Abstract

A beam that resembles a Bessel beam on two scales is generated using a tunable acoustic gradient index of refraction (TAG) lens. The minor scale of the TAG-generated Bessel beam is nondiffracting and self-healing. The major scale of the beam diffracts while still forming a Bessel pattern due to the specific geometry of the TAG lens. The acoustic and optical theory behind the TAG lens is outlined, and the experimental beam itself is presented. The major and minor rings are explained, and the TAG beam is compared with both axicon-generated and conventionally focused Gaussian beams.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  16. E. McLeod and C. B. Arnold, "Mechanics and refractive power optimization of tunable acoustic gradient index lenses," in preparation.

2005 (2)

D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
[CrossRef]

T. Cizmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

2004 (3)

V. A. Soifer, V. V. Kotlyar, and S. N. Khonina, Phys. Part. Nucl. 35, 733 (2004).

K. A. Higginson, M. A. Costolo, and E. A. Rietman, Appl. Phys. Lett. 84, 843 (2004).
[CrossRef]

K. A. Higginson, M. A. Costolo, and E. A. Rietman, J. Appl. Phys. 95, 5896 (2004).
[CrossRef]

2003 (2)

K. Wang, L. Zeng, and C. Yin, Opt. Commun. 216, 99 (2003).
[CrossRef]

Z. Bouchal, Czech. J. Phys. 53, 537 (2003).
[CrossRef]

2002 (1)

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002).
[CrossRef]

2001 (1)

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, Opt. Commun. 197, 239 (2001).
[CrossRef]

1999 (2)

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 60, 2438 (1999).
[CrossRef]

T. Aruga, S. W. Li, S. Yoshikado, M. Takabe, and R. Li, Appl. Opt. 38, 3152 (1999).
[CrossRef]

1997 (1)

1996 (1)

S. P. Tewari, H. Huang, and R. W. Boyd, Phys. Rev. A 54, 2314 (1996).
[CrossRef] [PubMed]

1993 (1)

T. Wulle and S. Herminghaus, Phys. Rev. Lett. 70, 1401 (1993).
[CrossRef] [PubMed]

1987 (1)

Allen, L.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 60, 2438 (1999).
[CrossRef]

Arlt, J.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, Opt. Commun. 197, 239 (2001).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 60, 2438 (1999).
[CrossRef]

Arnold, C. B.

E. McLeod and C. B. Arnold, "Mechanics and refractive power optimization of tunable acoustic gradient index lenses," in preparation.

Aruga, T.

Bouchal, Z.

Z. Bouchal, Czech. J. Phys. 53, 537 (2003).
[CrossRef]

Boyd, R. W.

S. P. Tewari, H. Huang, and R. W. Boyd, Phys. Rev. A 54, 2314 (1996).
[CrossRef] [PubMed]

Chávez-Cerda, S.

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002).
[CrossRef]

Cizmár, T.

T. Cizmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

Costolo, M. A.

K. A. Higginson, M. A. Costolo, and E. A. Rietman, Appl. Phys. Lett. 84, 843 (2004).
[CrossRef]

K. A. Higginson, M. A. Costolo, and E. A. Rietman, J. Appl. Phys. 95, 5896 (2004).
[CrossRef]

Dholakia, K.

T. Cizmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
[CrossRef]

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002).
[CrossRef]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, Opt. Commun. 197, 239 (2001).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 60, 2438 (1999).
[CrossRef]

Durnin, J.

Garces-Chavez, V.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, Opt. Commun. 197, 239 (2001).
[CrossRef]

Garcés-Chávez, V.

T. Cizmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002).
[CrossRef]

Herminghaus, S.

T. Wulle and S. Herminghaus, Phys. Rev. Lett. 70, 1401 (1993).
[CrossRef] [PubMed]

Higginson, K. A.

K. A. Higginson, M. A. Costolo, and E. A. Rietman, Appl. Phys. Lett. 84, 843 (2004).
[CrossRef]

K. A. Higginson, M. A. Costolo, and E. A. Rietman, J. Appl. Phys. 95, 5896 (2004).
[CrossRef]

Huang, H.

S. P. Tewari, H. Huang, and R. W. Boyd, Phys. Rev. A 54, 2314 (1996).
[CrossRef] [PubMed]

Khonina, S. N.

V. A. Soifer, V. V. Kotlyar, and S. N. Khonina, Phys. Part. Nucl. 35, 733 (2004).

Kotlyar, V. V.

V. A. Soifer, V. V. Kotlyar, and S. N. Khonina, Phys. Part. Nucl. 35, 733 (2004).

Li, R.

Li, S. W.

Maier, M.

McGloin, D.

D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
[CrossRef]

McLeod, E.

E. McLeod and C. B. Arnold, "Mechanics and refractive power optimization of tunable acoustic gradient index lenses," in preparation.

Niggl, L.

Padgett, M. J.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 60, 2438 (1999).
[CrossRef]

Rietman, E. A.

K. A. Higginson, M. A. Costolo, and E. A. Rietman, Appl. Phys. Lett. 84, 843 (2004).
[CrossRef]

K. A. Higginson, M. A. Costolo, and E. A. Rietman, J. Appl. Phys. 95, 5896 (2004).
[CrossRef]

Sibbett, W.

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002).
[CrossRef]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, Opt. Commun. 197, 239 (2001).
[CrossRef]

Soifer, V. A.

V. A. Soifer, V. V. Kotlyar, and S. N. Khonina, Phys. Part. Nucl. 35, 733 (2004).

Takabe, M.

Tewari, S. P.

S. P. Tewari, H. Huang, and R. W. Boyd, Phys. Rev. A 54, 2314 (1996).
[CrossRef] [PubMed]

Volke-Sepulveda, K.

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002).
[CrossRef]

Wang, K.

K. Wang, L. Zeng, and C. Yin, Opt. Commun. 216, 99 (2003).
[CrossRef]

Wulle, T.

T. Wulle and S. Herminghaus, Phys. Rev. Lett. 70, 1401 (1993).
[CrossRef] [PubMed]

Yin, C.

K. Wang, L. Zeng, and C. Yin, Opt. Commun. 216, 99 (2003).
[CrossRef]

Yoshikado, S.

Zemánek, P.

T. Cizmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

Zeng, L.

K. Wang, L. Zeng, and C. Yin, Opt. Commun. 216, 99 (2003).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

K. A. Higginson, M. A. Costolo, and E. A. Rietman, Appl. Phys. Lett. 84, 843 (2004).
[CrossRef]

T. Cizmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

Contemp. Phys. (1)

D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
[CrossRef]

Czech. J. Phys. (1)

Z. Bouchal, Czech. J. Phys. 53, 537 (2003).
[CrossRef]

J. Appl. Phys. (1)

K. A. Higginson, M. A. Costolo, and E. A. Rietman, J. Appl. Phys. 95, 5896 (2004).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (2)

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, Opt. Commun. 197, 239 (2001).
[CrossRef]

K. Wang, L. Zeng, and C. Yin, Opt. Commun. 216, 99 (2003).
[CrossRef]

Opt. Lett. (1)

Phys. Part. Nucl. (1)

V. A. Soifer, V. V. Kotlyar, and S. N. Khonina, Phys. Part. Nucl. 35, 733 (2004).

Phys. Rev. A (3)

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002).
[CrossRef]

S. P. Tewari, H. Huang, and R. W. Boyd, Phys. Rev. A 54, 2314 (1996).
[CrossRef] [PubMed]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 60, 2438 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

T. Wulle and S. Herminghaus, Phys. Rev. Lett. 70, 1401 (1993).
[CrossRef] [PubMed]

Other (1)

E. McLeod and C. B. Arnold, "Mechanics and refractive power optimization of tunable acoustic gradient index lenses," in preparation.

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Figures (4)

Fig. 1
Fig. 1

Experimental major and minor rings of the multiscale Bessel beam created by the TAG lens. The beam is imaged at a distance of 80 cm behind the back face of the lens. The TAG lens is driven at 257.0 kHz and 74.4 V pp . There are two major rings visible here.

Fig. 2
Fig. 2

Cross-section of the TAG lens showing its assembly.

Fig. 3
Fig. 3

Comparison between theoretical and experimental TAG beam and a simulated axicon. The experimental data are taken from Fig. 1, and the model uses n A = 4.4 × 10 5 . In these units, the theoretical TAG has a peak intensity of 1, and the axicon has a peak intensity of 1.32. The beams have been normalized to have equal power within a radius of 1.5 mm , the approximate limit of the central TAG minor scale Bessel beam.

Fig. 4
Fig. 4

Radial coordinate of the first local intensity minimum. For the Gaussian beam, the beam radius is the 1 e radius. The laser wavelength used here is 650 nm , and the TAG lens is driven at 74.4 V pp at 265.7 kHz . The axicon has a cone angle of 179.50°, and the simulated TAG beam uses n A = 5.5 × 10 5 .

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

n ( r , t ) = n 0 + n A J 0 ( ω f r v ) sin ( ω f t ) ,
I ( x img , y img , t ) = z 2 2 λ 0 2 ϵ 0 μ 0 U 0 ( x 0 , y 0 ) e i k 0 [ d + n ( x 0 , y 0 , t ) L ] d 2 d x 0 d y 0 2 ,
d = [ z 2 + ( x img x 0 ) 2 + ( y img y 0 ) 2 ] 1 2

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