Effective Nonlinear Parameter Research Articles

Concentration and wavelength dependence of the effective third-order susceptibility and optical limiting of C60 in toluene solution

The optical limiting action of C60 in toluene solution is mainly due to reverse saturable absorption (RSA). It is shown that the formalism describing nonlinear optical response due to instantaneous two-photon absorption can be used in the case of sequential two-photon absorption, yielding effective values of the relevant parameters of optical nonlinearity due to RSA. The effective two-photon absorption parameter beta eff and the effective nonlinear refractive index parameter gamma eff', which are related respectively to the imaginary and real parts of the effective third-order susceptibility chi eff(3) were measured by the z-scan technique as a function of fullerene concentration and of incident laser intensity and wavelength over the 420-640 nm region. The concentration dependence of these parameters indicates that the solution is optically thin as far as the ground state of C60 is concerned, whereas the wavelength dependence confirms the applicability of the formalism used in the sequential two-photon absorption model. Comparisons are made with other z-scan results on C60.

On the role of second-order nonlinearity in the evolution of shear-horizontal guided acoustic waves

Second-order nonlinearity causes acoustic waves of shear-horizontal polarization to couple to sagittal components of the displacement field. This coupling is usually nonresonant and merely alters the effective nonlinearity parameter in the equation governing the nonlinear evolution of guided acoustic waves which, in the linear limit, are of purely shear-horizontal polarization. Using plate modes as an example, we demonstrate how in the neighbourhood of a resonance of a fundamental wit its second harmonic, the effect of second-order nonlinearity greatly exceed those of the third-order nonlinearity which are the dominant nonlinear effects when only shear-horizontal displacements are considered.

Measurements of the effective nonlinearity parameter B/A of water containing trapped cylindrical bubbles

The effective nonlinearity parameter B/A of water containing a three-dimensional ensemble of randomly distributed uniform-sized trapped cylindrical bubbles was measured. The experimental results indicate that the dramatic enhancement of the effective nonlinear parameter B/A is due to the nonlinear resonance oscillation of the trapped bubbles. The measured effective B/A for the system is of the magnitude of 10(4) to 10(5).

Experimental studies of the enhanced effective nonlinearity parameter B/A of a bubbly medium

It has been known for some years that the presence of bubbles may enhance the nonlinearity parameter B/A of a medium. Two distinct physical mechanisms are believed to be involved. The first one is due to bubble nonlinear oscillations; bubbles are driven by an acoustic wave near resonance frequency. The second one is due to static properties of a bubbly medium. The effective nonlinearity parameter B/A of water containing a three-dimensional ensemble of randomly distributed uniformly-sized trapped cylindrical bubbles was measured. The measured effective B/A for the system is of the magnitude of 104 to 105. The experimental results also suggest that the dramatic enhancement of the effective nonlinear parameter B/A is mainly due to the nonlinear resonance oscillation of the trapped bubbles. [Work supported by the NIH via Grant No. CA42947 and by the NSF and Vermont Epscor.]

A corrected mixture law for B/A

A derivation is presented that corrects an expression for the effective acoustic nonlinearity parameter of a mixture of immiscible liquids. The derivation is based upon a mass fraction, rather than volume fraction, formulation.

Enhanced nonlinearity in a bubbly liquid considered as a mixture

During the past decade there has been an increasing interest in the nonlinear behavior of gas bubbles in liquids. Recent papers by Soviet investigators [e.g., Kustov et al., Sov. Phys. Acoust. 32(6), 500–503 (1986)] have concentrated on phenomena observed when sound interacts with a bubbly layer. These phenomena can include acoustic solitons, parametric radiation, self‐focusing, phase conjugation, and other effects that occur because the system is highly nonlinear. An investigation of the acoustic nonlinear parameter of mixtures was conducted to help infer the volume fractions of the mixture components. When a bubbly medium of known air volume fraction is considered as a two‐component mixture, its effective nonlinear parameter may be calculated using mixture methodologies [R. Apfel, J. Acoust. Soc. Am. 74, 1866–1869 (1983)]. The mixture analysis in this work, which is independent of any assumptions regarding bubble oscillation, yields nonlinear parameter values comparable to those of the Soviet investigators. For certain volume fractions, values of the nonlinear parameter of a bubbly liquid may be hundreds of times that of either the gas or the liquid host. Both experimental and theoretical work will be presented and the implications of this enhanced nonlinearity will be discussed. [Work supported by NIH through Grant 5‐R01‐GM30419.]

The effective nonlinearity parameter for immiscible liquid mixtures

A relation has been derived which gives the effective nonlinearity parameter of a system of immiscible liquids, given the individual nonlinearity parameters as well as the respective densities, compressibilities, and volume fractions in the mixture.

Effective acoustic nonlinear parameter (B/A) of a mixture

We derive an expression for the effective nonlinearity parameter, B/A, of a mixture for which the density, compressibility, B/A, and mass (volume) fraction of each component is known. We then compare the predictions with experimental results reported in the literature and with our own experimental results for compositions ranging from solutions to tissues. Finally, we attempt to rationalize differences between predictions and experimental results, where they exist. [Work supported by U.S. Office of Naval Research.]

Nonlinear Acoustical Parameters of Piezoelectric Crystals

The wave equation for elastic waves in piezoelectric crystals is found, including the third-order terms in the expansion of the thermodynamic potential in the strain and electric field. The effective nonlinear parameters for a general crystal are obtained. In the general case these parameters depend on the second-order and third-order coefficients: nonlinear piezoelectric, electrostrictive, and linear electro-optic. These coefficients are considered for piezoelectric and nonpiezoelectric crystals. Some estimates are given of the values of the nonlinear coefficients.

Nonlinear Acoustical Parameters of Piezoelectric Crystals

The wave equation for elastic waves in piezoelectric crystals is found, including the third-order terms in the expansion of the thermodynamic potential in the strain and electric field. The effective nonlinear acoustical parameters for a general crystal are obtained. In the general case these parameters depend on the second-order and third-order coefficients: nonlinear piezoelectric, electrostrictive, and linear electrooptic. These coefficients are considered for piezoelectric and nonpiezoelectric crystals. The properties of the nonlinear piezoelectric tensor are discussed giving some estimate of the value of the nonlinear coefficients. The dependence of sound velocity on the external fields (strain and electric field) and wave interaction is discussed. [Research carried out while visiting at the University of California, Berkeley 94720.]