Parametric array

In the field of acoustics, a parametric array 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. The main side lobe-free beam of low frequency sound is created as a result of nonlinear mixing of two high frequency sound beams at their difference frequency. Parametric arrays can be formed in water, air, and earth materials/rock.

Priority for discovery and explanation of the parametric array owes to Peter J. Westervelt, winner of the Lord Rayleigh Medal (currently Professor Emeritus at Brown University), although important experimental work was contemporaneously underway in the former Soviet Union.

According to Muir [16, p. 554] and Albers [17], the concept for the parametric array occurred to Dr. Westervelt while he was stationed at the London, England, branch office of the Office of Naval Research in 1951.

According to Albers [17], he (Westervelt) there first observed an accidental generation of low frequency sound in air by Captain H.J. Round (British pioneer of the superheterodyne receiver) via the parametric array mechanism.

The phenomenon of the parametric array, seen first experimentally by Westervelt in the 1950s, was later explained theoretically in 1960, at a meeting of the Acoustical Society of America. A few years after this, a full paper [2] was published as an extension of Westervelt's classic work on the nonlinear Scattering of Sound by Sound, as described in [8,6,12].

The foundation for Westervelt's theory of sound generation and scattering in nonlinear acoustic media owes to an application of Lighthill's equation (see Aeroacoustics) for fluid particle motion.

The application of Lighthill’s theory to the nonlinear acoustic realm yields the Westervelt–Lighthill Equation (WLE). Solutions to this equation have been developed using Green's functions [4,5] and Parabolic Equation (PE) Methods, most notably via the Kokhlov–Zablotskaya–Kuznetzov (KZK) equation.

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