Abstract

We theoretically demonstrate that long-period twisted elliptical fibers have the ability to change in a certain wavelength range the topological charge of the incoming field by two units. We also show that such fibers can generate charge-2 optical vortices from the incoming Gaussian beams.

© 2012 Optical Society of America

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References

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  1. M. Vasnetsov and K. Staliunas, Optical Vortices, Vol. 228 of Horizons of World Physics (Nova Science, 1999).
  2. M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
    [CrossRef]
  3. M. W. Beijersbergen, L. Allen, H. E. L. O. van der Ween, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
    [CrossRef]
  4. M. W. Bejersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
    [CrossRef]
  5. V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
    [CrossRef]
  6. Ya. V. Izdebskaya, V. G. Shvedov, and A. V. Volyar, “Generation of higher-order optical vortices by a dielectric wedge,” Opt. Lett. 30, 2472–2474 (2005).
    [CrossRef]
  7. K. J. Webb and M.-C. Yang, “Generation and control of optical vortices using left-handed materials,” Phys. Rev. E 74, 016601 (2006).
    [CrossRef]
  8. I. Skab, Y. Vasylkiv, B. Zapeka, V. Savaryn, and R. Vlokh, “Appearance of singularities of optical fields under torsion of crystals containing threefold symmetry axes,” J. Opt. Soc. Am. A 28, 1331–1340 (2011).
    [CrossRef]
  9. L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
    [CrossRef]
  10. L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
    [CrossRef]
  11. T. D. McGloin, N. B. Simpson, and M. J. Padgett, “Transfer of orbital angular momentum from a stressed fiber-optic waveguide to a light beam,” Appl. Opt. 37, 469–472 (1998).
    [CrossRef]
  12. C. D. Poole, C. D. Townsend, and K. T. Nelson, “Helical-grating two-mode fiber spatial-mode coupler,” J. Lightwave Technol. 9, 598–604 (1991).
    [CrossRef]
  13. K. S. Lee, “Coupling analysis of spiral fiber gratings,” Opt. Commun. 198, 317–324 (2001).
    [CrossRef]
  14. K. S. Lee and T. Erdogan, “Mode coupling in spiral fibre gratings,” Electron. Lett. 37, 156–157 (2001).
    [CrossRef]
  15. K. S. Lee and T. Erdogan, “Fiber mode conversion with tilted gratings in an optical fiber,” J. Opt. Soc. Am. A 18, 1176–1185 (2001).
    [CrossRef]
  16. C. N. Alexeyev, B. P. Lapin, and M. A. Yavorsky, “Helical core optical fibers maintaining propagation of a solitary optical vortex,” Phys. Rev. A 78, 013813 (2008).
    [CrossRef]
  17. C. N. Alexeyev, B. P. Lapin, and M. A. Yavorsky, “The effect of spin—orbit coupling on the structure of the stopband in helical-core optical fibres,” J. Opt. A: Pure Appl. Opt. 10, 085006 (2008).
    [CrossRef]
  18. C. N. Alexeyev, T. A. Fadeyeva, B. P. Lapin, and M. A. Yavorsky, “Generation of optical vortices in layered helical waveguides,” Phys. Rev. A 83, 063820 (2011).
    [CrossRef]
  19. V. I. Kopp, V. M. Churikov, G. Zhang, J. Singer, C. W. Draper, N. Chao, D. Neugroschl, and A. Z. Genack, “Single- and double-helix chiral fiber sensors,” J. Opt. Soc. Am. B 24, A48–A52 (2007).
    [CrossRef]
  20. S. Oh, K. R. Lee, U.-C. Paek, and Y. Chung, “Fabrication of helical long-period fiber gratings by use of a CO2 laser,” Opt. Lett. 29, 1464–1466 (2004).
    [CrossRef]
  21. V. I. Kopp and A. Z. Genack, “Double-helix chiral fibers,” Opt. Lett. 28, 1876–1878 (2003).
    [CrossRef]
  22. C. N. Alexeyev and M. A. Yavorsky, “Optical vortices and the higher order modes of twisted strongly elliptical optical fibres,” J. Opt. A: Pure Appl. Opt. 6, 824–832 (2004).
    [CrossRef]
  23. A. W. Snyder and J. D. Love, Optical Waveguide Theory(Chapman and Hall, 1985).
  24. A. S. Davydov, Quantum Mechanics (Pergamon, 1976).

2011 (3)

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

C. N. Alexeyev, T. A. Fadeyeva, B. P. Lapin, and M. A. Yavorsky, “Generation of optical vortices in layered helical waveguides,” Phys. Rev. A 83, 063820 (2011).
[CrossRef]

I. Skab, Y. Vasylkiv, B. Zapeka, V. Savaryn, and R. Vlokh, “Appearance of singularities of optical fields under torsion of crystals containing threefold symmetry axes,” J. Opt. Soc. Am. A 28, 1331–1340 (2011).
[CrossRef]

2008 (2)

C. N. Alexeyev, B. P. Lapin, and M. A. Yavorsky, “Helical core optical fibers maintaining propagation of a solitary optical vortex,” Phys. Rev. A 78, 013813 (2008).
[CrossRef]

C. N. Alexeyev, B. P. Lapin, and M. A. Yavorsky, “The effect of spin—orbit coupling on the structure of the stopband in helical-core optical fibres,” J. Opt. A: Pure Appl. Opt. 10, 085006 (2008).
[CrossRef]

2007 (1)

2006 (2)

K. J. Webb and M.-C. Yang, “Generation and control of optical vortices using left-handed materials,” Phys. Rev. E 74, 016601 (2006).
[CrossRef]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

2005 (1)

2004 (2)

S. Oh, K. R. Lee, U.-C. Paek, and Y. Chung, “Fabrication of helical long-period fiber gratings by use of a CO2 laser,” Opt. Lett. 29, 1464–1466 (2004).
[CrossRef]

C. N. Alexeyev and M. A. Yavorsky, “Optical vortices and the higher order modes of twisted strongly elliptical optical fibres,” J. Opt. A: Pure Appl. Opt. 6, 824–832 (2004).
[CrossRef]

2003 (1)

2001 (4)

K. S. Lee and T. Erdogan, “Fiber mode conversion with tilted gratings in an optical fiber,” J. Opt. Soc. Am. A 18, 1176–1185 (2001).
[CrossRef]

K. S. Lee, “Coupling analysis of spiral fiber gratings,” Opt. Commun. 198, 317–324 (2001).
[CrossRef]

K. S. Lee and T. Erdogan, “Mode coupling in spiral fibre gratings,” Electron. Lett. 37, 156–157 (2001).
[CrossRef]

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[CrossRef]

1998 (1)

1994 (1)

M. W. Bejersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

1993 (1)

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

1992 (1)

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

1991 (1)

C. D. Poole, C. D. Townsend, and K. T. Nelson, “Helical-grating two-mode fiber spatial-mode coupler,” J. Lightwave Technol. 9, 598–604 (1991).
[CrossRef]

Alexeyev, C. N.

C. N. Alexeyev, T. A. Fadeyeva, B. P. Lapin, and M. A. Yavorsky, “Generation of optical vortices in layered helical waveguides,” Phys. Rev. A 83, 063820 (2011).
[CrossRef]

C. N. Alexeyev, B. P. Lapin, and M. A. Yavorsky, “The effect of spin—orbit coupling on the structure of the stopband in helical-core optical fibres,” J. Opt. A: Pure Appl. Opt. 10, 085006 (2008).
[CrossRef]

C. N. Alexeyev, B. P. Lapin, and M. A. Yavorsky, “Helical core optical fibers maintaining propagation of a solitary optical vortex,” Phys. Rev. A 78, 013813 (2008).
[CrossRef]

C. N. Alexeyev and M. A. Yavorsky, “Optical vortices and the higher order modes of twisted strongly elliptical optical fibres,” J. Opt. A: Pure Appl. Opt. 6, 824–832 (2004).
[CrossRef]

Allen, L.

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

Bazhenov, V. Yu.

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

Beijersbergen, M. W.

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

Bejersbergen, M. W.

M. W. Bejersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Chao, N.

Chung, Y.

Churikov, V. M.

Coerwinkel, R. P. C.

M. W. Bejersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Davydov, A. S.

A. S. Davydov, Quantum Mechanics (Pergamon, 1976).

Draper, C. W.

Erdogan, T.

K. S. Lee and T. Erdogan, “Fiber mode conversion with tilted gratings in an optical fiber,” J. Opt. Soc. Am. A 18, 1176–1185 (2001).
[CrossRef]

K. S. Lee and T. Erdogan, “Mode coupling in spiral fibre gratings,” Electron. Lett. 37, 156–157 (2001).
[CrossRef]

Fadeyeva, T. A.

C. N. Alexeyev, T. A. Fadeyeva, B. P. Lapin, and M. A. Yavorsky, “Generation of optical vortices in layered helical waveguides,” Phys. Rev. A 83, 063820 (2011).
[CrossRef]

Genack, A. Z.

Izdebskaya, Ya. V.

Karimi, E.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

Kopp, V. I.

Kristensen, M.

M. W. Bejersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Lapin, B. P.

C. N. Alexeyev, T. A. Fadeyeva, B. P. Lapin, and M. A. Yavorsky, “Generation of optical vortices in layered helical waveguides,” Phys. Rev. A 83, 063820 (2011).
[CrossRef]

C. N. Alexeyev, B. P. Lapin, and M. A. Yavorsky, “The effect of spin—orbit coupling on the structure of the stopband in helical-core optical fibres,” J. Opt. A: Pure Appl. Opt. 10, 085006 (2008).
[CrossRef]

C. N. Alexeyev, B. P. Lapin, and M. A. Yavorsky, “Helical core optical fibers maintaining propagation of a solitary optical vortex,” Phys. Rev. A 78, 013813 (2008).
[CrossRef]

Lee, K. R.

Lee, K. S.

K. S. Lee, “Coupling analysis of spiral fiber gratings,” Opt. Commun. 198, 317–324 (2001).
[CrossRef]

K. S. Lee and T. Erdogan, “Fiber mode conversion with tilted gratings in an optical fiber,” J. Opt. Soc. Am. A 18, 1176–1185 (2001).
[CrossRef]

K. S. Lee and T. Erdogan, “Mode coupling in spiral fibre gratings,” Electron. Lett. 37, 156–157 (2001).
[CrossRef]

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory(Chapman and Hall, 1985).

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

Marrucci, L.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

McGloin, T. D.

Nagali, E.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

Nelson, K. T.

C. D. Poole, C. D. Townsend, and K. T. Nelson, “Helical-grating two-mode fiber spatial-mode coupler,” J. Lightwave Technol. 9, 598–604 (1991).
[CrossRef]

Neugroschl, D.

Oh, S.

Padgett, M. J.

Paek, U.-C.

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

Piccirillo, B.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

Poole, C. D.

C. D. Poole, C. D. Townsend, and K. T. Nelson, “Helical-grating two-mode fiber spatial-mode coupler,” J. Lightwave Technol. 9, 598–604 (1991).
[CrossRef]

Santamato, E.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

Savaryn, V.

Sciarrino, F.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

Shvedov, V. G.

Simpson, N. B.

Singer, J.

Skab, I.

Slussarenko, S.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory(Chapman and Hall, 1985).

Soskin, M. S.

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[CrossRef]

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

Staliunas, K.

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

Townsend, C. D.

C. D. Poole, C. D. Townsend, and K. T. Nelson, “Helical-grating two-mode fiber spatial-mode coupler,” J. Lightwave Technol. 9, 598–604 (1991).
[CrossRef]

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

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

Vasnetsov, M.

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

Vasnetsov, M. V.

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[CrossRef]

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

Vasylkiv, Y.

Vlokh, R.

Volyar, A. V.

Webb, K. J.

K. J. Webb and M.-C. Yang, “Generation and control of optical vortices using left-handed materials,” Phys. Rev. E 74, 016601 (2006).
[CrossRef]

Woerdman, J. P.

M. W. Bejersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

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

Yang, M.-C.

K. J. Webb and M.-C. Yang, “Generation and control of optical vortices using left-handed materials,” Phys. Rev. E 74, 016601 (2006).
[CrossRef]

Yavorsky, M. A.

C. N. Alexeyev, T. A. Fadeyeva, B. P. Lapin, and M. A. Yavorsky, “Generation of optical vortices in layered helical waveguides,” Phys. Rev. A 83, 063820 (2011).
[CrossRef]

C. N. Alexeyev, B. P. Lapin, and M. A. Yavorsky, “The effect of spin—orbit coupling on the structure of the stopband in helical-core optical fibres,” J. Opt. A: Pure Appl. Opt. 10, 085006 (2008).
[CrossRef]

C. N. Alexeyev, B. P. Lapin, and M. A. Yavorsky, “Helical core optical fibers maintaining propagation of a solitary optical vortex,” Phys. Rev. A 78, 013813 (2008).
[CrossRef]

C. N. Alexeyev and M. A. Yavorsky, “Optical vortices and the higher order modes of twisted strongly elliptical optical fibres,” J. Opt. A: Pure Appl. Opt. 6, 824–832 (2004).
[CrossRef]

Zapeka, B.

Zhang, G.

Appl. Opt. (1)

Electron. Lett. (1)

K. S. Lee and T. Erdogan, “Mode coupling in spiral fibre gratings,” Electron. Lett. 37, 156–157 (2001).
[CrossRef]

J. Lightwave Technol. (1)

C. D. Poole, C. D. Townsend, and K. T. Nelson, “Helical-grating two-mode fiber spatial-mode coupler,” J. Lightwave Technol. 9, 598–604 (1991).
[CrossRef]

J. Mod. Opt. (1)

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

J. Opt. (1)

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (2)

C. N. Alexeyev and M. A. Yavorsky, “Optical vortices and the higher order modes of twisted strongly elliptical optical fibres,” J. Opt. A: Pure Appl. Opt. 6, 824–832 (2004).
[CrossRef]

C. N. Alexeyev, B. P. Lapin, and M. A. Yavorsky, “The effect of spin—orbit coupling on the structure of the stopband in helical-core optical fibres,” J. Opt. A: Pure Appl. Opt. 10, 085006 (2008).
[CrossRef]

J. Opt. Soc. Am. A (2)

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

Opt. Commun. (3)

K. S. Lee, “Coupling analysis of spiral fiber gratings,” Opt. Commun. 198, 317–324 (2001).
[CrossRef]

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

M. W. Bejersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (2)

C. N. Alexeyev, T. A. Fadeyeva, B. P. Lapin, and M. A. Yavorsky, “Generation of optical vortices in layered helical waveguides,” Phys. Rev. A 83, 063820 (2011).
[CrossRef]

C. N. Alexeyev, B. P. Lapin, and M. A. Yavorsky, “Helical core optical fibers maintaining propagation of a solitary optical vortex,” Phys. Rev. A 78, 013813 (2008).
[CrossRef]

Phys. Rev. E (1)

K. J. Webb and M.-C. Yang, “Generation and control of optical vortices using left-handed materials,” Phys. Rev. E 74, 016601 (2006).
[CrossRef]

Phys. Rev. Lett. (1)

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef]

Prog. Opt. (1)

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[CrossRef]

Other (3)

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

A. W. Snyder and J. D. Love, Optical Waveguide Theory(Chapman and Hall, 1985).

A. S. Davydov, Quantum Mechanics (Pergamon, 1976).

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Figures (5)

Fig. 1.
Fig. 1.

Geometry of the problem: Schematically shown generation of the optical vortex OV from the incident Gaussian beam GB. Insets show intensity distribution of the corresponding fields.

Fig. 2.
Fig. 2.

Zero-approximation spectra of twisted elliptical fiber modes versus lattice vector q. The type of the mode is indicated at the corresponding curve. Insets show repulsion of spectral branches due to the effect of mode coupling; the fiber’s parameters are: nco=1.5, Δ=0.01, δ=0.05, r0=8λ0, λ0=632.8nm, qq0=11216.845m1.

Fig. 3.
Fig. 3.

Transmission coefficients |Pi|2 for the outcoming modes |1,0 (a) and |1,2 (b) versus wavelength of the incoming field |1,0; the fiber’s length d=2.55mm, Δ=0.01, δ=0.05, r0=8λ0, λ0=632.8nm, H=0,56mm. The coefficient for the outcoming mode |1,2 is negligibly small (not shown).

Fig. 4.
Fig. 4.

Transmission coefficients for the outcoming modes |1,0 (a) and |1,2 (b) versus wavelength of the incoming field |1,0; the fiber’s length d=207mm. The other parameters are the same as in Fig. 3.

Fig. 5.
Fig. 5.

Transmission coefficient for the outcoming vortex |1,3 versus wavelength of the incoming field |1,1. Fiber parameters: d=209.3mm, nco=1.5, Δ=0.01, δ=0.05, r0=8λ0, λ0=632.8nm, H=0.44mm.

Equations (18)

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

n2(r,φ,z)=nco2(12Δf(r))2nco2Δδrfrcos(2(φqz)),
ΔE⃗t+k2n2E⃗t=0,
{2r˜2+1r˜r˜+1r˜22φ˜2+(z˜qφ˜)2+k2n˜2(r˜)2k2nco2r˜Δδfr˜cos2φ˜}E⃗t=0,
{2r˜2+1r˜r˜+1r˜22φ˜2+(iβqφ˜)2+k2n˜22k2nco2r˜Δδfr˜cos2φ˜}et(r˜,φ˜)=0.
(H^0+V^)|e=β2|e,
H^0=(2r˜2+1r˜r˜+1r˜22φ˜2+k2n˜22iβqφ˜+q22φ˜2),
|σ,l=(1iσ)exp(ilφ˜)Fl(r),
(2r2+1rr+k2n˜2l2r2β˜l2)Fl(r)=0.
βl(1,2)=±β˜l+lq.
β1,2=±β˜0,β3,4=±β˜2+2q,β5,6=±β˜22q.
(β˜02β2AAβ˜22(β2q)2)x⃗a=0,
(2β˜0δAA2β˜2(2εδ))x⃗a=0.
β1,2(a)=β˜0+ε±ε2+Γ2,β1,2(b)=β˜0ε±ε2+Γ2,
|Ψ1a={c1|1,0exp[i(β˜0+ε)z]+c2|1,2exp[i(β˜2ε)z]}exp(izε2+Γ2),|Ψ2a={c2|1,0exp[i(β˜0+ε)z]+c1|1,2exp[i(β˜2ε)z]}exp(izε2+Γ2),
|Ψ1b={c2|1,0exp[i(β˜0+ε)z]+c1|1,2exp[i(β˜2ε)z]}exp(izε2+Γ2),|Ψ2b={c1|1,0exp[i(β˜0+ε)z]+c2|1,2exp[i(β˜2ε)z]}exp(izε2+Γ2).
|Φ1(z0)=|1,0eikz+R1|1,0eikz+R2|1,2eikz+R3|1,2eikz.
|Φ2=T1|ψ1a+T2|ψ2a+T3|ψ1b+T4|ψ2b+T5|1,2eiβ˜2z+T6|1,2eiβ˜2z,
|Φ3(zd)=(P1|1,0+P2|1,2+P3|1,2)eik(zd).

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