Abstract

In the present paper we have derived the analytical expressions for the modes of twisted elliptical fibers with torsional mechanical stress at various relationships of the fiber parameters. It was shown that circularly polarized optical vortices with the topological charges ±1 can propagate in elliptical fibers as generic modes if ellipticity and the twist-induced circular birefringence suppress the spin-orbit interaction. A comparison of the obtained results with the corresponding results for spun elliptical fibers is made.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  11. C. N. Alexeyev, E. V. Barshak, T. A. Fadeyeva, A. V. Volyar, and M. A. Yavorsky, “Generation of radially and azimuthally polarized beams with elliptical anisotropic twisted optical fibres,” J. Opt. 13, 075706 (2011).
    [CrossRef]
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    [CrossRef]
  17. C. N. Alexeyev and M. A. Yavorsky, “Optical vortices and the higher order modes of twisted strongly elliptical optical fibres,” J. Opt. A. 6, 824–832 (2004).
    [CrossRef]
  18. C. N Alexeyev, B A. Lapin, and M. A. Yavorsky, “Optical vortices and topological phase in strongly anisotropic coiled few-mode optical fibers,” J. Opt. Soc. Am. B 24, 2666–2675 (2007).
    [CrossRef]
  19. С. 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]
  20. 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]
  21. C. N. Alexeyev and M. A. Yavorsky, “Generation and conversion of optical vortices in long-period helical core optical fibers,” Phys. Rev. A 78, 043828 (2008).
    [CrossRef]
  22. C. N. Alexeyev, A. V. Volyar, and M. A. Yavorsky, “Fiber optical vortices,” in Lasers, Optics and Electro-Optics Research TrendsL. I. Chen, ed. (Nova, 2007), pp. 131–223.
  23. A. S. Davydov, Quantum Mechanics (Pergamon, 1976).
  24. A. W. Snyder and J. D. Love, Optical Waveguide Theory(Chapman and Hall, 1985).
  25. M. V. Berry, “Paraxial beams of spinning light,” Proc. SPIE 3487, 6–11 (1998).
    [CrossRef]

2011

C. N. Alexeyev, E. V. Barshak, T. A. Fadeyeva, A. V. Volyar, and M. A. Yavorsky, “Generation of radially and azimuthally polarized beams with elliptical anisotropic twisted optical fibres,” J. Opt. 13, 075706 (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]

2009

G. A. Swartzlander, “The optical vortex coronagraph,” J. Opt. A 11, 090422 (2009).
[CrossRef]

C. N. Alexeyev, E. V. Borshak, A. V. Volyar, and M. A. Yavorsky, “Angular momentum conservation and coupled vortex modes in twisted optical fibres with torsional stress,” J. Opt. A 11, 094011 (2009).
[CrossRef]

2008

G. A. Swartzlander, E. L. Ford, R. S. Abdul-Malik, L. M. Close, M. A. Peters, D. M. Palacios, and D. W. Wilson, “Astronomical demonstration of an optical vortex coronagraph,” Opt. Express 16, 10200–10207 (2008).
[CrossRef]

C. N. Alexeyev, A. V. Volyar, and M. A. Yavorsky, “Optical vortices in twisted optical fibres with torsional stress,” J. Opt. A 10, 095007 (2008).
[CrossRef]

C. N. Alexeyev and M. A. Yavorsky, “Generation and conversion of optical vortices in long-period helical core optical fibers,” Phys. Rev. A 78, 043828 (2008).
[CrossRef]

С. 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]

2007

2005

2004

2003

1998

N. J. Cerf, C. Adami, and P. G Kwiat, “Optical simulation of quantum logic,” Phys. Rev. A 57, R1477–R1480 (1998).
[CrossRef]

M. V. Berry, “Paraxial beams of spinning light,” Proc. SPIE 3487, 6–11 (1998).
[CrossRef]

1996

1995

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Cleeson, and D. H. O. Bebbington, “Theoretical analysis and measurement of effects of fibre twist on polarisation mode dispersion of optical fibres,” Electron. Lett. 31, 1772–1773 (1995).
[CrossRef]

1981

1979

1978

1944

V. L. Ginzburg, “Investigation of stress by the optical method,” Zh. Tekh. Fiz. 14, 181–192 (1944) (in Russian).

Abdul-Malik, R. S.

Adami, C.

N. J. Cerf, C. Adami, and P. G Kwiat, “Optical simulation of quantum logic,” Phys. Rev. A 57, R1477–R1480 (1998).
[CrossRef]

Alexeyev, ?. N.

С. 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]

Alexeyev, C. N

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, E. V. Barshak, T. A. Fadeyeva, A. V. Volyar, and M. A. Yavorsky, “Generation of radially and azimuthally polarized beams with elliptical anisotropic twisted optical fibres,” J. Opt. 13, 075706 (2011).
[CrossRef]

C. N. Alexeyev, E. V. Borshak, A. V. Volyar, and M. A. Yavorsky, “Angular momentum conservation and coupled vortex modes in twisted optical fibres with torsional stress,” J. Opt. A 11, 094011 (2009).
[CrossRef]

C. N. Alexeyev, A. V. Volyar, and M. A. Yavorsky, “Optical vortices in twisted optical fibres with torsional stress,” J. Opt. A 10, 095007 (2008).
[CrossRef]

C. N. Alexeyev and M. A. Yavorsky, “Generation and conversion of optical vortices in long-period helical core optical fibers,” Phys. Rev. A 78, 043828 (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. 6, 824–832 (2004).
[CrossRef]

C. N. Alexeyev, A. V. Volyar, and M. A. Yavorsky, “Fiber optical vortices,” in Lasers, Optics and Electro-Optics Research TrendsL. I. Chen, ed. (Nova, 2007), pp. 131–223.

Barlow, A. J.

Barnett, S.

Barshak, E. V.

C. N. Alexeyev, E. V. Barshak, T. A. Fadeyeva, A. V. Volyar, and M. A. Yavorsky, “Generation of radially and azimuthally polarized beams with elliptical anisotropic twisted optical fibres,” J. Opt. 13, 075706 (2011).
[CrossRef]

Bebbington, D. H. O.

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Cleeson, and D. H. O. Bebbington, “Theoretical analysis and measurement of effects of fibre twist on polarisation mode dispersion of optical fibres,” Electron. Lett. 31, 1772–1773 (1995).
[CrossRef]

Berry, M. V.

M. V. Berry, “Paraxial beams of spinning light,” Proc. SPIE 3487, 6–11 (1998).
[CrossRef]

Borshak, E. V.

C. N. Alexeyev, E. V. Borshak, A. V. Volyar, and M. A. Yavorsky, “Angular momentum conservation and coupled vortex modes in twisted optical fibres with torsional stress,” J. Opt. A 11, 094011 (2009).
[CrossRef]

Cerf, N. J.

N. J. Cerf, C. Adami, and P. G Kwiat, “Optical simulation of quantum logic,” Phys. Rev. A 57, R1477–R1480 (1998).
[CrossRef]

Chen, X.

Cleeson, L. M.

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Cleeson, and D. H. O. Bebbington, “Theoretical analysis and measurement of effects of fibre twist on polarisation mode dispersion of optical fibres,” Electron. Lett. 31, 1772–1773 (1995).
[CrossRef]

Close, L. M.

Courtial, J.

Davydov, A. S.

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

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]

C. N. Alexeyev, E. V. Barshak, T. A. Fadeyeva, A. V. Volyar, and M. A. Yavorsky, “Generation of radially and azimuthally polarized beams with elliptical anisotropic twisted optical fibres,” J. Opt. 13, 075706 (2011).
[CrossRef]

Ford, E. L.

Franke-Arnold, S.

Gahagan, K. T.

Gibson, G.

Ginzburg, V. L.

V. L. Ginzburg, “Investigation of stress by the optical method,” Zh. Tekh. Fiz. 14, 181–192 (1944) (in Russian).

Jian, S.

Kwiat, P. G

N. J. Cerf, C. Adami, and P. G Kwiat, “Optical simulation of quantum logic,” Phys. Rev. A 57, R1477–R1480 (1998).
[CrossRef]

Lapin, B A.

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]

С. 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]

Li, M. J.

Li, T.

Love, J. D.

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

Nolan, D. A.

Padgett, M.

Palacios, D. M.

Pas’ko, V.

Payne, D. N.

Peters, M. A.

Ramskov-Hansen, J. J.

Schuh, R. E.

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Cleeson, and D. H. O. Bebbington, “Theoretical analysis and measurement of effects of fibre twist on polarisation mode dispersion of optical fibres,” Electron. Lett. 31, 1772–1773 (1995).
[CrossRef]

Siddiqui, A. S.

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Cleeson, and D. H. O. Bebbington, “Theoretical analysis and measurement of effects of fibre twist on polarisation mode dispersion of optical fibres,” Electron. Lett. 31, 1772–1773 (1995).
[CrossRef]

Sikora, E. S. R.

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Cleeson, and D. H. O. Bebbington, “Theoretical analysis and measurement of effects of fibre twist on polarisation mode dispersion of optical fibres,” Electron. Lett. 31, 1772–1773 (1995).
[CrossRef]

Simon, A.

Smith, A.

Snyder, A. W.

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

Swartzlander, G. A.

Ulrich, R.

Vasnetsov, M.

Volyar, A. V.

C. N. Alexeyev, E. V. Barshak, T. A. Fadeyeva, A. V. Volyar, and M. A. Yavorsky, “Generation of radially and azimuthally polarized beams with elliptical anisotropic twisted optical fibres,” J. Opt. 13, 075706 (2011).
[CrossRef]

C. N. Alexeyev, E. V. Borshak, A. V. Volyar, and M. A. Yavorsky, “Angular momentum conservation and coupled vortex modes in twisted optical fibres with torsional stress,” J. Opt. A 11, 094011 (2009).
[CrossRef]

C. N. Alexeyev, A. V. Volyar, and M. A. Yavorsky, “Optical vortices in twisted optical fibres with torsional stress,” J. Opt. A 10, 095007 (2008).
[CrossRef]

C. N. Alexeyev, A. V. Volyar, and M. A. Yavorsky, “Fiber optical vortices,” in Lasers, Optics and Electro-Optics Research TrendsL. I. Chen, ed. (Nova, 2007), pp. 131–223.

Walker, N. G.

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Cleeson, and D. H. O. Bebbington, “Theoretical analysis and measurement of effects of fibre twist on polarisation mode dispersion of optical fibres,” Electron. Lett. 31, 1772–1773 (1995).
[CrossRef]

Wang, M.

Wilson, D. W.

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, E. V. Barshak, T. A. Fadeyeva, A. V. Volyar, and M. A. Yavorsky, “Generation of radially and azimuthally polarized beams with elliptical anisotropic twisted optical fibres,” J. Opt. 13, 075706 (2011).
[CrossRef]

C. N. Alexeyev, E. V. Borshak, A. V. Volyar, and M. A. Yavorsky, “Angular momentum conservation and coupled vortex modes in twisted optical fibres with torsional stress,” J. Opt. A 11, 094011 (2009).
[CrossRef]

C. N. Alexeyev, A. V. Volyar, and M. A. Yavorsky, “Optical vortices in twisted optical fibres with torsional stress,” J. Opt. A 10, 095007 (2008).
[CrossRef]

С. 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, “Generation and conversion of optical vortices in long-period helical core optical fibers,” Phys. Rev. A 78, 043828 (2008).
[CrossRef]

C. N Alexeyev, B A. Lapin, and M. A. Yavorsky, “Optical vortices and topological phase in strongly anisotropic coiled few-mode optical fibers,” J. Opt. Soc. Am. B 24, 2666–2675 (2007).
[CrossRef]

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

C. N. Alexeyev, A. V. Volyar, and M. A. Yavorsky, “Fiber optical vortices,” in Lasers, Optics and Electro-Optics Research TrendsL. I. Chen, ed. (Nova, 2007), pp. 131–223.

Yoshino, T.

Appl. Opt.

Electron. Lett.

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Cleeson, and D. H. O. Bebbington, “Theoretical analysis and measurement of effects of fibre twist on polarisation mode dispersion of optical fibres,” Electron. Lett. 31, 1772–1773 (1995).
[CrossRef]

J. Opt.

C. N. Alexeyev, E. V. Barshak, T. A. Fadeyeva, A. V. Volyar, and M. A. Yavorsky, “Generation of radially and azimuthally polarized beams with elliptical anisotropic twisted optical fibres,” J. Opt. 13, 075706 (2011).
[CrossRef]

J. Opt. A

C. N. Alexeyev, A. V. Volyar, and M. A. Yavorsky, “Optical vortices in twisted optical fibres with torsional stress,” J. Opt. A 10, 095007 (2008).
[CrossRef]

C. N. Alexeyev, E. V. Borshak, A. V. Volyar, and M. A. Yavorsky, “Angular momentum conservation and coupled vortex modes in twisted optical fibres with torsional stress,” J. Opt. A 11, 094011 (2009).
[CrossRef]

G. A. Swartzlander, “The optical vortex coronagraph,” J. Opt. A 11, 090422 (2009).
[CrossRef]

J. Opt. A.

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

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Phys. Rev. A

С. 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, 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 and M. A. Yavorsky, “Generation and conversion of optical vortices in long-period helical core optical fibers,” Phys. Rev. A 78, 043828 (2008).
[CrossRef]

N. J. Cerf, C. Adami, and P. G Kwiat, “Optical simulation of quantum logic,” Phys. Rev. A 57, R1477–R1480 (1998).
[CrossRef]

Proc. SPIE

M. V. Berry, “Paraxial beams of spinning light,” Proc. SPIE 3487, 6–11 (1998).
[CrossRef]

Zh. Tekh. Fiz.

V. L. Ginzburg, “Investigation of stress by the optical method,” Zh. Tekh. Fiz. 14, 181–192 (1944) (in Russian).

Other

C. N. Alexeyev, A. V. Volyar, and M. A. Yavorsky, “Fiber optical vortices,” in Lasers, Optics and Electro-Optics Research TrendsL. I. Chen, ed. (Nova, 2007), pp. 131–223.

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

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

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Figures (3)

Fig. 1.
Fig. 1.

Dependence of the propagation constants βi on the twist H in the case of twisted strongly elliptical optical fibers; the fiber parameters are nco=1.48, Δ=0.001, r0=10λHeNe, δ=0.01, andp44=0.075.

Fig. 2.
Fig. 2.

OAM in the direction of propagation (in relative units) Lz of the vortex modes [Eq. (11)] versus the twist pitch H; the fiber parameters are nco=1.48, Δ=0.001, r0=10λHeNe, δ=0.01, p44=0.075.

Fig. 3.
Fig. 3.

Dependence of the propagation constants βi on the twist H in the case of intensely twisted strongly elliptical optical fibers; the fiber parameters are nco=1.48, Δ=0.001, r0=10λHeNe, δ=0.01, and p44=0.075.

Equations (14)

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

n^2(r,ϕ)=n2(r)1^2nco2Δδrfrcos2ϕ1^+qp44nco4r(00sinϕ00cosϕsinϕcosϕ0).
(2+k2n^2(r,ϕ))E(r,ϕ,z)=((E·lnn2(r))+qp44nco4r(sinϕExzcosϕEyz)),
(H^0+V^ell+V^tw)|ψ=β2|ψ,
V^tw=k2qp44nco4r(00sinϕ00cosϕsinϕcosϕ0)++iqp44nco2β(0.5sin2ϕrrsin2ϕϕ1cos2ϕrr+0.5sin2ϕϕ01+sin2ϕrr+0.5sin2ϕϕ0.5sin2ϕrrcos2ϕϕ0irβsinϕirβcosϕ0)
|ψ1,n(0)1=(F1,n(r)iF1,n(r)iβ˜1,nr[rF1,nF1,n]eiϕ)eiϕ,|ψ1,n(0)2=(F1,n(r)iF1,n(r)iβ˜1,nr[rF1,nF1,n]eiϕ)eiϕ,|ψ1,n(0)3=(F1,n(r)sinϕF1,n(r)cosϕ0),|ψ1,n(0)4=(F1,n(r)cosϕF1,n(r)sinϕiβ˜1,nr[rF1,n+F1,n]),
Fl,n(r)={Jl(U˜nR)Jl(U˜n),R1,Kl(W˜nR)Kl(W˜n),R1,
H¯ij=ψl,n(0)|iH¯^|ψl,n(0)j,
Φ|Ψ=002π(Φx*Φy*Φz*)(ΨxΨyΨz)rdrdϕ.
H¯^=(β˜n2+An+Cn0iDnDn0β˜n2+AnCniDnDniDniDnβ˜n20DnDn0β˜n2+2Bn),
H^x=0.
|Ψ1=F1,n(r)cosϕ(sinγcosγi(sinγ+cosγ)),|Ψ2=F1,n(r)cosϕ(cosγ+sinγi(cosγsinγ)),|Ψ3=F1,n(r)sinϕ(sinγcosγi(sinγ+cosγ)),|Ψ4=F1,n(r)sinϕ(cosγ+sinγi(cosγsinγ)),
|Φ1=12F1(R)(sinθeiϕcosθeiϕ)(1i),|Φ2=12F1(R)(cosθeiϕ+sinθeiϕ)(1i),|Φ3=12F1(R)(sineiϕcosθeiϕ)(1i),|Φ4=12F1(R)(cosθeiϕ+sinθeiϕ)(1i),
sinθ|Bn|2|Dn|,4Σn|Bn|1.
Lz1,3=cos2θ,Lz2,4=cos2θ,

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