An Ultrasonic Analog for a Random Laser
Colleagues: Oleg Lobkis Research Scientist UIUC, Alexey Yamilov Professor U Missouri
We report measurements on ultrasonic systems analogous to random lasers. One system entails unstable ultrasonic feedback between distinct transducers, another involves a spontaneously emitting piezoelectric device that can also emit by stimulation. Both are found to exhibit behaviors similar to those of lasers. Over a wide range of parameters we observe narrow single emission lines, sensitivity to linear cavity properties, complex multi-mode emissions, and line narrowing. Line widths are more narrow than we can measure. Theory indicates they have natural widths of the order of 10^-9 Hz. See our JASA preprint on Larsen effect. See also a Preprint on entrainment and stimulated emission. There is an early version of our work on this at arXiv. Here find a brief discussion.
Stochastic Elastic Waves
Our longstanding interest in diffuse linear waves(funded by the NSF and the ONR) now has four relatively distinct sub efforts. Multiple Scattering, diffusion, and localization of ultrasound in solids. Ray chaos, level statistics, and response statistics in elastic wave "cavities." Stochastic structural vibrations in the mid frequency domain of complex systems, and Phase correlations of diffuse seismic and ultrasonic fields.
Multiple Scattering, diffusion, and localization of ultrasound in solids.
Energy distribution at times long after the action of a transient point tone burst source. The concentration near the source position is apparent. Results are from a numerical simulation of waves in a 2-d cavity with a rough boundary. From "Weak Anderson Localization and Enhanced Backscatter in Reverberation Rooms and Quantum Dots," J. Acoust Soc. Am., 96, 3186-3190 (1994)
Colleague: Oleg Lobkis, Research Scientist UIUC
Our work here dates to the 1980's, when the principles of equipartition and diffusion (in polycrystals and slurries) were established. This was followed by an unequivocal laboratory demonstration of Anderson localization of elastic waves in 2-d, and a concomitant study of localization in the time domain, and in the presence of dissipation. [R. Weaver, "Anderson Localization of Ultrasound," Wave Motion, 12, 129-142(1990)].
Radiative transfer equations were developed for elastic waves [ e.g. J. A. Turner and R.L. Weaver, " Radiative Transfer of Ultrasound," J.Acoust.Soc.Am. 96, 3654-74 (1994). More recent interest has focussed on enhanced backscatter ("Weak Anderson Localization") of elastic waves[ Richard L. Weaver, Oleg I. Lobkis "Enhanced Backscattering and Modal Echo of Reverberant Elastic Waves," Phys Rev Lett 84, 4942-5 (May 22, 2000)], and on localization in coupled elastic wave reverberation rooms[Richard L. Weaver and Oleg I. Lobkis , "Anderson Localization in Coupled Reverberation Rooms," J Sound Vibr 231 (4) 1111-1134 (2000).
Ray chaos, level statistics, and response statistics in elastic wave "cavities."
Colleagues: Dr Igor Rozhkov U KY; Oleg Lobkis, Research Scientist UIUC; Yan Fyodorov, Professor of Mathematics Brunel University London; Olivier Legrand, University of Nice, France
A decades-old puzzle as to the signature within the linear, and thus non chaotic, wave equation of the presence of ray chaos appears to have been clarified by recent acceptance of the Bohigas-Casati conjecture that ray chaos corresponds to the relevance of Random Matrix Theory. That is, the statistics of the eigensolutions of ray-chaotic structures are identical to those of the Gaussain Orthogonal Ensemble of random matrices. This was first demonstrated as relevant for elastic wave systems in "Spectral Statistics in Elastodynamics," J. Acoust. Soc. Am., 85, 1005-1013 (1989). One of the most striking features of these statistics is "spectral rigidity," in which eigenvalues tend to space themselves evenly, even over long ranges. This has consequencies for predictions of variance of reverberant responses, a subject for which there is a long history of failure on the part of theory. We are now attempting to improve that theory by extending Random Matrix theory to this long standing problem. An initial theoretical and laboratory effort [Oleg I. Lobkis, Richard L. Weaver, and Igor Rozhkov, "Power Variances and Decay Curvature in a Reverberant System," 237 281-302, J Sound Vibr (2000)] has shown that the eigenmodes of generic damped systems are not real, and that their complexity is critical for understanding response variance. We are now attemping to apply Supersymmetric Grassman integration techniques to better model generic dissipative structures.
Phase correlations of diffuse seismic and ultrasonic fields.
Colleagues: Dr Eric Larose, Postdoctoral Researcher; Oleg Lobkis, Research Scientist; Bart vanTiggelen U J Fourier Grenoble; Michel Campillo, U J Fourier, Grenoble
That fully diffuse fields have correlations equivalent to transient responses is not widely appreciated. This has been demonstrated to be the case in a recent PRL [Oleg I Lobkis and Richard L Weaver, "Ultrasonics without a source, Thermal fluctuation correlations at MHz frequencies," Phys Rev Lettvol87 art. no. 134301 (2001) ] where conventional piezoelectric receivers detected thermal motions with amplitudes of femptometers, motions with correlations identical to conventional pulse-echo waveforms. Other work has demonstrated that correlations of diffuse fields generated by distant deterministic sources also reveal local responses. At present we are engaged in studying the correlations of diffuse seismic signals [ See Physical Review Focus article ], in the hopes of extracting local lithographic structure. The radio program Science Update discussed this work in its show of Dec 28, 2001. This production of the American Association for the Advancement of Science ( 33K Real Audio File from 12/28/01) said that "Noise gets a bad rap as something unpleasant and to be eliminated. But now, one scientist has found something interesting lurking in the fuzz."
The work was also covered by an article in the Chicago Tribune Jan 07, 2002 and in the Elsevier publication MaterialsToday Jan 2002 p12.
Stochastic structural vibrations in the mid frequency domain of complex systems
Colleagues: Dr Igor Rozhkov U KY; Nicholas Wolff, Graduate Research Assistant; Alexei Akolzin, Graduate Research Assistant
This project investigates the statistics of vibrational and acoustic energy, its mean flow and its fluctuations, in complex irregular reverberant structures. The work is conceived with a view towards improved statistical energy theories for the mid-frequency range in such structures, and involves numerical simulations, analytic theory and laboratory measurements. The project consists of two parts. Methods for estimating flow of mean energy, and its distribution in frequency are beign developed. For undamped systems the method has already proven itself capable[R L Weaver, "Equipartition and mean square responses in large undamped structures," J Acoust Soc Am. 110 894-903 (2001) ] of describing gradual secular variations of spectral energy density that lie outside the capabilities of conventional Statistical Energy Analysis. The project also investigates the familiar rapid fluctuations in response spectra whose details cannot be predicted precisely without precise and reliable information about the structure, but whose statistics are presumably universal. These two thrusts are complementary in the sense that the first predicts mean energy, and the second considers the fluctuations around the mean, thus describing the variance and reliability of the predicted mean.
Phase Oscillators
This needs a write-up