ANALYSIS OF THE EFFECTIVE-INDEX METHOD FOR THE VECTOR MODES OF RECTANGULAR-CORE DIELECTRIC WAVE-GUIDES

The approximations involved in the effective-index method for analyzin g the vector modes of rectangular-core dielectric waveguides are exami ned in detail. It is shown that the effective-index method does not so lve the full vector-wave equation that governs the modes. Instead, it solves the reduced vector-wave equation, which is accurate only for ap proximately linearly polarized waves. Furthermore, in solving the redu ced vector-wave equation, the method of separation of variables is use d, which leads to additional errors as the waveguide being analyzed is a mathematically nonseparable structure. To characterize the performa nce of the effective-index method, asymptotic expressions are derived for the errors in the calculation of propagation constants. Apart from separating the effects of different approximations involved, these ex pressions show explicitly how the accuracy of the method depends on th e mode type, the normalized frequency, the mode orders, the dimensions of the waveguide, and the relative refractive-index differences betwe en the core and the surrounding media. With the help of these expressi ons, it is demonstrated that more accurate results can be obtained by combining various effective-index solutions.