Structure of laser-induced normal modes in finite inhomogeneous plasma

An analytic treatment of the problem of normal modes resulting from the decay of an electromagnetic pump wave propagating in a strongly inhomogeneous finite plasma is presented. Asymptotic solutions of the Weber equation and, alternatively, the WKB method, are applied to formulate dispersion relations which agree. Simple formulae for the complex growth rate pm = ρm±iΩm are obtained as functions of the coherence length κ−1/2 (κ being the wavenumber mismatch gradient), the plasma length L, and the basic gain length L0. Where numerical results are available, they agree with the eigenvalues from the formulae to within 10% or better. The mth mode appears if, and only if, the inequality amL0<κ−1/2