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Journal of the Optical Society of America B

Scaling laws and response-time effects in nonlinear Fabry-Perot resonators

W. J. Firth, A. G. Fitzgerald

Published Jan 1, 1986• 0 citations
OpenAlex

Abstract

We examine nonlinear Fabry-Perot resonators where the medium response time τ is, respectively, much less than, comparable to, and much greater than the cavity round-trip time tR. As in previous work1 we assume the cavity is filled with a Kerrlike medium in which diffusion washes out all phase gratings.

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We have studied theoretically and experimentally the dynamic behavior of a nonlinear Fabry-Perot interferrometer filled with a Kerr medium. The Fabry-Perot responses ranging from extremely transient to quasi-steady-state in various modes of operation are considered. The experimental results are in excellent agreement with theory. It is shown that the quasi-steady-state operation requires not only a medium response time much smaller than the cavity round-trip time, but also a characteristic time of the input intensity variation several hundred times larger than the cavity round-trip time. Even in the quasi-steady-state limit, optical switching is often featured by overshoot and ringing after switching. The switching speed is limited by the cavity buildup time.
Most of the intrinsic optical devices which have been studied in recent years consist of a Fabry-Perot resonator containing a nonlinear medium. The response time of such devices is determined by the transients associated with the high-Q resonator and the response time of the nonlinear medium. The fastest devices must be free of any Fabry-Perot cavity. The excitation of either surface plasmons at a nonlinear interface or guided waves in thin nonlinear films is a way to obtain an ultrafast bistable optical device. These two kinds of device have been studied.
In Chapters 8–13 we always assumed that the nonlinear medium is contained in a unidirectional ring cavity. The case of a Fabry–Perot cavity (Fig. 8.1) is substantially more complex because the interference of the two counterpropagating fields gives rise to a standing-wave pattern that modulates the population difference and the atomic polarization to form gratings with a spatial frequency equal to the inverse of the half-wavelength and its harmonics. Therefore the atomic variables exhibit, in addition to the slow spatial variation which characterizes the envelopes, also a fast spatial variation on the wavelength scale, and the coexistence of these two spatial scales poses a highly nontrivial problem that must be treated with care. In Chapters 9 and 11 we solved exactly the Maxwell–Bloch equations with the ring-cavity boundary conditions for both the active and the passive configuration. Exact solutions of this kind have been obtained also for the equations and boundary conditions of a Fabry–Perot cavity [117–119]. However, for the sake of simplicity we will pass directly to models that are valid in the low-transmission approximation. Again for the sake of simplicity, in this chapter we assume that n B = 1, so that the light velocity in the empty part of the cavity is the same as that in the atomic sample. By following the same line of reasoning as that which we pursued in Chapter 12, in Section 14.1 we introduce a spatial transformation of the electric-field envelopes, which leads to boundary conditions without parameters, while the parameters present in the boundary conditions of the original variables appear in the envelope equations. As in the ring-cavity case, this approach allows one to introduce the cavity modes in a natural way, and to derive a set of modal equations coupled to the equations for the atomic variables. Sets of equations of this kind are common in the laser literature, but are not derived from the true boundary conditions for the cavity.
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.