Abstract

We propose an optical element: a phase-shifted Fresnel axicon for generation of multiple Bessel beams. By giving a binary phase modulation to the standard Fresnel axicon, the proposed element is generated. The phase profile of the binary phase modulation is engineered to generate two and three Bessel beams of equal intensities. This composite optical element is fabricated using electron beam direct writing. The performance of the fabricated device is evaluated using a semiconductor laser, and the generation of two and three Bessel beams is successfully demonstrated.

© 2012 Optical Society of America

Full Article  |  PDF Article

Corrections

A. Vijaykumar and S. Bhattacharya, "Phase shifted Fresnel axicon: erratum," Opt. Lett. 38, 458-458 (2013)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-38-4-458

References

  • View by:
  • |
  • |
  • |

  1. J. H. McLeod, J. Opt. Soc. Am. 44, 592 (1954).
    [CrossRef]
  2. J. H. McLeod, J. Opt. Soc. Am. 50, 166 (1960).
    [CrossRef]
  3. O. Ren and R. Birngruber, IEEE J. Quantum Electron. 26, 2305 (1990).
    [CrossRef]
  4. M. Florjanczyk and R. Tremblay, Opt. Commun. 73, 448 (1989).
    [CrossRef]
  5. M. Rioux, R. Tremblay, and P. A. Bélanger, Appl. Opt. 17, 1532 (1978).
    [CrossRef]
  6. S. K. Eah, W. Jhe, and Y. Arakawa, Rev. Sci. Instrum. 74, 4969 (2003).
    [CrossRef]
  7. V. V. Kotlyar, A. A. Kovalev, V. A. Soifer, C. Stewart Tuvey, and Jeffrey A. Davis, Opt. Lett. 32, 921 (2007).
    [CrossRef]
  8. A. Burvall, K. Kołacz, V. G. Alexander, Z. Jaroszewicz, and C. Dainty, Appl. Opt. 46, 312 (2007).
    [CrossRef]
  9. C. Yu, M. R. Wang, A. J. Varela, and B. Chen, Opt. Commun. 177, 369 (2000).
    [CrossRef]
  10. R. Grunwald, U. Griebner, F. Tschirschwitz, E. T. J. Nibbering, T. Elsaesser, V. Kebbel, H.-J. Hartmann, and W. Juptner, Opt. Lett. 25, 981 (2000).
    [CrossRef]
  11. I. Golub, Opt. Lett. 31, 1890 (2006).
    [CrossRef]
  12. K. Gourley, I. Golub, and B. Chebbi, Appl. Opt. 50, 303 (2011).
    [CrossRef]
  13. G. Roy and R. Tremblay, Opt. Commun. 34, 1(1980).
    [CrossRef]
  14. S. A. Rishton and D. P. Kern, J. Vac. Sci. Technol. B 5, 135 (1987).
    [CrossRef]
  15. T. K. Lean, J. Appl. Phys. 65, 1776 (1989).
    [CrossRef]
  16. T. Abe, S. Yamasaki, T. Yamaguchi, R. Yoshikawa, and T. Takigawa, Jpn. J. Appl. Phys. 30, 2965(1991).
    [CrossRef]

2011 (1)

2007 (2)

2006 (1)

2003 (1)

S. K. Eah, W. Jhe, and Y. Arakawa, Rev. Sci. Instrum. 74, 4969 (2003).
[CrossRef]

2000 (2)

1991 (1)

T. Abe, S. Yamasaki, T. Yamaguchi, R. Yoshikawa, and T. Takigawa, Jpn. J. Appl. Phys. 30, 2965(1991).
[CrossRef]

1990 (1)

O. Ren and R. Birngruber, IEEE J. Quantum Electron. 26, 2305 (1990).
[CrossRef]

1989 (2)

M. Florjanczyk and R. Tremblay, Opt. Commun. 73, 448 (1989).
[CrossRef]

T. K. Lean, J. Appl. Phys. 65, 1776 (1989).
[CrossRef]

1987 (1)

S. A. Rishton and D. P. Kern, J. Vac. Sci. Technol. B 5, 135 (1987).
[CrossRef]

1980 (1)

G. Roy and R. Tremblay, Opt. Commun. 34, 1(1980).
[CrossRef]

1978 (1)

1960 (1)

1954 (1)

Abe, T.

T. Abe, S. Yamasaki, T. Yamaguchi, R. Yoshikawa, and T. Takigawa, Jpn. J. Appl. Phys. 30, 2965(1991).
[CrossRef]

Alexander, V. G.

Arakawa, Y.

S. K. Eah, W. Jhe, and Y. Arakawa, Rev. Sci. Instrum. 74, 4969 (2003).
[CrossRef]

Bélanger, P. A.

Birngruber, R.

O. Ren and R. Birngruber, IEEE J. Quantum Electron. 26, 2305 (1990).
[CrossRef]

Burvall, A.

Chebbi, B.

Chen, B.

C. Yu, M. R. Wang, A. J. Varela, and B. Chen, Opt. Commun. 177, 369 (2000).
[CrossRef]

Dainty, C.

Davis, Jeffrey A.

Eah, S. K.

S. K. Eah, W. Jhe, and Y. Arakawa, Rev. Sci. Instrum. 74, 4969 (2003).
[CrossRef]

Elsaesser, T.

Florjanczyk, M.

M. Florjanczyk and R. Tremblay, Opt. Commun. 73, 448 (1989).
[CrossRef]

Golub, I.

Gourley, K.

Griebner, U.

Grunwald, R.

Hartmann, H.-J.

Jaroszewicz, Z.

Jhe, W.

S. K. Eah, W. Jhe, and Y. Arakawa, Rev. Sci. Instrum. 74, 4969 (2003).
[CrossRef]

Juptner, W.

Kebbel, V.

Kern, D. P.

S. A. Rishton and D. P. Kern, J. Vac. Sci. Technol. B 5, 135 (1987).
[CrossRef]

Kolacz, K.

Kotlyar, V. V.

Kovalev, A. A.

Lean, T. K.

T. K. Lean, J. Appl. Phys. 65, 1776 (1989).
[CrossRef]

McLeod, J. H.

Nibbering, E. T. J.

Ren, O.

O. Ren and R. Birngruber, IEEE J. Quantum Electron. 26, 2305 (1990).
[CrossRef]

Rioux, M.

Rishton, S. A.

S. A. Rishton and D. P. Kern, J. Vac. Sci. Technol. B 5, 135 (1987).
[CrossRef]

Roy, G.

G. Roy and R. Tremblay, Opt. Commun. 34, 1(1980).
[CrossRef]

Soifer, V. A.

Stewart Tuvey, C.

Takigawa, T.

T. Abe, S. Yamasaki, T. Yamaguchi, R. Yoshikawa, and T. Takigawa, Jpn. J. Appl. Phys. 30, 2965(1991).
[CrossRef]

Tremblay, R.

M. Florjanczyk and R. Tremblay, Opt. Commun. 73, 448 (1989).
[CrossRef]

G. Roy and R. Tremblay, Opt. Commun. 34, 1(1980).
[CrossRef]

M. Rioux, R. Tremblay, and P. A. Bélanger, Appl. Opt. 17, 1532 (1978).
[CrossRef]

Tschirschwitz, F.

Varela, A. J.

C. Yu, M. R. Wang, A. J. Varela, and B. Chen, Opt. Commun. 177, 369 (2000).
[CrossRef]

Wang, M. R.

C. Yu, M. R. Wang, A. J. Varela, and B. Chen, Opt. Commun. 177, 369 (2000).
[CrossRef]

Yamaguchi, T.

T. Abe, S. Yamasaki, T. Yamaguchi, R. Yoshikawa, and T. Takigawa, Jpn. J. Appl. Phys. 30, 2965(1991).
[CrossRef]

Yamasaki, S.

T. Abe, S. Yamasaki, T. Yamaguchi, R. Yoshikawa, and T. Takigawa, Jpn. J. Appl. Phys. 30, 2965(1991).
[CrossRef]

Yoshikawa, R.

T. Abe, S. Yamasaki, T. Yamaguchi, R. Yoshikawa, and T. Takigawa, Jpn. J. Appl. Phys. 30, 2965(1991).
[CrossRef]

Yu, C.

C. Yu, M. R. Wang, A. J. Varela, and B. Chen, Opt. Commun. 177, 369 (2000).
[CrossRef]

Appl. Opt. (3)

IEEE J. Quantum Electron. (1)

O. Ren and R. Birngruber, IEEE J. Quantum Electron. 26, 2305 (1990).
[CrossRef]

J. Appl. Phys. (1)

T. K. Lean, J. Appl. Phys. 65, 1776 (1989).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Vac. Sci. Technol. B (1)

S. A. Rishton and D. P. Kern, J. Vac. Sci. Technol. B 5, 135 (1987).
[CrossRef]

Jpn. J. Appl. Phys. (1)

T. Abe, S. Yamasaki, T. Yamaguchi, R. Yoshikawa, and T. Takigawa, Jpn. J. Appl. Phys. 30, 2965(1991).
[CrossRef]

Opt. Commun. (3)

G. Roy and R. Tremblay, Opt. Commun. 34, 1(1980).
[CrossRef]

M. Florjanczyk and R. Tremblay, Opt. Commun. 73, 448 (1989).
[CrossRef]

C. Yu, M. R. Wang, A. J. Varela, and B. Chen, Opt. Commun. 177, 369 (2000).
[CrossRef]

Opt. Lett. (3)

Rev. Sci. Instrum. (1)

S. K. Eah, W. Jhe, and Y. Arakawa, Rev. Sci. Instrum. 74, 4969 (2003).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

Schematic of the optical setup for generation of multiple Bessel beams.

Fig. 2.
Fig. 2.

Generation of PSFx phase from the phase profile of fraxicon (ΦF) and a binary phase modulation (ΦB).

Fig. 3.
Fig. 3.

Optical micrograph of phase-shifted fraxicon.

Fig. 4.
Fig. 4.

Cross-sectional image of the two Bessel beams and their intensity profile.

Fig. 5.
Fig. 5.

Cross-sectional image of the three Bessel beams and their intensity profile.

Equations (4)

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

I(r,z)=2πk(tΛ1)2(nr1)2zI0e2(nr1)2z2t2Λ12w02J02(k(nr1)rtΛ1),
r0=1.22λπsinβ,
β=arcsin(nrt[Λ12+t2]1/2)arctan(tΛ1).
ΦB(x)={Φ,nxΛ2xc<(nx+1/2)Λ20,(nx+1/2)Λ2xc<(nx+1)Λ2,nx=,2,1,0,1,2,,

Metrics