Nondiffracting X Waves-Exact Solutions to Free-Space Scalar Wave Equation and Their Finite Aperture Realizations

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

Volumn 39, Issue 1, 1992, Pages 19-31

  Lu, Jian Yu ^a   Greenleaf, James F ^a  

^a MAYO CLINIC   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC IMAGING; ACOUSTIC TRANSDUCERS--APPLICATIONS;

ELECTROMAGNETIC ENERGY TRANSMISSION; FINITE APERTURE REALIZATION; FREE-SPACE SCALAR WAVE EQUATION; NONDIFFRACTING ANNULAR ARRAY TRANSDUCER; NONDIFFRACTING X WAVES;

ELECTROMAGNETIC WAVES;

EID: 0026678389     PISSN: 08853010     EISSN: None     Source Type: Journal    
DOI: 10.1109/58.166806     Document Type: Article

References (41)

1. J. B. Brittingham, “Focus wave modes in homogeneous Maxwell's equations: transverse electric mode,” J. Appl. Phys., vol 54, no. 3, pp. 1179-1189, 1983.
2. R. W. Ziolkowski, “Exact solutions of the wave equation with complex source locations,” J. Math. Phys., vol. 26, no. 4, pp. 861-863, Apr., 1985.
3. R. W. Ziolkowski, D. K. Lewis, and B. D. Cook, “Evidence of localized wave transmission,” Phys. Rev. Lett., vol. 62, no. 2, pp. 147-150, Jan. 9, 1989.
4. A. M. Shaarawi, I. M. Besieris, and R. W. Ziolkowski, “Localized energy pulse train launched from an open, semi-infinite, circular waveguide,” J. Appl. Phys., vol. 65, no. 2, pp. 805-813, 1989.
5. I. M. Besieris, A. M. Shaarawi, and R. W. Ziolkowski, “A bidirectional traveling plane wave representation of exact solutions of the scalar wave equation,” J. Math. Phys., vol. 30, no. 6, pp. 1254-1269, 1989.
6. E. Heyman, B. Z. Steinberg, and L. B. Felsen, “Spectral analysis of focus wave modes,” J. Opt. Soc. Am. A, vol. 4, no. 11, pp. 2081-2091, Nov., 1987.
7. R. W. Ziolkowski, “Localized transmission of electromagnetic energy,” Phys. Rev. A., vol. 39, no. 4, pp. 2005-2033, Feb. 15, 1989.
8. J. V. Candy, R. W. Ziolkowski, and D. K. Lewis, “Transient waves: reconstruction and processing,” J. Acoust. Soc. Am., vol. 88, no. 5, pp. 2248-2258, Nov., 1990.
9. “Transient wave estimation: a multichannel deconvolution application,” J. Acoust. Soc. Am., vol. 88, no. 5, pp. 2235-2247, Nov., 1990.
10. R. W. Ziolkowski and D. K. Lewis, “Verification of the localized wave transmission effect,” J. Appl. Phys., vol. 68, no. 12, pp. 6083-6086, Dec. 15, 1990.
11. J. Durnin, “Exact solutions for nondiffracting beams-I: The scalar theory,” J. Opt. Soc., vol. 4, no. 4, pp. 651-654, 1987.
12. J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett., vol. 58, no. 15, pp. 1499-1501, Apr. 13, 1987.
13. J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, “Experiments with nondiffracting needle beams,” Optical Soc. Amer., Washington, DC, available from IEEE Service Center (cat. no. 87CH2391-1), Piscataway, NJ, p. 208, 1987.
14. G. Indebetow, “Nondiffracting optical fields: Some remarks on their analysis and synthesis,” J. Opt. Soc. Am. A, vol. 6, no. 1, pp. 150-152, Jan., 1989.
15. F. Gori, G. Guattari, and C. Padovani, “Model expansion for Jo-correlated Schell-model sources,” Optics Commun., vol. 64, no. 4, pp. 311-316, Nov. 15, 1987.
16. K. Uehara and H. Kikuchi, “Generation of near diffraction-free laser beams,” Appl. Physics B, vol. 48, pp. 125-129, 1989.
17. L. Vicari, “Truncation of nondiffracting beams,” Optics Commun., vol. 70, no. 4, pp. 263-266, Mar. 15, 1989.
18. M. Zahid and M. S. Zubairy, “Directionally of partially coherent Bessel-Gauss beams,” Optics Commun., vol. 70, no. 5, pp. 361-364, Apr. 1, 1989.
19. S. Y. Cai, A. Bhattacharjee, and T. C. Marshall, “ ‘Diffraction-free’ optical beams in inverse free electron laser acceleration,” Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors, and Associated Equipment, vol. 272, no. 1-2, pp. 481-184, Oct., 1988.
20. D. K. Hsu, F. J. Margetan, and D. O. Thompson, “Bessel beam ultrasonic transducer: fabrication method and experimental results,” Appl. Phys. Lett., vol. 55, no. 20, pp. 2066-2068, Nov. 13, 1989.
21. J. Lu and J. F. Greenleaf, “Ultrasonic nondiffracting transducer for medical imaging,” IEEE Trans. Ultrason., Ferroelec., Freq. Contr., vol. 37, no. 5, pp. 438-447, Sept. 1990.
22. “Pulse-echo imaging using a nondiffracting beam transducer,” U.S. Med. Biol., vol. 17, no. 3, pp. 265-281, May 1991.
23. “Evaluation of a nondiffracting transducer for tissue characterization,” in Proc. 1990 Ultrason. Symp., Honolulu, HI, 90CH2938-9, vol. 2, Dec. 4-7, 1990, pp. 795-798.
24. “A computational and experimental study of nondiffracting transducer for medical ultrasound,” Ultrason. Imag., vol. 12, no. 2, pp. 146-147, Apr. 1990. (abst)
25. “Simulation of imaging contrast of nondiffracting beam transducers”, J. Ultrasound Med., vol. 10, no. 3, (suppl), p. S4, Mar. 1991. (abst)
26. J. A. Campbell and S. Soloway, “Generation of a nondiffracting beam with frequency independent beam width,” J. Acoust. Soc. Am., vol. 88, no. 5, pp. 2467-2477, Nov., 1990.
27. J. H. Mcleod, “The Axicon: a new type of optical element,” J. Opt. Soc. Am., vol. 44, p. 592, 1954.
28. S. Fujiwara, “Optical properties of conic surfaces. I. Reflecting Cone,” J. Opt. Soc. Am., vol. 52, pp. 287-292, 1962.
29. C. B. Burckhardt, H. Hoffmann, and P. A. Grandchamp, “Ultrasound axicon: A device for focusing over a large depth,” J. Acoust. Soc. Am., vol. 54, no. 6, pp. 1628-1630, Dec., 1973.
30. K. Yamada and H. Shimizu, “Conical and toroidal piezoelectric polymer transducers for long range focusing,” IEEE Trans. Sonics Ultrason., vol. SU-30, p. 215, 1983.
31. M. S. Patterson and F. S. Foster, “Acoustic fields of conical radiators,” IEEE Trans. Sonics Ultrason., vol. SU-29, no. 2, pp. 83-92, Mar. 1982.
32. D. R. Dietz, “Apodized conical focusing for ultrasound imaging,” IEEE Trans. Sonics Ultrason., SU-29, no. 3, pp. 128-138, May 1982.
33. M. Moshfeghi, “Sidelobe suppression in annular array and axicon imaging systems,” J. Acoust. Soc. Am., vol. 83, no. 6, pp. 2202-2209, June 1988.
34. Jian-yu Lu and J. F. Greenleaf, “Experimental verification of Nondiffracting X waves,” IEEE Trans. Ultrason. Ferroelec., Freq. Contr., submitted for publication.
35. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, corrected and enlarged ed. New York: Academic, 1980, ch. 17.
36. A. V. Oppenheim and R. W. Schafer, Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, Inc., 1975, ch. 5.
37. R. Bracewell, The Fourier Transform and its Applications. New York: McGraw-Hill, 1965, chs. 4 and 6.
38. J. W. Goodman, Introduction to Fourier Optics. New York: McGraw-Hill, 1968, chs. 2-4.
39. T. K. Song and S. B. Park, “Analysis of broadband ultrasonic field response and its application to the design of focused annular array imaging systems,” Ultrason. Technol. 1987, Toyohashi Int. Conf. Ultrason. Technol, Toyohashi, Japan, Edited by Kohji Toda, MYU Res., Tokyo, 1987.
40. J. Lu and J. F. Greenleaf, “Nondiffracting electromagnetic X waves,” IEEE Trans. Antennas Propag., submitted for review.
41. P. M. Moise and H. Feshbach, Methods of Theoretical Physics, Part I. New York: McGraw-Hill, 1953, chs. 4 and 7.