Second-harmonic generation in a Bessel beam is investigated analytically, with emphasis on the effect of absorption. It is shown that absorption has a strong influence on the far-field beam profile. Numerical results are presented for higher harmonics and for waveform distortion in a Bessel beam that forms a shock.
Generation of intense, phase-conjugated ultrasonic beams by a single active magnetic element in a supercritical parametric mode has been demonstrated experimentally and theoretically. Specifically, phase conjugation with amplification greater than 80 dB, producing intensities of several hundred W/cm2 at MHz frequencies, is accomplished via parametric electromagnetic pumping of magnetoelastic solids. Reversal of the sound field incident on the conjugator has been confirmed by observation of the self-targeting of beams on scattering sites in water [Usp. Fiz. Nauk 168, 877–890 (1998) (in Russian)]. The large amplification provided by the conjugator leads to nonlinear distortion and shock formation in the conjugate field. These nonlinear effects are studied experimentally with measurements based on light diffraction for conjugated beams in water having intensities of 2 W/cm2 and frequencies near 5 MHz. Numerical simulations corresponding to experimental conditions take into account absorption, diffraction, nonlinearity, and the finite size of the conjugator. The simulations reveal the presence of shocks, yet accurate reversal of the incident field despite the strong waveform distortion [Phys. Acoust. (in press (1998)]. Potential applications of this technololgy are discussed. [Work supported by RFBR (Grants 96-02-17301, 98-02-16761), CRDF (Project RE1-270), and ONR.]
Numerical simulations based on the nonlinear parabolic wave equation are used to investigate time reversal of sound beams radiated by unfocused and focused sources. Emphasis is placed on nonlinear propagation distortion in the time-reversed beam, and specifically its effect on field reconstruction. Distortion of this kind, due to amplification during time reversal, has been observed in recent experiments [A. P. Brysev et al., Acoust. Phys. 44, 641-650 (1998)]. Effects of diffraction introduced by time-reversal mirrors with finite apertures are also considered. It is shown that even in the presence of shock formation, the ability of time reversal to retarget most of the energy on the source or focal region of the incident beam is quite robust.
The profile of a Bessel beam is J0(ρ), where J0 is the zeroth-order Bessel function and ρ is a dimensionless distance from the axis. The beam propagates without diffraction, a property that has stimulated interest in connection with medical ultrasound imaging. Previous analyses of second-harmonic generation in Bessel beams are limited to lossless media. Du, Zhang, and Zhu [Proc. 14th Intl. Symp. Nonlin. Acoust., edited by R. J. Wei (Nanjing U.P., Nanjing, 1996), pp. 189–194] showed that the beam profile of the second harmonic in the near field is given approximately by J20(ρ). Ding and Lu [Appl. Phys. Lett. 68, 608 (1996)] obtained J0(2ρ) for the far field. We provide a more general analysis of second-harmonic generation, first by investigating solutions for lossless propagation in greater detail, and second by including absorption. It is shown that the far-field beam profile is J0(2ρ) only for very small values of a characteristic absorption parameter. As the absorption parameter increases, the beam profile evolves toward a distribution given approximately (i.e., away from minima) by J20(ρ). Numerical results are presented for higher harmonics and for waveform distortion in a Bessel beam that forms a shock. [Work supported by ONR.]
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