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Physical Review A

Effects of stimulated radiative processes on the spectral structure of amplified spontaneous emission

Hans R. Griem

Published Oct 1, 1989• 7 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.40.3706

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arXiv:0802.0913•Journal of Experimental and Theoretical Physics Letters•Dec 1, 2008•1 citation
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.
Introduction When an electromagnetic wave propagates through amedium stimulated emissions increase the intensity of the wave, while absorptions diminish it. The overall intensity will increase if the number of stimulated emissions can be made larger than the number of absorptions. If we can create such a situation then we have built an amplifier that operates through the mechanism of stimulated emission. This laser amplifier , in common with electronic amplifiers, has useful gain only over a particular frequency bandwidth. Its operating frequency range will be determined by the lineshape of the transition, and we expect the frequency width of its useful operating range to be of the same order as the width of the lineshape. It is very important to consider how this frequencywidth is related to the various mechanisms by which transitions between different energy states of a particle are smeared out over a range of frequencies. This line broadening affects in a fundamental way not only the frequency bandwidth of the amplifier, but also its gain. A laser amplifier can be turned into an oscillator by supplying an appropriate amount of positive feedback. The level of oscillation will stabilize because the amplifier saturates. Laser amplifiers fall into two categories, which saturate in different ways. A homogeneously broadened amplifier consists of a number of amplifying particles that are essentially equivalent, whereas an inhomogeneously broadened amplifier contains amplifying particles with a distribution of amplification characteristics. Homogeneous line broadening All energy states, except the lowest energy state of a particle (the ground state) cover a range of possible energies.
The output of pulsed, homogeneously broadened amplified spontaneous emission (ASE) lasers operating under conditions of strong saturation is considered. An expression for the maximum power (energy) per unit volume that may be extracted from steady-state (pulsed) systems is derived and shown to be independent of the saturation intensity. Numerical calculations of the temporal evolution of the populations in the laser levels and the growth in the ASE fluence, peak intensity, and spectral width are presented for three types of laser system: quasi steady state, short pump pulses, and self-termination. In all cases the growth in the fluence of the ASE pulse is found to agree with an analytic solution derived for conditions of strong saturation. The calculated growth in intensity of the ASE pulse is compared with expressions derived by Pert [J. Opt. Soc. Am. B11, 1425 (1994)] for the steady-state case. As expected, good agreement is found for the quasi-steady-state system, but in the limit of strong saturation significant differences occur for the short pump pulse and self-terminating laser systems considered. For all cases considered, the variation of the spectral width of the ASE pulse is found to be in reasonable agreement with that predicted by Pert for steady-state conditions.
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.
Amplification of probe radiation by an inversionless two-level system in the 'red' wing of its spectral line is studied theoretically during the resonance absorption of intense cw laser radiation. The effect is caused by the inequality of the spectral densities of the Einstein coefficients for absorption and stimulated emission outside the absorption line under conditions when homogeneous broadening, due to the interaction of particles with the buffer gas, significantly exceeds the natural broadening (at high pressures of the buffer gas). It is found that the larger the inversionless gain, the higher the buffer gas pressure and the pump radiation intensity. It is established that at high enough pump intensity, the probe field is amplified along the entire region of the 'red' wing of the line (at any negative detunings of the probe field frequency).
A previously developed theory of spontaneous emission from driven systems has been applied to the case of a Doppler broadened gas of two level atoms radiating into free space. The power spectrum of those photons radiated nearly parallel to the propagation vector of the driving field is predicted to differ from that of the undriven system. The case of zero attenuation coefficient (population equality in the two resonance levels) and the driving field tuned to the center of the Doppler line, is investigated in particular. When the saturation parameter is large there is strong suppression, in an interval about the central frequency comparable to the saturated width, of the spontaneous emission whose spectral components are phased for amplitude modulation relative to the driving field. An amount of power equal to that suppressed, but with spectral components phased for phase modulation relative to the driving field, is radiated in an interval about the central frequency comparable to the homogeneous width.
The observable line shape of the spontaneous emission depends on the procedure of atom’s excitation. The spectrum of radiation emitted by a two-level atom excited from the ground state by a π pulse of the resonant pump field is calculated for the case when the Rabi frequency is much larger than the relaxation rate. It is shown that the central part of the spectral distribution has a standard Lorentzian form, whereas for detunings from the resonance that are larger than the Rabi frequency the spectral density falls off faster. The shape of the wings of the spectral line is sensitive to the form of the π pulse. The implications for the quantum Zeno effect theory and for the estimates of the duration of quantum jumps are discussed.