Linearized Theory of Laser-Induced Instabilities in Liquids and Gases

Abstract

A macroscopic linearized instability theory is developed to describe a class of instabilities resulting from optical-acoustic coupling of a laser beam in fluids and gases. A phenomenon of particular interest is the initial phase in the development of the high-intensity optical filaments which are observed when an intense laser beam propagates through certain fluids. It is suggested that for certain laser cell geometries and a sufficiently high power flux density, filament formation may be preceded by a breakdown in the mode structure of the incident laser beam as a result of coupling to the eigenmodes of the medium. The interaction mechanisms considered are stimulated Raman scattering, electrostriction, the high-frequency Kerr effect, and thermal-energy deposition, while the response of the laser-fluid system is described by Maxwell's equations combined with the appropriately modified conservation equations from hydrodynamics. On the basis of this model, it is proposed that inhomogeneities in the laser intensity, or in the density and temperature of the fluid, act as sources of instability growth for the induced waves which are generated when the primary and scattered optical waves interfere. The dispersion relation for the problem is derived and a procedure for calculating the growth rates of this instability is outlined. The method is illustrated by detailed computations on carbon disulfide covering a range of laser intensities, and it is shown that the laser-Stokes coupling terms do not significantly affect the initial growth rates. In the case of gases, where the electrostrictive effect can be ignored, analytic expressions for the spatial and temporal gains are derived. Under the assumption that the first-order contributions in the linear theory become important after they have undergone several $e$ foldings, these results indicate—for a power flux density, optical-absorption coefficient product of ${10}^{-8\mathrm{}}$ MW/${\mathrm{cm}}^3$—that mode degeneration is expected to occur in a laser beam which has propagated a distance of the order of a few kilometers through air at a pressure of 1 atm or which has a pulse length of several microseconds.