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Quantum Electronics

Dynamics of superradiance in an optical cavity

Anatolii V Andreev

Published Jun 30, 1993• 4 citations
Publisher

Abstract

The dynamics of superradiance in an optical cavity is analyzed under conditions such that a population grating is induced through degenerate four-wave mixing of counterpropagating waves. The initial field distribution which maximizes the radiative decay rate is determined.
DOI
10.1070/qe1993v023n06abeh003106

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Mode superradiance (i.e. superfluorescence) in an open Fabry—Perot resonator is characterised by simultaneous emission of counterpropagating coherent pulses even when the mirrors have very low (but finite) reflection coefficients, beginning from R cr ≪ 1. It is shown that for any value of the resonator Q factor, even when R ≫ R cr or R ~ 1, a self-matched λ /2 grating of the population inversion in a two-level medium does not result in significant Bragg reflection which would exceed the reflection from the mirrors. A consistent allowance for the interference of inhomogeneous conterpropagating waves significantly alters the spatial and temporal dynamics of depletion of the population inversion and, consequently, greatly changes he profile of collective spontaneous radiation pulses, compared with the predictions of the mean field and unidirectional superradiance theories. A new nonlinear equation for superradiance in an open resonator is derived.
A theoretical investigation is made of parametric generation of light by four-wave mixing in an optical cavity with two pump fields of different frequencies. Mixing configurations resulting in the excitation of one and three cavity modes are considered taking into account the effects of phase modulation and of depletion of the pump fields. An analysis is made of stable steady-state oscillation regimes. Calculations are reported of the intensities of the generated radiation modes at the exit from the cavity above the threshold. An analysis is made of the conditions for the appearance of optical bistability at nonzero values of the cavity detuning.
Cooperative radiation emitted by an ensemble of three-level optical systems with a doublet in the ground state (Λ scheme), which is placed into a cyclic cavity, is studied theoretically. In contrast to the two-level model of emitters, this process with such a configuration of operating transitions may occur without population inversion in the whole, if the doublet is prepared at the initial instant in a superposition (coherent) state. In the ideal case of a Hamilton system, in which the cavity losses and relaxation in the radiator ensemble are disregarded, the conservation laws are derived, which allow a substantial reduction of the dimension of the phase space of the model (ℝ 11 → ℝ 5 ) and the application of methods of dynamics of nonlinear systems for analyzing the three-level superradiance under these conditions. The possibility of different (both quasiperiodic and chaotic) scenarios of the three-level superradiance is demonstrated on the basis of Poincaré’s mappings. Global bifurcation of the system upon a transition from the conventional superradiance regime to inversionless one is revealed. The effects of cavity losses, as well as homogeneous and inhomogeneous broadening in the system of radiators on the regularities found are also discussed.