Abstract

We study the structure of l=1 modes of strongly anisotropic coiled weakly guiding optical fibers. By solving the vector wave equation within the framework of the perturbation theory with degeneracy, we analytically establish the expressions for modes and their polarization corrections. We show that, at certain parameters of the fiber helix, the l=1 modes are represented by almost pure optical vortices that maintain a linear polarization in the Frenet frame. We demonstrate that, in this case, the propagation constants comprise geometrically induced terms that are proportional to the orbital angular momentum (OAM) of the mode. We show that the vortex modes acquire upon propagation additional topological phases proportional to their intrinsic OAM and to the solid angle subtended by one helix coil. The presence of such a topological phase results in rotation (at a constant polarization) of the intensity patterns; after one coil the rotation angle equals the solid angle subtended by a coil.

© 2007 Optical Society of America

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    [CrossRef] [PubMed]
  50. I. V. Kataevskaya and N. D. Kundikova, "Influence of the helical shape of a fibre waveguide on the propagation of light," Quantum Electron. 25, 927-928 (1995).
    [CrossRef]
  51. C. N. Alexeyev and M. A. Yavorsky, "Topological phase evolving from the orbital angular momentum of "coiled" quantum vortices," J. Opt. A, Pure Appl. Opt. 8, 752-758 (2006).
    [CrossRef]

2007 (4)

A. Ya. Bekshaev, M. S. Soskin, "Transverse energy flows in vectorial fields of paraxial beams with singularities," Opt. Commun. 271, 332-348 (2007).
[CrossRef]

C. N. Alexeyev, A. V. Volyar, and M. A. Yavorsky, "Transformation of optical vortices in elliptical and anisotropic optical fibres," J. Opt. A, Pure Appl. Opt. 9, 387-394 (2007).
[CrossRef]

C. N. Alexeyev and M. A. Yavorsky, "Berry's phase for optical vortices in coiled optical fibres," J. Opt. A, Pure Appl. Opt. 9, 6-14 (2007).
[CrossRef]

K. Yu. Bliokh, D. Yu. Frolov, and Yu. A. Kravtsov, "Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium," Phys. Rev. A 75, 053821 (2007).
[CrossRef]

2006 (4)

C. N. Alexeyev and M. A. Yavorsky, "Topological phase evolving from the orbital angular momentum of "coiled" quantum vortices," J. Opt. A, Pure Appl. Opt. 8, 752-758 (2006).
[CrossRef]

K. Yu. Bliokh, "Geometrical optics of beams with vortices: Berry phase and orbital angular momentum Hall effect," Phys. Rev. Lett. 97, 043901 (2006).
[CrossRef]

C. N. Alexeyev and M. A. Yavorsky, "Hybridisation of the topological and dynamical phase in coiled optical fibres," J. Opt. A, Pure Appl. Opt. 8, 647-651 (2006).
[CrossRef]

Z. Menachem and M. Mond, "Infrared wave propagation in a helical waveguide with inhomogeneous cross section and application," Electromagn. Waves 61, 159-192 (2006).
[CrossRef]

2005 (3)

K. N. Alekseev and M. A. Yavorskii, "Twisted optical fibers sustaining propagation of optical vortices," Opt. Spectrosc. 98, 59-66 (2005).
[CrossRef]

A. Desyatnikov, Yu. Kivshar, and L. Torner, "Optical vortices and vortex solitons," Prog. Opt. 47, 291-391 (2005).
[CrossRef]

G. Foo, D. M. Palacios, and G. A. Swartzlander, Jr., "Optical vortex coronograph," Opt. Lett. 30, 3308-3310 (2005).
[CrossRef]

2004 (6)

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas'ko, S. M. Barnett, and S. Franke-Arnold, "Free-space information transfer using light beams carrying orbital angular momentum," Opt. Express 12, 5448-5556 (2004).
[CrossRef] [PubMed]

C. N. Alexeyev, A. V. Volyar, and M. A. Yavorsky, "Vortex-preserving weakly guiding anisotropic twisted fibres," J. Opt. A, Pure Appl. Opt. 6, S162-S165 (2004).
[CrossRef]

M. V. Berry, "The electric and magnetic polarization singularities of paraxial waves," J. Opt. A, Pure Appl. Opt. 6, 475-481 (2004).
[CrossRef]

M. V. Berry and M. R. Dennis, "Quantum cores of optical phase singularities," J. Opt. A, Pure Appl. Opt. 6, S178-S180 (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]

S. Franke-Arnold, S. Barnett, E. Yao, J. Leach, J. Courtial, and M. Padgett, "Uncertainty principle for angular position and angular momentum," New J. Phys. 6, 103 (2004).
[CrossRef]

2003 (2)

D. B. S. Soh, J. Nilsson, J. K. Sahu, and L. J. Cooper, "Geometrical factor modification of helical-core fiber radiation loss formula," Opt. Commun. 222, 235-242 (2003).
[CrossRef]

A. G. Peele and K. A. Nugent, "X-ray vortex beams: a theoretical analysis," Opt. Express 11, 2315-2322 (2003).
[CrossRef] [PubMed]

2002 (3)

G. S. Agarwal and J. Banerji, "Spatial coherence and information entropy in optical vortex fields," Opt. Lett. 27, 800-802 (2002).
[CrossRef]

I. Freund, M. S. Soskin, and A. I. Mokhun, "Elliptic critical points in paraxial optical fields," Opt. Commun. 207, 223-253 (2002).
[CrossRef]

K. N. Alekseev, A. V. Volyar, and T. A. Fadeeva, "Spin-orbit interaction and evolution of optical eddies in perturbed weakly directing optical fibers," Opt. Spectrosc. 93, 639-649 (2002).
[CrossRef]

2001 (1)

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

1999 (2)

A. V. Volyar, V. Z. Zhilaitis, and V. G. Shvedov, "Optical eddies in small-mode fibers: II. The spin-orbit interaction," Opt. Spectrosc. 86, 593-598 (1999).

E. J. Galvez and C. D. Holmes, "Geometric phase of optical rotators," J. Opt. Soc. Am. A 16, 1981-1985 (1999).
[CrossRef]

1998 (4)

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1998).
[CrossRef]

K. N. Alexeyev, T. A. Fadeyeva, A. V. Volyar, and M. S. Soskin, "Optical vortices and the flow of their angular momentum in a multi mode fiber," Semicond. Phys., Quantum Electron. Optoelectron. 1, 1-8 (1998).

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]

F. Wassmann and A. Ankiewicz, "Berry's phase analysis of polarization rotation in helicoidal fibers," Appl. Opt. 37, 3902-3911 (1998).
[CrossRef]

1997 (1)

1996 (1)

1995 (2)

I. V. Kataevskaya and N. D. Kundikova, "Influence of the helical shape of a fibre waveguide on the propagation of light," Quantum Electron. 25, 927-928 (1995).
[CrossRef]

C. G. Chen and Q. Wang, "Local fields in single-mode helical fibres," Opt. Quantum Electron. 27, 1069-1074 (1995).
[CrossRef]

1992 (2)

V. S. Liberman and B. Ya. Zel'dovich, "Spin-orbit interaction of a photon in an inhomogeneous medium," Phys. Rev. A 45, 5199-5207 (1992).
[CrossRef]

M. Segev, R. Solomon, and A. Yariv, "Manifestation of Berry's phase in image-bearing optical beams," Phys. Rev. Lett. 69, 590-593 (1992).
[CrossRef] [PubMed]

1991 (1)

1988 (1)

M. V. Berry, "The geometric phase," Sci. Am. 259, 26-34 (1988).
[CrossRef]

1987 (2)

1986 (2)

R. Y. Chiao and Y.-S. Wu, "Manifestation of Berry's topological phase for the photon," Phys. Rev. Lett. 57, 933-936 (1986).
[CrossRef] [PubMed]

A. Tomita and R. Y. Chiao, "Observation of Berry's topological phase by use of an optical fibre," Phys. Rev. Lett. 57, 937-940 (1986).
[CrossRef] [PubMed]

1984 (1)

J. N. Ross, "The rotation of the polarization in low birefringence monomode optical fibers due to geometric effects," Opt. Quantum Electron. 16, 455-461 (1984).
[CrossRef]

1980 (1)

1974 (1)

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

Agarwal, G. S.

Alekseev, K. N.

K. N. Alekseev and M. A. Yavorskii, "Twisted optical fibers sustaining propagation of optical vortices," Opt. Spectrosc. 98, 59-66 (2005).
[CrossRef]

K. N. Alekseev, A. V. Volyar, and T. A. Fadeeva, "Spin-orbit interaction and evolution of optical eddies in perturbed weakly directing optical fibers," Opt. Spectrosc. 93, 639-649 (2002).
[CrossRef]

Alexeyev, C. N.

C. N. Alexeyev, A. V. Volyar, and M. A. Yavorsky, "Transformation of optical vortices in elliptical and anisotropic optical fibres," J. Opt. A, Pure Appl. Opt. 9, 387-394 (2007).
[CrossRef]

C. N. Alexeyev and M. A. Yavorsky, "Berry's phase for optical vortices in coiled optical fibres," J. Opt. A, Pure Appl. Opt. 9, 6-14 (2007).
[CrossRef]

C. N. Alexeyev and M. A. Yavorsky, "Topological phase evolving from the orbital angular momentum of "coiled" quantum vortices," J. Opt. A, Pure Appl. Opt. 8, 752-758 (2006).
[CrossRef]

C. N. Alexeyev and M. A. Yavorsky, "Hybridisation of the topological and dynamical phase in coiled optical fibres," J. Opt. A, Pure Appl. Opt. 8, 647-651 (2006).
[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]

C. N. Alexeyev, A. V. Volyar, and M. A. Yavorsky, "Vortex-preserving weakly guiding anisotropic twisted fibres," J. Opt. A, Pure Appl. Opt. 6, S162-S165 (2004).
[CrossRef]

Alexeyev, K. N.

K. N. Alexeyev, T. A. Fadeyeva, A. V. Volyar, and M. S. Soskin, "Optical vortices and the flow of their angular momentum in a multi mode fiber," Semicond. Phys., Quantum Electron. Optoelectron. 1, 1-8 (1998).

Allen, L.

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (IOP, 2003).
[CrossRef]

Ankiewicz, A.

Banerji, J.

Barnett, S.

S. Franke-Arnold, S. Barnett, E. Yao, J. Leach, J. Courtial, and M. Padgett, "Uncertainty principle for angular position and angular momentum," New J. Phys. 6, 103 (2004).
[CrossRef]

Barnett, S. M.

Bekshaev, A. Ya.

A. Ya. Bekshaev, M. S. Soskin, "Transverse energy flows in vectorial fields of paraxial beams with singularities," Opt. Commun. 271, 332-348 (2007).
[CrossRef]

Berry, M. V.

M. V. Berry and M. R. Dennis, "Quantum cores of optical phase singularities," J. Opt. A, Pure Appl. Opt. 6, S178-S180 (2004).
[CrossRef]

M. V. Berry, "The electric and magnetic polarization singularities of paraxial waves," J. Opt. A, Pure Appl. Opt. 6, 475-481 (2004).
[CrossRef]

M. V. Berry, "The geometric phase," Sci. Am. 259, 26-34 (1988).
[CrossRef]

M. V. Berry, "Interpreting the anholonomy of coiled light," Nature 326, 277-278 (1987).
[CrossRef]

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

Brown, C. S.

Chen, C. G.

C. G. Chen and Q. Wang, "Local fields in single-mode helical fibres," Opt. Quantum Electron. 27, 1069-1074 (1995).
[CrossRef]

Chiao, R. Y.

R. Y. Chiao and Y.-S. Wu, "Manifestation of Berry's topological phase for the photon," Phys. Rev. Lett. 57, 933-936 (1986).
[CrossRef] [PubMed]

A. Tomita and R. Y. Chiao, "Observation of Berry's topological phase by use of an optical fibre," Phys. Rev. Lett. 57, 937-940 (1986).
[CrossRef] [PubMed]

Choi, S. S.

Cooper, L. J.

D. B. S. Soh, J. Nilsson, J. K. Sahu, and L. J. Cooper, "Geometrical factor modification of helical-core fiber radiation loss formula," Opt. Commun. 222, 235-242 (2003).
[CrossRef]

Courtial, J.

S. Franke-Arnold, S. Barnett, E. Yao, J. Leach, J. Courtial, and M. Padgett, "Uncertainty principle for angular position and angular momentum," New J. Phys. 6, 103 (2004).
[CrossRef]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas'ko, S. M. Barnett, and S. Franke-Arnold, "Free-space information transfer using light beams carrying orbital angular momentum," Opt. Express 12, 5448-5556 (2004).
[CrossRef] [PubMed]

Davydov, A. S.

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

Dennis, M. R.

M. V. Berry and M. R. Dennis, "Quantum cores of optical phase singularities," J. Opt. A, Pure Appl. Opt. 6, S178-S180 (2004).
[CrossRef]

Desyatnikov, A.

A. Desyatnikov, Yu. Kivshar, and L. Torner, "Optical vortices and vortex solitons," Prog. Opt. 47, 291-391 (2005).
[CrossRef]

Eickhoff, W.

Fadeeva, T. A.

K. N. Alekseev, A. V. Volyar, and T. A. Fadeeva, "Spin-orbit interaction and evolution of optical eddies in perturbed weakly directing optical fibers," Opt. Spectrosc. 93, 639-649 (2002).
[CrossRef]

Fadeyeva, T. A.

K. N. Alexeyev, T. A. Fadeyeva, A. V. Volyar, and M. S. Soskin, "Optical vortices and the flow of their angular momentum in a multi mode fiber," Semicond. Phys., Quantum Electron. Optoelectron. 1, 1-8 (1998).

Foo, G.

Franke-Arnold, S.

S. Franke-Arnold, S. Barnett, E. Yao, J. Leach, J. Courtial, and M. Padgett, "Uncertainty principle for angular position and angular momentum," New J. Phys. 6, 103 (2004).
[CrossRef]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas'ko, S. M. Barnett, and S. Franke-Arnold, "Free-space information transfer using light beams carrying orbital angular momentum," Opt. Express 12, 5448-5556 (2004).
[CrossRef] [PubMed]

Freund, I.

I. Freund, M. S. Soskin, and A. I. Mokhun, "Elliptic critical points in paraxial optical fields," Opt. Commun. 207, 223-253 (2002).
[CrossRef]

Gahagan, T.

Galvez, E. J.

Gibson, G.

Gorshkov, V. N.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1998).
[CrossRef]

Heckenberg, N. R.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1998).
[CrossRef]

Holmes, C. D.

Jarzynski, J.

Kataevskaya, I. V.

I. V. Kataevskaya and N. D. Kundikova, "Influence of the helical shape of a fibre waveguide on the propagation of light," Quantum Electron. 25, 927-928 (1995).
[CrossRef]

Kivshar, Yu.

A. Desyatnikov, Yu. Kivshar, and L. Torner, "Optical vortices and vortex solitons," Prog. Opt. 47, 291-391 (2005).
[CrossRef]

Korn, G. A.

G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, 1968).

Korn, T. M.

G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, 1968).

Kravtsov, Yu. A.

K. Yu. Bliokh, D. Yu. Frolov, and Yu. A. Kravtsov, "Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium," Phys. Rev. A 75, 053821 (2007).
[CrossRef]

Kundikova, N. D.

I. V. Kataevskaya and N. D. Kundikova, "Influence of the helical shape of a fibre waveguide on the propagation of light," Quantum Electron. 25, 927-928 (1995).
[CrossRef]

Kwon, O. J.

Leach, J.

S. Franke-Arnold, S. Barnett, E. Yao, J. Leach, J. Courtial, and M. Padgett, "Uncertainty principle for angular position and angular momentum," New J. Phys. 6, 103 (2004).
[CrossRef]

Lee, H. T.

Lee, S. B.

Liberman, V. S.

V. S. Liberman and B. Ya. Zel'dovich, "Spin-orbit interaction of a photon in an inhomogeneous medium," Phys. Rev. A 45, 5199-5207 (1992).
[CrossRef]

Love, J. D.

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

Malos, J. T.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1998).
[CrossRef]

McGloin, D.

Menachem, Z.

Z. Menachem and M. Mond, "Infrared wave propagation in a helical waveguide with inhomogeneous cross section and application," Electromagn. Waves 61, 159-192 (2006).
[CrossRef]

Mokhun, A. I.

I. Freund, M. S. Soskin, and A. I. Mokhun, "Elliptic critical points in paraxial optical fields," Opt. Commun. 207, 223-253 (2002).
[CrossRef]

Mond, M.

Z. Menachem and M. Mond, "Infrared wave propagation in a helical waveguide with inhomogeneous cross section and application," Electromagn. Waves 61, 159-192 (2006).
[CrossRef]

Nilsson, J.

D. B. S. Soh, J. Nilsson, J. K. Sahu, and L. J. Cooper, "Geometrical factor modification of helical-core fiber radiation loss formula," Opt. Commun. 222, 235-242 (2003).
[CrossRef]

Nugent, K. A.

Nye, J. F.

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

J. F. Nye, Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocation (IOP, 1999).

Padgett, M.

S. Franke-Arnold, S. Barnett, E. Yao, J. Leach, J. Courtial, and M. Padgett, "Uncertainty principle for angular position and angular momentum," New J. Phys. 6, 103 (2004).
[CrossRef]

Padgett, M. J.

Palacios, D. M.

Pas'ko, V.

Peele, A. G.

Rashleigh, S. G.

Ross, J. N.

J. N. Ross, "The rotation of the polarization in low birefringence monomode optical fibers due to geometric effects," Opt. Quantum Electron. 16, 455-461 (1984).
[CrossRef]

Sahu, J. K.

D. B. S. Soh, J. Nilsson, J. K. Sahu, and L. J. Cooper, "Geometrical factor modification of helical-core fiber radiation loss formula," Opt. Commun. 222, 235-242 (2003).
[CrossRef]

Segev, M.

M. Segev, R. Solomon, and A. Yariv, "Manifestation of Berry's phase in image-bearing optical beams," Phys. Rev. Lett. 69, 590-593 (1992).
[CrossRef] [PubMed]

Shute, M. W.

Shvedov, V. G.

A. V. Volyar, V. Z. Zhilaitis, and V. G. Shvedov, "Optical eddies in small-mode fibers: II. The spin-orbit interaction," Opt. Spectrosc. 86, 593-598 (1999).

Simpson, N. B.

Snyder, A. W.

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

Soh, D. B. S.

D. B. S. Soh, J. Nilsson, J. K. Sahu, and L. J. Cooper, "Geometrical factor modification of helical-core fiber radiation loss formula," Opt. Commun. 222, 235-242 (2003).
[CrossRef]

Solomon, R.

M. Segev, R. Solomon, and A. Yariv, "Manifestation of Berry's phase in image-bearing optical beams," Phys. Rev. Lett. 69, 590-593 (1992).
[CrossRef] [PubMed]

Soskin, M. S.

A. Ya. Bekshaev, M. S. Soskin, "Transverse energy flows in vectorial fields of paraxial beams with singularities," Opt. Commun. 271, 332-348 (2007).
[CrossRef]

I. Freund, M. S. Soskin, and A. I. Mokhun, "Elliptic critical points in paraxial optical fields," Opt. Commun. 207, 223-253 (2002).
[CrossRef]

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

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1998).
[CrossRef]

K. N. Alexeyev, T. A. Fadeyeva, A. V. Volyar, and M. S. Soskin, "Optical vortices and the flow of their angular momentum in a multi mode fiber," Semicond. Phys., Quantum Electron. Optoelectron. 1, 1-8 (1998).

Staliunas, K.

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

Swartzlander, G. A.

Tomita, A.

A. Tomita and R. Y. Chiao, "Observation of Berry's topological phase by use of an optical fibre," Phys. Rev. Lett. 57, 937-940 (1986).
[CrossRef] [PubMed]

Torner, L.

A. Desyatnikov, Yu. Kivshar, and L. Torner, "Optical vortices and vortex solitons," Prog. Opt. 47, 291-391 (2005).
[CrossRef]

Tsao, C. Y. H.

Ulrich, S.

Vasnetsov, M.

Vasnetsov, M. V.

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

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1998).
[CrossRef]

Volyar, A. V.

C. N. Alexeyev, A. V. Volyar, and M. A. Yavorsky, "Transformation of optical vortices in elliptical and anisotropic optical fibres," J. Opt. A, Pure Appl. Opt. 9, 387-394 (2007).
[CrossRef]

C. N. Alexeyev, A. V. Volyar, and M. A. Yavorsky, "Vortex-preserving weakly guiding anisotropic twisted fibres," J. Opt. A, Pure Appl. Opt. 6, S162-S165 (2004).
[CrossRef]

K. N. Alekseev, A. V. Volyar, and T. A. Fadeeva, "Spin-orbit interaction and evolution of optical eddies in perturbed weakly directing optical fibers," Opt. Spectrosc. 93, 639-649 (2002).
[CrossRef]

A. V. Volyar, V. Z. Zhilaitis, and V. G. Shvedov, "Optical eddies in small-mode fibers: II. The spin-orbit interaction," Opt. Spectrosc. 86, 593-598 (1999).

K. N. Alexeyev, T. A. Fadeyeva, A. V. Volyar, and M. S. Soskin, "Optical vortices and the flow of their angular momentum in a multi mode fiber," Semicond. Phys., Quantum Electron. Optoelectron. 1, 1-8 (1998).

Wang, Q.

C. G. Chen and Q. Wang, "Local fields in single-mode helical fibres," Opt. Quantum Electron. 27, 1069-1074 (1995).
[CrossRef]

Wassmann, F.

Wu, Y.-S.

R. Y. Chiao and Y.-S. Wu, "Manifestation of Berry's topological phase for the photon," Phys. Rev. Lett. 57, 933-936 (1986).
[CrossRef] [PubMed]

Yao, E.

S. Franke-Arnold, S. Barnett, E. Yao, J. Leach, J. Courtial, and M. Padgett, "Uncertainty principle for angular position and angular momentum," New J. Phys. 6, 103 (2004).
[CrossRef]

Yariv, A.

M. Segev, R. Solomon, and A. Yariv, "Manifestation of Berry's phase in image-bearing optical beams," Phys. Rev. Lett. 69, 590-593 (1992).
[CrossRef] [PubMed]

Yavorskii, M. A.

K. N. Alekseev and M. A. Yavorskii, "Twisted optical fibers sustaining propagation of optical vortices," Opt. Spectrosc. 98, 59-66 (2005).
[CrossRef]

Yavorsky, M. A.

C. N. Alexeyev, A. V. Volyar, and M. A. Yavorsky, "Transformation of optical vortices in elliptical and anisotropic optical fibres," J. Opt. A, Pure Appl. Opt. 9, 387-394 (2007).
[CrossRef]

C. N. Alexeyev and M. A. Yavorsky, "Berry's phase for optical vortices in coiled optical fibres," J. Opt. A, Pure Appl. Opt. 9, 6-14 (2007).
[CrossRef]

C. N. Alexeyev and M. A. Yavorsky, "Topological phase evolving from the orbital angular momentum of "coiled" quantum vortices," J. Opt. A, Pure Appl. Opt. 8, 752-758 (2006).
[CrossRef]

C. N. Alexeyev and M. A. Yavorsky, "Hybridisation of the topological and dynamical phase in coiled optical fibres," J. Opt. A, Pure Appl. Opt. 8, 647-651 (2006).
[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]

C. N. Alexeyev, A. V. Volyar, and M. A. Yavorsky, "Vortex-preserving weakly guiding anisotropic twisted fibres," J. Opt. A, Pure Appl. Opt. 6, S162-S165 (2004).
[CrossRef]

Yu. Bliokh, K.

K. Yu. Bliokh, D. Yu. Frolov, and Yu. A. Kravtsov, "Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium," Phys. Rev. A 75, 053821 (2007).
[CrossRef]

K. Yu. Bliokh, "Geometrical optics of beams with vortices: Berry phase and orbital angular momentum Hall effect," Phys. Rev. Lett. 97, 043901 (2006).
[CrossRef]

Yu. Frolov, D.

K. Yu. Bliokh, D. Yu. Frolov, and Yu. A. Kravtsov, "Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium," Phys. Rev. A 75, 053821 (2007).
[CrossRef]

Zel'dovich, B. Ya.

V. S. Liberman and B. Ya. Zel'dovich, "Spin-orbit interaction of a photon in an inhomogeneous medium," Phys. Rev. A 45, 5199-5207 (1992).
[CrossRef]

Zhilaitis, V. Z.

A. V. Volyar, V. Z. Zhilaitis, and V. G. Shvedov, "Optical eddies in small-mode fibers: II. The spin-orbit interaction," Opt. Spectrosc. 86, 593-598 (1999).

Appl. Opt. (2)

Electromagn. Waves (1)

Z. Menachem and M. Mond, "Infrared wave propagation in a helical waveguide with inhomogeneous cross section and application," Electromagn. Waves 61, 159-192 (2006).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (8)

C. N. Alexeyev and M. A. Yavorsky, "Hybridisation of the topological and dynamical phase in coiled optical fibres," J. Opt. A, Pure Appl. Opt. 8, 647-651 (2006).
[CrossRef]

C. N. Alexeyev and M. A. Yavorsky, "Topological phase evolving from the orbital angular momentum of "coiled" quantum vortices," J. Opt. A, Pure Appl. Opt. 8, 752-758 (2006).
[CrossRef]

C. N. Alexeyev, A. V. Volyar, and M. A. Yavorsky, "Transformation of optical vortices in elliptical and anisotropic optical fibres," J. Opt. A, Pure Appl. Opt. 9, 387-394 (2007).
[CrossRef]

C. N. Alexeyev, A. V. Volyar, and M. A. Yavorsky, "Vortex-preserving weakly guiding anisotropic twisted fibres," J. Opt. A, Pure Appl. Opt. 6, S162-S165 (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]

C. N. Alexeyev and M. A. Yavorsky, "Berry's phase for optical vortices in coiled optical fibres," J. Opt. A, Pure Appl. Opt. 9, 6-14 (2007).
[CrossRef]

M. V. Berry, "The electric and magnetic polarization singularities of paraxial waves," J. Opt. A, Pure Appl. Opt. 6, 475-481 (2004).
[CrossRef]

M. V. Berry and M. R. Dennis, "Quantum cores of optical phase singularities," J. Opt. A, Pure Appl. Opt. 6, S178-S180 (2004).
[CrossRef]

J. Opt. Soc. Am. A (3)

Nature (1)

M. V. Berry, "Interpreting the anholonomy of coiled light," Nature 326, 277-278 (1987).
[CrossRef]

New J. Phys. (1)

S. Franke-Arnold, S. Barnett, E. Yao, J. Leach, J. Courtial, and M. Padgett, "Uncertainty principle for angular position and angular momentum," New J. Phys. 6, 103 (2004).
[CrossRef]

Opt. Commun. (3)

A. Ya. Bekshaev, M. S. Soskin, "Transverse energy flows in vectorial fields of paraxial beams with singularities," Opt. Commun. 271, 332-348 (2007).
[CrossRef]

I. Freund, M. S. Soskin, and A. I. Mokhun, "Elliptic critical points in paraxial optical fields," Opt. Commun. 207, 223-253 (2002).
[CrossRef]

D. B. S. Soh, J. Nilsson, J. K. Sahu, and L. J. Cooper, "Geometrical factor modification of helical-core fiber radiation loss formula," Opt. Commun. 222, 235-242 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Opt. Quantum Electron. (2)

J. N. Ross, "The rotation of the polarization in low birefringence monomode optical fibers due to geometric effects," Opt. Quantum Electron. 16, 455-461 (1984).
[CrossRef]

C. G. Chen and Q. Wang, "Local fields in single-mode helical fibres," Opt. Quantum Electron. 27, 1069-1074 (1995).
[CrossRef]

Opt. Spectrosc. (3)

A. V. Volyar, V. Z. Zhilaitis, and V. G. Shvedov, "Optical eddies in small-mode fibers: II. The spin-orbit interaction," Opt. Spectrosc. 86, 593-598 (1999).

K. N. Alekseev, A. V. Volyar, and T. A. Fadeeva, "Spin-orbit interaction and evolution of optical eddies in perturbed weakly directing optical fibers," Opt. Spectrosc. 93, 639-649 (2002).
[CrossRef]

K. N. Alekseev and M. A. Yavorskii, "Twisted optical fibers sustaining propagation of optical vortices," Opt. Spectrosc. 98, 59-66 (2005).
[CrossRef]

Phys. Rev. A (3)

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1998).
[CrossRef]

K. Yu. Bliokh, D. Yu. Frolov, and Yu. A. Kravtsov, "Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium," Phys. Rev. A 75, 053821 (2007).
[CrossRef]

V. S. Liberman and B. Ya. Zel'dovich, "Spin-orbit interaction of a photon in an inhomogeneous medium," Phys. Rev. A 45, 5199-5207 (1992).
[CrossRef]

Phys. Rev. Lett. (4)

M. Segev, R. Solomon, and A. Yariv, "Manifestation of Berry's phase in image-bearing optical beams," Phys. Rev. Lett. 69, 590-593 (1992).
[CrossRef] [PubMed]

R. Y. Chiao and Y.-S. Wu, "Manifestation of Berry's topological phase for the photon," Phys. Rev. Lett. 57, 933-936 (1986).
[CrossRef] [PubMed]

A. Tomita and R. Y. Chiao, "Observation of Berry's topological phase by use of an optical fibre," Phys. Rev. Lett. 57, 937-940 (1986).
[CrossRef] [PubMed]

K. Yu. Bliokh, "Geometrical optics of beams with vortices: Berry phase and orbital angular momentum Hall effect," Phys. Rev. Lett. 97, 043901 (2006).
[CrossRef]

Proc. R. Soc. London, Ser. A (1)

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

Prog. Opt. (2)

A. Desyatnikov, Yu. Kivshar, and L. Torner, "Optical vortices and vortex solitons," Prog. Opt. 47, 291-391 (2005).
[CrossRef]

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

Quantum Electron. (1)

I. V. Kataevskaya and N. D. Kundikova, "Influence of the helical shape of a fibre waveguide on the propagation of light," Quantum Electron. 25, 927-928 (1995).
[CrossRef]

Sci. Am. (1)

M. V. Berry, "The geometric phase," Sci. Am. 259, 26-34 (1988).
[CrossRef]

Semicond. Phys., Quantum Electron. Optoelectron. (1)

K. N. Alexeyev, T. A. Fadeyeva, A. V. Volyar, and M. S. Soskin, "Optical vortices and the flow of their angular momentum in a multi mode fiber," Semicond. Phys., Quantum Electron. Optoelectron. 1, 1-8 (1998).

Other (7)

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (IOP, 2003).
[CrossRef]

G. A. Swartzlander, Jr., "Singular optics/optical vortex references," http://www.u.arizona.edu/~grovers/SO/so.html.

J. F. Nye, Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocation (IOP, 1999).

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

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

G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, 1968).

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

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Figures (4)

Fig. 1
Fig. 1

Model of a helical optical fiber; H is the pitch, R is the offset, and ( X , Y , Z ) is the laboratory frame.

Fig. 2
Fig. 2

Local helical coordinates ( r , φ , s ) in the Frenet frame ν , β , τ , where ν is the unit vector of the principal normal, β is the unit vector of the binormal, and τ is the unit vector in the tangent direction.

Fig. 3
Fig. 3

Dependence of squared decomposition coefficients ratio ( cot 2 γ ) on pitch for modes (17) of a coiled anisotropic fiber; R = 0.1 m , waveguide parameter V = 4.2 , and n e n o = 4 × 10 5 ; anisotropy is assumed to be independent on the geometric parameters of the helix. The insets show the intensity distribution of the mode ψ 1 at some values of pitch (optimal, 2 m , 3 m ).

Fig. 4
Fig. 4

Polarization corrections Δ β i = β i β ̃ versus pitch for modes (17) of a coiled anisotropic fiber: R = 0.1 m , waveguide parameter V = 4.2 , and n e n o = 4 × 10 5 . Anisotropy is assumed to be independent on geometric parameters of the helix.

Equations (51)

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

( 2 + n 2 ( x , y , z ) k 2 ) E ( x , y , z ) = ( E ( x , y , z ) ln n 2 ( x , y , z ) ) ,
n ̂ co , t 2 = ( n e 2 0 0 n o 2 ) ,
α ̂ = [ cos φ sin φ sin φ cos φ ]
n ̂ co , t 2 ( φ ) = n ¯ 2 1 ̂ + Δ n 2 [ cos 2 φ sin 2 φ sin 2 φ cos 2 φ ] ,
n 2 ( r , φ , s ) n co 2 ( 1 2 Δ f ( r ) ) 1 ̂ + Δ n 2 [ cos 2 φ sin 2 φ sin 2 φ cos 2 φ ] ,
x = R cos K s r cos ϕ cos K s + r v sin ϕ sin K s ,
y = R sin K s r cos ϕ sin K s r v sin ϕ cos K s ,
z = v s + r R K sin φ .
div A = 1 G x i ( A i G g i i ) , ( Φ ) k = g k k g k i Φ x i ,
( curl A ) i = g i i G [ x j ( g k n A n g n n ) x k ( g j n A n g n n ) ] ,
g i j = [ 1 0 0 0 r 2 r 2 υ 0 r 2 υ g 33 ]
( H ̂ 0 + V ̂ ) Φ h = β 2 Φ h ,
Φ h ( e r ( r , φ ) e φ ( r , φ ) )
H ̂ 0 = ( 2 r 2 + 1 r r + 1 r 2 2 φ 2 1 r 2 + k 2 n ̃ 2 ( r ) ) σ ̂ 0 + 2 i r 2 φ σ ̂ 2 ,
V ̂ = { ( κ cos φ r κ 2 cos 2 φ ) r ( 2 r κ cos φ + 3 r 2 κ 2 cos 2 φ ) β 2 + υ 2 2 φ 2 + 1 G [ κ sin φ φ 2 i β ( r υ + r 2 κ υ cos φ ) φ ] κ 2 2 } σ ̂ 0 + σ ̂ 1 [ 1 G r 2 κ 2 sin 2 φ + β r 2 G κ υ cos φ ] + σ ̂ 2 [ i G κ sin φ i β r 2 G κ υ cos φ ] + σ ̂ 3 [ κ 2 cos 2 φ + r 2 G κ υ i β sin φ + υ 2 K 2 2 ] + ψ r 2 { r σ ̂ 0 + 1 r φ σ ̂ 1 i 1 r φ σ ̂ 2 + r σ ̂ 3 } + k 2 Δ n 2 ( σ ̂ 3 cos 2 φ σ ̂ 1 sin 2 φ ) ,
1 h = e i ( l + 1 ) ϕ ( 1 i ) F l ( r ) , 2 h = e i ( 1 l ) ϕ ( 1 i ) F l ( r ) ,
3 h = e i ( l 1 ) ϕ ( 1 i ) F l ( r ) , 4 h = e i ( l 1 ) ϕ ( 1 i ) F l ( r ) ,
( 2 r 2 + 1 r r + k 2 n ̃ 2 ( r ) l 2 r 2 β ̃ 2 ) F l ( r ) = 0 .
1 = e i l ϕ ( 1 i ) F l ( r ) , 2 = e i l ϕ ( 1 i ) F l ( r ) ,
3 = e i l ϕ ( 1 i ) F l ( r ) 4 = e i l ϕ ( 1 i ) F l ( r ) .
1 = 1 , l , 2 = 1 , l , 3 = 1 , l , 4 = 1 , l .
± 1 , ± l = H E l + 1 , m e v ± i H E l + 1 , m o d ,
1 , ± l = E H l 1 , m e v ± i E H l 1 , m o d ,
Φ Ψ = 0 0 2 π ( Φ ν * Φ β * ) ( Ψ ν Ψ β ) r d r d φ .
V x = Δ β 2 x ,
V 1 = [ A 1 + 4 β υ 0 0 E 0 B 1 E B 1 0 E A 1 4 β υ 0 E B 1 0 B 1 ] ,
A 1 = Δ Q 1 r 0 2 ( F 1 F 1 F 1 2 ) R = 1 , B 1 = Δ Q 1 r 0 2 ( F 1 2 + F 1 F 1 ) R = 1 ,
x 1 = ( 1 , 0 , 0 , 0 ) T , x 2 = ( 0 , 0 , 1 , 0 ) T ,
x 3 = ( 0 , 1 , 0 , 1 ) T , x 4 = ( 0 , 1 , 0 , 1 ) T .
ψ 1 = 1 , 1 , ψ 2 = 1 , 1 , ψ 3 = 1 , 1 + 1 , 1 ,
ψ 4 = 1 , 1 1 , 1 .
ψ 3 ( cos φ sin φ ) F l , ψ 4 ( sin φ cos φ ) F l .
ψ 1 = F 1 ( R ) ( cos γ e i φ sin γ e i φ ) ( 1 0 ) ,
ψ 2 = F 1 ( R ) ( sin γ e i φ + cos γ e i φ ) ( 1 0 ) ,
ψ 3 = F 1 ( R ) ( cos γ e i φ + sin γ e i φ ) ( 0 1 ) ,
ψ 4 = F 1 ( R ) ( sin γ e i φ + cos γ e i φ ) ( 0 1 ) ,
β 1 , 2 = β ̃ + 1 4 β ̃ ( 2 E + A 1 + B 1 ± ( 4 β ̃ υ ) 2 + B 1 2 ) ,
β 3 , 4 = β ̃ + 1 4 β ̃ ( 2 E + A 1 + B 1 ± ( 4 β ̃ υ ) 2 + B 1 2 ) .
ψ 1 = F 1 ( R ) ( sin φ 0 ) , ψ 2 = F 1 ( R ) ( cos φ 0 ) ,
ψ 3 = F 1 ( R ) ( 0 cos φ ) , ψ 4 = F 1 ( R ) ( 0 sin φ ) ,
ψ 1 L V 1 x = F 1 ( R ) ( e i φ 0 ) , ψ 2 L V 1 x = F 1 ( R ) ( e i φ 0 ) ,
ψ 3 L V 1 y = F 1 ( R ) ( 0 e i φ ) , ψ 4 L V 1 y = F 1 ( R ) ( 0 e i φ ) ,
β 1 , 2 β ̃ ± υ + 1 2 β ̃ ( E + A 1 + B 1 2 ± B 1 2 8 β ̃ υ ) ,
β 3 , 4 β ̃ ± υ + 1 2 β ̃ ( E + A 1 + B 1 2 ± B 1 2 8 β ̃ υ ) .
Δ n = 0.25 n co 3 ( p 11 p 12 ) ( 1 + ν ) κ 2 r f 2 ,
γ = ( l + σ ) Ω ,
γ = Ω sgn l ,
L V in = 1 2 ( 1 + 4 ) 1 2 ( 1 , l + 1 , l ) .
L V out = 1 2 ( 1 , l exp [ i Ω ( l + 1 ) ] + 1 , l exp [ i Ω ( l 1 ) ] ) .
Ψ i ( s 0 ) = L ̂ ( 2 π v ) e i γ d Ψ i ( 0 ) ,
Φ 1 ( s 0 ) = L ̂ ( 2 π v 1 ) k C k exp ( i γ k ) Ψ k ( 0 ) L ̂ ( 2 π v 1 ) Φ ̃ .

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