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By the Gaussian expansion approach we investigate fundamental- and second-harmonic generation in practical Bessel beams of several lobes. The analysis is based on the integral solutions of the Khokhlov-Zabolotskaya-Kuznetsov equation under the quasilinear approximation. The influence of the medium attenuation on beam profile is considered. Numerical results show that the absorption parameter has a significant effect on the beam profile of the second harmonic. Under certain circumstances, the second harmonic of a practical Bessel beam with several lobes still has the main properties of an ideal Bessel beam of infinite aperture when it propagates within its depth of field.
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Keywords:
- second-harmonic generation /
- Bessel sound beam /
- sound attenuation /
- sound beams of limited aperture
[1] Durnin J 1987 J. Opt. Soc. Am. A 4 651
[2] [3] Durnin J, Miceli J J, Eberly J H 1987 Phys. Rev. Lett. 58 1499
[4] [5] Vasara A, Turunen J, Friberg A T 1989 J. Opt. Soc. Am. A 6 1748
[6] Wulle T, Herminghaus S 1993 Phys. Rev. Lett. 70 1401
[7] [8] [9] Arlt J, Dholakia K, Allen L, Padgett M J 1999 Phys. Rev. E 60 2438
[10] [11] Hsu D K, Margetan F J, Thompson D O 1989 Appl. Phys. Lett. 55 2066
[12] Compbell J A, Soloway S 1990 J. Acoust. Soc. Am. 88 2667
[13] [14] Stepanishen P R, Sun J 1997 J. Acoust. Soc. Am. 102 3308
[15] [16] [17] Lu J Y, Greenleaf J F 1991 Ultrasound Med. Biol. 17 265
[18] [19] Lu J Y 1997 IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 44 839
[20] Lu J Y 1998 IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 45 84
[21] [22] Ding D S, Lu Z H 1996 Appl. Phys. Lett. 71 723
[23] [24] [25] Synnevag J, Holm S 1998 IEEE Ultrason. Symp. 2 1885
[26] [27] Ding D S, Liu X J 1998 J. Acoust. Soc. Am. 104 2645
[28] Ding D S, Wang S J, Wang Y J 1999 J. Appl. Phys. 86 1716
[29] [30] Ding D S, Lu J Y 2000 Phys. Rev. E 61 2038
[31] [32] [33] Ding D S, Lu J Y 2000 J. Acoust. Soc. Am. 107 1212
[34] Cunningham K B, Hamilton M F 2000 J. Acoust. Soc. Am. 108 519
[35] [36] Ding D S, Xu J Y, Wang Y J 2002 Chin. Phys. Lett. 19 689
[37] [38] Huang J H, Ding D S, Hsu Y S 2009 J. Sound Vib. 328 148
[39] [40] Holm S, Prieur F 2010 J. Acoust. Soc. Am. 128 1015
[41] [42] [43] Aanonsen S I, Barkve T, Tjotta J N, Tjotta S 1984 J. Acoust. Soc. Am. 75 749
[44] Hamilton M F, Tjotta J N, Tjotta S 1985 J. Acoust. Soc. Am. 78 202
[45] [46] [47] Hamilton M F 1998 Sound Beams in Nonlinear Acoustics (Boston: Academic) Chap 8
[48] Wen J J, Breazeale M A 1988 J. Acoust. Soc. Am. 83 1752
[49] [50] Huang D, Breazeale M A 1999 J. Acoust. Soc. Am. 106 1771
[51] [52] Ding D S, Liu X J 1999 J. Opt. Soc. Am. A 16 1286
[53] [54] [55] Ding D S, Zhang Y, Liu J Q 2003 J. Acoust. Soc. Am. 113 3043
[56] Ding D S, Zhang Y 2004 J. Acoust. Soc. Am. 116 1401
[57] [58] [59] Ding D S, Tong X J, He P Z 2005 J. Acoust. Soc. Am. 118 608
[60] [61] Ding D S, Xu J Y 2006 IEEE Trans. Ultrason. Ferroelectr. Freq. Contr. 53 246
[62] Ding D S, Shui Y G, Lin J B, Zhang D 1996 J. Acoust. Soc. Am. 100 727
[63] [64] Ding D S 2000 J. Acoust Soc. Am. 108 2759
[65] [66] Ding D S 2004 J. Acoust. Soc. Am. 115 35
[67] -
[1] Durnin J 1987 J. Opt. Soc. Am. A 4 651
[2] [3] Durnin J, Miceli J J, Eberly J H 1987 Phys. Rev. Lett. 58 1499
[4] [5] Vasara A, Turunen J, Friberg A T 1989 J. Opt. Soc. Am. A 6 1748
[6] Wulle T, Herminghaus S 1993 Phys. Rev. Lett. 70 1401
[7] [8] [9] Arlt J, Dholakia K, Allen L, Padgett M J 1999 Phys. Rev. E 60 2438
[10] [11] Hsu D K, Margetan F J, Thompson D O 1989 Appl. Phys. Lett. 55 2066
[12] Compbell J A, Soloway S 1990 J. Acoust. Soc. Am. 88 2667
[13] [14] Stepanishen P R, Sun J 1997 J. Acoust. Soc. Am. 102 3308
[15] [16] [17] Lu J Y, Greenleaf J F 1991 Ultrasound Med. Biol. 17 265
[18] [19] Lu J Y 1997 IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 44 839
[20] Lu J Y 1998 IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 45 84
[21] [22] Ding D S, Lu Z H 1996 Appl. Phys. Lett. 71 723
[23] [24] [25] Synnevag J, Holm S 1998 IEEE Ultrason. Symp. 2 1885
[26] [27] Ding D S, Liu X J 1998 J. Acoust. Soc. Am. 104 2645
[28] Ding D S, Wang S J, Wang Y J 1999 J. Appl. Phys. 86 1716
[29] [30] Ding D S, Lu J Y 2000 Phys. Rev. E 61 2038
[31] [32] [33] Ding D S, Lu J Y 2000 J. Acoust. Soc. Am. 107 1212
[34] Cunningham K B, Hamilton M F 2000 J. Acoust. Soc. Am. 108 519
[35] [36] Ding D S, Xu J Y, Wang Y J 2002 Chin. Phys. Lett. 19 689
[37] [38] Huang J H, Ding D S, Hsu Y S 2009 J. Sound Vib. 328 148
[39] [40] Holm S, Prieur F 2010 J. Acoust. Soc. Am. 128 1015
[41] [42] [43] Aanonsen S I, Barkve T, Tjotta J N, Tjotta S 1984 J. Acoust. Soc. Am. 75 749
[44] Hamilton M F, Tjotta J N, Tjotta S 1985 J. Acoust. Soc. Am. 78 202
[45] [46] [47] Hamilton M F 1998 Sound Beams in Nonlinear Acoustics (Boston: Academic) Chap 8
[48] Wen J J, Breazeale M A 1988 J. Acoust. Soc. Am. 83 1752
[49] [50] Huang D, Breazeale M A 1999 J. Acoust. Soc. Am. 106 1771
[51] [52] Ding D S, Liu X J 1999 J. Opt. Soc. Am. A 16 1286
[53] [54] [55] Ding D S, Zhang Y, Liu J Q 2003 J. Acoust. Soc. Am. 113 3043
[56] Ding D S, Zhang Y 2004 J. Acoust. Soc. Am. 116 1401
[57] [58] [59] Ding D S, Tong X J, He P Z 2005 J. Acoust. Soc. Am. 118 608
[60] [61] Ding D S, Xu J Y 2006 IEEE Trans. Ultrason. Ferroelectr. Freq. Contr. 53 246
[62] Ding D S, Shui Y G, Lin J B, Zhang D 1996 J. Acoust. Soc. Am. 100 727
[63] [64] Ding D S 2000 J. Acoust Soc. Am. 108 2759
[65] [66] Ding D S 2004 J. Acoust. Soc. Am. 115 35
[67]
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