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Journal of Optical Technology

Superradiance of the polaritons of a two-level medium in a low-Q Fabry-Perot cavity

E. R. Kocharovskaya

Published Sep 1, 2004• 0 citations
Publisher

Abstract

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

DOI
10.1364/jot.71.000588

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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
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.
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 ).
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.
The superradiance (SR) of initially inverted two-level active medium in a cavity is considered. We discuss the results specific for the rigorous simulation of the SR pulse (obtained on the basis of 1D Maxwell-Bloch equations solution without slowly varying envelope approximation (SVEA) in the spatial variable): the strong dependencies of the counter-propagating waves correlation and pulse development acceleration not only on the module of the cavity mirrors reflection coefficient, but on the integer- factor of the ratio of the sample length and half of the resonant wavelength. The simple modification of the SVEA model approximately describing the above features is considered.
The intracavity absorption (or gain) coefficient of two-level atoms embedded inside a Fabry–Perot cavity has been demonstrated to be well represented by an equivalent two-level system. The parameters of this new two-level system are simply related to that of the medium and to the cavity characteristics. When associated with well-known results of fluorescence spectra and nearly degenerate four-wave mixing in two-level media, this equivalence provides a universal description of intracavity resonance fluorescence and relaxation oscillations in any nonlinear absorptive, amplifying, or dispersive Fabry–Perot cavities.