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Physical Review A

Quantum theory of a swept-gain laser amplifier

Frederic A. Hopf, Pierre Meystre

Published Dec 1, 1975• 47 citations
Publisher

Abstract

The buildup of radiation from noise is considered in the case of the small-signal regime of a swept-gain amplifier with small Doppler width, of the sort indicated in recent schemes for an x-ray laser. The treatment uses the fully quantized electromagnetic field in order to take into account the spontaneous emission. The pulse is seen to grow nonexponentially with a rate that vanishes in the limit of large distances. The gain is generally much smaller than would be expected on the basis of the usual development. Many of the features normally associated with the small-signal regime of an amplifier, such as threshold conditions and spectral narrowing, are not seen. Instead we find spectral broadening, saturation, and the formation of steady states.

DOI
10.1103/physreva.12.2534

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Quantum theory of a swept-gain amplifier. II

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The steady-state behavior of amplifiers in which the excitation is swept at the speed of light is discussed in the semiclassical approximation. In the present work we examine the case where the decay time of the population is comparable to that of the polarization. Pulse propagation is shown to obey a generalized sine-Gordon equation which contains the effects of atomic relaxations. The analytical expression of the steady-state pulses (SSP) gives two threshold conditions. In the region of limited gain the SSP is a broad pulse with small area which can be obtained by small signal theory. In the second region of high gain the SSP is the superradiant $\ensuremath{\pi}$ pulse. Its pulse power is not limited as in usual superradiant theory because, as we show, for a swept excitation the cooperation-length limit does not exist.

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Small-signal gain in lethargic and conventional laser amplifiers

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The lethargic regime of a swept-gain laser amplifier is investigated theoretically to determine the procedure for passing over to the conventional limit ${T}_{1}(\mathrm{level}\mathrm{lifetime}) \ensuremath{\gg}{T}_{2} (\mathrm{phase}\mathrm{memory}\mathrm{time})$ of laser amplifiers. The calculation is done with a model in which the transit time of the atoms ${t}_{0}$, is less than ${T}_{1}$, which is soluble in closed form. The conventional limit is taken as ${t}_{0}\ensuremath{\rightarrow}\ensuremath{\infty}$. The general and conventional limits involve contradictory conditions of operation; nonetheless, both agree with experiment. This apparent contradiction is resolved by our finding that the conventional limit is a singular case.

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MIRADCOM Program in Swept-Gain Superradiance,

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Recently, Bonifacio, Hopf, Meystre and Scully, using amplifier theory, predicted that under certain conditions, a noise amplifier, pumped by an impulse excitation traveling at the speed of light in the active material, can produce highly nonlinear spacially asymptotic coherent pulses of electromagnetic energy of anomalous intensity and of anomalously short temporal width. The pulse intensities were predicted to increase as the square of the density of the active material, whereas the temporal width should decreased as the inverse of the density. Also, the pulses are characterized by a temporal delay from the pump cutoff to the peak of the pulse evolution. This process has come to be known as swept-gain superradiance. Electromangetic energy having these general characteristics would be useful in application to LADAR systems for propagation, ranging, discrimination and coherent imaging. Other applications would include coupling to plasmas for efficient energy delivery needed for laser induced fusion and for plasma diagnostics. Since the pulses are produced in the amplifier configuration without mirrors, this presents an attractive scheme for production of unidirectional coherent VUV and X-ray radiation.

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Coherent Amplification of an Ultrashort Pulse in a High- and Swept-Gain Medium with Level Degeneracy

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A one-dimensional model of the coherent amplification in a high- and swept-gain amplifier in the presence of strong spontaneous emission is presented and applied to seeding an x-ray laser with a high harmonic pulse. The atomic structure of the amplifying medium includes level degeneracy, and the Maxwell-Bloch equations are used to describe the propagation and interaction processes. This analysis elucidates, in the most comprehensive way, the influence of the random spontaneous emission on the coherent amplification process, as reflected in the basic pulse parameters such as its shape, polarization, and coherence.

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Amplified-spontaneous-emission intensity fluctuations

N. B. Abraham, John C. Huang, David A. Kranz +1 more

Intensity fluctuation characteristics of amplified-spontaneous emission are found using intensity rate equations and the noise-amplifier approximation for saturation coupling between two and four competing modes. The existence of more than one mode leads to the retention of relatively large fluctuations in each mode even as the amplifier gain is saturated, an operating regime which by contrast has been shown to reduce significantly the fluctuations when only a single beam is present. The noise-amplifier approximation is found to be an adequate approximation of the effects of the spontaneous emission distributed along the length of a laser amplifier. The intensity fluctuations in all cases approach limiting distributions functions as the amplifier becomes heavily saturated. Characteristics of these limiting distributions are found for one, two, and four beams; for combinations of beams copropagating and counterpropagating; in the presence and absence of loss; for differences in gain; and for saturation of the sources due to high intensities.

Physical Review A•Nov 1, 1981•14 citations
The buildup of radiation from noise is considered in the case of the small-signal regime of a swept-gain amplifier with small Doppler width, of the sort indicated in recent schemes for an x-ray laser. The treatment uses the fully quantized electromagnetic field in order to take into account the spontaneous emission. The pulse is seen to grow nonexponentially with a rate that vanishes in the limit of large distances. The gain is generally much smaller than would be expected on the basis of the usual development. Many of the features normally associated with the small-signal regime of an amplifier, such as threshold conditions and spectral narrowing, are not seen. Instead we find spectral broadening, saturation, and the formation of steady states.
The steady-state behavior of amplifiers in which the excitation is swept at the speed of light is discussed in the semiclassical approximation. In the present work we examine the case where the decay time of the population is comparable to that of the polarization. Pulse propagation is shown to obey a generalized sine-Gordon equation which contains the effects of atomic relaxations. The analytical expression of the steady-state pulses (SSP) gives two threshold conditions. In the region of limited gain the SSP is a broad pulse with small area which can be obtained by small signal theory. In the second region of high gain the SSP is the superradiant $\ensuremath{\pi}$ pulse. Its pulse power is not limited as in usual superradiant theory because, as we show, for a swept excitation the cooperation-length limit does not exist.
The lethargic regime of a swept-gain laser amplifier is investigated theoretically to determine the procedure for passing over to the conventional limit ${T}_{1}(\mathrm{level}\mathrm{lifetime}) \ensuremath{\gg}{T}_{2} (\mathrm{phase}\mathrm{memory}\mathrm{time})$ of laser amplifiers. The calculation is done with a model in which the transit time of the atoms t0{t}_{0}t0​, is less than T1{T}_{1}T1​, which is soluble in closed form. The conventional limit is taken as ${t}_{0}\ensuremath{\rightarrow}\ensuremath{\infty}$. The general and conventional limits involve contradictory conditions of operation; nonetheless, both agree with experiment. This apparent contradiction is resolved by our finding that the conventional limit is a singular case.
Recently, Bonifacio, Hopf, Meystre and Scully, using amplifier theory, predicted that under certain conditions, a noise amplifier, pumped by an impulse excitation traveling at the speed of light in the active material, can produce highly nonlinear spacially asymptotic coherent pulses of electromagnetic energy of anomalous intensity and of anomalously short temporal width. The pulse intensities were predicted to increase as the square of the density of the active material, whereas the temporal width should decreased as the inverse of the density. Also, the pulses are characterized by a temporal delay from the pump cutoff to the peak of the pulse evolution. This process has come to be known as swept-gain superradiance. Electromangetic energy having these general characteristics would be useful in application to LADAR systems for propagation, ranging, discrimination and coherent imaging. Other applications would include coupling to plasmas for efficient energy delivery needed for laser induced fusion and for plasma diagnostics. Since the pulses are produced in the amplifier configuration without mirrors, this presents an attractive scheme for production of unidirectional coherent VUV and X-ray radiation.
A one-dimensional model of the coherent amplification in a high- and swept-gain amplifier in the presence of strong spontaneous emission is presented and applied to seeding an x-ray laser with a high harmonic pulse. The atomic structure of the amplifying medium includes level degeneracy, and the Maxwell-Bloch equations are used to describe the propagation and interaction processes. This analysis elucidates, in the most comprehensive way, the influence of the random spontaneous emission on the coherent amplification process, as reflected in the basic pulse parameters such as its shape, polarization, and coherence.
Intensity fluctuation characteristics of amplified-spontaneous emission are found using intensity rate equations and the noise-amplifier approximation for saturation coupling between two and four competing modes. The existence of more than one mode leads to the retention of relatively large fluctuations in each mode even as the amplifier gain is saturated, an operating regime which by contrast has been shown to reduce significantly the fluctuations when only a single beam is present. The noise-amplifier approximation is found to be an adequate approximation of the effects of the spontaneous emission distributed along the length of a laser amplifier. The intensity fluctuations in all cases approach limiting distributions functions as the amplifier becomes heavily saturated. Characteristics of these limiting distributions are found for one, two, and four beams; for combinations of beams copropagating and counterpropagating; in the presence and absence of loss; for differences in gain; and for saturation of the sources due to high intensities.