Abstract

A vortex lens is a useful optical device having applications ranging from astronomy to microscopy. Current vortex masks operate across a narrow bandwidth. Two design schemes are proposed for creating a vortex across a bandwidth exceeding 100nm in the visible region of the spectrum.

© 2006 Optical Society of America

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References

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  1. M.Vasnetsov and K.Staliunas, eds., Optical Vortices, Vol. 228 of Horizons in World Physics (Nova Science, 1999).
  2. S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
    [CrossRef]
  3. A. Ashkin, Biophys. J. 61, 569 (1992).
    [CrossRef] [PubMed]
  4. V. Westphal and S. W. Hell, Phys. Rev. Lett. 94, 143903 (2005).
    [CrossRef] [PubMed]
  5. M. D. Levenson, T. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and S. M. Tan, J. Microlithogr., Microfabr., Microsyst. 3, 293 (2004).
    [CrossRef]
  6. H. Sasada and M. Okamoto, Phys. Rev. A 68, 12323 (2003).
    [CrossRef]
  7. J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, Phys. Rev. Lett. 92, 013601 (2004).
    [CrossRef] [PubMed]
  8. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 27, 285 (2002).
    [CrossRef]
  9. G. Foo, D. M. Palacios, and G. A. Swartzlander, Opt. Lett. 30, 3308 (2005).
    [CrossRef]
  10. D. Mawet, P. Riaud, O. Absil, and J. Surdej, Astrophys. J. 633, 1191 (2005).
    [CrossRef]
  11. D. M. Palacios, "The low-order aberration sensitivity of an optical vortex coronagraph," submitted to Opt. Lett.
  12. M. V. Berry and S. Klein, Proc. Natl. Acad. Sci. U.S.A. 93, 2614 (1996).
    [CrossRef] [PubMed]
  13. G. Gbur, T. D. Visser, and E. Wolf, Phys. Rev. Lett. 88, 013901 (2002).
    [CrossRef] [PubMed]
  14. G. Popescu and A. Dogariu, Phys. Rev. Lett. 88, 183902 (2002).
    [CrossRef] [PubMed]
  15. J. T. Foley and E. Wolf, J. Opt. Soc. Am. A 19, 2510 (2002).
    [CrossRef]
  16. G. A. Swartzlander, Jr., and J. Schmit, Phys. Rev. Lett. 93, 093901 (2004).
    [CrossRef] [PubMed]
  17. G. A. Swartzlander, Jr., Opt. Lett. 30, 2876 (2005).
    [CrossRef] [PubMed]
  18. F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, Chaos, Solitons Fractals 4, 1575 (1994).
    [CrossRef]
  19. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
    [CrossRef]
  20. J. W. Sung, H. Hockel, H. D. Brown, and E. G. Johnson, Appl. Opt. 45, 33 (2006).
    [CrossRef] [PubMed]

2006 (1)

2005 (4)

G. A. Swartzlander, Jr., Opt. Lett. 30, 2876 (2005).
[CrossRef] [PubMed]

G. Foo, D. M. Palacios, and G. A. Swartzlander, Opt. Lett. 30, 3308 (2005).
[CrossRef]

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

D. Mawet, P. Riaud, O. Absil, and J. Surdej, Astrophys. J. 633, 1191 (2005).
[CrossRef]

2004 (3)

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] [PubMed]

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

2003 (1)

H. Sasada and M. Okamoto, Phys. Rev. A 68, 12323 (2003).
[CrossRef]

2002 (4)

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

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

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, Opt. Lett. 27, 285 (2002).
[CrossRef]

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

1996 (1)

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

1994 (2)

F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, Chaos, Solitons Fractals 4, 1575 (1994).
[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

1992 (2)

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]

Absil, O.

D. Mawet, P. Riaud, O. Absil, and J. Surdej, Astrophys. J. 633, 1191 (2005).
[CrossRef]

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] [PubMed]

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Berry, M. V.

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

Biener, G.

Bomzon, Z.

Brennan, T. M.

F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, Chaos, Solitons Fractals 4, 1575 (1994).
[CrossRef]

Brown, H. D.

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[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] [PubMed]

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]

de Colstoun, F. B.

F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, Chaos, Solitons Fractals 4, 1575 (1994).
[CrossRef]

Dogariu, A.

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

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]

Fedorov, A. V.

F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, Chaos, Solitons Fractals 4, 1575 (1994).
[CrossRef]

Foley, J. T.

Foo, G.

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] [PubMed]

Gbur, G.

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

Hammons, B. G.

F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, Chaos, Solitons Fractals 4, 1575 (1994).
[CrossRef]

Hasman, E.

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] [PubMed]

Hockel, H.

Johnson, E. G.

Khitrova, G.

F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, Chaos, Solitons Fractals 4, 1575 (1994).
[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] [PubMed]

Kleiner, V.

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]

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[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] [PubMed]

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]

Lowry, C.

F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, Chaos, Solitons Fractals 4, 1575 (1994).
[CrossRef]

Maker, P. D.

F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, Chaos, Solitons Fractals 4, 1575 (1994).
[CrossRef]

Mawet, D.

D. Mawet, P. Riaud, O. Absil, and J. Surdej, Astrophys. J. 633, 1191 (2005).
[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]

Nelson, T. R.

F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, Chaos, Solitons Fractals 4, 1575 (1994).
[CrossRef]

Okamoto, M.

H. Sasada and M. Okamoto, Phys. Rev. A 68, 12323 (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] [PubMed]

Palacios, D. M.

G. Foo, D. M. Palacios, and G. A. Swartzlander, Opt. Lett. 30, 3308 (2005).
[CrossRef]

D. M. Palacios, "The low-order aberration sensitivity of an optical vortex coronagraph," submitted to Opt. Lett.

Popescu, G.

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

Riaud, P.

D. Mawet, P. Riaud, O. Absil, and J. Surdej, Astrophys. J. 633, 1191 (2005).
[CrossRef]

Sasada, H.

H. Sasada and M. Okamoto, Phys. Rev. A 68, 12323 (2003).
[CrossRef]

Schmit, J.

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

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] [PubMed]

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]

Sung, J. W.

Surdej, J.

D. Mawet, P. Riaud, O. Absil, and J. Surdej, Astrophys. J. 633, 1191 (2005).
[CrossRef]

Swartzlander, G. A.

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] [PubMed]

Westphal, V.

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

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Wolf, E.

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

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

Appl. Opt. (1)

Astrophys. J. (1)

D. Mawet, P. Riaud, O. Absil, and J. Surdej, Astrophys. J. 633, 1191 (2005).
[CrossRef]

Biophys. J. (1)

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

Chaos, Solitons Fractals (1)

F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, Chaos, Solitons Fractals 4, 1575 (1994).
[CrossRef]

J. Microlithogr., Microfabr., Microsyst. (1)

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. (1)

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. Soc. Am. A (1)

Opt. Commun. (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (1)

H. Sasada and M. Okamoto, Phys. Rev. A 68, 12323 (2003).
[CrossRef]

Phys. Rev. Lett. (5)

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

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

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

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

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

Proc. Natl. Acad. Sci. U.S.A. (1)

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

Other (2)

D. M. Palacios, "The low-order aberration sensitivity of an optical vortex coronagraph," submitted to Opt. Lett.

M.Vasnetsov and K.Staliunas, eds., Optical Vortices, Vol. 228 of Horizons in World Physics (Nova Science, 1999).

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Figures (3)

Fig. 1
Fig. 1

Lower substrate and upper superstrate layers of vortex lenses (phase masks) of topological charge m and pitch multiplicity μ, where (A) μ = 1 and (B) μ = 2 .

Fig. 2
Fig. 2

Achromatic vortex lens having m 0 = 2 at λ 0 = 0.55 μ m for Schott glasses N-LASF44 and N-SF14. (A) Relative topological charge and transmission into the intended mode. (B) Transmission into neighboring modes.

Fig. 3
Fig. 3

Achromatic vortex lens having m 0 = 2 at λ = 0.5 μ m and 0.6 μ m for Schott glasses F5 and N-SK15. (A) Relative topological charge and transmission into the intended mode. (B) Transmission into neighboring modes.

Tables (1)

Tables Icon

Table 1 Pairs of Schott Glasses that Satisfy the Achromatic Condition to Within ε at a Single Wavelength ( 550 nm ) and at Two Wavelengths (500 and 600 nm )

Equations (8)

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

t ( θ , ω ) = exp [ i m ( ω ) θ ] = 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 ,
d ( θ ) = d base + θ m 0 λ 0 2 π ( n s n 0 ) λ 0 ,
Δ d = m 0 λ 0 μ ( n s n 0 ) λ 0 .
m ( λ ) = m 0 ( λ 0 λ ) ( n s n 0 λ ( n s n 0 ) λ 0 .
n ( λ ) = n ( λ 0 ) + n ( λ 0 ) ( λ λ 0 ) + ( 1 2 ) n ( λ 0 ) ( λ λ 0 ) 2 ,
n ( λ ) = n ( λ 0 ) + n ( λ 0 ) δ λ + ( 1 2 ) n ( λ 0 ) δ λ 2 ,
( λ max λ min ) 1 λ min λ max C m 0 2 d λ = 0.998 .

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