Abstract

We deduce and study an analytical expression for Fresnel diffraction of a plane wave by a spiral phase plate (SPP) that imparts an arbitrary-order phase singularity on the light field. Estimates for the optical vortex radius that depends on the singularity’s integer order n (also termed topological charge, or order of the dislocation) have been derived. The near-zero vortex intensity is shown to be proportional to ρ2n, where ρ is the radial coordinate. Also, an analytical expression for Fresnel diffraction of the Gaussian beam by a SPP with nth-order singularity is analyzed. The far-field intensity distribution is derived. The radius of maximal intensity is shown to depend on the singularity number. The behavior of the Gaussian beam intensity after a SPP with second-order singularity (n=2) is studied in more detail. The parameters of the light beams generated numerically with the Fresnel transform and via analytical formulas are in good agreement. In addition, the light fields with first- and second-order singularities were generated by a 32-level SPP fabricated on the resist by use of the electron-beam lithography technique.

© 2005 Optical Society of America

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    [CrossRef]
  2. S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
    [CrossRef]
  3. V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
    [CrossRef]
  4. I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, J. Turunen, “Generation of rotating Gauss–Laguerre modes with binary-phase diffractive optics,” J. Mod. Opt. 46, 227–238 (1999).
  18. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristiensen, J. P. Woerdman, “Helical-wave front laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
    [CrossRef]
  19. S. S. R. Oemrawsingh, J. A. W. van Houwelingen, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, G. W. Hooft, “Production and characterization of spiral phase plates for optical wavelengths,” Appl. Opt. 43, 688–694 (2004).
    [CrossRef] [PubMed]

2004

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, J. Turunen, “Generation and selection of laser beams represented by a superposition of two angular harmonics,” J. Mod. Opt. 51, 761–773 (2004).
[CrossRef]

S. S. R. Oemrawsingh, J. A. W. van Houwelingen, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, G. W. Hooft, “Production and characterization of spiral phase plates for optical wavelengths,” Appl. Opt. 43, 688–694 (2004).
[CrossRef] [PubMed]

2003

2001

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Paakkonen, J. Simonen, J. Turunen, “An analysis of the angular momentum of a light field in terms of angular harmonics,” J. Mod. Opt. 48, 1543–1557 (2001).
[CrossRef]

2000

1999

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, J. Turunen, “Generation of rotating Gauss–Laguerre modes with binary-phase diffractive optics,” J. Mod. Opt. 46, 227–238 (1999).

1998

1997

E. Abramochkin, N. Losevsky, V. Volostnikov, “Generation of spiral-type laser beams,” Opt. Commun. 141, 59–64 (1997).
[CrossRef]

D. Rozas, C. T. Law, G. A. Swartzlander, “Propagation dynamics of optical vortices,” J. Opt. Soc. Am. B 14, 3054–3065 (1997).
[CrossRef]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

1994

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristiensen, J. P. Woerdman, “Helical-wave front laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

1993

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
[CrossRef]

1992

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[CrossRef] [PubMed]

1974

J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
[CrossRef]

Abramochkin, E.

E. Abramochkin, N. Losevsky, V. Volostnikov, “Generation of spiral-type laser beams,” Opt. Commun. 141, 59–64 (1997).
[CrossRef]

Allen, L.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

Basistiy, I. V.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

Bazhenov, V. Yu.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristiensen, J. P. Woerdman, “Helical-wave front laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

Berry, M. V.

J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
[CrossRef]

Brichkov, Y. A.

P. Prudnikov, Y. A. Brichkov, O. I. Marichev, Integrals and Series. Special Functions (Nauka, Moscow, 1983).

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristiensen, J. P. Woerdman, “Helical-wave front laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Davidson, N.

Eliel, E. R.

Friesem, A. A.

Gorshkov, V. N.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

Heckenberg, N. R.

Honkanen, M.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, J. Turunen, “Generation of rotating Gauss–Laguerre modes with binary-phase diffractive optics,” J. Mod. Opt. 46, 227–238 (1999).

Hooft, G. W.

Indebetouw, G.

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
[CrossRef]

Jefimovs, K.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, J. Turunen, “Generation and selection of laser beams represented by a superposition of two angular harmonics,” J. Mod. Opt. 51, 761–773 (2004).
[CrossRef]

Khonina, S. N.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, J. Turunen, “Generation and selection of laser beams represented by a superposition of two angular harmonics,” J. Mod. Opt. 51, 761–773 (2004).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Paakkonen, J. Simonen, J. Turunen, “An analysis of the angular momentum of a light field in terms of angular harmonics,” J. Mod. Opt. 48, 1543–1557 (2001).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, J. Turunen, “Generation of rotating Gauss–Laguerre modes with binary-phase diffractive optics,” J. Mod. Opt. 46, 227–238 (1999).

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

Kloosterboer, J. G.

Kotlyar, V. V.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, J. Turunen, “Generation and selection of laser beams represented by a superposition of two angular harmonics,” J. Mod. Opt. 51, 761–773 (2004).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Paakkonen, J. Simonen, J. Turunen, “An analysis of the angular momentum of a light field in terms of angular harmonics,” J. Mod. Opt. 48, 1543–1557 (2001).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, J. Turunen, “Generation of rotating Gauss–Laguerre modes with binary-phase diffractive optics,” J. Mod. Opt. 46, 227–238 (1999).

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

Kristiensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristiensen, J. P. Woerdman, “Helical-wave front laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Lautanen, J.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, J. Turunen, “Generation of rotating Gauss–Laguerre modes with binary-phase diffractive optics,” J. Mod. Opt. 46, 227–238 (1999).

Law, C. T.

Losevsky, N.

E. Abramochkin, N. Losevsky, V. Volostnikov, “Generation of spiral-type laser beams,” Opt. Commun. 141, 59–64 (1997).
[CrossRef]

Marichev, O. I.

P. Prudnikov, Y. A. Brichkov, O. I. Marichev, Integrals and Series. Special Functions (Nauka, Moscow, 1983).

McDuff, R.

Nugent, K. A.

Nye, J. F.

J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
[CrossRef]

Oemrawsingh, S. S. R.

Oron, R.

Paakkonen, P.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Paakkonen, J. Simonen, J. Turunen, “An analysis of the angular momentum of a light field in terms of angular harmonics,” J. Mod. Opt. 48, 1543–1557 (2001).
[CrossRef]

Peele, G.

Prudnikov, P.

P. Prudnikov, Y. A. Brichkov, O. I. Marichev, Integrals and Series. Special Functions (Nauka, Moscow, 1983).

Rozas, D.

Sacks, Z. S.

Shinkaryev, M. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

Simonen, J.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Paakkonen, J. Simonen, J. Turunen, “An analysis of the angular momentum of a light field in terms of angular harmonics,” J. Mod. Opt. 48, 1543–1557 (2001).
[CrossRef]

Smith, C. P.

Soifer, V. A.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, J. Turunen, “Generation and selection of laser beams represented by a superposition of two angular harmonics,” J. Mod. Opt. 51, 761–773 (2004).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Paakkonen, J. Simonen, J. Turunen, “An analysis of the angular momentum of a light field in terms of angular harmonics,” J. Mod. Opt. 48, 1543–1557 (2001).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, J. Turunen, “Generation of rotating Gauss–Laguerre modes with binary-phase diffractive optics,” J. Mod. Opt. 46, 227–238 (1999).

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

Soskin, M. S.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

Swartzlander, G. A.

Turunen, J.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, J. Turunen, “Generation and selection of laser beams represented by a superposition of two angular harmonics,” J. Mod. Opt. 51, 761–773 (2004).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Paakkonen, J. Simonen, J. Turunen, “An analysis of the angular momentum of a light field in terms of angular harmonics,” J. Mod. Opt. 48, 1543–1557 (2001).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, J. Turunen, “Generation of rotating Gauss–Laguerre modes with binary-phase diffractive optics,” J. Mod. Opt. 46, 227–238 (1999).

Uspleniev, G. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

van der Veen, H. E. L. O.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

van Houwelingen, J. A. W.

Vasnetsov, M. V.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

Verstegen, E. J. K.

Volostnikov, V.

E. Abramochkin, N. Losevsky, V. Volostnikov, “Generation of spiral-type laser beams,” Opt. Commun. 141, 59–64 (1997).
[CrossRef]

White, A. G.

Woerdman, J. P.

S. S. R. Oemrawsingh, J. A. W. van Houwelingen, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, G. W. Hooft, “Production and characterization of spiral phase plates for optical wavelengths,” Appl. Opt. 43, 688–694 (2004).
[CrossRef] [PubMed]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristiensen, J. P. Woerdman, “Helical-wave front laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

Appl. Opt.

J. Mod. Opt.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Paakkonen, J. Simonen, J. Turunen, “An analysis of the angular momentum of a light field in terms of angular harmonics,” J. Mod. Opt. 48, 1543–1557 (2001).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, M. Honkanen, J. Lautanen, J. Turunen, “Generation of rotating Gauss–Laguerre modes with binary-phase diffractive optics,” J. Mod. Opt. 46, 227–238 (1999).

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, J. Turunen, “Generation and selection of laser beams represented by a superposition of two angular harmonics,” J. Mod. Opt. 51, 761–773 (2004).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristiensen, J. P. Woerdman, “Helical-wave front laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

E. Abramochkin, N. Losevsky, V. Volostnikov, “Generation of spiral-type laser beams,” Opt. Commun. 141, 59–64 (1997).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

Proc. R. Soc. London Ser. A

J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
[CrossRef]

Other

P. Prudnikov, Y. A. Brichkov, O. I. Marichev, Integrals and Series. Special Functions (Nauka, Moscow, 1983).

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