Floquet-Bloch theory is used to calculate the electromagnetic fields in a leaky-mode grating-assisted directional coupler (LM-GADC) fabricated with semiconductor and glass materials. One waveguide is made from semiconductor materials (refractive index \approx3.2) while the second is made from glass (refractive index \approx1.45). The coupling of light between the two waveguides is assisted by a grating fabricated at the interface of the glass and semiconductor materials. Unlike typical GADC structures where power is exchanged between two waveguides using bound modes, this semiconductor/glass combination couples power between two waveguides using a bound mode (confined to the semiconductor) and a leaky mode (associated with the glass). The characteristics of the LM-GADC are discussed. Such LM-GADC couplers are expected to have numerous applications in areas such as laser-fiber coupling, photonic integrated circuits, and on-chip optical clock distribution. Analyses indicate that simple LM-GADC's can couple over 40% of the optical power from one waveguide to another in distances less than 1.25 mm.
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