Leaky Modes in Nonlinear Optical Resonators

Yuan-Ping Cai, Li 丽 Jiang 姜, Ren-Gang Wan

Abstract We investigate the nonlinear Goos–Hänchen shift of a light beam reflected from a prism-coupled leaky waveguide containing a Kerr medium. As the incident power varies, the system can switch between two states, total internal reflection and frustrated total reflection, owing to the inherent positive feedback arising from the intensity-dependent guiding mode resonance. The reflectance exhibits optical bistability; meanwhile, the lateral shift of the reflected beam also shows hysteresis behavior. It is found that the transition between the two stable states is related to the excitation of a leaky mode in the waveguide, which results from the modulation of the electric field in the nonlinear substrate. We also analyze the effects of system parameters on the bistable Goos–Hänchen shift. The thresholds as well as the width of the hysteresis curve are sensitive to the thicknesses of the gap layer and the guiding layer, which determine the resonance angle. The bistable lateral displacement in the slab waveguide may have potential applications in optical switching, beam steering, etc.

Andrea M. Armani, Rigoberto Castro‐Beltrán, Vinh M. Diep +4 more

V. K. Ablekov, Vadim S. Belyaev, V. P. Vasil'ev +3 more

M. Nevière, E. Popov, R. Reinisch +1 more

Kerr-type leaky resonators are distributed couplers. They can be prism or \ngrating couplers, Fabry-Pérot's or multilayer devices all which include a nonlinear \nmedium that exhibits the optical Kerr effect [IX. 1 and IX.2]. One of the key features of \nthe optical Kerr effect is that it gives rise to a light-intensity dependent refractive index, \nallowing in this way to control light with light [IX.3]. This constitutes a fascinating field \nof nonlinear optics. The resulting all-optical interactions lead to numerous manifestations \nranging from optical bistability to "exotic" behavior such as self-pulsing, chaos, strange \npattern, light bullets, etc. The first observations of optical bistability date back to the \n1970s [ІХ.4-ІХ.7]. A proper study of these effects requires the development of a spatiotemporal theory of the optical Kerr effect in leaky resonators [IX.8].

R. Reinisch, P. Vincent, M. Nevière +1 more

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, βpL, 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, tp, of the incident plane wave, iii) use the coupled-mode formalism to derive the analytical expression(4) of the complex nonlinear longitudinal wavevector component βpNL.

A. Dorsel, W. J. Firth, A. Guzman de Garcia +10 more