Parametric Acoustic Array Formation via Weak Collinear and Noncollinear Interaction in Dispersive Fluids.

The effect of dispersion on parametric arrays formed by Gaussian beams is investigated via solutions of the nonlinear paraxial wave equation. Analytical solutions are obtained by employing the quasilinear approximation; the results are thus restricted to weakly nonlinear interactions. Both (i) collinear and (ii) noncollinear interaction of the primary beams are considered. (i) Dispersion noticeably affects nonlinear interaction only when (VBAR)(delta)(VBAR) > (alpha)(,T)/k(,-), where (delta) = 1 - (k(,1) - k(,2))/k(,-) is the dispersion parameter, k(,j) (j = 1,2) and k(,-) are the primary and difference -frequency wave numbers, and (alpha)(,T) = (alpha)(,1) + (alpha)(,2) - (alpha)(,-) is the combined attenuation coefficient. Within the interaction region, dispersion causes the difference -frequency field to experience spatial oscillations. For an absorption-limited array, the interaction region behaves as a line array whose phasing depends on (delta). When (delta) (GREATERTHEQ) 0, the direction of maximum radiation is shifted off axis to the angle cos('-1)(1 - (delta)), whereas when (delta) < 0, the field is evanescent and the maximum remains on axis. Diffraction of the primaries also introduces slight phase mismatching, the effect of which is reduced for appropriate values of (delta) > 0. (ii) When (delta) > 0, compensation for the detrimental effects of dispersion in plane-wave interaction is attained when the primaries intersect at such an angle that k(,1)(' )-(' )k(,2)(' )=(' )k(,-). However, for arrays formed by narrow, noncollinear primaries, no amount of compensation is possible when (delta) > 0. When (delta) < 0, slight compensation is sometimes possible for highly collimated plane waves, for which the phase matching angle is SQRT.( -8(delta)) radians. No similar compensation is possible with Gaussian beams. The price paid for phase matching via collinear interaction is reduction in size of the interaction region, and therefore only marginal compensation for dispersion is ever possible.