Spontaneous Emission and Coupled-Mode Theory in Multimode 1-D Systems with Contradirectional Coupling

By means of source terms and coupled-mode theory, the essential features of spontaneous emission in multimode waveguides with counterdirectional feedback, such as corrugated and photonic crystal waveguides, are described in a heuristic manner. These multimode source terms generalize a similar approach evoked in multilayer structures. We account for features such as the "mini-stopband," and the "stripe of minigaps" of broad photonic crystal waveguides, modeling previous experimental data. The result holds in several situations for which the differences in source terms for the uncoupled waveguide modes are not important. The approach yields significant results through a simple path.