Theory of quantum nonlinear resonance

G. Grynberg

Edward Shuryak

R. Reinisch, Guy Vitrant, Marc Haelterman

We develop a one-dimensional theory of diffraction-induced transverse effects in nonlinear Fabry-P\'erot resonators addressed by finite-width incident beams. This is achieved in the framework of the coupled-mode analysis, which takes full advantage of the fact that nonlinear Fabry-P\'erot devices are resonant. As compared with a recently published theory dealing with the same subject [M. Haelterman, Opt. Commun. 75, 165 (1990); M. Haelterman, G. Vitrant, and R. Reinisch, J. Opt. Soc. Am. B 7, 1309 (1990); and G. Vitrant, M. Haelterman, and R. Reinisch, ibid. 7, 1319 (1990)], where the nonlinearity is introduced in an approximate way, the formalism developed here takes the nonlinearity associated with the optical Kerr effect rigorously into account. This feature has an important consequence: It leads to a theory that can be generalized to the TM case and also to anisotropic nonlinear media. The theory presented here is valid for any value of the angle of incidence. Under normal (or quasinormal) incidence, two counterpropagating modes, having the same absolute value of the wave-vector component parallel to the plane of the mirrors, are resonantly (or nearly resonantly) excited, whereas under oblique incidence, only one of these modes is excited.This allows us to point out that the feedback leading to optical bistability occurs along the direction of propagation of these resonantly excited counterpropagating modes of the nonlinear optical resonator. This explains why optical bistability disappears under oblique incidence. Although developed in the case of nonlinear Fabry-P\'erot resonators, this theory applies to a wide range of nonlinear optical resonators such as nonlinear prism couplers, nonlinear grating couplers, nonlinear interference filters, etc. The theory developed here applies whenever the excited electromagnetic field can be accurately described by a single mode or two counterpropagating modes of the nonlinear device. As an example, numerical results are given in the case of a nonlinear multiple-quantum-well Fabry-P\'erot-type structure of ${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ga}}_{\mathit{x}}$As/GaAs with ${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ga}}_{\mathit{x}}$As/AlAs mirrors.

G. P. Berman

Fabio Mauceri, Alberto Mercurio, Salvatore Savasta +1 more

The authors study the quantum Rabi model in the ultrastrong regime in the presence of cavity nonlinearities and identify inconsistencies from various nonlinear Hamiltonians. To resolve the issues, the authors develop a microscopic theory and provide a consistent nonlinear-resonator quantum Rabi model satisfying the gauge principle.

Guy Vitrant, Marc Haelterman, R. Reinisch

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.