We explore the discrete nature of waveguide modes and the effective medium concept to achieve an ultra-compact highly efficient mode conversion device in a high-index platform such as a silicon waveguide. The proposed device is based on a co-directional coupler that has a periodic variation in its refractive index along the propagation direction. The transverse variation of the index profile is calculated based on the interference pattern between the modes of interest. We show that mode conversion can be realized with dielectric metasurfaces engraved in the silicon waveguide. We derive the equation for effective index and show proof-of-concept numerical results of the device performance. We obtain conversion efficiencies of 95.4% between the TE0-TE1 modes over 8.91 mu m interaction distance and 96.4% between the TE0-TE2 over 6.32 mu m. The resulting coupling coefficient changes as a function of the interaction distance in a sinusoidal manner, which is crucial for constructive energy transfer from one mode to another. Such mode coupling devices have the potential for application in dispersion compensations, wavelength division multiplexing systems, and sensing. (C) 2019 Optical Society of America
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