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Higher order modes and topological phase in the coiled elliptical weakly guiding optical fibres
Alexeyev C.N., Lapin B.P., Yavorsky M.A.

Taurida National V.I. Vernadsky University, 4 Vernadsky Ave., 95007 Simferopol, Crimea, Ukraine

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We study the structure of  l = 1 modes in strongly elliptical coiled weakly guiding optical fibres. We establish analytically the expressions for the modes and their polarization corrections. We show that, at certain parameters of the fibre helix, the l = 1 modes are represented in the local Frenet frame by uniform elliptically polarized fields. We demonstrate that the modes turn into circularly polarized fields if the coiling-induced perturbation becomes larger than the intrinsic spin-orbit coupling. In this case the propagation constants comprise geometrically in-duced terms proportional to the spin angular momentum of the mode and a topological phase appears in the system. We show that the presence of such a geometric phase exhibits itself in the rotation of polarization plane of LP mode excited in the fibre. The rotation angle is found to be equal to the solid angle subtended by the coil.

Keywords: helical fibre, Berry’s phase, topological phase, elliptical fibre

PACS: 42.25.Bs, 42.81.Q
UDC: 535.1
Ukr. J. Phys. Opt. 9 34-50   doi: 10.3116/16091833/9/1/34/2008
Received: 08.11.2007

REFERENCES

1. Berry MV, 1984. Quantum phase factor accompanying adiabatic changes. Proc Roy. Soc. Lond. A 392: 45-57.
2. Shapere A. and Wilczek F. Geometric phases in physics. World Scientific: Singapore, (1989).
3.Tomita A and Chiao RY, 1986. Observation of Berry’s topological phase by use of an optical fibre. Phys. Rev. Lett. 57: 937-940.
        doi:10.1103/PhysRevLett.57.937 http://dx.doi.org/10.1103/PhysRevLett.57.937
4. Chiao RY and Wu Y-S, 1986. Manifestation of Berry’s topological phase for the phton, Phys. Rev. Lett. 57: 933-936.
        doi:10.1103/PhysRevLett.57.933 http://dx.doi.org/10.1103/PhysRevLett.57.933
5. Berry MV, 1988. The geometric phase. Scient. Amer. 259: 26-34.
6. Ross JN, 1984. The rotation of the polarization in low birefringence single-mode optical fibres due to geometric effects. Opt. Quant. Electron. 16: 455-461.
        doi:10.1007/BF00619638 http://dx.doi.org/10.1007/BF00619638
7. Berry MV, 1987. Interpreting the anholonomy of coiled light. Nature 326: 277-278.
        doi:10.1038/326277a0 http://dx.doi.org/10.1038/326277a0
8. Galvez EJ and Holmes CD, 1999. Geometric phase of optical rotators. J. Opt. Soc. Am. A. 16: 1981-1985.
        doi:10.1364/JOSAA.16.001981 http://dx.doi.org/10.1364/JOSAA.16.001981
9. Segev M, Solomon R and Yariv A, 1992. Manifestation of Berry’s phase in im-agebearing optical beams. Phys. Rev. Lett. 69: 590-593 .
        doi:10.1103/PhysRevLett.69.590 http://dx.doi.org/10.1103/PhysRevLett.69.590
10. Kataevskaya IV and Kundikova ND, 1995. Influence of the helical shape of a fibre waveguide on the propagation of ligh. Quant. Electron. 25: 927-928 .
        doi:10.1070/QE1995v025n09ABEH000504 http://dx.doi.org/10.1070/QE1995v025n09ABEH000504
11. Vasnetsov M. and Staliunas K. Optical Vortices, Vol. 228 in Horizons of World Physics, Nova Science: Huntington, N.Y. (1999).
12. Mokhun I.I. Introduction to linear singular optics. In Optical Correlation Techniques and Applications, Bellingham: SPIE Press PM168. (2007).
13. Alexeyev CN and Yavorsky MA, 2006. Topological phase evolving from the orbital angular momentum of “coiled” quantum vortices. J. Opt. A: Pure Appl. Opt. 8: 752-758
        doi:10.1088/1464-4258/8/9/008 http://dx.doi.org/10.1088/1464-4258/8/9/008
14. Soskin MS, Gorshkov VN, Vasnetsov MV, Malos JT and Heckenberg NR, 1998. Topological charge and angular momentum of light carrying optical vortices. Phys. Rev. A. 56: 4064-4075.
        doi:10.1103/PhysRevA.56.4064 http://dx.doi.org/10.1103/PhysRevA.56.4064
15. Bliokh KYu, 2006. Geometrical optics of beams with vortices: Berry phase and or-bital angular momentum Hall effect. Phys. Rev. Lett. 97: 043901 .
        doi:10.1103/PhysRevLett.97.043901 http://dx.doi.org/10.1103/PhysRevLett.97.043901
16. Alexeyev CN and Yavorsky MA, 2007. Berry's phase for optical vortices in coiled optical fibres. J. Opt. A: Pure Appl. Opt. 9: 6-14.
        doi:10.1088/1464-4258/9/1/002 http://dx.doi.org/10.1088/1464-4258/9/1/002
17. Alexeyev CN, Lapin BA and Yavorsky MA, 2007. Optical vortices and topological phase in strongly anisotropic coiled few-mode optical fibres. J. Opt. Soc. Am. B. 24, 2666-2675.
        doi:10.1364/JOSAB.24.002666 http://dx.doi.org/10.1364/JOSAB.24.002666
18. Alexeyev CN and Yavorsky MA, 2007 Propagation of optical vortices in coiled weakly guiding optical fibres. Opt. Spektrosk. 102: 754-759 .
        doi:10.1134/S0030400X07050177 http://dx.doi.org/10.1134/S0030400X07050177
19. Alexeyev CN and Yavorsky MA, 2006. Hybridisation of the topological and dynami-cal phase in coiled optical fibres. J. Opt. A: Pure Appl. Opt. 8: 647-651 .
        doi:10.1088/1464-4258/8/8/005 http://dx.doi.org/10.1088/1464-4258/8/8/005
20. Snyder A.W. and Love J.D. Optical Waveguide Theory. Chapman and Hall: London, New York, (1985).
21. Chen G and Wang Q, 1995. Mode coupling in single-mode helical fibres under perturbation. Opt. Quant. Electron. 27: 1069-74 .
22. Chen G and Wang Q, 1995. Local fields in single-mode helical fibres,” Opt. Quant. Electron. 27: 1069-1074.
        doi:10.1007/BF00292136 http://dx.doi.org/10.1007/BF00292136
23. Soh DBS, Nilsson J, Sahu JK and Cooper LJ, 2003. Geometrical factor modification of helical-core fibre radiation loss formula. Opt. Comm. 222: 235-242.
        doi:10.1016/S0030-4018(03)01599-2 http://dx.doi.org/10.1016/S0030-4018(03)01599-2
24. Shute MW, Sr., Brown CS and Jarzynski J, 1997. Polarization model for a helically wound optical fibre. J. Opt. Soc. Am. A. 14: 3251-3261 .
25. Tsao CYH, 1987. Polarization parameters of plane waves in hybrid birefringent optcal fibres. J. Opt. Soc. Am. A. 4: 1407-1412 .
26. Alexeyev CN, Soskin MS and Volyar AV, 2000. Spin-orbit interaction in a generic vortex field transmitted through an elliptic fibre. Semicond. Phys., Quant. Electron. and Optoelectron. 3: 501-513.
27. Menachem Z and Mond M, 2006. Infrared wave propagation in a helical waveguide with inhomogeneous cross section and application. Electromagn. Waves. 61: 159-192.
        doi:10.2528/PIER06020205 http://dx.doi.org/10.2528/PIER06020205
28. Korn G.A. and Korn T.M., Mathematical handbook for scientists and engineers. McGrawhill: New-York, (1968).
29. V.S. Liberman and B.Ya. Zel’dovich, Spin-orbit interaction of a photon in an inhmo-geneous medium. Phys. Rev. A. 45, 5199-5207 (1992).
        doi:10.1103/PhysRevA.46.5199 http://dx.doi.org/10.1103/PhysRevA.46.5199
30. Volyar AV, Zhilaitis VZ and Shvedov VG, 1999. Optical eddies in small-mode fbres: II. The spin–orbit interaction. Opt. Spektrosk. 86: 593-598.
31. Dooghin AV, Kundikova ND, Liberman VS and Zel’dovich BYa, 1992. Optical Magnus effect. Phys. Rev. A 45: 8204 - 8208 .
        doi:10.1103/PhysRevA.45.8204 http://dx.doi.org/10.1103/PhysRevA.45.8204
32. Bliokh KYu and Bliokh YuP, 2004. Modified geometrical optics of a smoothly inhmogeneous isotropic medium: The anisotropy, Berry phase, and the optical Magnus efect. Phys. Rev. E 70: 026605.
        doi:10.1103/PhysRevE.70.026605 http://dx.doi.org/10.1103/PhysRevE.70.026605
33. Davydov A.S. Quantum mechanics. Pergamon: Oxford, (1976).
34. Alexeyev CN and Yavorsky MA, 2004. Optical vortices and the higher order modes of twisted strongly elliptical optical fibres. J. Opt. A: Pure Appl. Opt. 6: 824-832.
        doi:10.1088/1464-4258/6/9/002 http://dx.doi.org/10.1088/1464-4258/6/9/002
35. Alexeyev CN and Yavorsky MA, 2007. Pancharatnam’s phase induced by spin-orbit interaction in weakly guiding twisted elliptical fibres. Ukr. J. Phys. Opt. 8: 1-12 .
        doi:10.3116/16091833/8/1/1/2007 http://dx.doi.org/10.3116/16091833/8/1/1/2007
36. Pancharatnam S., Collected works of S. Pancharatnam. Oxford: University Press, (1975).
37. Berry MV, 1987. The adiabatic phase and Pancharatnam’s phase for polarized light. J. Mod. Opt. 34: 1401-07 .
        doi:10.1080/09500348714551321 http://dx.doi.org/10.1080/09500348714551321

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