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Physical Review A

Anomalous frequency pulling in the photorefractive oscillators

R. Herrero, Daniel Hennequin

Published Aug 1, 1999• 0 citations
Publisher

Abstract

The emission frequency of an optical oscillator is not, in general, the cavity frequency, because it results from a compromise between the cavity and the material (atom, crystal) frequencies: this phenomenon is known as frequency pulling. We study in this paper the mechanisms leading to frequency pulling in oscillators with photorefractive gain (OPG), and compare them with those of lasers. We find that because the pulling in OPG does not depend explicitly on the empty cavity mode frequency, behaviors different from those observed in lasers are obtained. In particular, for a given set of parameters, the frequency pulling has a constant sign, so that the emission frequency is always larger (or smaller) than the maximum gain frequency. This leads to the counterintuitive effect that, in some conditions, the emitted intensity could decrease as the losses are decreased.

DOI
10.1103/physreva.60.1679

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The emission frequency of an optical oscillator is not, in general, the cavity frequency, because it results from a compromise between the cavity and the material (atom, crystal) frequencies: this phenomenon is known as frequency pulling. We study in this paper the mechanisms leading to frequency pulling in oscillators with photorefractive gain (OPG), and compare them with those of lasers. We find that because the pulling in OPG does not depend explicitly on the empty cavity mode frequency, behaviors different from those observed in lasers are obtained. In particular, for a given set of parameters, the frequency pulling has a constant sign, so that the emission frequency is always larger (or smaller) than the maximum gain frequency. This leads to the counterintuitive effect that, in some conditions, the emitted intensity could decrease as the losses are decreased.
A theoretical analysis of the oscillator with a photorefractive gain is presented. The steady multimode oscillation is considered. In such a system, the cavity light beam undergoes a frequency ``pulling'' due to the nonlinear interaction between light and matter. This frequency shift is evaluated with respect to the empty-cavity frequency. We show that it can be as large as necessary depending on the experimental parameters. This can be a physical interpretation for the periodic (and chaotic) oscillation of several transverse family modes already observed in these setups.
A self-consistent theory is used to derive the frequency shift presented by the oscillating mode in a cavity that contains a photorefractive crystal. A long-time-limit theory has been used to get the steady characteristics of the cavity field. The problem of the weak-field approximation is avoided. This approximation is useless in the case studied because the interaction along the crystal is so strong that one has to take in account the intensity exchange occurring inside the material between the pump and oscillating beams (two-wave mixing). We have fully analyzed the influence of the transverse nature of the beams on the intensity exchange in the two-wave mixing situation. In the photorefractive resonator case, the frequency shift of the oscillating beam is expressed in terms of a ratio that presents poles. The dependence on the problem parameters of these poles is studied and a perturbative method is developed; it is based on the smallness of the transverse overlap between the pump and cavity modes. An analytical expression for this frequency shift is obtained.
Photorefractive resonators exhibit an extremely small frequency difference (Deltaomega/omega~10(-15)) between the oscillating and pumping beams. The observed frequency difference is proportional to cavity-length detuning. This dependence is explained by a photorefractive phase shift that is due to slightly nondegenerate two-wave mixing that compensates for cavity detuning and satisfies the round-trip phase condition for steady-state oscillation. The measured onset or threshold of oscillation as a function of photorefractive gain and intensity agrees with theory.
The value of the Einstein BBB coefficient for stimulated emission for a collection of atoms interacting with a radiation field is shown to depend upon the velocity distribution of the excited atoms and also upon the variation of field intensity with frequency. An emission line narrowing phenomenon for radiating matter enclosed in a nonresonant cavity with reflecting walls is predicted. It is shown that a loss mechanism must be introduced if significant line narrowing is to result from a single pass of radiation through an amplifying medium. An additional contributing effect to the mode pushing and mode pulling phenomena in a gas laser is demonstrated. A method of setting a gas laser to a predetermined frequency is described.
The paper presents a detailed analysis of FM laser oscillation which includes the effect of arbitrary atomic lineshape, saturation, and mode pulling. Such oscillation is achieved by means of an intracavity phase perturbation, and is a parametric oscillation wherein the laser modes oscillate with FM phases and nearly Bessel function amplitudes. One principal idea is that of the competition between different FM oscillations. The effect of the intracavity phase perturbation is to associate a set of sidebands with each of the previously free-running laser modes. While the free-running laser modes experienced their gain from essentially independent atomic populations, the competing FM oscillations to a large extent see the same atomic population; and in cases of interest the strongest of these oscillations is able to quench the competing weaker oscillations and establish the desired steady state condition. Results of the analysis include the following: threshold and power output, amplitudes and phases of all sidebands, frequency pulling of the entire oscillation, time domain behavior, distortion, super-mode conversion efficiency, and effect of mirror motion. Results of numerical application of the theory to a number of specific cases are given.
We study the collective emission of a beam of atomic dipoles into an optical cavity. Our focus lies on the effect of a finite detuning between the atomic transition frequency and the cavity resonance frequency. By developing a theoretical description of the coupled atom-cavity dynamics we analyze the stationary atomic configurations including a superradiant phase where the atoms undergo continuous monochromatic collective emission. In addition, we derive an analytical formula for the cavity pulling coefficient which characterizes the displacement of the emission frequency towards the cavity frequency. We find that the pulling is small if the cavity linewidth is much larger than the collective linewidth of the atomic beam. This regime is desired for building stable lasers because the emission frequency is robust against cavity length fluctuations. Furthermore, we investigate the stability of the atomic phases and compare our theoretical predictions with numerical results. Remarkably, we also find polychromatic emission regimes, where the spectrum has several frequency components while the light output is still superradiant.