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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 6 — Mar. 17, 2008
  • pp: 3918–3923
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Single-polarization ultra-large-mode-area Yb-doped photonic crystal fiber

O. Schmidt, J. Rothhardt, T. Eidam, F. Röser, J. Limpert, A. Tünnermann, K.P. Hansen, C. Jakobsen, and J. Broeng  »View Author Affiliations


Optics Express, Vol. 16, Issue 6, pp. 3918-3923 (2008)
http://dx.doi.org/10.1364/OE.16.003918


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Abstract

We report on an ytterbium-doped single-transverse-mode rod-type photonic crystal fiber that combines the advantages of low nonlinearity and intrinsic polarization stability. The mode-field-area of the fundamental mode is as large as 2300 µm2. An output power of up to 163 W with a degree of polarization better than 85% has been extracted from a simple fiber laser setup without any additional polarizing element within the cavity than the fiber itself. The beam quality has been characterized by a M2 value of 1.2. The single-polarization window ranges from 1030 to 1080 nm, hence possesses an excellent overlap with the gain profile of ytterbium-doped silica fibers. To the best of our knowledge this fiber design has the largest mode-field-diameter ever reported for polarizing or even polarization maintaining rare-earth-doped double-clad fibers.

© 2008 Optical Society of America

1. Introduction

Rare-earth-doped fiber laser systems have themselves established as a power scalable solid-state laser concept for a variety of operation regimes ranging from ultrafast to narrow linewidth continuous-wave. However, the performance of fiber laser and amplifiers is primarily limited by nonlinear effects, which scale with the core intensity and the interaction length. Hence, over the recent years every endeavor has been made to develop fiber designs with reduced nonlinearity. Conventional actively doped step-index fibers with reduced numerical aperture assisted by coiling or tapered sections to achieve single-mode performance allow for core diameters of up to 40 µm [1

1. Y. Jeong, J. Sahu, D. Payne, and J. Nilsson, “Ytterbium-doped large-core fiber laser with 1.36 kW continuous-wave output power,” Opt. Express 12, 6088–6092 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-25-6088 [CrossRef] [PubMed]

]. Rare-earth-doped photonic crystal fibers (PCF) allow for significantly large core sizes of up to 100 µm [2–4

2. 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.opticsinfobase.org/abstract.cfm?URI=oe-12-7-1313 [CrossRef] [PubMed]

] due to the significantly better control of the index step between a nano-structured core and the holey photonic crystal cladding. As an alternative to this weakly confined large-mode PCF other approaches have been pursued such as the excitation of a single higher-order mode (HOM) in a highly multimode fiber [5

5. S. Ramachandran, J. W. Nicholson, S. Ghalmi, M. F. Yan, P. Wisk, E. Monberg, and F. V. Dimarcello, “Light propagation with ultralarge modal areas in optical fibers,” Opt. Lett. 31, 1797–1799 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=ol-31-12-1797 [CrossRef] [PubMed]

] or tailored propagation loss for higher-order modes as demonstrated in chirally coupled core (CCC) fibers [6

6. C. -H. Liu, G. Chang, N. Litchinitser, A. Galvanauskas, D. Guertin, N. Jabobson, and K. Tankala, “Effectively Single-Mode Chirally-Coupled Core Fiber,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper ME2. http://www.opticsinfobase.org/abstract.cfm?URI=ASSP-2007-ME2

] or fibers with a single ring of large air holes [7

7. W. S. Wong, X. Peng, J. M. McLaughlin, and L. Dong, “Breaking the limit of maximum effective area for robust single-mode propagation in optical fibers,” Opt. Lett. 30, 2855–2857 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=ol-30-21-2855 [CrossRef] [PubMed]

].

However, a degradation of the degree of polarization (DOP) is typically observed when using non-polarization maintaining fibers. To overcome this problem and especially to simplify the laser setup in terms of polarization control there is a great interest in combining large-mode-area fibers and polarization maintaining elements. Several approaches have been reported to introduce the necessary birefringence, such as the well-known technique of stress-applying parts (SAP) inside a step-index large-mode-area low-numerical aperture fiber [8

8. C.-H. Liu, A. Galvanauskas, V. Khitrov, B. Samson, U. Manyam, K. Tankala, D. Machewirth, and S. Heinemann, “High-power single-polarization and single-transverse-mode fiber laser with an all-fiber cavity and fiber-grating stabilized spectrum,” Opt. Lett. 31, 17–19 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=ol-31-1-17 [CrossRef] [PubMed]

], asymmetric hole arrangements in leakage channel fibers possessing mode-field-areas of up to 1400 µm2 [9

9. X. Peng and L. Dong, “Fundamental-mode operation in polarization-maintaining ytterbium-doped fiber with an effective area of 1400 µm2,” Opt. Lett. 32, 358–360 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-4-358 [CrossRef] [PubMed]

] or an index-matched SAP region in combination with the photonic crystal cladding in photonic crystal fibers. The latter technique gives even the possibility to split (due to introduced birefringence) the two polarization states of the weakly guided fundamental mode in that way, that the effective index of one polarization is below the cladding index, thus, resulting in a single polarization large mode area fiber. An Ytterbium-doped single-polarization fiber with mode-field-area of about 700 µm2 has been reported recently [10

10. T. Schreiber, F. Röser, O. Schmidt, J. Limpert, R. Iliew, F. Lederer, A. Petersson, C. Jacobsen, K. Hansen, J. Broeng, and A. Tünnermann, “Stress-induced single-polarization single-transverse mode photonic crystal fiber with low nonlinearity,” Opt. Express 13, 7621–7630 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-19-7621 [CrossRef] [PubMed]

].

In this contribution we report on a continuous-wave fiber laser comprising a 70 µm core single-polarization, single-transverse mode photonic crystal fiber. The fiber laser shows a high DOP without any additional polarization controlling intracavity element up to a pump-power limited output power as high as 163 W. The mode-area of the fundamental mode is ~2300 µm2, corresponding to a mode-field-diameter larger than 50 µm. The comparison with a standard (non-polarizing) fiber with similar dimension shows the advantages and the potential of the fiber including SAPs in terms of polarization control. The fiber design bases on the rod-type photonic crystal fiber concept [3

3. J. Limpert, O. Schmidt, J. Rothhardt, F. Röser, T. Schreiber, A. Tünnermann, S. Ermeneux, P. Yvernault, and F. Salin, “Extended single-mode photonic crystal fiber lasers,” Opt. Express 14, 2715–2720 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-7-2715 [CrossRef] [PubMed]

] combined with a region of boron-doped SAP in the photonic crystal cladding. Hence, polarizing properties are added to a fiber which distinguishes itself by a very large mode-area together with a very short absorption length (below 1 meter), hence, possessing an ultra-low nonlinearity. The waveguide structures for signal and pump radiation are surrounded by a very large fused silica outer cladding making the fiber stiff and self-supporting without the need of protective polymer coating. Therefore, the large fundamental core mode is protected from any bending induced distortion and mode area reduction, which is typically observed when large mode area fibers are coiled [11

11. J. M. Fini, “Bend-resistant design of conventional and microstructure fibers with very large mode area,” Opt. Express 14, 69–81 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-1-69 [CrossRef] [PubMed]

]. The rod-type fiber concept allows for maintaining the large mode size over the entire fiber length leading to most effective exploitation of the low-nonlinearity. In addition, the lack of the polymer coating makes high average power extraction possible without thermal issues.

2. The 70 µm core ytterbium-doped single-transverse-mode polarizing rod-type fiber

A cross section of the ultra-large mode area ytterbium-doped single-polarization rod-type PCF (Crystal Fibre DC-200/70-PM-Yb-ROD) is shown in Fig. 1. Clearly visible are the boron-doped stress applying parts within the outer four rings of the photonic crystal structure which are responsible for the birefringence and thus the polarizing properties of the fiber.

The 200 µm inner cladding (pump waveguide) is surrounded by an air-clad consisting of ninety 400 nm thick and 7 µm long silica bridges. This structure leads to a numerical aperture of ~0.6 at 976 nm allowing for efficient launch of the multimode pump radiation into the fiber. 19 missing holes in the center of the fiber form the Yb/Al co-doped active core region with a corner-to-corner distance of 70 µm. Five rings of small, carefully dimensioned air-holes (pitch Λ~11 µm, relative hole size d/Λ = 0.1) around this core provide the guidance of the fundamental mode only, whereby the inner ring maintains free from SAPs. A theoretical consideration of such structures has revealed that the induced stress is not screened by the photonic crystal structure for relative hole sizes below 0.5 [12

12. 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/abstract.cfm?URI=oe-13-10-3637 [CrossRef] [PubMed]

].

Due to the small ratio of pump- to active core area resulting in an increased pump overlap the pump light absorption is enhanced. Thus, the fiber possesses a small signal absorption of about 30 dB/m at 976 nm. The whole inner structure is surrounded by a stiff 1.5 mm thick fused silica outer cladding to prevent the weakly guided fundamental mode from bend-induced losses or distortions. No coating material is applied allowing for straightforward high power extraction

Fig. 1. Cross-section of the polarizing large-mode-area PCF with a zoom on the embedded stress applying parts.

3. Characterization results

To measure the polarization properties of the polarizing large-mode-area PCF a simple laser setup has been build up, as shown in Fig. 2. The laser cavity consists of a high reflective mirror (M1) and the 4 % Fresnel reflection at the perpendicularly cleaved output facet of the 1.2 m long fiber. It is important to mention that there is no polarizing element placed intra-cavity than the fiber itself. The fiber is pumped by a fiber coupled (400 µm, NA = 0.22) laser diode emitting at a wavelength of 976 nm. The degree of polarization (DOP = (Pmax - Pmin) / (Pmax + Pmin)) is characterized by a combination of a zero-order achromatic half wave plate and a polarization beam splitter.

Fig. 2. Experimental laser setup (M1 - high reflectivity mirror, M2 - dichroic mirror (HT < 990 nm, HR > 1010 nm), PH - pinhole to block unabsorbed pump light, HWP - half wave plate, PBS - polarization beam splitter, PZ-PCF - single-polarization photonic crystal fiber.

Figure 3 shows the measured output power as a function of the launched pump power. At maximum available pump power (220 W) an output power of 163 W is reached with a slope efficiency of approximately 75 %. No wavelength selection is introduced, hence, the laser shows broadband emission around 1035 nm. As seen in the graph no roll-over effect of the slope is detectable. A misalignment of the cavity caused a reduction of output power but not a change in output mode profile, therefore, the 70 µm active core can be considered as intrinsically single-mode. Generated by the implementation of the stress applying parts and thus inhomogeneous spatial guiding conditions the near-field image reveals a slightly asymmetric mode, possessing mode-field-diameters of 50 and 57 µm, respectively (see inset of Fig. 3) and a core NA of ~0.015. The corresponding mode-field-area is as large as 2300 µm2. The emitted beam quality is characterized for the complete power range mentioned above to a M2 value of about 1.2. (device: SPIRICON beam propagation analyzer model M2- 200), as shown in Fig. 4.

Fig. 3. Laser performance of the 1.2 m polarizing rodtype LMA-PCF. The inset shows a near-field image of the fundamental mode.
Fig. 4. Characterization of beam quality at the highest power level.

In comparison to polarization maintaining fibers a polarizing fiber inherently suppresses the evolution of the fast axis polarization state. Figure 5 shows the DOP as a function of the launched pump power. The results obtained for the fiber with SAPs are compared to a very similar rod-type fiber without SAPs possessing an 80 µm core and a 200 µm inner cladding. An identical length of 1.2 m of fiber is used in the same experimental setup. As shown, the DOP of the large-mode-area single-polarization PCF maintains the linear polarization state with increasing pump power (DOP > 85 %, equivalent to a polarization extinction ratio (PER) of >11 dB). At 20 W output power a maximum DOP of ~90 % (PER ~13 dB) has been measured. In contrast, the non-PZ fiber shows more or less uncontrolled as well as temporally unstable polarization output.

Fig. 5. DOP vs. launched pump power for the polarizing and a non-polarizing rod-type fiber.

In order to gain information about the spectral range in which the fiber is polarizing (polarization window) the passive transmission characteristics have been investigated by launching a widely tunable narrow linewidth diode laser into the 70 µm active core. Figure 6 shows near field intensity distributions for the slow- and fast axis modes which are characteristic for three wavelength ranges. The measurement reveals a high guidance loss for both polarization states below 1030 nm, low-loss propagation for the slow axis and still high losses for the fast axis mode for wavelengths ranging from 1030 to 1080 nm with a maximum polarization extinction around ~1050 nm. Above 1080 nm even the fast axis polarization state is getting more confined and the fiber structure acts in a polarization maintaining manner. It should be mentioned that the transitions between the regimes are rather smooth than discrete. This spectral single-polarization window matches well with the typical spectral gain distribution of Yb-doped silica fibers.

Fig. 6. Near field intensity distributions for the slow (upper row) and fast axis at four different wavelengths.

The birefringence of the large-mode-area PCF above the polarization window (>1080 nm) has been characterized by launching linearly polarized white light at 45° to slow and fast axis into a 60 cm long fiber sample. At a wavelength of 1150 nm the spectral interference pattern between both polarization modes has a period of 7 nm, corresponding to a birefringence of 3.1 × 10−4.

4. Conclusion

In conclusion, we report on a large-mode-area (2300 µm2) single-transverse mode single-polarization ytterbium-doped photonic crystal fiber. To our knowledge this is the largest polarizing or even polarization maintaining fiber design ever demonstrated. The polarizing properties have been proven in a high power fiber laser setup without any additional polarization control. An output power of 163 W has been demonstrated with a degree of polarization higher than 85 % for the whole power range. The single-polarization window of the presented fiber design ranges from 1030 to 1080 nm, hence possessing a good overlap with the Yb gain profile, making this fiber suitable for high peak power and high energy fiber laser and amplifier configurations.

References

1.

Y. Jeong, J. Sahu, D. Payne, and J. Nilsson, “Ytterbium-doped large-core fiber laser with 1.36 kW continuous-wave output power,” Opt. Express 12, 6088–6092 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-25-6088 [CrossRef] [PubMed]

2.

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.opticsinfobase.org/abstract.cfm?URI=oe-12-7-1313 [CrossRef] [PubMed]

3.

J. Limpert, O. Schmidt, J. Rothhardt, F. Röser, T. Schreiber, A. Tünnermann, S. Ermeneux, P. Yvernault, and F. Salin, “Extended single-mode photonic crystal fiber lasers,” Opt. Express 14, 2715–2720 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-7-2715 [CrossRef] [PubMed]

4.

C. D. Brooks and F. Di Teodoro “Multimegawatt peak-power, single-transverse-mode operation of a 100 µm core diameter, Yb-doped rodlike photonic crystal fiber amplifier,” Appl. Phys. Lett. 89, 111119 (2006). [CrossRef]

5.

S. Ramachandran, J. W. Nicholson, S. Ghalmi, M. F. Yan, P. Wisk, E. Monberg, and F. V. Dimarcello, “Light propagation with ultralarge modal areas in optical fibers,” Opt. Lett. 31, 1797–1799 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=ol-31-12-1797 [CrossRef] [PubMed]

6.

C. -H. Liu, G. Chang, N. Litchinitser, A. Galvanauskas, D. Guertin, N. Jabobson, and K. Tankala, “Effectively Single-Mode Chirally-Coupled Core Fiber,” in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper ME2. http://www.opticsinfobase.org/abstract.cfm?URI=ASSP-2007-ME2

7.

W. S. Wong, X. Peng, J. M. McLaughlin, and L. Dong, “Breaking the limit of maximum effective area for robust single-mode propagation in optical fibers,” Opt. Lett. 30, 2855–2857 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=ol-30-21-2855 [CrossRef] [PubMed]

8.

C.-H. Liu, A. Galvanauskas, V. Khitrov, B. Samson, U. Manyam, K. Tankala, D. Machewirth, and S. Heinemann, “High-power single-polarization and single-transverse-mode fiber laser with an all-fiber cavity and fiber-grating stabilized spectrum,” Opt. Lett. 31, 17–19 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=ol-31-1-17 [CrossRef] [PubMed]

9.

X. Peng and L. Dong, “Fundamental-mode operation in polarization-maintaining ytterbium-doped fiber with an effective area of 1400 µm2,” Opt. Lett. 32, 358–360 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-4-358 [CrossRef] [PubMed]

10.

T. Schreiber, F. Röser, O. Schmidt, J. Limpert, R. Iliew, F. Lederer, A. Petersson, C. Jacobsen, K. Hansen, J. Broeng, and A. Tünnermann, “Stress-induced single-polarization single-transverse mode photonic crystal fiber with low nonlinearity,” Opt. Express 13, 7621–7630 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-19-7621 [CrossRef] [PubMed]

11.

J. M. Fini, “Bend-resistant design of conventional and microstructure fibers with very large mode area,” Opt. Express 14, 69–81 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-1-69 [CrossRef] [PubMed]

12.

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/abstract.cfm?URI=oe-13-10-3637 [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
(060.5295) Fiber optics and optical communications : Photonic crystal fibers
(060.3510) Fiber optics and optical communications : Lasers, fiber

ToC Category:
Photonic Crystal Fibers

History
Original Manuscript: January 2, 2008
Revised Manuscript: March 3, 2008
Manuscript Accepted: March 3, 2008
Published: March 10, 2008

Citation
O. Schmidt, J. Rothhardt, T. Eidam, F. Röser, J. Limpert, A. Tünnermann, K. P. Hansen, C. Jakobsen, and J. Broeng, "Single-polarization ultra-large-mode-area Yb-doped photonic crystal fiber," Opt. Express 16, 3918-3923 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-6-3918


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References

  1. Y. Jeong, J. Sahu, D. Payne, and J. Nilsson, "Ytterbium-doped large-core fiber laser with 1.36 kW continuous-wave output power," Opt. Express 12, 6088-6092 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-25-6088 [CrossRef] [PubMed]
  2. 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.opticsinfobase.org/abstract.cfm?URI=oe-12-7-1313 [CrossRef] [PubMed]
  3. J. Limpert, O. Schmidt, J. Rothhardt, F. Röser, T. Schreiber, A. Tünnermann, S. Ermeneux, P. Yvernault, and F. Salin, "Extended single-mode photonic crystal fiber lasers," Opt. Express 14, 2715-2720 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-7-2715 [CrossRef] [PubMed]
  4. C. D. Brooks and F. Di Teodoro "Multimegawatt peak-power, single-transverse-mode operation of a 100 µm core diameter, Yb-doped rodlike photonic crystal fiber amplifier," Appl. Phys. Lett. 89, 111119 (2006). [CrossRef]
  5. S. Ramachandran, J. W. Nicholson, S. Ghalmi, M. F. Yan, P. Wisk, E. Monberg, and F. V. Dimarcello, "Light propagation with ultralarge modal areas in optical fibers," Opt. Lett. 31, 1797-1799 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=ol-31-12-1797 [CrossRef] [PubMed]
  6. C. -H. Liu, G. Chang, N. Litchinitser, A. Galvanauskas, D. Guertin, N. Jabobson, and K. Tankala, " Effectively Single-Mode Chirally-Coupled Core Fiber," in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper ME2. http://www.opticsinfobase.org/abstract.cfm?URI=ASSP-2007-ME2
  7. W. S. Wong, X. Peng, J. M. McLaughlin, and L. Dong, "Breaking the limit of maximum effective area for robust single-mode propagation in optical fibers," Opt. Lett. 30, 2855-2857 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=ol-30-21-2855 [CrossRef] [PubMed]
  8. C.-H. Liu, A. Galvanauskas, V. Khitrov, B. Samson, U. Manyam, K. Tankala, D. Machewirth, S. Heinemann, "High-power single-polarization and single-transverse-mode fiber laser with an all-fiber cavity and fiber-grating stabilized spectrum," Opt. Lett. 31, 17-19 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=ol-31-1-17 [CrossRef] [PubMed]
  9. X. Peng and L. Dong, "Fundamental-mode operation in polarization-maintaining ytterbium-doped fiber with an effective area of 1400 µm2," Opt. Lett. 32, 358-360 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-4-358 [CrossRef] [PubMed]
  10. T. Schreiber, F. Röser, O. Schmidt, J. Limpert, R. Iliew, F. Lederer, A. Petersson, C. Jacobsen, K. Hansen, J. Broeng, and A. Tünnermann, "Stress-induced single-polarization single-transverse mode photonic crystal fiber with low nonlinearity," Opt. Express 13, 7621-7630 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-19-7621 [CrossRef] [PubMed]
  11. J. M. Fini, "Bend-resistant design of conventional and microstructure fibers with very large mode area," Opt. Express 14, 69-81 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-1-69 [CrossRef] [PubMed]
  12. 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/abstract.cfm?URI=oe-13-10-3637 [CrossRef] [PubMed]

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