The self focusing of a quadruple Gaussian laser beam, comprising four coherent identical Gaussian beams with axes parallel to ẑ but shifted from z-axis by −x0x̂,x0x̂,−x0ŷ,x0ŷ in a collisionless plasma, is investigated in the paraxial ray approximation. The nonlinearity arises through the ponderomotive force led plasma density redistribution. As the beam propagates, it maintains the shape of its intensity profile with spot size r0 of each of the four distributions modified from r0 to r0f, x0, modified to x0f and the axial intensity enhanced by 1/f2, where f is the beam width parameter. In the regime of quadratic nonlinearity, the threshold beam power for self focusing, Pth, increases with x0 as the laser intensity gradient decreases and the ponderomotive force becomes weaker. At beam power greater than Pth, the beam focuses in an oscillatory manner, i.e., f varies periodically with z due to the saturating effect of nonlinearity. The locations of intensity maxima of the four beams also vary periodically with z. As x0 increases from 0 to 0.6r0, the transverse intensity gradient becomes weaker and the rate of self focusing, i.e., the rate of variation of f with z decreases.

An analytical model for the avalanche breakdown of water by an intense short laser pulse of finite spot size is developed. Initially, the laser undergoes self-focusing due to Kerr nonlinearity. As it acquires large intensity, it causes heating and avalanche breakdown of water. The plasma thus created on the laser axis causes nonlinear refraction induced defocusing of the laser. Thermal conduction tends to flatten the temperature profile and reduce the nonlinear refraction. The plasma density modification leads to frequency broadening of the laser.

The presence of a density ripple in an unmagnetized plasma is shown to allow parametric decay of an electromagnetic wave into two electromagnetic waves, which is otherwise not allowed due to wave number mismatch between the decay waves. The static density ripple accounts for the mismatch. The decay occurs at plasma densities below the quarter critical density and the decay electromagnetic waves propagate at angles to the pump laser. The requisite ripple wave number q increases with the increase in pump wave frequency. However, as the ripple orientation with respect to the pump θR increases, q decreases. The growth rate for the parametric instability initially decreases with the frequency of the lower frequency electromagnetic wave, attains a minimum and then increases. The growth rate is higher for lower values of θR.

Parametric decay of a large amplitude electromagnetic wave into two electromagnetic modes in a rippled density plasma channel is investigated. The channel is taken to possess step density profile besides a density ripple of axial wave vector. The density ripple accounts for the momentum mismatch between the interacting waves and facilitates nonlinear coupling. For a given pump wave frequency, the requisite ripple wave number varies only a little w.r.t. the frequency of the low frequency decay wave. The radial localization of electromagnetic wave reduces the growth rate of the parametric instability. The growth rate decreases with the frequency of low frequency electromagnetic wave. V C 2012 American Institute of Physics. [http://dx.

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