A parametric array, in the field of acoustics, is a nonlinear transduction mechanism that generates narrow, nearly side lobe-free beams of low frequency sound, through the mixing and interaction of high frequency sound waves, effectively overcoming the diffraction limit (a kind of spatial 'uncertainty principle') associated with linear acoustics.
[4][5] Priority for discovery and explanation of the parametric array owes to Peter J. Westervelt,[6] winner of the Lord Rayleigh Medal[7] (currently Professor Emeritus at Brown University), although important experimental work was contemporaneously underway in the former Soviet Union.
[11][12][13] The foundation for Westervelt's theory of sound generation and scattering in nonlinear acoustic[14] media owes to an application of Lighthill's equation for fluid particle motion.
[18] An alternate mathematical formalism using Fourier operator methods in wavenumber space, was also developed and generalized by Westervelt.
[19] The solution method is formulated in Fourier (wavenumber) space in a representation related to the beam patterns of the primary fields generated by linear sources in the medium.