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Journal of Applied Physics

Operational characteristics of a light amplifier

T. Urisu, Kenji Kajiyama, Y. Mizushima

Published Oct 1, 1977• 3 citations
Publisher

Abstract

A general operation diagram of a traveling unidirectional light amplifier is proposed by theoretical analysis, wherein different regimes are specified by a noise condition and the several threshold conditions of gain. The effects of hole burning and cross relaxation on the amplified spontaneous-emission (AES) noise and the gain saturation threshold were formulated. The transient operation diagram was determined by a numerical calculation of the rate equations in dye-laser amplifier with a rhodamine 6G methanol solution system. The numerically calculated diagram agreed well with the general analytical results.

DOI
10.1063/1.323453

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A general operation diagram of a traveling unidirectional light amplifier is proposed by theoretical analysis, wherein different regimes are specified by a noise condition and the several threshold conditions of gain. The effects of hole burning and cross relaxation on the amplified spontaneous-emission (AES) noise and the gain saturation threshold were formulated. The transient operation diagram was determined by a numerical calculation of the rate equations in dye-laser amplifier with a rhodamine 6G methanol solution system. The numerically calculated diagram agreed well with the general analytical results.
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.
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.
Interaction of two coherent fields of arbitrary intensity with a general homogeneously broadened three-level molecular system for both an amplifier as well as a laser oscillator under general conditions of pumping is discussed. The amplifier solution is obtained through the time-averaged density-matrix formalism with two coherent fields treated classically. A detailed consideration of both real and imaginary parts of the electric susceptibility at pump and emission frequencies, corresponding to gain and dispersion in the active medium has been taken into account. The results obtained are used to study a number of situations for weak and strong pumping in the laser amplifier. Subsequently these are applied to a mode analysis of a unidirectional single-mode laser oscillator to determine the output characteristics of the laser and to establish conditions under which emission becomes dynamically unstable resulting in sustained oscillatory emission. The results obtained are found to be in good agreement with those of a full numerical analysis of the atomic and field coupled equations describing the system.
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.
Amplified spontaneous emission of laser media having a spherical or disk shape is numerically analyzed. Some properties are discussed and a comparison with linear systems is made. Analytical approximations, for the case of high pumping rates and high efficiency, are obtained. Energy level schemes of dye systems are used in the analysis and in the numerical calculations. A coupled set of radiative transfer and rate equations is solved under quasi-steady-state conditions. The model takes into account the fluorescence spectrum and gain saturation effects with radially symmetric distributions of the active dye molecular densities. As a comparison, the numerical examples also include an H2O system which is relevant in astrophysics.
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.