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Quantum Electronics and Laser Science Conference

An analogue to sound propagation in a nonlinear Fabry-Perot cavity

J. Boyce, R. Y. Chiao

Published Jan 20, 2003• 0 citations
Publisher

Abstract

Summary form only given. The phenomena of self-focusing and defocusing in nonlinear optics can be viewed as arising from interactions between photons when the light propagation is paraxial and the Kerr nonlinearity is fast. We investigate one novel consequence of this, the existence of sound-like propagating photon density waves in a planar Fabry-Perot cavity containing a self-defocusing (n/sub 2/<0) nonlinear medium.

DOI
10.1109/qels.1999.807143

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Summary form only given. The phenomena of self-focusing and defocusing in nonlinear optics can be viewed as arising from interactions between photons when the light propagation is paraxial and the Kerr nonlinearity is fast. We investigate one novel consequence of this, the existence of sound-like propagating photon density waves in a planar Fabry-Perot cavity containing a self-defocusing (n/sub 2/<0) nonlinear medium.
In this complement we discuss several examples of optical phenomena in media where the refractive index depends nonlinearly on the intensity , known as optical Kerr media. This nonlinear effect exists in all materials, even isotropic ones, like glass or fused silica, but it is particularly marked in certain physical systems to be exemplified in Section 7B.1. After investigating the propagation of light through such media in Section 7B.2, we shall discuss three applications of the optical Kerr effect (which can be studied in any order). We begin by describing a bistable optical system , when this nonlinear medium is inserted in a Fabry–Perot cavity (Section 7B.3). We then study phase conjugate mirrors and examine their potential applications in adaptive optics (Section 7B.4). Finally, we discuss certain effects occurring during the propagation of an isolated wave, bounded either transversely or temporally, in a Kerr medium, and describe self-focusing effects (Section 7B.5) and self-phase-modulation effects (Section 7B.6). In particular, we shall show that nonlinear effects and dispersion effects can compensate to produce stable structures known as solitons , which maintain their shape during propagation. Examples of third-order nonlinearities Nonlinear response of two-level atoms We begin by studying a simple case of a nonlinear interaction, namely a two-level quantum system under the effects of a plane wave.
Propagation of light beams in a Fabry-Perot resonator filled with a self-focusing Kerr material is described by the nonlinear Schrodinger equation. If the degrees of freedom are restricted to one transverse dimension through the use of a line focus at the input face, the system possesses classical soliton solutions analogous to those for travelling-wave self-trapped beams. When the classical field theory is quantized, one obtains an effective nonrelativistic many-body field theory in which pairs of photons interact through attractive delta function potentials. The existence of bound states between photons is the microscopic phenomenon that prevents beams from spreading by diffraction. The fundamental bound state consists of two photons, which we call the "diphoton." We consider production of these quasi-particles in a single longitudinal mode Fabry-Perot resonator filled with an alkali vapor. The injected light is strongly attenuated to excite few photons in the cavity and is detuned slightly above the atomic resonance, giving rise to the self-focusing nonlinearity. Detection of the diphoton can be achieved by rejecting the unbound component by using a spatial filter and detecting the remaining signal in coincidence counting. The diphoton signature is a characteristic Lorentzian-squared two-point correlation profile.1
An analysis is made of the propagation of an optical wave parallel to reflecting planes in an extended nonlinear Fabry-Perot interferometer pumped by a strong wave of the same intensity. It is shown that the nonlinear-optics self-interaction of the first wave changes drastically near certain parts of the main experimental characteristic of the interferometer, which is the dependence of the intensity of the transmitted light on the intensity of the pump wave. The acoustooptic interaction can change similarly in this interferometer.
Optical Kerr nonlinearity is central to optical bistability in high-Q microcavities. Here, we show that optical Kerr nonlinearities in Fabry Perot resonators can also result in self-focusing effects, that can substantially modify the Q-factors of the resonators. For the studied cavities, up to five-fold increase in Q-factors is predicted, attributed to reduction of sidewall leakage, confirmed via simulations performed on curved cavities. We also show that for high Q-factor cavities, the higher-order Kerr effect can become relevant already at modest input intensities scaling inversely with Q-factor for a particular n2/n4 ratio. We investigate numerically the role of higher-order Kerr effect on optical bistability responses and find that its inclusion can shift the bistability threshold to higher input intensities than predicted by the standard n2-only model.