-coordinate regions. The form of the normal modes are simple in each separable-coordinate region. symmetric slab waveguide modes for the central region and plane waves for the other regions. The electromagnetic fields are expanded in terms of the normal modes in each region. Imposing the condition upon the modal coefficients that the tangential fields are continuous at the boundaries with other regions and increaing the number of the normal modes used in the analysis, we may find the guided modes in those structures as accurate as possible. Extension to array structures is straightforward in our formulation, since the number of the separable-coordinate regions is fixed to three. Accurate results are obtained for the rectangular dielectric waveguides and significant corrections are made to the previous estimations of coupling length is a directional couple with rectangular core. By successive approximation the effective index method for the rectangular dielectric waveguides is derived from the fourier integral method. During the calculations for the strip waveguides, only TM modes are used within the central slab waveguide region that includes a loading strip. When the width of the uniform slab decreases, the Fourier integral analysis becomes more simple while the previous methods become more complicated. To prevent the leakages of the fie...