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Journal of physics. A, Proceedings of the Physical Society. General

Spectral distribution of amplified spontaneous emission

L. Allen, G I Peters

Published May 1, 1972• 21 citations
Publisher

Abstract

A theory is described which accounts for the dependence of the spectral distribution of amplified spontaneous emission on the length and inversion density of the active medium. For an inhomogeneously broadened line an unanticipated dip occurs in the plot of linewidth against length at lengths slightly greater than the critical length, but is explained by a simple physical analysis. Agreement occurs between the theory and that of Yariv and Leite (1963) in the regime over which their theory is expected to work. Observations by other workers on the spectral distribution of amplified spontaneous emission systems are discussed.

DOI
10.1088/0305-4470/5/5/011

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Amplified Spontaneous Emission and External Signal Amplification in an Inverted Medium

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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.

Physical Review A•Oct 1, 1973•109 citations
A theory is described which accounts for the dependence of the spectral distribution of amplified spontaneous emission on the length and inversion density of the active medium. For an inhomogeneously broadened line an unanticipated dip occurs in the plot of linewidth against length at lengths slightly greater than the critical length, but is explained by a simple physical analysis. Agreement occurs between the theory and that of Yariv and Leite (1963) in the regime over which their theory is expected to work. Observations by other workers on the spectral distribution of amplified spontaneous emission systems are discussed.
The theory of amplified spontaneous emission (ASE) and the gain–length product at saturation is revised. Formulas valid for both peak and integrated lines are given. In the latter case the solution for a general Voigt stimulated-emission line shape is presented, whereas in the two limiting cases of Gaussian and Lorentzian line shapes an approximation better than the one obtained by the steepest-descent method is successfully achieved. Various parameters that take into account the ratio of spontaneous to stimulated linewidths, the form factor depending on the linewidths of the inhomogeneous and homogeneous convoluted line shapes, and the population inversion fraction arise from the theory, giving the complete functional dependence for both the ASE photon flux and the gain–length product.
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.
Spectral line broadening due to resonance absorption and induced emission is investigated for general spectral distributions of the radiation field using the frequency-dependent relaxation operator method. An analytic self-consistent solution is found for the case of equal spectral profiles of field and radiative cross sections. The often-assumed Gaussian distribution of the field in saturated amplifiers is shown to yield symmetrical doublet structure for the radiative cross sections if the induced rates are larger than or comparable to the Gaussian width. A similar calculation was therefore performed for double Gaussian field spectra that reproduces such doublet structure for the cross sections in the case of narrowly spaced Gaussians. Self-consistent solutions of gain and line-broadening equations are accordingly expected to favor the sidebands, and at very high powers and gains amplified-spontaneous-emission lines should generally split into two lines of equal intensity separated by an averaged Rabi frequency. Since the cross-section profiles vary along the amplifier, the overall gain may be diminished, although the local cross sections have enhanced maxima at high powers.
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.