Effective Index Series Analysis of Ridge Waveguides with Arbitrarily Sloped Sidewalls,

Semiconductor ridge waveguide structures are widely used in many integrated optical circuits and devices, including low threshold current, single-mode diode lasers. Although computer-intensive numerical techniques are required to completely analyze these structures, reasonable accuracy can be obtained with simple effective index methods, in cases where the ridge is not etched into the guiding layer. However, effective index methods to date have been restricted to ridges with vertical sidewalls, while many actual structures have sloped sidewalls. In this paper, an effective index series technique for analyzing ridge waveguide structures with arbitrarily sloped sidewalls is presented. A simple ridge waveguide with sloped sidewalls is illustrated. For this ridge structure, the effective index at each position in the lateral direction, y, is calculated assuming a slab waveguide of infinite extent with upper cladding thickness, h. The square of the effective index of a typical four-layer slab guide as a function of the upper cladding thickness, h, is shown. Once the effective index is known as a function of y, another slab waveguide analysis is used in the transverse y-direction. For quasi-TE modes in the ridge structure i.e., predominant electric field in the y-direction, TE boundary conditions are used to calculate the effective index as a function of h, and TM boundary conditions are used in the transverse direction. For quasi-TM modes, the boundary conditions used in the two parts of the solution are reversed. Since TM boundary conditions are more difficult in the presence of graded indices, the quasi-TE mode case is treated here.