Abstract
There exists an intensive effort to design specific wave patterns in classical fields as well as in quantum chemistry 1–9. In particular, there are a number of physical situations such as internal material diagnostics and modifications10 where it would be useful to produce a specified acoustic wave structure within a solid by applying a pattern of forces on the solid’s surface. The surface loads are created by using lasers, electron beams as well as through transducer arrays 11–15, Waves in a solid are of two types as compressional and shear waves with respectively longitudinal and transverse propagation character. This added complexity offers in fact an additional flexibility for achieving a desired output. The design of a surface load pattern in both space and time for the coherent focusing of waves at a prescribed target volume at a prescribed time is studied in this paper. Posed in this manner, such a design is an inverse problem. In general, the guessing of the input surface load to achieve a prescribed wave pattern as output is very complicated and relies heavily on experience and intuition in the absence of a rational design procedure. The proposed scheme provides a rational design procedure to substitute intuition and to achieve constructions where intuition would fail. This is particularly true for generating coherent waves that interfere constructively as well as destructively in specific regions of space.
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References
J. N. Brittingham, J. Appl. Phys. 54, 1179 (1983).
R. W. Ziolkowski, Phys. Rev. A39, 2005(1989).
R. W. Ziolkowski, D. K. Lewis, B. D. Cook, Phys.Rev. Lett. 62,147 (1989).
P.Hillion, J. Appl.Phys 60, 2981 (1986); J. Math.Phys.28,1743 (1987).
T. T. Wu,J. Appl.Phys. 57, 2370 (1985); T.T. Wu, R.W.P. King and H.-M. Shen, J. Appl. Phys. 62, 4036 (1987).
J. Durnin, J. Opt. Soc. Am. A4, 651 (1987); J. Durnin, J. J. Miceli, Jr. and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
H. E. Moses, J. Math. Phys. 25, 1905 (1984); H. E. Moses and R.T. Prosser, IEEE Trans. Antenna Propag. AP-34, 188 (1988).
E. Heyman and L.P. Felsen, IEEE Trans. Antenna Propag. AP-34, 1602 (1986); E. Heyman and B. Z. Steinberg, J. Opt. Soc.Am.A4, 473 (1987); E. Heyman, B. Z. Steinberg and L. P. Felsen, J. Opt. Soc. Am. A4,2801 (1987).
S S. Shi, A. Woody, H. Rabitz, J. Chem. Phys. 88, 6870 (1988).
F. R. Breckenbridge, C. E. Tschiegg and M. Greenspan, J. Acoust. Soc. Am.57, 626 (1975); N. N. Hsu and S. C. Hardy, xxx in Elastic Waves and Non-Destructive Testing, Edited by Y. H. Pao (ASME, New York, 1978), pp. 85–106; For rewiev, see, e.g., R. B. Thompson, ASME J. Appl. Mech. 50, 1191 (1983).
H. W. Jones and H. W. Kwan, Ultrasonics 23, 63 (1985).
C. B. Scruby, R. J. Dewhurst, D. A. Hutchins and S. B. Palmer, J. Appl.Phys. 51, 6210 (1980); R. J. Dewhurst, D. A. Hutchins, S. B. Palmer and C. B. Scruby, J. Appl. Phys. Lett. 38, 677 (1981); J. Appl. Phys. 53, 4064 (1982).
R. M. White, J. Appl. Phys. 34, 3559 (1963); J. E. Sinclair, J. Phys.D: Appl. Phys. 12, 1309 (1979); L. R. F. Rose, J.,Acoust. Soc. Am. 75,723 (1984).
R. R. Boade and O. L. Burchett, J. Appl. Phys. 47, 3412 (1976); L. J. Balk, Can. J. Phys. 64, 1238 (1986).
A. J. A. Bruinsma, J. A. Vogel, Appl. Opt. 27, 4690 (1988).
D. G. Luenberger, “Introduction to Dynamical Systems: Theory, Models and Applications,” [Wiley, New York, 1979]; A. Bryson and Y. Ho, Applied Optimal Control, Blaisdell, Waltham, Mass. (1969)
A. C. Eringen, Mechanics of Continua John Wiley and Sons (1967)
Y. S. Kim, H. Rabitz, A. Askar, J. B. McManus, “Optimal control of acoustic waves in solids,”Accepted for publication,Phys.Rev.B,1991.
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Kim, Y.S., Rabitz, H., Askar, A., McManus, J.B. (1992). Designing Coherent Acoustic Waves by Optimal Control Theory. In: Bandrauk, A.D., Wallace, S.C. (eds) Coherence Phenomena in Atoms and Molecules in Laser Fields. NATO ASI Series, vol 287. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3364-1_35
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DOI: https://doi.org/10.1007/978-1-4615-3364-1_35
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