Leaky modes in coupled photonic bandgap waveguides

Abstract

We identify and analyze a class of leaky modes in two coupled identical photonic bandgap (PBG) slab waveguides. These leaky modes originate from the modes of the array structure that separates the two waveguides and may introduce additional losses to the coupled PBG waveguides when operating as a directional coupler. We derive an approximate formula to show explicitly how the leakage losses of such modes decrease exponentially with an increase in the thickness of the guiding layers. With numerical examples, we show that the leakage losses vary over a wide range, depending on the waveguide parameters. These leaky modes precede the guided modes according to the ranking of the mode indices and thus affect the orders of the guided modes. Their presence provides a simple physical explanation of the unusual phenomenon that the orders of the symmetric and antisymmetric guided modes of two coupled PBG waveguides depend on the number of the high-index elements in the array structure between the waveguides.