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Physical Review A

Amplified Spontaneous Emission and External Signal Amplification in an Inverted Medium

L. Allen, G I Peters

Published Oct 1, 1973• 109 citations
Publisher

Abstract

An improved version of the theory of amplified spontaneous emission (ASE) is presented and shown to be satisfied by experimental data obtained using the 3.39-\ensuremath{\mu}m transition of He-Ne. The new approach allows the effect of an external signal injected at one end of the system to be investigated and its influence on both the positive-going and negative-going waves to be calculated for He-Ne. A special case occurs when the injected signal is replaced by a mirror which reflects the negative-going wave back into the medium and the theory of this commonly occurring laboratory system is experimentally verified at 3.39 \ensuremath{\mu}m. The treatment allows the importance of the interaction between spontaneous and stimulated emission to be considered. The beam divergence predicted by the theory is evaluated and compared with experiment. The spectral distribution for a pure ASE system is considered, as is the distribution of inversion which results from the positive- and negative-going waves and which is shown to have minima at the medium extremities. Finally the implications of this work for the problem of interstellar OH emission is considered.

DOI
10.1103/physreva.8.2031

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Amplified spontaneous emission. IV. Beam divergence and spatial coherence

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For pt. III see abstr. A54492 of 1971. The origins of beam divergence in amplified spontaneous emission are discussed and theoretical models are developed to predict what their effect would be in real systems. The divergence of the beam is experimentally investigated for the 3.39 mu m He-Ne and the 0.614 mu m Ne systems and compared with the theories. Good agreement is achieved in pure neon for a theory which depends upon the parametric relationship between intensity and length of active medium. In the case of He-Ne although the theory gives the correct qualitative prediction, the absolute magnitude of the effect is wrong by a factor of about 1.7. Measurements of the degree of spatial coherence as a function of length and inversion density of the medium and for the variation of spatial coherence across the tube for a given length and inversion density of medium, are presented for the neon system.

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Amplified spontaneous emission III. Intensity and saturation

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For pt. II see abstr. A35654 of 1971. A theory is developed to account for the intensity of ASE as a function of the length and diameter of the amplifying medium and of its inversion density. Detailed results are presented from a study of the 3.39 mu m transition in He-Ne which verify the theory. The theory is also shown to fit the experimental data obtained from the 0.337 mu m transition in N 2 .

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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.

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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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Amplified spontaneous emission (ASE) occurs in media with large gain, and affects both the magnitude and the spatial distribution of the inversion. In this work we theoretically study the effect of ASE in three-dimensional, rectangular slab amplifiers, using Monte Carlo type computer simulations. We found that in one-dimensional amplifiers ASE is always larger at the edges so that the inversion has a maxima at the center of the amplifier. However, in two- and three-dimensional amplifiers, the inversion has a minimum at the center of the amplifier for low gain, and a maximum at the center of the amplifier for high gain. Thus, the inversion profile can be changed by increasing the gain from a minimum at the center, through a plateau, to a maximum at the center. A simple analytical theory was developed and agrees with these results.

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Bidirectional description of amplified spontaneous emission induced by three-photon absorption

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)].

Journal of the Optical Society of America B•Feb 1, 2005•8 citations
An improved version of the theory of amplified spontaneous emission (ASE) is presented and shown to be satisfied by experimental data obtained using the 3.39-\ensuremath{\mu}m transition of He-Ne. The new approach allows the effect of an external signal injected at one end of the system to be investigated and its influence on both the positive-going and negative-going waves to be calculated for He-Ne. A special case occurs when the injected signal is replaced by a mirror which reflects the negative-going wave back into the medium and the theory of this commonly occurring laboratory system is experimentally verified at 3.39 \ensuremath{\mu}m. The treatment allows the importance of the interaction between spontaneous and stimulated emission to be considered. The beam divergence predicted by the theory is evaluated and compared with experiment. The spectral distribution for a pure ASE system is considered, as is the distribution of inversion which results from the positive- and negative-going waves and which is shown to have minima at the medium extremities. Finally the implications of this work for the problem of interstellar OH emission is considered.
For pt. III see abstr. A54492 of 1971. The origins of beam divergence in amplified spontaneous emission are discussed and theoretical models are developed to predict what their effect would be in real systems. The divergence of the beam is experimentally investigated for the 3.39 mu m He-Ne and the 0.614 mu m Ne systems and compared with the theories. Good agreement is achieved in pure neon for a theory which depends upon the parametric relationship between intensity and length of active medium. In the case of He-Ne although the theory gives the correct qualitative prediction, the absolute magnitude of the effect is wrong by a factor of about 1.7. Measurements of the degree of spatial coherence as a function of length and inversion density of the medium and for the variation of spatial coherence across the tube for a given length and inversion density of medium, are presented for the neon system.
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.
Amplified spontaneous emission (ASE) occurs in media with large gain, and affects both the magnitude and the spatial distribution of the inversion. In this work we theoretically study the effect of ASE in three-dimensional, rectangular slab amplifiers, using Monte Carlo type computer simulations. We found that in one-dimensional amplifiers ASE is always larger at the edges so that the inversion has a maxima at the center of the amplifier. However, in two- and three-dimensional amplifiers, the inversion has a minimum at the center of the amplifier for low gain, and a maximum at the center of the amplifier for high gain. Thus, the inversion profile can be changed by increasing the gain from a minimum at the center, through a plateau, to a maximum at the center. A simple analytical theory was developed and agrees with these results.
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)].