Coupled mode formulation by reciprocity and a variational principle
Abstract
A coupled mode formulation for parallel dielectric waveguides is presented via two methods: a reciprocity theorem and a variational principle. In the first method, a generalized reciprocity relation for two sets of field solutions satisfying Maxwell's equations and the boundary conditions in two different media, respectively, is derived. Based on the generalized reciprocity theorem, the coupled mode equations can then be formulated. The second method using a variational principle is also presented for a general waveguide system which can be lossy. The results of the variational principle can also be shown to be identical to those from the reciprocity theorem. The exact relations governing the 'conventional' and the new coupling coefficients are derived. It is shown analytically that the present formulation satisfies the reciprocity theorem and power conservation exactly, while the conventional theory violates the power conservation and reciprocity theorem by as much as 55 percent and the HardyStreifer (1985, 1986) theory by 0.033 percent, for example.
 Publication:

Journal of Lightwave Technology
 Pub Date:
 January 1987
 Bibcode:
 1987JLwT....5....5C
 Keywords:

 Coupled Modes;
 Dielectrics;
 Lossy Media;
 Reciprocity Theorem;
 Variational Principles;
 Waveguides;
 Computer Programs;
 Electric Fields;
 Matrices (Mathematics);
 Maxwell Equation;
 Polarization (Waves);
 Optics;
 WAVEGUIDES;
 COUPLING;
 MODES