Guy Vitrant

Transverse effects in nonlinear planar resonators. I. Modal theory

On the basis of a pole analysis, we derive a simple and powerful model of the nonlinear Fabry–Perot resonator. Our theory extends the modal approach, which was already developed for the nonlinear prism coupler, to the Fabry–Perot resonator for any angle of incidence. The main advantage of the modal approach is that it greatly simplifies the numerical study of transverse effects and provides a deep understanding of physical phenomena related to optical bistability. By means of a simple analysis of the equations, our model permits us to discuss the role of diffraction and the influence of the incident angle on the nonlinear Fabry–Perot behavior.

Transverse effects in nonlinear planar resonators. II. Modal analysis for normal and oblique incidence

A unified nonlinear modal theory that is valid not only for waveguide couplers but also for nonlinear Fabry–Perot resonators has recently been proposed. The validity of this new approach is numerically demonstrated by comparison with the well-known bidimensional theory. The unified modal theory appears to be a powerful tool for studying transverse effects in a broad class of nonlinear resonators. It has been used to derive the main characteristics of the stationary behavior of the optical resonators in the case of a local nonlinearity. In particular, the disappearance of optical bistability when the resonator is tilted is predicted. Optical bistability at nearly normal incidence is interpreted by the coupling between two resonantly excited counterpropagating modes that are at the origin of the required transverse feedback.

Demonstration of optical bistability with a nonlinear prism coupler

A guided wave is launched through a nonlinear prism coupler whose prism‐waveguide gap is filled with a liquid crystal. We observed that the intensity of the excited guided wave exhibits optical bistability when the incident intensity is modulated. This result, which is rather surprising when compared to recent theoretical predictions, is shown to arise from a thermal averaging process in the liquid crystal.

Drift instability and spatiotemporal dissipative structures in a nonlinear Fabry–Perot resonator under oblique incidence

By means of a simplified model we study the dynamics of transverse effects in the nonlinear Fabry–Perot resonator illuminated under both normal and oblique incidences. We show that oblique incidence leads to a new kind of instability characterized by the onset of periodic self-pulsing. On the basis of a simple linear stability analysis, we interpret this instability in terms of a drift of spatial dissipative structures.

Radiated diffracted orders in Kerr-type grating couplers

Abstract A theory is developed which allows deriving, in a simple way, the intensity dependence of the diffracted orders radiated, in reflexion or transmission, by a Kerr-type grating coupler. The accuracy of this method can be easily checked. This formalism leads to the possibility of studying the influence of transverse effects on the field map of diffracted orders whatever their type, evanescent or radiated, may be.

Modulational instabilities in diffusive Kerr-type resonators

Abstract A modulational stability analysis of Kerr-type nonlinear resonators is performed, revealing that the stability properties of these devices are fundamentally altered by the Debye time and the diffusion length of the nonlinearity. The main new feature, as compared to the case of a local and instantaneous nonlinearity, is the presence of Hopf-bifurcations located on the upper branch of the bistable loop and resulting in time-dependent transverse patterns. Numerical simulations show the existence of self-pulsing and turbulent patterns, both for self-focusing and self-defocusing media.

Transverse effects in optical bistability with the nonlinear Fabry–Pérot étalon: A new theoretical approach

On the basis of a plane‐wave analysis we develop an original one‐dimensional model for the nonlinear Fabry–Perot etalon. This model facilitates numerical analysis and physical interpretations. We discuss the role of diffraction and the influence of the incident angle on bistability. A preliminary numerical study of the model is proposed.

Engineering and application of functionalized polymers in nonlinear optics

The engineering of functionalized polymers for second order nonlinear optical applications is shortly described and discussed. The ways of chromophore orientation are also discussed with a special emphasis on static field poling. Practical application applications of these polymers are overviewed and an integrated optical amplifier is described in more details.

Coupled-mode theory of optical bistability in a locally nonlinear waveguide

Abstract On the basis of the coupled-mode theory we analyse the physical properties of a nonlinear waveguide section laid between two linear waveguides. We assume a local Kerr nonlinearity and we study the role of the rapidly varying terms of the nonlinear wave equation which come from the presence of two counterpropagating guided waves. We discuss the origin of optical bistability in this device. In particular, we investigate the role of the backward mode generation recently studied by Karpierz [Optics Comm. 73 (1989) 203].

Demonstration Of Optical Bistability By Resonant Excitation Of Nonlinear Guided Waves

A guided wave is launched through a nonlinear prism coupler whose prism-waveguide gap is filled with a liquid crystal. We observe that the intensity of the guided wave may exhibit optical bistability. Tests are realized which proove that the loops are true bistable cycles and not only hysteresis. The experimental results are in good agreement with plane-wave calculations. The disagreement with finite-width incident beam calculations is explained by a thermal averaging process within the liquid crystal.