Pulse propagation in a partially homogeneously broadened linear gas laser amplifier: Determination of line-shape parameters

Abstract

A new method for determining the Lorentzian linewidth Δν_L, Doppler linewidth Δν_D, and gain parameter G of a partially homogeneously broadened linear laser amplifier is developed here. This method is based on the measurements of the following pulse propagation parameters: the incremental pulse intensity gain γ_I, the increments of pulse duration, and pulse delay time per unit plasma length ∂τ′/∂z and ∂T′/∂z, respectively. Assuming that the gain medium is uniformly distributed, the pulse width is narrower than the gain bandwidth, the waveform of an incident pulse is Gaussian and its mean frequency is tuned to the line center of the gain medium, the γ_I, ∂τ′/∂z, and ∂T′/∂z are expressed in terms of the Voigt function ψ (0,y), and its second derivative ψ^″ (0,y), and the first derivative of its Hilbert conjugate φ′ (0,y), respectively. The parameter y= (ln2)^1/2 Δν_L/Δν_D is obtained by solving a transcendental equation; S (0,y) =Q, where S (0,y) =ψ (0,y) ‖ψ^″ (0,y) ‖/φ′ (0,y)². The function S (0,y) is numerically tabulated and Q=γ_I(∂τ′²/∂z)/8 ln2(Λ T′/∂z)² consists of the observable quantities. By substituting the values of ψ (0,y), ψ^″ (0,y), and φ′ (0,y) for the y obtained in the numerical tables into the formulas for γ_I, ∂τ′/∂z, and ∂T′/∂z, we obtain Δν_L, Δν_D, and G. The line‐shape parameters of the 3.5‐μm high‐gain xenon transition are determined by applying this pulse propagation method, where the experimental setup consists of a self‐mode‐locked xenon laser, a xenon laser amplifier with variable plasma lengths, infrared isolators, InAs photovoltaic detectors, and a sampling scope controlled by a signal‐averaging computer. The results are consistent with those obtained by the cw method based on the line‐narrowing and gain measurements.