Grating Couplers for Kerr Type Nonlinear Waveguides: A Simplified Theory,

Abstract : We consider grating induced optical bistability (OB) arising from the resonant excitation of a given nonlinear guided mode. In that case it can be shown, using the coupled-mode formalism, that in the whole bistable domain : (a) the transverse field map of the resonantly excited nonlinear guided mode corresponds to that of the associated linear one which is known. (b) the Kerr-type nonlinearity only modifies the longitudinal wavevector component. Thus the rigorous theory of diffraction, previously used to study grating-induced plane wave OB, can be replaced by a much more simple one which works as follows: (1) determine the complex longitudinal wavevector component of the linear leaky guided mode p, Beta sub p L, through the solution of the associated linear homogeneous grating problem, (2) use the rigorous theory of diffraction in linear optics to determine the in-coupling efficiency, t sub p, of the incident plane wave, (3) use the coupled-mode formalism to derive the analytical expression of the complex nonlinear longitudinal wavevector component Beta sub p NL.