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 formalismi⁽¹⁾, 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⁽²⁾, previously used to study grating-induced plane wave OB⁽³⁾, can be replaced by a much more simple one which works as follows : i) determine the complex longitudinal wavevector component of the linear leaky guided mode p, β_p^L, through the solution of the associated linear homogeneous grating problem⁽²⁾, ii) use the rigorous theory of diffraction in linear optics⁽²⁾ to determine the in-coupling efficiency, t_p, of the incident plane wave, iii) use the coupled-mode formalism to derive the analytical expression⁽⁴⁾ of the complex nonlinear longitudinal wavevector component β_p^NL.

© 1991 Optical Society of America