Effect of Spectral Hole-Burning and Cross Relaxation on the Gain Saturation of Laser Amplifiers

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Abstract
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*3+:glass broadband and narrow‐band amplification; an approximate lower bound of 4×105 sec−1 is determined for F.

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