Parametric amplification near resonance in non-linear dispersive media

Abstract

The behaviour of collinear signal, idler and pump waves in a non-linear medium without inversion symmetry is investigated under small-signal conditions when the frequency ω of either the signal or the idler approaches a transition frequency of the medium. The three waves are coupled together by the first-, second- and third-order susceptibility tensors of the medium. All three tensors exhibit a resonance in the case under consideration. The first-order resonance creates an absorption band and the third-order resonance produces stimulated Raman amplification. It is shown that the strength of the second-order resonance, which enters into the parametric effect, is determined by the product of the strengths of the other two. The growth constant of the signal and idler waves is a maximum when the mismatch of the propagation constants Δk in the presence of the pump field takes a non-zero value equal to the decay constant at frequency ω times the ratio of the imaginary and real parts of the complex parametric growth constant, a quantity which is independent of the pump field strength. Except in the immediate neighbourhood of resonance, the frequency dependence of the optimum growth constant is controlled by the ratio of the peak Raman growth constant to the off-resonance parametric growth constant. When this ratio is small the optimum growth constant is never significantly larger than the off-resonance parametric value; when it is large the optimum growth constant slightly exceeds the peak Raman growth constant over a frequency range of 10-103 linewidths on one side of resonance. In the immediate neighbourhood of the resonance the optimum growth constant exhibits structure which is controlled by the anomalous dispersion and absorption resulting from the first-order resonance.