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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 10 — May. 16, 2005
  • pp: 3637–3646
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Stress-induced birefringence in large-mode-area micro-structured optical fibers

T. Schreiber, H. Schultz, O. Schmidt, F. Röser, J. Limpert, and A. Tünnermann  »View Author Affiliations


Optics Express, Vol. 13, Issue 10, pp. 3637-3646 (2005)
http://dx.doi.org/10.1364/OPEX.13.003637


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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

1. Introduction

Currently, micro-structured optical fibers (also called photonic crystal fibers (PCF)) are under intensive research due to their superior properties compared to standard single mode fibers [1

1. P.St.J. Russell, J.C. Knight, T.A. Birks, B.J. Mangan, and W.J. Wadsworth, “Photonic Crystal Fibres,” Science 299, 358–362 (2003). [CrossRef] [PubMed]

]. They consist of a regular micro-structured array of holes, where the core is formed by a solid- or air-filled defect (Fig. 1). The freedom in the design parameters allows for new properties like dispersion shift, endlessly single mode operation [2

2. T.A. Birks, J.C. Knight, and P.St.J. Russell, “Endlessly single-mode photonic crystal fibre,” Opt. Lett. 22, 961–963 (1997). [CrossRef] [PubMed]

] and even low-index bandgap guidance, e.g. in air. In combination with the precision in the fabrication process, exceptional fiber parameters have been achieved. For instance, shifting the zero dispersion wavelength in a fused silica fiber into the visible spectral region [3

3. J.K. Ranka, R.S. Windeler, and A.J. Stentz, “Optical properties of high-delta air silica microstructure optical fibers,” Opt. Lett. 25, 796–798 (2000). [CrossRef]

], truly single-mode extended large-mode-area (LMA) fibers [4

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

] and even low-loss propagation in air-core fibers have been demonstrated [5

5. 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, and P. St. J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express 13, 236–244 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-236 [CrossRef] [PubMed]

]. Beside these extended fiber parameters, completely new experiments in different areas of research have been developed using micro-structured fibers [6

6. 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). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-21-1195 [PubMed]

8

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

].

2. Theory

The stresses resulting from thermal expansion and/or external forces can be calculated according to the equilibrium equation (Eq. 1), where σ is the stress tensor, εx/y are the normal strain components, γxy is the shear strain component, D is the elasticity matrix describing an isotropic material using Young’s modulus E and Poisson’s ratio ν, α is the expansion coefficient, F the force, T the high temperature and Tref the reference temperature, e.g. room temperature. In this equation small displacements and the plain-strain approximation, meaning zero axial strain in z-direction, are assumed [18

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

].

σ=.([εxεyγxy][αα0](1+v)(TTref))=Fwhereσ=Dε
(1)

The elasto-optical effect relates the stress σ to a change of the refractive index Δn according to

Δn=Cσ
(2)

B=(C2C1)(σxσy)
Bav=(C2C1)(σxσy)rdrdφ
(3)

It is now possible to calculate the birefringence created by external forces like twists or lateral forces as well as birefringence induced by SAP [17

17. Z. Zhu and T. G. Brown, “Stress-induced birefringence in microstructured optical fibers,” Opt. Lett. 28, 2306–2308 (2003). [CrossRef] [PubMed]

,10

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

]. For some cases, analytical solutions of equation 1 are available. For complex geometries, like in our case of photonic crystal fibers, one has to solve the problem numerically. One flexible and easy way is the use of the finite element method (FEM), where commercial products are available [19].

Because most of the calculations in this paper refer to photonic crystal fibers, all calculations are done using FEM. A finite element analysis solves a numerical problem by subdividing it’s objects into very small but finite-size elements, where each element is described by equations concerning physical and boundary properties as well as their behaviors. Solving these equations predicts the behavior of the whole object. The quality of the results clearly depends on the shape and number of elements used. For our calculations, a triangulation is done and the element size is decreased until the calculated results have been converged. To reduce calculation time and memory requirements, the object is reduced according to symmetries by means of the right boundary conditions.

Table 1. Parameters used in the calculations.

table-icon
View This Table

Our investigation concerns two cases: firstly, lateral external forces are applied to a micro-structured fiber and the dependence on the outer diameter is evaluated. Secondly, SAPs are placed outside the micro-structured core region. For both stress fields, the screening of the stresses due to the air-hole structure is evaluated in the following sections.

A fiber with SAPs in a circular shape (stress rods) is shown in Fig. 2. This type of fiber is called PANDA type fiber. Different thermal expansion coefficients for the material of the fiber and SAPs generate a permanent stress field when cooling the fiber below the softening temperature during the drawing process. Beside the physical parameters of the materials (E, ν, α, C), which cannot be changed greatly, the geometry parameters (the diameter of the stress rods R, the distance from the center r1 and the diameter of the fiber D) influence the value of the birefringence in the fiber center B following the analytical expression of equation 4 [20

20. P. L. Chu and 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).

].

BR2(r1+R2)2·(13(r1+R2)4(D2)4)
(4)

Generally, the distance r1 has to be minimized without influencing the guided mode. In the case of photonic crystal fibers, the SAPs can only be applied outside the air-hole cladding. A hexagonal holey cladding is shown in Fig. 1. The guiding properties in such solid core PCFs are only determined by the structural parameters, where d is the air-hole diameter and Λ is the pitch [2

2. T.A. Birks, J.C. Knight, and P.St.J. Russell, “Endlessly single-mode photonic crystal fibre,” Opt. Lett. 22, 961–963 (1997). [CrossRef] [PubMed]

,21

21. N.A. Mortensen, J.R. Folkenberg, M.D. Nielsen, and K.P. Hansen, “Modal cutoff and the V parameter in photonic crystal fibers,” Opt. Lett. 28, 1879–1881 (2003). [CrossRef] [PubMed]

]. Clearly, the minimum distance of the SAPs has to be at least r1 =(N+0.5)Λ, where N is the number of air-hole rings surrounding the core. It has already been proven that 4 to 5 rings allow for low loss guidance [22

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

].

Fig. 1. Design and parameters of a micro-structured fiber: Λ — pitch, d — hole diameter
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

The results for these micro-structured PANDA type fibers are presented in section 3.2 and general conclusions for actively doped low-nonlinearity polarization-maintaining fibers will be drawn in section 4.

3. Screening and enhancement of induced stresses

3.1 Stresses by lateral forces

The schematic representation of our calculations for a lateral external force is shown in Fig. 3. A point force is acting in x-direction, which induces a stress distribution inside the fiber. As a result of the FEM calculation, all components of the stress tensor are available. From this, the birefringence B or Bav is calculated using equation 3. A typical result of such a calculation is shown in Fig. 3 containing the principle stress components σx and σy as well as the birefringence B.

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

The air-hole structure influences the induced stress distribution. The relative size of the hole is characterized by the quantity d/Λ, which is also responsible for the guiding properties of such a fiber. It is clear that in the limit of d/Λ=0 the birefringence becomes that of a standard step index fiber. If d/Λ reaches 1 the stresses and birefringence are screened completely, which means that the core is isolated from the cladding. We calculated the exact behavior of this screening effect. For this calculation a large mode area fiber with a pitch of Λ=12 µm is chosen, which expands the holey cladding to a diameter of ~130 µm. The results of the birefringence Bav (averaged over a radius of 6 µm) are shown in Fig. 4 for different outer diameters D of the fiber; 170 µm, 250 µm and 400 µm. The acting force F is chosen in a way that the birefringence obtained without holey cladding is the same for all three fibers. This is an easy task, because the problem scales linearly with the force F (Eq. 1). As the air-hole size increases, a continuous drop in the birefringence is expected, but the calculations show that the birefringence remains almost constant and even increases for the smallest outer diameter of 170 µm until a certain value of d/Λ is reached. Furthermore, the screening depends on the outer diameter. To give some quantities: the value d/Λ where a 10 % drop in the value of the birefringence is observed due to the screening of the holey cladding is ~0.65 for D=400 µm, ~0.75 for D=250 µm and ~0.9 for D=170 µm. This result does not change significantly for the birefringence B in the core center (inset of Fig. 4). From this it can be concluded that the air-hole cladding does not introduce any disadvantages in terms of screening a stress field in a PCF up to a value of d/Λ>0.65. Just to remember: the condition for endlessly single mode operation for a one-hole missing fiber, where most of the photonic crystal fibers usually work, is d/Λ<0.45. Even if d/Λ needs to be larger and a high stress difference in the core region is required, the outer diameter can be chosen to be as small as the holey cladding diameter.

The reason why the screening of the stress is strongly dependent on the outer diameter, especially if the diameter of the holey cladding is comparable to the outer diameter, can be explained as following. The distribution of the induced stresses is visualized in terms of the Von Mises stress σv. This quantity is usually used to summarize the stress tensor to estimate yield criteria for ductile materials [23

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

]. In the case of plane stress it is defined as:

σv=σx2+σy2+(σxσy)22
(5)

Beside the differential stress (σxy)2 responsible of birefringence it also represents the absolute value of the stresses. Fig. 5 shows the distribution of σv for the fiber with D=170 µm (a) and D=400 µm (b) around the holey cladding. For the thinner fiber, it can clearly be seen that the main part of the stresses are influenced by a smaller part of the holey cladding. In the thicker fiber the stress distribution is more uniform across the whole holey cladding. Thus, if less holes effectively influence the stress distribution, a larger hole diameter is necessary to screen the birefringence significantly, which is indeed observed (d/Λ~0.9 for the D=170 µm fiber) and therefore indicates the dependence on D. Furthermore, for a force placed close to the air-holes, the stress is enhanced between the holes due to the decreased area, if d/Λ increases. These stresses are channeled further in direction towards the core, acting against the screening. This is the reason for the increase of the birefringence with increased air-hole size in the 170 µm fiber. For the other fibers this effect is probably hidden due to the effect of screening by the whole cladding.

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

3.2. PANDA-type induced stresses

If stress rods are placed inside a fiber, a different stress distribution is obtained compared to a point force acting on the fiber as done in the last section. Beside the obvious forces along the axes connecting the two stress rods, perpendicular forces act due to the dimension and shape of the rods. For a given fiber diameter D and a minimum distance of the stress rods r1 an optimum rods diameter R can be calculated according to equation 4 to maximize the birefringence in the core center. By varying all geometric parameters including the position of the rods we checked numerically that this law also holds if a holey cladding is placed between the rods, which means that a further optimization is neither necessary nor possible.

Fig. 6. Stress induced birefringence as a function of the relative air-hole size d/Λ for a PANDA type fiber.
Fig. 7. Movie showing the stress induced birefringence distribution in a PANDA type fiber.
Fig. 8. Stress-induced birefringence as a function of the number of rings removed from the outside of the holey cladding.
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. Stress-induced birefringence as a function of the number of rings removed from the inside of the holey cladding.
Fig. 11. Movie showing the birefringence distribution as a function of the number of rings removed from the outside of the holey cladding.

4. Birefringence in rare earth doped, low nonlinearity photonic crystal fibers

Many experiments have proven the potential of power scaling when using rare earth doped fibers as a gain medium in lasers and amplifiers [24

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

]. In these fibers, the actively doped core is usually surrounded by a second highly multimode waveguide, which is called inner cladding or pump core. This has the advantage, that low brightness high power diode lasers can be launched into this core. The pump light is then gradually absorbed over the entire fiber length and is converted into high brightness high power laser radiation. For power scaling it is necessary to have reduced nonlinear interaction of the laser light with the fiber material. In principle, the nonlinear effects scales with the length of the fiber and the intensity of the laser light. The intensity can be lowered using larger core diameters. The length of the fiber is given by the absorption length. Thus, assuming a fixed rare-earth doping concentration the overlap of the pump light with the active core has to be maximized, meaning the ratio of core diameter to outer diameter (here: ~pump core). On the one hand, the scaling of the laser core is limited by low loss single-mode conditions. On the other hand, for polarization maintaining fibers the size of the pump core is limited as it might include SAPs and the micro-structured core.

In Fig. 12, a conventional LMA step index fiber is compared to a micro-structured LMA fiber in terms of achievable birefringence for different outer diameters. Both fibers exhibit the same core diameter of 30 µm. For the step index fiber the minimum distance is set to r1 =40 µm, which is a common distance for stress rods to not disturb the guided mode. Due to the expansion of the holey cladding in the PCF (d/Λ=0.25 and Λ=12 µm) r1 has to be as high as r1 =66 µm. A simple scaling of the geometry will change neither the birefringence nor the nonlinearity as defined above. The blue line in Fig. 12 indicates this fact, where the fiber with an original diameter of 400 µm has been scaled. To compare the achievable birefringence, the outer diameter is changed and the stress rods parameters are optimized, whereas the core region is kept constant. The main difference in achieved birefringence is only attributed to the difference in r1 - no screening is expected for that holey cladding. As a result, the birefringence is decreased by more than 50%. To compensate for that, one has to use almost twice the outer diameter, which also means four times the length and therefore nonlinearity compared to a step index fiber. For actively doped low-nonlinearity photonic crystal fibers, the application of SAP to introduce birefringence seems to be questionable. Anyway, although the birefringence is lowered, photonic crystal fiber can provide true single-mode operation even at this large mode field diameter. On the other hand half of the birefringence could be enough to achieve polarization maintenance. Furthermore, several options are available to increase the birefringence in the fiber, which have not been included in the calculation. For instance, it is well known that pre-treatment of the fiber pre-form, e.g. preheating, is beneficial to maximize the birefringence. Additionally, the actual value of the expansion coefficients of the fiber materials will define the birefringence and changes are expected in a linear manner [25

25. Yueai Liu, B. M. A Rahman, and K. T. V. Grattan, “Thermal-stress-induced birefringence in bow-tie optical fibers,” Appl. Opt. 33, 5611–5616 (1994). [CrossRef] [PubMed]

].

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).

5. Conclusion

We analyzed the influence of a holey cladding to stress distributions inside a fiber induced by a point force acting on the fiber and stress applying parts inside the fiber.

For the first case, we found that the induced birefringence depends on the ratio of holey cladding diameter and outer fiber diameter, e.g. the distance of the force from the holey cladding. As a result, it could be shown that the closer the force is acting, the less screening is observed by the air-holes even at high air-hole diameters. This could be explained by the smaller effective number of holes influencing the stress distribution significantly. For thin fibers, the screening does not occur before a relative air-hole size d/Λ of ~0.9. In any other case the holey cladding does not influence the birefringence in the core center unless a value of d/Λ of above 0.65 is reached, which is well above the condition for endlessly single mode operation of d/Λ<0.45. Furthermore, we explained the fact that an enhancement of birefringence can be observed if the air-hole diameter is large and the fiber is made thin compared to the holey cladding. This could be interesting for sensor applications.

Secondly, we showed, that the birefringence induced by stress applying parts is significantly screened at value of d/Λ>0.65. We explained this by the fact, that again the whole holey cladding influences the stress distribution.

Finally, with the results obtained during our analysis we discussed the birefringence that can be achieved in LMA PCFs when stress-applying parts are placed outside the holey cladding. In comparison to LMA step index fibers, the birefringence is only half that value. The main reason is found to be the distance of the stress rods to the core.

Acknowledgments

This work was supported by the Bundesministerium für Bildung und Forschung (BMBF) under contract number 13 N 8336.

References and links

1.

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

2.

T.A. Birks, J.C. Knight, and P.St.J. Russell, “Endlessly single-mode photonic crystal fibre,” Opt. Lett. 22, 961–963 (1997). [CrossRef] [PubMed]

3.

J.K. Ranka, R.S. Windeler, and A.J. Stentz, “Optical properties of high-delta air silica microstructure optical fibers,” Opt. Lett. 25, 796–798 (2000). [CrossRef]

4.

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

5.

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, and P. St. J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express 13, 236–244 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-236 [CrossRef] [PubMed]

6.

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). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-21-1195 [PubMed]

7.

Th. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416, 233–237 (2002). [CrossRef] [PubMed]

8.

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

9.

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

10.

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

11.

A. Ortigosa-Blanch, J. C. Knight, W. J. Wadsworth, J. Arriaga, B. J. Mangan, T. A. Birks, and P. St. J. Russell, “Highly birefringent photonic crystal fibers,” Opt. Lett. 25, 1325–1327 (2000). [CrossRef]

12.

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

13.

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). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-5931 [CrossRef] [PubMed]

14.

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). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-5-956 [CrossRef] [PubMed]

15.

http://www.crystal-fibre.com

16.

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

17.

Z. Zhu and T. G. Brown, “Stress-induced birefringence in microstructured optical fibers,” Opt. Lett. 28, 2306–2308 (2003). [CrossRef] [PubMed]

18.

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

19.

http://www.femlab.com

20.

P. L. Chu and 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).

21.

N.A. Mortensen, J.R. Folkenberg, M.D. Nielsen, and K.P. Hansen, “Modal cutoff and the V parameter in photonic crystal fibers,” Opt. Lett. 28, 1879–1881 (2003). [CrossRef] [PubMed]

22.

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

23.

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

24.

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

25.

Yueai Liu, B. M. A Rahman, and K. T. V. Grattan, “Thermal-stress-induced birefringence in bow-tie optical fibers,” Appl. Opt. 33, 5611–5616 (1994). [CrossRef] [PubMed]

OCIS Codes
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(060.2420) Fiber optics and optical communications : Fibers, polarization-maintaining

ToC Category:
Research Papers

History
Original Manuscript: April 8, 2005
Revised Manuscript: April 29, 2005
Published: May 16, 2005

Citation
T. Schreiber, H. Schultz, O. Schmidt, F. Röser, J. Limpert, and A. Tünnermann, "Stress-induced birefringence in large-mode-area micro-structured optical fibers," Opt. Express 13, 3637-3646 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-10-3637


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References

  1. 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]
  2. T.A. Birks, J.C. Knight, P.St.J. Russell, �??Endlessly single-mode photonic crystal fibre,�?? Opt. Lett. 22, 961-963 (1997). [CrossRef] [PubMed]
  3. J.K. Ranka, R.S. Windeler, A.J. Stentz, �??Optical properties of high-delta air silica microstructure optical fibers,�?? Opt. Lett. 25, 796-798 (2000). [CrossRef]
  4. 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]
  5. 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]
  6. 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]
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