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

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Abstract
A new method for determining the Lorentzian linewidth ΔνL, Doppler linewidth ΔνD, 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 γI, 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 γI, ∂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 ΔνL/ΔνD 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=γI(∂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 γI, ∂τ′/∂z, and ∂T′/∂z, we obtain ΔνL, ΔνD, 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.