Abstract

Spontaneous Pattern Formation in an Acoustical Resonator

V.J.Sanchez-Morcillo, V.Espinosa, J.Alba (Departamento de Fisica Aplicada, Universidad Politecnica de Valencia, Spain)

e-mail: victorsm@fis.upv.es

The problem of spontaneous emergence of patterns in the transverse section of an acoustical interferometer is studied from the theoretical point of view. A model for parametric sound generation in a large aspect-ratio dispersive cavity is derived, taking into account the effects of diffraction. It is shown that the subharmonic field can be excited, when a threshold pump value is reached, and presents a non-uniform distribution in the transverse plane, or pattern. This occurs when the field frequency is tuned below the frequency of the closest resonator mode (negative detuning). On the contrary, an on-axis field, with homogeneous distribution, is emmited. Traditionally, patterns arise from the imposition of external constraints (waveguiding). The field then oscillates in modes of the resonator. The spontaneous emergence of patterns considered in here presupposes no external transverse mode selection mechanism, but instead allows the system to choose a pattern through the nonlinear interaction of a tipically infinite set of degenerate modes. The pattern formation process described here is related with the competing effects of nonlinearity and diffraction, and presents many analogies with similar systems studied in nonlinear optics, such as the two-level laser or the optical parametric oscillator, to which the model derived is isomorphous.

Section : 9