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Physical Review A

Wave-optics description of amplified spontaneous emission

J. C. Garrison, Burke Ritchie, Howard Nathel, C. K. Hong, L. Minner

Published May 1, 1991• 9 citations
Publisher

Abstract

Paraxial Maxwell-Bloch theory is used to describe amplified spontaneous emission (ASE) in strongly inverted media. Counterpropagation of waves coupled through gain saturation and diffraction, and pumping by a laser beam which propagates transverse to the amplifier are included in the treatment. The reactive part of the medium polarization is calculated by population-rate equations in the limit of rapid dephasing of the atomic dipoles. The spontaneous emission noise source needed for the numerical simulation of Maxwell's equations is derived from microscopic theory by coarse-graining, thereby establishing the compatibility of the spherically symmetric microscopic source with paraxial propagation theory. The three coupled Maxwell equations for the counterpropagating ASE waves and the transversely propagating pump wave are solved numerically in time and two spatial dimensions. This simulation is used to calculate the longitudinal profile of the transverse fluorescence, which measures the saturation of the gain, the longitudinal profile of the transmitted pump wave, which measures the saturation of pump absorption, and the transverse coherence function of the radiation emitted from the ends of the amplifier.

DOI
10.1103/physreva.43.4941

Related papers

Theory of optical pulse propagation in the region between superfluorescence and amplified spontaneous emission

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The coupling of forward and backward propagating waves is studied theoretically in the transition region between superfluorescence (SF) and amplified spontaneous emission (ASE). To accomplish this a computer code has been written that solves Maxwell's equations in time and two spatial dimensions and accounts for counter-propagation, diffraction, and temporal coherence in the Bloch equations. Diffraction is ignored in the present calculations. In the SF regime the coupling is generally weak, as found by others; however, I have found a randomly occurring shot-to-shot coupling that is quite significant in cases where one wave, forward or backward, becomes established from quantum noise first in the amplified rod. In this case the wave that arises second is strongly coupled to the first. In the ASE regime the propagation shows strong forward-backward coupling and the characteristic spatial profile of the inversion that tends to zero at either end and to the small signal value of one in the middle of the amplifier. In the transion region the propagation shows mixed SF and ASE behavior.

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Amplification of spontaneous emission and coherence in three-dimensional systems

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The steady-state wave equation, used in the literature for the description of amplified spontaneous emission (ASE) in a refractive medium with inverted atoms, focuses on a narrow frequency band at the atomic line center. In the present work, the effect of this approximation was studied by comparison to an alternative procedure that accounts for the full line shape. The three-dimensional time-dependent Maxwell-Bloch equations for ASE in a refraction guided system were solved as an initial-value problem by using transverse-mode expansion. The steady-state limit was approached only for quantities that are bilinear in the field (autorcorrelation function, complex degree of coherence, and radiation intensity). It was found that, except for a gain narrowing factor, the inclusion of the full line shape (or equivalently the detailed dynamics of atomic polarization) does not change the theoretical prediction for the amplification of mode intensities. However, it drastically changes the prediction for the behavior of cross correlations of mode amplitudes. In the high-gain limit the steady-state wave equation predicts that these cross correlations, normalized to the intensity of the involved modes, are independent of the system length and of the excitation strength of the modes. The solution of the Maxwell-Bloch equations predicts that the normalized cross correlations are exponentially decreasing functions of the system length and of the difference between the excitation strengths of the modes. It is therefore argued that the inclusion of the detailed atomic line shape is essential to the analysis of spatial coherence in ASE systems.

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Amplified spontaneous emission of laser media having a spherical or disk shape is numerically analyzed. Some properties are discussed and a comparison with linear systems is made. Analytical approximations, for the case of high pumping rates and high efficiency, are obtained. Energy level schemes of dye systems are used in the analysis and in the numerical calculations. A coupled set of radiative transfer and rate equations is solved under quasi-steady-state conditions. The model takes into account the fluorescence spectrum and gain saturation effects with radially symmetric distributions of the active dye molecular densities. As a comparison, the numerical examples also include an H2O system which is relevant in astrophysics.

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We present a Hamiltonian-based, 3D theory in paraxial approximation for X-ray amplified spontaneous emission (or superfluorescence) pumped by X-ray free-electron laser. The seed field is included. The ensemble-averaged Heisenberg equations become Maxwell-Bloch equations if factorization of operator products is assumed and are adequate when the stimulated emission is dominant. The spontaneous emission is accounted for by adding a random noise term to the atomic coherence, the magnitude of which is uniquely determined from the fact that the expectation value of the normally-ordered product electric field operators associated with an atom does not factorize. The modified Maxwell-Bloch equation we developed reproduces the results of the previous 1D theory based on correlation functions.

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Alexander S. Baev, Viktor Kimberg, Sergey P. Polyutov +2 more

A semiclassical dynamic theory of the nonlinear propagation of a few interacting intense light pulses is applied to study the nonlinear counterpropagation of amplified spontaneous emission (ASE) induced by three-photon absorption of short intense laser pulses in a chromophore solution. Several important results from the modeling are reached for the ASE process developing in the regime of strong saturation. Accounting for ASE in both forward and backward directions with respect to the pump pulse results in a smaller efficiency of nonlinear conversion for the forward ASE compared with the case in which forward emission is considered alone, something that results from the partial repump of the absorbed energy to the backward ASE component; the overall efficiency is nevertheless higher than for the forward emission considered alone. The efficiency of nonlinear conversion of the pump energy to the counterpropagating ASE pulses is strongly dependent on the concentration of active molecules so that a particular combination of concentration versus cell length optimizes the conversion coefficient. Under certain specified conditions, the ASE effect is found to be oscillatory; the origin of oscillations is dynamical competition between stimulated emission and off-resonant absorption. This result can be considered one of the possible explanations of the temporal fluctuations of the forward ASE pulse [Nature 415, 767 (2002)].

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Amplification without inversion in transversely limited beams

Vladimir Leonardovich Derbov, Inna L. Plastun

Propagation of a weak probe optical beam through a three-level medium pumped with a microwave strong beam is numerically studied. P-scheme of transitions under the conditions providing the amplification of the probe field without inversion is taken to calculate the atomic polarization which enters the paraxial wave equations. Diffraction and self-action of beams due to nonlinear absorption and refraction are properly taken into account. These effects together with linear absorption and refraction form a complex distribution of gain across the beams. As a result the amplified beam acquires ring transverse patterns and slight asymmetry in the frequency characteristics.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 10, 1996•0 citations
Paraxial Maxwell-Bloch theory is used to describe amplified spontaneous emission (ASE) in strongly inverted media. Counterpropagation of waves coupled through gain saturation and diffraction, and pumping by a laser beam which propagates transverse to the amplifier are included in the treatment. The reactive part of the medium polarization is calculated by population-rate equations in the limit of rapid dephasing of the atomic dipoles. The spontaneous emission noise source needed for the numerical simulation of Maxwell's equations is derived from microscopic theory by coarse-graining, thereby establishing the compatibility of the spherically symmetric microscopic source with paraxial propagation theory. The three coupled Maxwell equations for the counterpropagating ASE waves and the transversely propagating pump wave are solved numerically in time and two spatial dimensions. This simulation is used to calculate the longitudinal profile of the transverse fluorescence, which measures the saturation of the gain, the longitudinal profile of the transmitted pump wave, which measures the saturation of pump absorption, and the transverse coherence function of the radiation emitted from the ends of the amplifier.
The coupling of forward and backward propagating waves is studied theoretically in the transition region between superfluorescence (SF) and amplified spontaneous emission (ASE). To accomplish this a computer code has been written that solves Maxwell's equations in time and two spatial dimensions and accounts for counter-propagation, diffraction, and temporal coherence in the Bloch equations. Diffraction is ignored in the present calculations. In the SF regime the coupling is generally weak, as found by others; however, I have found a randomly occurring shot-to-shot coupling that is quite significant in cases where one wave, forward or backward, becomes established from quantum noise first in the amplified rod. In this case the wave that arises second is strongly coupled to the first. In the ASE regime the propagation shows strong forward-backward coupling and the characteristic spatial profile of the inversion that tends to zero at either end and to the small signal value of one in the middle of the amplifier. In the transion region the propagation shows mixed SF and ASE behavior.
The steady-state wave equation, used in the literature for the description of amplified spontaneous emission (ASE) in a refractive medium with inverted atoms, focuses on a narrow frequency band at the atomic line center. In the present work, the effect of this approximation was studied by comparison to an alternative procedure that accounts for the full line shape. The three-dimensional time-dependent Maxwell-Bloch equations for ASE in a refraction guided system were solved as an initial-value problem by using transverse-mode expansion. The steady-state limit was approached only for quantities that are bilinear in the field (autorcorrelation function, complex degree of coherence, and radiation intensity). It was found that, except for a gain narrowing factor, the inclusion of the full line shape (or equivalently the detailed dynamics of atomic polarization) does not change the theoretical prediction for the amplification of mode intensities. However, it drastically changes the prediction for the behavior of cross correlations of mode amplitudes. In the high-gain limit the steady-state wave equation predicts that these cross correlations, normalized to the intensity of the involved modes, are independent of the system length and of the excitation strength of the modes. The solution of the Maxwell-Bloch equations predicts that the normalized cross correlations are exponentially decreasing functions of the system length and of the difference between the excitation strengths of the modes. It is therefore argued that the inclusion of the detailed atomic line shape is essential to the analysis of spatial coherence in ASE systems.
Amplified spontaneous emission of laser media having a spherical or disk shape is numerically analyzed. Some properties are discussed and a comparison with linear systems is made. Analytical approximations, for the case of high pumping rates and high efficiency, are obtained. Energy level schemes of dye systems are used in the analysis and in the numerical calculations. A coupled set of radiative transfer and rate equations is solved under quasi-steady-state conditions. The model takes into account the fluorescence spectrum and gain saturation effects with radially symmetric distributions of the active dye molecular densities. As a comparison, the numerical examples also include an H2O system which is relevant in astrophysics.
We present a Hamiltonian-based, 3D theory in paraxial approximation for X-ray amplified spontaneous emission (or superfluorescence) pumped by X-ray free-electron laser. The seed field is included. The ensemble-averaged Heisenberg equations become Maxwell-Bloch equations if factorization of operator products is assumed and are adequate when the stimulated emission is dominant. The spontaneous emission is accounted for by adding a random noise term to the atomic coherence, the magnitude of which is uniquely determined from the fact that the expectation value of the normally-ordered product electric field operators associated with an atom does not factorize. The modified Maxwell-Bloch equation we developed reproduces the results of the previous 1D theory based on correlation functions.
A semiclassical dynamic theory of the nonlinear propagation of a few interacting intense light pulses is applied to study the nonlinear counterpropagation of amplified spontaneous emission (ASE) induced by three-photon absorption of short intense laser pulses in a chromophore solution. Several important results from the modeling are reached for the ASE process developing in the regime of strong saturation. Accounting for ASE in both forward and backward directions with respect to the pump pulse results in a smaller efficiency of nonlinear conversion for the forward ASE compared with the case in which forward emission is considered alone, something that results from the partial repump of the absorbed energy to the backward ASE component; the overall efficiency is nevertheless higher than for the forward emission considered alone. The efficiency of nonlinear conversion of the pump energy to the counterpropagating ASE pulses is strongly dependent on the concentration of active molecules so that a particular combination of concentration versus cell length optimizes the conversion coefficient. Under certain specified conditions, the ASE effect is found to be oscillatory; the origin of oscillations is dynamical competition between stimulated emission and off-resonant absorption. This result can be considered one of the possible explanations of the temporal fluctuations of the forward ASE pulse [Nature 415, 767 (2002)].
Propagation of a weak probe optical beam through a three-level medium pumped with a microwave strong beam is numerically studied. P-scheme of transitions under the conditions providing the amplification of the probe field without inversion is taken to calculate the atomic polarization which enters the paraxial wave equations. Diffraction and self-action of beams due to nonlinear absorption and refraction are properly taken into account. These effects together with linear absorption and refraction form a complex distribution of gain across the beams. As a result the amplified beam acquires ring transverse patterns and slight asymmetry in the frequency characteristics.