A Circular-Harmonic Computer Analysis Of Rectangular Dielectric Waveguide

It is anticipated that dielectric waveguides will be used as the fundamental building blocks of integrated optical circuits. These waveguides can serve not only as a transmission medium to confine and direct optical signals, but also as the basis for circuits such as filters and directional couplers.1 Thus, it is important to have a thorough knowledge of the properties of their modes. Circular dielectric waveguides have received considerable attention because circular geometry is commonly used in fiber optics.2-5 In many integrated optics applications it is expected that waveguides will consist of a rectangular, or near rectangular, dielectric core embedded in a dielectric medium of slightly lower refractive index. The modes 2133 2146 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 11MM) for this geometry are more difficult to analyze than those of the metallic rectangular waveguide because of the nature of the boundary. Marcatili, using approximations based on the assumption that most of the power flow is confined to the waveguide core, has derived in closed form the properties of a rectangular dielectric waveguide.6 In his solution, fields with sinusoidal variation in the core are matched to exponentially decaying fields in the external medium. In each region only a single mode is used. The results of this method are obtained in a relatively simple form for numerical evaluation. The properties of the principal mode of the rectangular dielectric waveguide have been studied by Schlosser and Unger using a highspeed digital computer.7 In their approach the transverse plane was divided into regions, as shown in Fig.