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Quantum Electronics

Nonlinear Bragg scattering and mode superradiance in an open Fabry—Perot resonator

E. R. Golubyatnikova, Vitalii V Kocharovskii, Vladimir V Kocharovskii

Published Sep 30, 1994• 2 citations
Publisher

Abstract

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.

DOI
10.1070/qe1994v024n09abeh000243

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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.
An analytical theory has been developed for the superradiance of hot polariton modes formed by an inverted two-level medium in an open low-Q Fabry-Perot cavity. A qualitative analysis is proposed for the nonlinear stage of single-mode and multimode superradiance, and its difference from unidirectional superradiance is indicated. The characteristic shapes of the pulses and the common properties of single-pulse and oscillatory regimes are discussed for a cavity of arbitrary Q, as well as the correlation and the Bragg-rescattering features of pulses emitted from the opposite ends of a sample. © 2004 Optical Society of America
We carry out numerical modelling of the Maxwell-Bloch equations for a CW superradiant lasing of a homogeneous two-level active medium in a symmetric low-Q Fabry-Perot cavity and find a remarkable phase transition. Namely, at a pumping level n > n ( a ) exceeding by several times the lasing threshold, n ( s ) , a stationary (or nonstationary multimode) lasing of more or less symmetric counter-propagating electromagnetic waves is replaced with a steady-state monochromatic (or weakly modulated) lasing of asymmetric counter-propagating waves with different amplitudes a + , a − . The spontaneous transition to a new field structure is accompanied by formation of a highly asymmetric strongly nonlinear half-wavelength grating of the self-consistent polarization and population inversion of active medium n z [1] , [2] . Many similar numerical runs with noise taking into account show that in a rather wide range of laser parameters the grating appears with equal probabilities 50:50 at one and the same distance from left or right ends of an active sample and has always one and the same asymmetric profile n z ( ζ ) with maximum at symmetric points with respect to the cavity center ζ = 0. As a rule, a formation of the steady-state grating takes a long transient period of time and includes generation of several superradiant pulses (see Fig. 1a ).
The recent experiments on a pulsed superfluorescence and prospects of a CW superradiant lasing in various active media, especially semiconductor heterostructures, [1] attract much attention to new coherent dynamical effects in such lasers. These effects take place in the case of very dense active medium and low-Q cavities when a photon (cavity) lifetime is much shorter than a polarization (optical dipole) lifetime of an active center. Here, on the basis of numerical modeling of the Maxwell-Bloch equations, we describe the steady and dynamic spontaneous symmetry breaking of the structure of the field, polarization and population inversion of an active medium with almost homogeneously broadened spectral line placed into a symmetric low-Q combined distributed feedback (DFB) Fabry-Perot cavity.
By means of numerical modeling of nonlinear and analytical solution of linearized Maxwell-Bloch equations, we find an intriguing regime of a superradiant laser with a symmetric low-Q Fabry-Perot cavity equipped with a distributed feedback of counter-propagating waves. We find that, in a wide range of parameters, there is lasing of a strongly-asymmetric self-modulated powerful polariton mode accompanied by excitation of several almost symmetric weak polariton or electromagnetic modes. The frequency of the powerful mode is approximately coincides with a center of the laser spectral line, and the frequencies of the weak modes are outside the spectral line of an active medium. We show that such a lasing takes place due to formation of a self-consistent inhomogeneous asymmetric grating of population inversion of active centers that provides undamped Rabi oscillations of the population inversion and dipole moments of centers. The grating makes the powerful ‘central’ mode strongly asymmetric, and the Rabi oscillations of active centers excite the weak ‘sideband’ modes due to the quadratic resonant nonlinearity of the two-level active medium.