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Physical Review A

Spatial response of cavity systems

Andrew J. Scroggie, John Jeffers, G.J. McCartney, Gian‐Luca Oppo

Published Aug 29, 2005• 1 citation
Publisher

Abstract

We show that a plane-mirror Fabry-Perot cavity is capable of converting a spatially phase (amplitude) modulated input beam into an amplitude (phase) modulated output. For a cavity close to resonance the effect is most easily seen for negative detunings. When nonlinear elements are added to the mean-field cavity, the effect persists but acquires an intensity dependence, while the requirement of net negative dispersion remains. In addition, the output of a near-resonant nonlinear cavity can have the same type of modulation as the input, something which is impossible in the corresponding linear cavity. These results are demonstrated in cavities containing Kerr or two-level materials, as well as in optical parametric oscillators.

DOI
10.1103/physreva.72.023824

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We show that a plane-mirror Fabry-Perot cavity is capable of converting a spatially phase (amplitude) modulated input beam into an amplitude (phase) modulated output. For a cavity close to resonance the effect is most easily seen for negative detunings. When nonlinear elements are added to the mean-field cavity, the effect persists but acquires an intensity dependence, while the requirement of net negative dispersion remains. In addition, the output of a near-resonant nonlinear cavity can have the same type of modulation as the input, something which is impossible in the corresponding linear cavity. These results are demonstrated in cavities containing Kerr or two-level materials, as well as in optical parametric oscillators.
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With the exception of Chapter 1, up to this point we have considered cavityless optical systems. With this chapter, instead, we start focussing on the case that the atomic medium is located in an optical cavity. We describe in detail the case of a unidirectional ring resonator, the boundary condition which characterizes it and the relations between its output fields and the intracavity field (Sections 8.1–8.3). We discuss the transmission of an empty cavity (Section 8.4) and of a cavity that contains a linear medium (Section 8.5). Optical cavities An optical cavity or optical resonator is formed by at least two mirrors, appropriately arranged in such a way that the radiation beam follows a closed path. The beam splitters allow the radiation to escape from the cavity (output) and allow one to inject radiation into the cavity (input). In order to confine the radiation transversally with respect to the direction of propagation, the mirrors are usually spherical (see Fig. 1.2). The case of cavities with spherical mirrors will be described in Part III of this volume. On the other hand, an analytical treatment of the problems is possible only within the plane-wave approximation which we will use in the remainder of Part I and in Part II. In accord with this, we assume here that the mirrors are planar. The two most common types of optical resonator are the Fabry–Perot cavity and the ring cavity . The planar Fabry–Perot cavity consists in two beam splitters in a parallel configuration as shown in Fig. 8.1. Within the cavity there are two counterpropagating fields, E F propagating in the forward direction and E B propagating in the backward direction with respect to the input field E I . Because we have derived the Maxwell–Bloch equations for the unidirectional configuration, in this and the following chapters we focus on the case of a ring cavity, which allows unidirectionality. The Fabry–Perot case will be considered in Chapter 14.
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.
A Fabry-Perot resonator filled with second-order nonlinear optical material is investigated. Attention is devoted to making the resonator act as a nonlinear mirror for ultralow-intensity light signals that can be switched by a control beam at the second-harmonic frequency. The interaction process is an input-phase-independent parametric downconversion. The theoretical problem is solved through implementation of a dummy variable method optimized for a parametric process. Efficient amplification and bistability of low-intensity signals have been found.
A theory of modulation of optical bistability of a main (signal) beam by an additional (control) beam is presented. It is supposed that the mirrors composing a Fabry-Perot cavity are highly reflective to the signal beam but transparent to the control beam. We show that the property of a medium in the cavity, and hence the transmission of the signal beam through the cavity, is modulated by the control beam which changes the dielectric susceptibility of the intracavity medium. Amplification of the signal beam occurs in the limit of a strong control beam. The process can be viewed as a parametric transfer of energy between the signal beam and the control beam with the nonlinear medium providing the nonlinear susceptibility that couples the beams. In addition, multibistability in the transmission characteristics of the signal beam is predicted and attributed to the saturation effect of the multiphoton processes.