Third-order parametric array generated by distantly spaced primary ultrasonic tones

Traditional parametric arrays are produced by a second-order nonlinear interaction between two primary ultrasonic tones that are close in frequency, resulting in a difference tone that is in the audio band. This article presents a parametric array produced by a third-order nonlinear interaction between two primary ultrasonic tones that are distantly spaced in frequency such that one tone is approximately the second harmonic of the other. The result is a third-order lower intermodulation (IM3) tone in the audio band with greater directivity and lower side lobe amplitude than comparable second-order fields. Measurements are presented that compare the directivity of 1-, 2-, and 4-kHz difference tones to that of 1-, 2-, and 4-kHz IM3 lower tones. Furthermore, a cascaded second-order approach for N-element transducer arrays is used to model third-order scattering with good agreement between measurement and theory.