Abstract

We report on detailed numerical investigation of stress-induced birefringence in micro-structured solid-core optical fibers. The stress is induced either by external forces or stress applying parts inside the fiber. Both methods lead to different stress distributions where screening as well as enhancement effects due to the air-hole micro-structuring could be observed. Furthermore, we discuss the potential of the realization of polarization-maintaining low-nonlinearity micro-structured fibers that are suitable for applications in ultrafast optics.

© 2005 Optical Society of America

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References

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Appl. Opt. (1)

Conference on Lasers and Electro-Optics (1)

J. Limpert, A. Liem, T. Schreiber, S. Nolte, H. Zellmer, A. Tünnermann, J. Broeng, A. Petersson, Ch. Jacobsen, H. Simonsen, N.A. Mortensen, �??Extended large-mode-area single-mode microstructured fiber laser," Conference on Lasers and Electro-Optics 2004, San Francisco, session CMS.

Electron. Lett. (1)

M.D. Nielsen, J.R. Folkenberg, N.A. Mortensen, �??Singlemode photonic crystal fibre with effective area of 600 µm2 and low bending loss,�?? Electron. Lett. 39, 25, 1802 (2003).
[CrossRef]

IEEE J. Quantum Electron. (1)

A.J. Barlow, D.N. Payne, �??The stress-optic effect in optical fibres,�?? IEEE J. Quantum Electron. QE-19 (5), 834-839 (1983).
[CrossRef]

J. Lightwave Technol. (2)

P. L. Chu, R. A. Sammut, �??Analytical method for calculation of stresses and material birefringence in polarization-maintaining optical fiber,�?? J. Lightwave Technol. LT-2, 650-662 (1984).

J. Noda, K. Okamoto, Y. Sasaki, �??Polarization-maintaining fibers and their applications,�?? J. Lightwave Technol. LT-4, 1071-1088 (1986).
[CrossRef]

Nature (1)

Th. Udem, R. Holzwarth, T. W. Hänsch, �??Optical frequency metrology,�?? Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

Opt. Expres (1)

F. Benabid, J. C. Knight, and P. S. J. Russell, "Particle levitation and guidance in hollow-core photonic crystal fiber," Opt. Express 10, 1195-1203 (2002). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-21-1195">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-21-1195</a>
[PubMed]

Opt. Express (5)

J. R. Folkenberg, M. D. Nielsen, N. A. Mortensen, C. Jakobsen, and H. R. Simonsen, "Polarization maintaining large mode area photonic crystal fiber," Opt. Express 12, 956-960 (2004). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-5-956">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-5-956</a>
[CrossRef] [PubMed]

J. Limpert, A. Liem, M. Reich, T. Schreiber, S. Nolte, H. Zellmer, A. Tünnermann, J. Broeng, A. Petersson, C. Jakobsen, "Low-nonlinearity single-transverse-mode ytterbium-doped photonic crystal fiber amplifier," Opt. Express 12, 1313-1319 (2004). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1313">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1313</a>
[CrossRef] [PubMed]

X. Chen, M. Li, N. Venkataraman, M. T. Gallagher, W. A. Wood, A. M. Crowley, J. P. Carberry, L. A. Zenteno, K. W. Koch, "Highly birefringent hollow-core photonic bandgap fiber," Opt. Express 12, 3888-3893 (2004). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-16-3888">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-16-3888</a>
[CrossRef] [PubMed]

T. Ritari, H. Ludvigsen, M. Wegmuller, M. Legré, N. Gisin, J. R. Folkenberg, and M. D. Nielsen, "Experimental study of polarization properties of highly birefringent photonic crystal fibers,�?? Opt. Express 12, 5931-5939 (2004). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-5931">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-5931</a>
[CrossRef] [PubMed]

P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, P. St. J. Russell, "Ultimate low loss of hollow-core photonic crystal fibres," Opt. Express 13, 236-244 (2005). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-236">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-236</a>
[CrossRef] [PubMed]

Opt. Lett. (5)

Photonics Spectra (1)

J. Limpert, A. Liem, T. Schreiber, F. Röser, H. Zellmer, A. Tünnermann, �??Scaling Single-Mode Photonic Crystal Fiber Lasers to Kilowatts,�?? Photonics Spectra 38, 54-65 (2004).

Science (2)

P.St.J. Russell, J.C. Knight, T.A. Birks, B.J. Mangan, W.J. Wadsworth, �??Photonic Crystal Fibres,�?? Science 299, 358-362 (2003).
[CrossRef] [PubMed]

F. Benabid, J. C. Knight, G. Antonopoulos, P. St. J. Russell, �??Stimulated Raman Scattering in Hydrogen-Filled Hollow-Core Photonic Crystal Fiber,�?? Science 11, 298, 399-402 (2002).
[CrossRef]

Other (4)

<a href="http://www.crystal-fibre.com">http://www.crystal-fibre.com</a>

A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity (Dover, New York, 1944).

<a href="http://www.femlab.com">http://www.femlab.com</a>

R. Hill, The Mathematical Theory of Plasticity (Oxford University Press, 1998).

Supplementary Material (3)

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Figures (12)

Fig. 1.
Fig. 1.

Design and parameters of a micro-structured fiber: Λ — pitch, d — hole diameter

Fig. 2.
Fig. 2.

Design and parameters of a PANDA type fiber: r1 — distance of the stress rods from the center of the fiber, R — diameter of the stress rods, D — diameter of the fiber

Fig. 3.
Fig. 3.

Principal stresses σx and σy, and resulting birefringence B introduced by an external force (F=1000 N) applied to a fiber with an outer diameter of 170 µm

Fig. 4.
Fig. 4.

Average birefringence Bav as a function of the relative airhole size d/Λ for different outer diameters of the fiber (inset: birefringence in the center of the core).

Fig. 5.
Fig. 5.

Von Mises stress distribution σv [Pa] in the holey cladding for an outer diameter of (a) 170 µm and (b) 400 µm

Fig. 6.
Fig. 6.

Stress induced birefringence as a function of the relative air-hole size d/Λ for a PANDA type fiber.

Fig. 7.
Fig. 7.

Movie showing the stress induced birefringence distribution in a PANDA type fiber.

Fig. 8.
Fig. 8.

Stress-induced birefringence as a function of the number of rings removed from the outside of the holey cladding.

Fig. 9.
Fig. 9.

Movie showing the birefringence distribution as a function of the number of rings removed from the outside of the holey cladding.

Fig. 10.
Fig. 10.

Stress-induced birefringence as a function of the number of rings removed from the inside of the holey cladding.

Fig. 11.
Fig. 11.

Movie showing the birefringence distribution as a function of the number of rings removed from the outside of the holey cladding.

Fig. 12.
Fig. 12.

Birefringence that can be obtained from a large-mode area step index fibers with r1=40 µm (a) and photonic crystal fibers with r1=66 µm (b). Simple scaling of the whole PCF structure of a seven-missing air-hole, 400 µm PCF does not change the birefringence but the core diameter (c).

Tables (1)

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Table 1. Parameters used in the calculations.

Equations (6)

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σ = . ( [ ε x ε y γ xy ] [ α α 0 ] ( 1 + v ) ( T T ref ) ) = F where σ = D ε
Δ n = C σ
B = ( C 2 C 1 ) ( σ x σ y )
B av = ( C 2 C 1 ) ( σ x σ y ) r dr d φ
B R 2 ( r 1 + R 2 ) 2 · ( 1 3 ( r 1 + R 2 ) 4 ( D 2 ) 4 )
σ v = σ x 2 + σ y 2 + ( σ x σ y ) 2 2

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