Transmission of coherent light through photonic gratings with varying Kerr nonlinearity is modeled within a coupled-mode system derived from the Maxwell equations. The incident light waves are uniformly stable in time-dependent dynamics if the photonic grating has zero net-average Kerr nonlinearity. When the average nonlinearity is weak but nonzero, light waves exhibit oscillatory instabilities and long-term high-amplitude oscillations in the out-of-phase linear gratings. We show that a two-step transmission map between lower-transmissive and higher-transmissive states has a narrow stability domain, which limits its applicability for logic and switching functions. Light waves exhibit cascades of real and complex instabilities in the multistable gratings with strong net-average Kerr nonlinearity. Only the first lower-transmissive stationary state can be stimulated by the incident light of small intensities. Light waves of moderate and large intensities are essentially nonstationary in the multistable gratings, and they exhibit periodic generation of Bragg solitons and blowup.
© 2002 Optical Society of America
(190.1450) Nonlinear optics : Bistability
(190.3100) Nonlinear optics : Instabilities and chaos
(190.4360) Nonlinear optics : Nonlinear optics, devices
(230.1480) Optical devices : Bragg reflectors
(230.4320) Optical devices : Nonlinear optical devices
Dmitry Pelinovsky and Edward H. Sargent, "Stable all-optical limiting in nonlinear periodic structures. II. Computations," J. Opt. Soc. Am. B 19, 1873-1889 (2002)