Analysis of grating couplers for planar dielectric waveguides

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Abstract
Output and input grating couplers for step index planar dielectric waveguides are investigated taking into account the interaction between a guided mode with a finite number of radiative and an infinite number of nonradiative space harmonics. For transverse electric and transverse magnetic modes, and for shallow gratings of arbitrary profiles located at either the upper or the lower guide surface, the governing equation for the slowly varying amplitude of the guided wave is deduced, and therefrom the real and the imaginary parts of the correction to the wave number of unperturbed guide are evaluated, the power conservation relation is established, and the output and the input coupling efficiencies are defined. For the input coupler, the excitation by a two-dimensional radiation beam is also included. The role of the space harmonics which, like the guided wave, carry power along the guide in modifying the real and the imaginary parts of the wave number of the guided wave is discussed. The effect of the choice of the profile and location of the grating on the distribution of the outgoing radiation between the cover and the substrate, and between harmonics of different orders are examined. In a multimode coupler, significant improvements in input coupling efficiency can be achieved by a suitable choice of the grating profile and the excitation region. The effect of tapering the relative depth of the grating on the amplitude profile of the radiated beam of the output coupler, and on the coupling efficiency of the input coupler are investigated.

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