Oscillations in harmonics generated by the interaction of acoustic beams

A numerical model of nonlinear propagation is used to investigate two cases of monochromatic ultrasonic beams interacting at small angles in a nonline ar medium. Two finite Young's slits are seen to produce fringes at harmonic frequencies of the source in places where the source frequency is absent, which can be seen as a combination of harmonic generation near the source a nd in the beam. Two intersecting beams with shaded edges are seen to produc e similar fringes in the near field, with an oscillatory structure. Algebra ic solutions to a simplified model, using the weak-field Khokhlov-Zabolotsk aya equation, are invoked to illustrate the origin of the oscillations, and of the far-field directivity, providing an alternative view of the fringes due to Young's slits. It is seen that two weakly interacting beams can pro duce fringes of second harmonic where the source frequency has low amplitud e, if the beams coincide at the point of observation, or if a boundary cond ition is imposed on the second harmonic where the beams coincide. (C) 1999 Acoustical Society of America. [S0001-4966(99)03103-3].