Abstract

A splitting of modes in a cylindrical graded-index optical fiber is demonstrated by solving the full Maxwell equations using the perturbation analysis. It is shown that the degeneracy of vortex Laguerre–Gauss modes with distinct orbital angular momentum and polarization (spin) but the same total angular momentum is lifted due to the spin–orbit (vector) and tensor forces. Numerical estimations of group delays of modes in optical fiber and frequency splitting in Fabry–Perot and ring resonators are presented.

© 2013 Optical Society of America

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References

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2011

T. W. Allen, J. Silverstone, N. Ponnampalam, T. Olsen, A. Meldrum, and R. G. DeCorby, Opt. Express 19, 18903 (2011).
[CrossRef]

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, W. E. Santamato, E. Nagali, and F. Sciarrino, J. Opt. 13, 064001 (2011).
[CrossRef]

2008

N. I. Petrov, Laser Phys. 18, 522 (2008).
[CrossRef]

2007

2006

2005

K. Yu. Bliokh and D. Yu. Frolov, Opt. Commun. 250, 321 (2005).
[CrossRef]

2004

1996

N. I. Petrov, J. Mod. Opt. 43, 2239 (1996).
[CrossRef]

1984

P. K. Yu and K. Luk, IEEE Trans. Microwave Theory Tech. 32, 641 (1984).
[CrossRef]

1975

C. W. Erickson, IEEE Trans. Microwave Theory Tech. 23, 218 (1975).
[CrossRef]

1974

K. Thyagarajan and A. K. Chatak, Opt. Commun. 11, 417 (1974).
[CrossRef]

1973

Alessandro, G. D.

Allen, T. W.

Baumberg, J.

A. Kavokin, J. Baumberg, G. Malpuech, and F. P. Laussy, Microcavities (Oxford University, 2007), pp. 1–21.

Baumberg, J. J.

Bhongale, S.

Bliokh, K. Yu.

K. Yu. Bliokh and D. Yu. Frolov, Opt. Commun. 250, 321 (2005).
[CrossRef]

Chatak, A. K.

K. Thyagarajan and A. K. Chatak, Opt. Commun. 11, 417 (1974).
[CrossRef]

Chatterjee, S.

Cui, G.

DeCorby, R. G.

Erickson, C. W.

C. W. Erickson, IEEE Trans. Microwave Theory Tech. 23, 218 (1975).
[CrossRef]

Foster, D. H.

Frolov, D. Yu.

K. Yu. Bliokh and D. Yu. Frolov, Opt. Commun. 250, 321 (2005).
[CrossRef]

Gibbs, H. M.

Hannigan, J. M.

Holland, M.

Kaczmarek, M.

Karimi, E.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, W. E. Santamato, E. Nagali, and F. Sciarrino, J. Opt. 13, 064001 (2011).
[CrossRef]

Kavokin, A.

A. Kavokin, J. Baumberg, G. Malpuech, and F. P. Laussy, Microcavities (Oxford University, 2007), pp. 1–21.

Khitrova, G.

Laussy, F. P.

A. Kavokin, J. Baumberg, G. Malpuech, and F. P. Laussy, Microcavities (Oxford University, 2007), pp. 1–21.

Loeckenhoff, R.

Luk, K.

P. K. Yu and K. Luk, IEEE Trans. Microwave Theory Tech. 32, 641 (1984).
[CrossRef]

Malpuech, G.

A. Kavokin, J. Baumberg, G. Malpuech, and F. P. Laussy, Microcavities (Oxford University, 2007), pp. 1–21.

Marrucci, L.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, W. E. Santamato, E. Nagali, and F. Sciarrino, J. Opt. 13, 064001 (2011).
[CrossRef]

Matinaga, F. M.

Matsuhara, M.

Meldrum, A.

Mosor, S.

Nagali, E.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, W. E. Santamato, E. Nagali, and F. Sciarrino, J. Opt. 13, 064001 (2011).
[CrossRef]

Nockel, J. U.

Olsen, T.

Pennington, R. C.

Petrov, N. I.

N. I. Petrov, Laser Phys. 18, 522 (2008).
[CrossRef]

N. I. Petrov, J. Mod. Opt. 43, 2239 (1996).
[CrossRef]

Piccirillo, B.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, W. E. Santamato, E. Nagali, and F. Sciarrino, J. Opt. 13, 064001 (2011).
[CrossRef]

Ponnampalam, N.

Raymer, M. G.

Santamato, W. E.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, W. E. Santamato, E. Nagali, and F. Sciarrino, J. Opt. 13, 064001 (2011).
[CrossRef]

Sciarrino, F.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, W. E. Santamato, E. Nagali, and F. Sciarrino, J. Opt. 13, 064001 (2011).
[CrossRef]

Silverstone, J.

Slussarenko, S.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, W. E. Santamato, E. Nagali, and F. Sciarrino, J. Opt. 13, 064001 (2011).
[CrossRef]

Thyagarajan, K.

K. Thyagarajan and A. K. Chatak, Opt. Commun. 11, 417 (1974).
[CrossRef]

Yu, P. K.

P. K. Yu and K. Luk, IEEE Trans. Microwave Theory Tech. 32, 641 (1984).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

C. W. Erickson, IEEE Trans. Microwave Theory Tech. 23, 218 (1975).
[CrossRef]

P. K. Yu and K. Luk, IEEE Trans. Microwave Theory Tech. 32, 641 (1984).
[CrossRef]

J. Mod. Opt.

N. I. Petrov, J. Mod. Opt. 43, 2239 (1996).
[CrossRef]

J. Opt.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, W. E. Santamato, E. Nagali, and F. Sciarrino, J. Opt. 13, 064001 (2011).
[CrossRef]

J. Opt. Soc. Am.

Laser Phys.

N. I. Petrov, Laser Phys. 18, 522 (2008).
[CrossRef]

Opt. Commun.

K. Thyagarajan and A. K. Chatak, Opt. Commun. 11, 417 (1974).
[CrossRef]

K. Yu. Bliokh and D. Yu. Frolov, Opt. Commun. 250, 321 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Other

A. Kavokin, J. Baumberg, G. Malpuech, and F. P. Laussy, Microcavities (Oxford University, 2007), pp. 1–21.

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Figures (3)

Fig. 1.
Fig. 1.

Electric field profiles of (a) even modes |00, |20, |22 and (b) odd modes |11, |31.

Fig. 2.
Fig. 2.

(a) Delay time and (b) group delay splitting as a function of radial and azimuthal indices, accordingly, z=1km, n0=1.5.

Fig. 3.
Fig. 3.

(a) Mode splitting and (b) degeneracy lifting as function of azimuthal index, p=0, n0=1.5.

Equations (14)

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

(2+k2n2)e⃗iβeze⃗=β2e⃗(2+k2n2)ez+iβe⃗lnn2=β2ez,
(2+k2n2+W0+14P2)E⃗=(β12P)2E⃗,
E⃗=(exeyez),W0=(2x22xy02yx2y2000),P=(00ix00iyin2n2xin2n2y0).
H^Ψ=εΨ,
H^=H^(0)+H^(1)+,
H^(0)=H0R,H0=H^012k2n02W^0,H^0=12k2n022+12n02(n02n2),
H(1)=12H0212R2,R=P2kn0.
n2(r)=n02ω2r2,
ε(1)=η232[11(v+1)2j22jσ],
βvls=kn0{1η(v+1)η232[11(v+1)2j22jσ]}.
τ=zcβkzn0c+zn0cη232[11(ν+1)2j22jσ],
Δff=Δλλ=11(v+1)2j22jσ8k4n04w04,
ε1,2(1)=(η2/32)[11(v+1)2j2+2j±10(v+1)(p+1)(p+l)].
ψvl(r,φ)=a||v,l,i|v,l,ez1+b||v,l2,i|v,l2,ez2.

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