Extraneous self-imaging phenomenon with weak-guiding condition

We discuss a self-imaging phenomenon in a multimode interference (MMI) coupler. From experiment, different self-images, which are undefined in MMI theory, are observed. These undefined self-images are named “extraneous self-images” (Ex̱SIs) for convenience. To estimate the applicability of the Ex̱SIs, the characteristics of both the single self-image ($0\mathrm{dB}$ self-image, $0\mathrm{dB}$ SI), which is defined in MMI theory, and the Ex̱SI are compared and analyzed through simulation and experiment. The results show that the Ex̱SI has an imaging period that is the same as the $0\mathrm{dB}$ SI and that the excess loss and the extinction ratio of the Ex̱SI improve more than that of the $0\mathrm{dB}$ SI as the imaging period increases.