Abstract

A pulse transmitted through a helical vortex phase mask undergoes a temporal Hilbert transform. The fluence transmitted into the unfavorable plane wave mode is found to increase as the square of the bandwidth and, to first order, is independent of the topological charge.

© 2005 Optical Society of America

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References

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  1. S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
    [CrossRef]
  2. A. Ashkin, Biophys. J. 61, 569 (1992).
    [CrossRef] [PubMed]
  3. H. Sasada and M. Okamoto, Phys. Rev. A 68, 012323 (2003).
    [CrossRef]
  4. J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, Phys. Rev. Lett. 92, 013601 (2004).
    [CrossRef]
  5. V. Westphal and S. W. Hell, Phys. Rev. Lett. 94, 143903 (2005).
    [CrossRef]
  6. M. D. Levenson, T. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and S. M. Tan, J. Microlithogr., Microfabr., Microsyst. 3, 293 (2004).
    [CrossRef]
  7. M. V. Berry and S. Klein, Proc. Natl. Acad. Sci. U.S.A. 93, 2614 (1996).
    [CrossRef]
  8. G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2002).
    [CrossRef]
  9. G. Popescu and A. Dogariu, Phys. Rev. Lett. 88, 183902 (2002).
    [CrossRef]
  10. J. T. Foley and E. Wolf, J. Opt. Soc. Am. A 19, 2510 (2002).
    [CrossRef]
  11. G. A. Swartzlander and J. Schmit, Phys. Rev. Lett. 93, 093901 (2004).
    [CrossRef]
  12. G. A. Swartzlander, Opt. Lett. 26, 497 (2001).
    [CrossRef]
  13. For a review of singular optics, see M. Vasnetsov and K. Staliunas, eds., Optical Vortices, Vol. 228 of Horizons in World Physics (Nova Science, 1999), andG. A. Swartzlander, “Singular optics/optical vortex references,” http://www.u.arizona.edu/~grovers/SO/so.html.
  14. M. V. Berry, J. Opt. A, Pure Appl. Opt. 6, 259 (2004).
    [CrossRef]
  15. D. Palacios, “An optical vortex coherence filter,” PhD. dissertation (Worcester Polytechnic Institute, June 2004).

2005

V. Westphal and S. W. Hell, Phys. Rev. Lett. 94, 143903 (2005).
[CrossRef]

2004

M. D. Levenson, T. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and S. M. Tan, J. Microlithogr., Microfabr., Microsyst. 3, 293 (2004).
[CrossRef]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, Phys. Rev. Lett. 92, 013601 (2004).
[CrossRef]

G. A. Swartzlander and J. Schmit, Phys. Rev. Lett. 93, 093901 (2004).
[CrossRef]

M. V. Berry, J. Opt. A, Pure Appl. Opt. 6, 259 (2004).
[CrossRef]

2003

H. Sasada and M. Okamoto, Phys. Rev. A 68, 012323 (2003).
[CrossRef]

2002

G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef]

G. Popescu and A. Dogariu, Phys. Rev. Lett. 88, 183902 (2002).
[CrossRef]

J. T. Foley and E. Wolf, J. Opt. Soc. Am. A 19, 2510 (2002).
[CrossRef]

2001

1996

M. V. Berry and S. Klein, Proc. Natl. Acad. Sci. U.S.A. 93, 2614 (1996).
[CrossRef]

1992

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

A. Ashkin, Biophys. J. 61, 569 (1992).
[CrossRef] [PubMed]

Ashkin, A.

A. Ashkin, Biophys. J. 61, 569 (1992).
[CrossRef] [PubMed]

Barnett, S. M.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, Phys. Rev. Lett. 92, 013601 (2004).
[CrossRef]

Berry, M. V.

M. V. Berry, J. Opt. A, Pure Appl. Opt. 6, 259 (2004).
[CrossRef]

M. V. Berry and S. Klein, Proc. Natl. Acad. Sci. U.S.A. 93, 2614 (1996).
[CrossRef]

Courtial, J.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, Phys. Rev. Lett. 92, 013601 (2004).
[CrossRef]

Dai, G.

M. D. Levenson, T. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and S. M. Tan, J. Microlithogr., Microfabr., Microsyst. 3, 293 (2004).
[CrossRef]

Dogariu, A.

G. Popescu and A. Dogariu, Phys. Rev. Lett. 88, 183902 (2002).
[CrossRef]

Ebihara, T.

M. D. Levenson, T. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and S. M. Tan, J. Microlithogr., Microfabr., Microsyst. 3, 293 (2004).
[CrossRef]

Foley, J. T.

Franke-Arnold, S.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, Phys. Rev. Lett. 92, 013601 (2004).
[CrossRef]

Gbur, G.

G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef]

Hayashi, N.

M. D. Levenson, T. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and S. M. Tan, J. Microlithogr., Microfabr., Microsyst. 3, 293 (2004).
[CrossRef]

Hell, S. W.

V. Westphal and S. W. Hell, Phys. Rev. Lett. 94, 143903 (2005).
[CrossRef]

Khonina, S. N.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Klein, S.

M. V. Berry and S. Klein, Proc. Natl. Acad. Sci. U.S.A. 93, 2614 (1996).
[CrossRef]

Kotlyar, V. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Leach, J.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, Phys. Rev. Lett. 92, 013601 (2004).
[CrossRef]

Levenson, M. D.

M. D. Levenson, T. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and S. M. Tan, J. Microlithogr., Microfabr., Microsyst. 3, 293 (2004).
[CrossRef]

Morikawa, Y.

M. D. Levenson, T. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and S. M. Tan, J. Microlithogr., Microfabr., Microsyst. 3, 293 (2004).
[CrossRef]

Okamoto, M.

H. Sasada and M. Okamoto, Phys. Rev. A 68, 012323 (2003).
[CrossRef]

Padgett, M. J.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, Phys. Rev. Lett. 92, 013601 (2004).
[CrossRef]

Palacios, D.

D. Palacios, “An optical vortex coherence filter,” PhD. dissertation (Worcester Polytechnic Institute, June 2004).

Popescu, G.

G. Popescu and A. Dogariu, Phys. Rev. Lett. 88, 183902 (2002).
[CrossRef]

Sasada, H.

H. Sasada and M. Okamoto, Phys. Rev. A 68, 012323 (2003).
[CrossRef]

Schmit, J.

G. A. Swartzlander and J. Schmit, Phys. Rev. Lett. 93, 093901 (2004).
[CrossRef]

Shinkaryev, M. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Skeldon, K.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, Phys. Rev. Lett. 92, 013601 (2004).
[CrossRef]

Soifer, V. A.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Swartzlander, G. A.

G. A. Swartzlander and J. Schmit, Phys. Rev. Lett. 93, 093901 (2004).
[CrossRef]

G. A. Swartzlander, Opt. Lett. 26, 497 (2001).
[CrossRef]

Tan, S. M.

M. D. Levenson, T. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and S. M. Tan, J. Microlithogr., Microfabr., Microsyst. 3, 293 (2004).
[CrossRef]

Uspleniev, G. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Visser, T. D.

G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef]

Westphal, V.

V. Westphal and S. W. Hell, Phys. Rev. Lett. 94, 143903 (2005).
[CrossRef]

Wolf, E.

G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef]

J. T. Foley and E. Wolf, J. Opt. Soc. Am. A 19, 2510 (2002).
[CrossRef]

Biophys. J.

A. Ashkin, Biophys. J. 61, 569 (1992).
[CrossRef] [PubMed]

J. Microlithogr., Microfabr., Microsyst.

M. D. Levenson, T. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and S. M. Tan, J. Microlithogr., Microfabr., Microsyst. 3, 293 (2004).
[CrossRef]

J. Mod. Opt.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

J. Opt. A, Pure Appl. Opt.

M. V. Berry, J. Opt. A, Pure Appl. Opt. 6, 259 (2004).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Lett.

Phys. Rev. A

H. Sasada and M. Okamoto, Phys. Rev. A 68, 012323 (2003).
[CrossRef]

Phys. Rev. Lett.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, Phys. Rev. Lett. 92, 013601 (2004).
[CrossRef]

V. Westphal and S. W. Hell, Phys. Rev. Lett. 94, 143903 (2005).
[CrossRef]

G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2002).
[CrossRef]

G. Popescu and A. Dogariu, Phys. Rev. Lett. 88, 183902 (2002).
[CrossRef]

G. A. Swartzlander and J. Schmit, Phys. Rev. Lett. 93, 093901 (2004).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A.

M. V. Berry and S. Klein, Proc. Natl. Acad. Sci. U.S.A. 93, 2614 (1996).
[CrossRef]

Other

For a review of singular optics, see M. Vasnetsov and K. Staliunas, eds., Optical Vortices, Vol. 228 of Horizons in World Physics (Nova Science, 1999), andG. A. Swartzlander, “Singular optics/optical vortex references,” http://www.u.arizona.edu/~grovers/SO/so.html.

D. Palacios, “An optical vortex coherence filter,” PhD. dissertation (Worcester Polytechnic Institute, June 2004).

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Figures (2)

Fig. 1
Fig. 1

Vortex spectra for the orders l = 0 , + 1 , 1 for the case m 0 = 1 .

Fig. 2
Fig. 2

Transmitted fluence (joules per square centimeter) of the plane-wave mode through a vortex mask (design parameters, m 0 = 1 and ω 0 ), normalized to the net fluence of the input pulse having a uniform band-limited frequency distribution of half-width Δ ω and center Ω.

Equations (17)

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F m ( r , θ , z ) = A m ( r , z ) exp ( i m θ ) ,
t ( θ ) = exp ( i m θ ) .
d ( θ ) = d base + Δ d ( 1 θ 2 π ) ,
m ( ω ) = m 0 ω ω 0 [ n s ( ω ) n 0 ( ω ) n s ( ω 0 ) n 0 ( ω 0 ) ] ,
m ( ω ) = m 0 ω ω 0 .
t ( θ , ω ) = l = C l ( ω ) exp ( i l θ ) ,
C l ( ω ) = ( 2 π ) 1 π π t ( θ , ω ) exp ( i l θ ) d θ ,
C l ( ω ) = sinc ( m 0 π ω ω 0 l π ) .
E in ( r , θ , z ; t ) = G ( t ) F ( r , z ) exp ( i Ω t ) exp ( i k z z ) ,
g ( ω ) = G ( t ) exp ( i Ω t ) exp ( i ω t ) d t ,
G ( t ) exp ( i Ω t ) = 1 2 π g ( ω ) exp ( i ω t ) d ω .
E out ( r , θ , z = 0 ; t ) = l = E l ( r , θ , z = 0 ; t ) ,
E l ( r , θ , z = 0 ; t ) = G l ( t ) F ( r , z = 0 ) exp ( i l θ ) exp ( i Ω t ) ,
G l ( t ) = ( 2 π ) 1 exp ( i Ω t ) g ( ω ) C l ( ω ) exp ( i ω t ) d ω ,
g l ( ω ) = C l ( ω ) g ( ω ) .
η = E l = 0 ( r , θ , z = 0 ; t ) 2 d t E in ( r , θ , z = 0 ; t ) 2 d t = G l = 0 ( t ) 2 d t G ( t ) 2 d t = g l = 0 ( ω ) 2 d ω g ( ω ) 2 d ω .
η = 1 2 Δ ω Ω Δ ω Ω + Δ ω sinc 2 ( m 0 π ω Ω ) d ω = ( 1 2 ( m 0 π ) 2 Δ ω ) Δ ω Ω Δ ω Ω sin 2 ( m 0 π ω ) ( ω + 1 ) 2 d ω 1 3 ( Δ ω Ω ) 2 .

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