## Berry’s Phase Analysis of Polarization Rotation in Helicoidal Fibers

Applied Optics, Vol. 37, Issue 18, pp. 3902-3911 (1998)

http://dx.doi.org/10.1364/AO.37.003902

Acrobat PDF (241 KB)

### Abstract

We relate Berry’s topological phase to the polarization rotation of linearly polarized light in helicoidal single-mode ideal fibers where the pitch length and coil radius are allowed to change adiabatically. First we present an alternative derivation for this phase using the Serret–Frenet coordinate system and show that this phase can be derived and interpreted in terms of both solid and planar angles. The results obtained are then applied to various helicoidal fiber structures, and from this we show that the total change in the polarization rotation angle can be tailored through a judicious choice of the fiber geometry. Finally, we propose that certain helicoidal fiber configurations can be used as fiber sensors.

© 1998 Optical Society of America

**OCIS Codes**

(060.0060) Fiber optics and optical communications : Fiber optics and optical communications

(080.0080) Geometric optics : Geometric optics

(130.6010) Integrated optics : Sensors

(260.5430) Physical optics : Polarization

**Citation**

Frank Wassmann and Adrian Ankiewicz, "Berry’s Phase Analysis of Polarization Rotation in Helicoidal Fibers," Appl. Opt. **37**, 3902-3911 (1998)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-18-3902

Sort: Year | Journal | Reset

### References

- J. N. Ross, “The rotation of the polarization in low birefringence monomode optical fibres due to geometric effects,” Opt. Quantum Electron. 16, 455–461 (1984).
- 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).
- X. S. Fang and Z. Q. Lin, “Field in single-mode helically-wound optical fibers,” IEEE Trans. Microwave Theory Tech. MTT-33, 1150–1154 (1985).
- G. Chen and Q. Wang, “Local fields in single-mode helical fibres,” Opt. Quantum Electron. 27, 1069–1074 (1995).
- R. Ulrich and A. Simon, “Polarization optics of twisted single-mode fibers,” Appl. Opt. 18, 2241–2251 (1979).
- A. M. Smith, “Birefringence induced by bends and twists in single-mode optical fiber,” Appl. Opt. 19, 2606–2611 (1980).
- M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. London Ser. A 392, 45–57 (1984).
- B. Markovski and V. I. Vinitsky, Topological Phases in Quantum Theory (World Scientific, Singapore, 1989).
- A. Shapere and F. Wilczek, Geometric Phases in Physics (World Scientific, Singapore, 1989).
- S. Pancharatnam, “Generalized theory of interference and its application,” Proc. Indian Acad. Sci. A 44, 247–262 (1956).
- M. P. Varnham, R. D. Birch, and D. N. Payne, “Helical-core circularly-birefringent fibers,” in Proceedings of the International Conference on Integrated Optics and Optical Fibre Communications–European Conference on Optical Communications (Instituto Internazionale delle Communicazione, Genova, Italy, 1985), pp. 135–138.
- M. V. Berry, “The adiabatic phase and Pancharatnam’s phase for polarized light,” J. Mod. Opt. 34, 1401–1407 (1987a).
- M. V. Berry, “Interpreting the anholonomy of coiled light,” Nature (London) 326, 277–278 (1987).
- M. V. Berry, “Classical adiabatic angles and quantal adiabatic phase,” J. Phys. A 18, 15–27 (1985).
- J. H. Hannay, “Angle variable holonomy in adiabatic excursion of an integrable Hamiltonian,” J. Phys. A 18, 221–230 (1985).
- R. Y. Chiao and Y-S. Wu, “Manifestations of Berry’s topological phase for the photon,” Phys. Rev. Lett. 57, 933–936 (1986).
- V. S. Liberman and B. Ya. Zel’dovich, “Birefringence by a smoothly inhomogeneous locally isotropic medium,” Phys. Rev. E 49, 2389–2396 (1994).
- A. Yu. Savchenko and B. Ya. Zel’dovich, “Birefringence by a smoothly inhomogeneous locally isotropic medium: three-dimensional case,” Phys. Rev. E 50, 2287–2292 (1994).
- V. S. Liberman and B. Ya. Zel’dovich, “Spin-orbit interaction of a photon in an inhomogeneous medium,” Phys. Rev. A 46, 5199–5207 (1992).
- F. D. M. Haldane, “Path dependence of the geometric rotation of polarization in optical fibers,” Opt. Lett. 11, 730–732 (1986).
- L. H. Ryder, “The optical Berry phase and the Gauss-Bonnet theorem,” Eur. J. Phys. 12, 15–18 (1991).
- L. Lewin, D. C. Chang, and E. F. Kuester, Electromagnetic Waves and Curved Structures (Peregrinus, London, 1977).
- C. H. Tang, “An orthogonal coordinate system for curved pipes,” IEEE Trans. Microwave Theory Tech. MTT-18, 69 (1970).
- A. Altintas and J. D. Love, “Effective cut-offs for modes on helical fibres,” Opt. Quantum Electron. 22, 213–226 (1990).
- R. Bhandari and J. Samuel, “Observation of topological phase by use of a laser interferometer,” Phys. Rev. Lett. 60, 1211–1213 (1988).
- R. Y. Chiao, A. Antaramian, K. M. Ganga, H. Jiao, S. R. Wilkinson, and H. Nathel, “Observation of a topological phase by means of a nonplanar Mach–Zehnder interferometer,” Phys. Rev. Lett. 60, 1214–1217 (1988).
- P. Hariharan and M. Roy, “A geometric phase interferometer,” J. Mod. Opt. 39, 1811–1815 (1992).
- E. Frins and W. Dultz, “Direct observation of Berry’s topological phase by using an optical fibre ring interferometer,” Opt. Commun. 136, 354–356 (1997).
- P. Hariharan, K. G. Larkin, and M. Roy, “The geometric phase: interferometric observations with white light,” J. Mod. Opt. 41, 663–667 (1994).
- J. Liñares, M. C. Nistal, and D. Baldomin, “Beam modes in graded-index media and topological phases,” Appl. Opt. 33, 4293–4299 (1994).
- D. Subbarao, “Topological phase in Gaussian beam optics,” Opt. Lett. 16, 223–225 (1995).
- T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, and R. G. Priest, “Optical fiber sensor technology,” IEEE J. Quantum Electron. QE-18, 626–665 (1982).
- G. Davis and A. Mazzolini, “A new biomedical sensor utilizing macrobending losses in optical fibers,” Proc. Aust. Conf. Opt. Fibre Technol. 21, 129–132 (1996).
- S. K. Yao and C. K. Asawa, “Microbending fiber optic sensing,” in Fiber Optic and Laser Sensors I, E. L. Moore and O. G. Ramer, eds., Proc. SPIE 412, 9–13 (1983).
- N. Lagakos, J. H. Cole, and J. A. Bucaro, “Microbend fiber-optic sensor,” Appl. Opt. 26, 2171–2180 (1987).
- T. Abe, Y. Mitsunaga, and H. Koga, “A strain sensor using twisted optical fibers,” J. Lightwave Technol. 7, 525–529 (1989).
- T. Yoshino, K. Inoue, and Y. Kobayashi, “Spiral fibre microbend sensors,” IEE Proc. Optoelectron. 144, 145–150 (1997).
- D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. Am. 66, 216–220 (1976).
- I. Bassett, “Design principle for a circularly birefringent optical fiber,” Opt. Lett. 13, 844–846 (1988).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.