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Physical Review A

Collisional-cross-relaxation effects in amplified-spontaneous-emission lasers

G. J. Pert

Published Nov 1, 1994• 12 citations
Publisher

Abstract

The role of collisional cross relaxation in saturated laser amplification is considered by using a simple strong-collisional model. Expressions for the particle-state density distribution and gain are derived for a four-level system. These are reduced to a simple analytic form, subject to an approximation of wide applicability. The role of collisions in changing an inhomogeneous-broadened line to homogeneous, with a change from rebroadening to narrowing on saturation, is demonstrated. The results are shown to be consistent with the existing limited experimental data.

DOI
10.1103/physreva.50.4412

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A theory is presented for the effect of cross relaxation (CR) on the saturation with driving-signal intensity of the steady-state gain of a laser amplifier with an inhomogeneously broadened linewidth. The condition of steady-state gain results when the amplifier excitation level W and the driving-signal intensity are constant for about 3τ or longer, where τ is the fluorescence lifetime of the upper laser level. The driving signal is derived from an oscillator operated in the normal mode and which does not saturate the amplifier inversion density over times short compared with τ. We assume that CR, at a rate F, restores to thermal equilibrium any distortion of the spectral inversion density caused by the driving signal. Formulas are derived for steady-state gain saturation with arbitrary F for two cases: the spectral width of the driving signal is (1) narrow and (2) broad relative to the ionic or homogeneous line. The ionic linewidth Δvi is assumed to be much less than the inhomogeneous linewidth Δva and refers to the minimum frequency interval for which infinitely fast CR is operative. The theory also yields the CR coefficients f=(Δvi/Δva) [F/(τ−1+W)] for the narrow-band case and f*=(Δvs/Δva) [F/(τ−1+W)] for the broadband case, where Δvs is the driving-signal bandwidth. These coefficients significantly parametrize the CR effect: for f, f*>1, hole-burning is not severe, whereas for f, f*<1, considerable hole-burning takes place and the gain saturates faster. Finally, the theory is applied to experimental results obtained for Nd3+:glass broadband and narrow-band amplification; an approximate lower bound of 4×105 sec−1 is determined for F.

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Cambridge University Press eBooks•Mar 20, 2014•0 citations
The role of collisional cross relaxation in saturated laser amplification is considered by using a simple strong-collisional model. Expressions for the particle-state density distribution and gain are derived for a four-level system. These are reduced to a simple analytic form, subject to an approximation of wide applicability. The role of collisions in changing an inhomogeneous-broadened line to homogeneous, with a change from rebroadening to narrowing on saturation, is demonstrated. The results are shown to be consistent with the existing limited experimental data.
A theory is presented for the effect of cross relaxation (CR) on the saturation with driving-signal intensity of the steady-state gain of a laser amplifier with an inhomogeneously broadened linewidth. The condition of steady-state gain results when the amplifier excitation level W and the driving-signal intensity are constant for about 3τ or longer, where τ is the fluorescence lifetime of the upper laser level. The driving signal is derived from an oscillator operated in the normal mode and which does not saturate the amplifier inversion density over times short compared with τ. We assume that CR, at a rate F, restores to thermal equilibrium any distortion of the spectral inversion density caused by the driving signal. Formulas are derived for steady-state gain saturation with arbitrary F for two cases: the spectral width of the driving signal is (1) narrow and (2) broad relative to the ionic or homogeneous line. The ionic linewidth Δvi is assumed to be much less than the inhomogeneous linewidth Δva and refers to the minimum frequency interval for which infinitely fast CR is operative. The theory also yields the CR coefficients f=(Δvi/Δva) [F/(τ−1+W)] for the narrow-band case and f*=(Δvs/Δva) [F/(τ−1+W)] for the broadband case, where Δvs is the driving-signal bandwidth. These coefficients significantly parametrize the CR effect: for f, f*>1, hole-burning is not severe, whereas for f, f*<1, considerable hole-burning takes place and the gain saturates faster. Finally, the theory is applied to experimental results obtained for Nd3+:glass broadband and narrow-band amplification; an approximate lower bound of 4×105 sec−1 is determined for F.
We report experiments which show that saturation of the inhomogeneously broadened 6328-\AA{} neon-laser line is strongly affected by cross relaxation which tends to redistribute the excited atoms over the Maxwellian velocity distribution and thus leads to partially homogeneous line saturation. Our results for Ne20{\mathrm{Ne}}^{20}Ne20 discharges agree well with theoretical calculations based on a "strong-collision" model. Results for He3{\mathrm{He}}^{3}He3:Ne20{\mathrm{Ne}}^{20}Ne20x mixtures show deviations from this model that we attribute to the "weak" cross relaxation caused by He-Ne collisions.
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.
Spectral broadening and cross relaxation of an aggregate of highly carrier-injected quantum dots have been studied experimentally by evaluating the gain saturation and optical-wave mixing characteristics of traveling-wave laser amplifiers that include self-assembled 0.98-µm InGaAs dots. Measured signal-gain spectra at room temperature showed that the gain decreases over the entire gain spectra when an intense and narrow-linewidth saturating signal is injected at a higher-order subband transition of the quantum dot. Differential-gain spectrum was calculated from the saturated and unsaturated signal gain spectra, and revealed asymmetric gain saturation with respect to the wavelength of the saturating signal. These results suggest that cross relaxation is so fast that the dot aggregate has a homogeneously broadened gain spectrum. Self-saturation and cross-saturation characteristics, and the detuning characteristics of highly nondegenerate four-wave mixing were also investigated. The latter revealed that the characteristic times of two cross-relaxation processes are about 1 ps and 100 fs.
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.