A theoretical analysis of graded-index optical channel waveguides and directional couplers fabricated by the beam-writing technique is presented. The analysis is based on a combination of the effective-index-of-refraction method and the WKB method, which is shown to apply for directional couplers as well as for channel waveguides, when special care is taken in connecting the field at the gap region. The mode dispersion characteristics and the field profile of a channel waveguide were derived. The conversion length of a directional coupler was also determined as a function of the coupler parameters and the mode order. The guided mode field has long evanescent tails outside the guide, and the positions of the turning points are located further away from the guide center for higher-order modes. Accordingly, the conversion length of a coupler increases slowly with the waveguide spacing and exhibits a strong dependence on the transverse mode order. The results are summarized in a few practically useful design charts by employing the normalizations of the device parameters. Some design examples are given and the fabrication tolerances are discussed.
© 1979 Optical Society of AmericaPDF Article