Dispersion relationships of leaky-mode grating-assisted directional couplers

Summary form only given. Grating assisted coupling between highly asymmetric dielectric waveguides provides a monolithic, low cost solution to coupling fibers to lasers and eliminates the need for external optics. One of the two modes of this tandem waveguide system is a leaky mode. We find that leaky-mode grating-assisted directional couplers (LM-GADCs), unlike conventional GADCs, have three distinct dispersion relationships and that the transition between the different dispersion relationships depends strongly on the depth of the grating. We consider a semiconductor-glass waveguide system and explore the relationship between the dispersion curves and the coupling strength as the grating depth is varied. We analyze LM-GADCs by using the Floquet-Bloch theory.