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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 23 — Nov. 10, 2008
  • pp: 18752–18763
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Birefringent all-solid hybrid microstructured fiber

Ryuichiro Goto, Stuart D. Jackson, Simon Fleming, Boris T. Kuhlmey, Benjamin J. Eggleton, and Kuniharu Himeno  »View Author Affiliations


Optics Express, Vol. 16, Issue 23, pp. 18752-18763 (2008)
http://dx.doi.org/10.1364/OE.16.018752


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Abstract

We report the characterization of a birefringent all-solid hybrid microstructured fiber, in which the core-modes are guided by both the photonic bandgap (PBG) effect and total internal reflection (TIR). Due to the twofold symmetry, modal birefringence of 1.5×10-4 and group birefringence of 2.1×10-4 were measured at 1.31 μm, which is in the middle of the second bandgap. The band structure was calculated to be different from conventional 2-D PBG fibers due to the 1-D arrangement of high-index regions. The bend loss has a strong directional dependence due to the coexistence of the two guiding mechanisms. The fiber has two important properties pertinent to PBG fibers; spectral filtering, and chromatic dispersion specific to PBG fibers. The number of high-index regions, which trap pump power (by index guiding) when the fiber is used in cladding-pumped fiber lasers, is greatly reduced so that this fiber should enable efficient cladding pumping. This structure is suitable for linearly-polarized, cladding-pumped fiber lasers utilizing the properties of PBG fibers.

© 2008 Optical Society of America

1. Introduction

All-solid photonic bandgap (PBG) fibers [1

1. F. Brechet, P. Roy, J. Marcou, and D. Pagnoux, “Single-mode propagation into depressed-core-index photonic-bandgap fibre designed for zero-dispersion propagation at short wavelengths,” Electron. Lett. 36, 514–515 (2000). [CrossRef]

4

4. A. Argyros, T. A. Birks, S. G. Leon-Saval, C. M. Cordeiro, F. Luan, and P. St. J. Russell, “Photonic bandgap with an index step of one percent,” Opt. Express 13, 309–314 (2005). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-13-1-309. [CrossRef] [PubMed]

] are one configuration of PBG fibers [5

5. P. Yeh, A. Yariv, and E. Marom, “Theory of Bragg fiber,” J. Opt. Soc. Am. 68, 1196–1199 (1978). [CrossRef]

, 6

6. J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic Band Gap Guidance in Optical Fibers,” Science 282, 1476–1478 (1998). [CrossRef] [PubMed]

] in which a low-index glass core is surrounded by a microstructured cladding, which typically comprises isolated high-index glass regions embedded in a low-index glass background. The core-modes are guided not by total internal reflection (TIR) but by coherent multiple scattering from the microstructured cladding, and the guidance mechanism is explained by the PBG effect [7

7. T. A. Birks, P. J. Roberts, P. St. J. Russell, D. M. Atkin, and T. J. Shepherd, “Full 2-D photonic bandgaps in silica/air structures,” Electron. Lett. 31, 1941–1943 (1995). [CrossRef]

,8

8. J. Lægsgaard, “Gap formation and guided modes in photonic bandgap fibres with high-index rods,” J. Opt. A 6, 798–804 (2004). [CrossRef]

] or, more generally, by anti-resonant reflection [9

9. T. P. White, R. C. McPhedran, C. Martjin de Sterke, N. M. Litchinitser, and B. J. Eggleton, “Resonance and scattering in microstructured optical fibers,” Opt. Lett. 27, 1977–1979 (2002). [CrossRef]

,10

10. N. M. Litchinitser, A. K. Abeeluck, C. Headley, and B. J. Eggleton, “Antiresonant reflecting photonic crystal optical waveguides,” Opt. Lett. 27, 1592–1594 (2002). [CrossRef]

]. A particularly interesting aspect of all-solid PBG fibers is that their core can be doped with rare-earth ions to make fiber lasers. Such fiber lasers then benefit from the properties of all-solid PBG fibers, such as spectral filtering [11

11. A. Wang, A. K. George, and J. C. Knight, “Three-level neodymium fiber laser incorporating photonic bandgap fiber,” Opt. Lett. 31, 1388–1390 (2006). [CrossRef] [PubMed]

, 12

12. V. Pureur, L. Bigot, G. Bouwmans, Y. Quiquempois, M. Douay, and Y. Jaouen, “Ytterbium-doped solid core photonic bandgap fiber for laser operation around 980 nm,” Appl. Phys. Lett. 92, 061113 (2008). [CrossRef]

], chromatic dispersion adjustable by design [1

1. F. Brechet, P. Roy, J. Marcou, and D. Pagnoux, “Single-mode propagation into depressed-core-index photonic-bandgap fibre designed for zero-dispersion propagation at short wavelengths,” Electron. Lett. 36, 514–515 (2000). [CrossRef]

, 2

2. J. Riishede, J. Lægsgaard, J. Broeng, and A. Bjarklev, “All-silica photonic bandgap fibre with zero dispersion and a large mode area at 730 nm,” J. Opt. A 6, 667–670 (2004). [CrossRef]

, 13

13. A. Isomäki and O. G. Okhotnikov, “Femtosecond soliton mode-locked laser based on ytterbium-doped photonic bandgap fiber,” Opt. Express 14, 9238–9243 (2006). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-14-20-9238. [CrossRef] [PubMed]

], and the potential to achieve large mode area [2

2. J. Riishede, J. Lægsgaard, J. Broeng, and A. Bjarklev, “All-silica photonic bandgap fibre with zero dispersion and a large mode area at 730 nm,” J. Opt. A 6, 667–670 (2004). [CrossRef]

, 14

14. G. Bouwmans, L. Bigot, Y. Quiquempois, F. Lopez, L. Provino, and M. Douay, “Fabrication and characterization of an all-solid 2D photonic bandgap fiber with a low-loss region (< 20 dB/km) around 1550 nm,” Opt. Express 13, 8452–8459 (2005). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-13-21-8452. [CrossRef] [PubMed]

, 15

15. S. Février, R. Jamier, J.-M. Blondy, S. L. Semjonov, M. E. Likhachev, M. M. Bubnov, E. M. Dianov, V. F. Khopin, M. Y. Salganskii, and A. N. Guryanov, “Low-loss singlemode large mode area all-silica photonic bandgap fiber,” Opt. Express 14, 562–569 (2006). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-14-2-562. [CrossRef] [PubMed]

].

Many applications of all-solid PBG fibers in fiber lasers require birefringence and the capacity for efficient cladding pumping. For example, when a high power fiber laser is used for frequency doubling, linearly polarized output from a fiber laser is required, so that the laser cavity preferably consists of cladding-pumped birefringent fibers and a polarizer [16

16. Y. Barannikov, A. Oussov, F. Shcherbina, R. Yagodkin, V. Gapontsev, and N. Platonov, “250W, single-mode, CW, linearly-polarized fibre source in Yb wavelength range,” in Proceedings of Conference on Lasers and Electro-Optics (Optical Society of America, 2004), paper CMS3 (2004).

]. To obtain high cladding pumping efficiency in all-solid PBG fibers, it is necessary to minimize the amount of pump power which is trapped (by index guiding) in the high-index regions, and hence not absorbed by the rare-earth doped core. It has been reported that birefringence in an all-solid PBG fiber can be realized by incorporating stress elements in a 2-D structure [17

17. J. K. Lyngsø, B. J. Mangan, and P. J. Roberts, “Polarization maintaining hybrid TIR/bandgap all-solid photonic crystal fiber,” in Proceedings of Conference on Lasers and Electro-Optics, and Conference on Quantum Electronics and Laser Science (Optical Society of America, 2008), paper CThV1 (2008). [PubMed]

], however the reported structure has many high-index regions and therefore may suffer low cladding pumping efficiency.

With the aim of improving the cladding pumping efficiency of all-solid PBG fibers, we have previously reported a cladding-pumped, ytterbium-doped, all-solid hybrid microstructured fiber [18

18. R. Goto, K. Takenaga, K. Okada, M. Kashiwagi, T. Kitabayashi, S. Tanigawa, K. Shima, S. Matsuo, and K. Himeno, “Cladding-Pumped Yb-Doped Solid Photonic Bandgap Fiber for ASE Suppression in ShorterWavelength Region,” in Proceedings of Conference on Optical Fiber communication/National Fiber Optic Engineers Conference (Optical Society of America, 2008), paper OTuJ5 (2008). [CrossRef] [PubMed]

]. The fiber is based on a recently reported new form of microstructured fiber, in which the guidance mechanism is based on both the PBG effect and TIR [19

19. A. Cerqueira. S. Jr., F. Luan, C. M. B. Cordeiro, A. K. George, and J. C. Knight, “Hybrid photonic crystal fiber,” Opt. Express 14, 926–931 (2006). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-14-2-926. [CrossRef] [PubMed]

]. The number of high-index regions is reduced more than ten times (from 126 to 12) compared to comparable 2-D structures, therefore high cladding pumping efficiency is expected. As a result of the twofold rotational symmetry of the fiber, birefringence is also expected.

2. Fiber structure

The cross section of the fiber is schematically shown in Fig. 1(a). In the silica cladding (shown in light gray), the Ge-doped high-index regions (shown in white) with pure silica jackets (shown in light gray) are positioned periodically in the x-direction with pitch Λ. The diameters of the high-index regions and pure silica jackets are dhigh and dsi. The remainder of the cross section comprises fluoride(F)-doped low-index uniform glass (shown in dark gray). The core is formed by replacing one high-index region with pure silica and the core diameter is dcore. Figure 1(b) shows the refractive index profiles along with the x- and y-axis of the fiber cross section. In the x-direction, the core is surrounded by the high-index regions and the guidance mechanism is based on the PBG effect. Along the y-axis, the core is surrounded by the low-index cladding and the guidance mechanism is based on TIR. The outer pure silica cladding surrounding the low-index cladding is far from the core and the leakage loss through the low-index cladding is negligibly small.

The cross section of the fabricated hybrid microstructured fiber is shown in Fig. 2. The stack and draw method was used for fiber fabrication. First, a Ge-doped silica preform with pure silica cladding and a uniformly F-doped silica preform were both drawn into rods. These rods were then hexagonally stacked in a pure silica tube and drawn to a fiber. The pitch of the high-index regions, Λ, is 8.0 µm. According to the measurement of the Ge-doped silica preform before being drawn into rods, Δnhigh is about 2.8% and dhigh/Λ is ~0.5. The relative refractive index profile of the high-index regions is approximated by Δn(r)=Δnhigh[1-(r/R)4.25], where r is the distance from the center of the high-index region and R=dhigh/2. The relative refractive index difference of the low-index cladding Δnlow is -0.35%. The fiber diameter is 148 µm.

Fig. 1. Schematic cross section and refractive index profile of all-solid hybrid microstructured fiber.
Fig. 2. Cross section of the hybrid microstructured fiber.

3. Fiber characterization

3.1. Transmission

Fig. 3. Transmission spectra of the hybrid microstructured fiber.

Fig. 4. Calculated band structure and fundamental core-mode of the hybrid and 2-D structure. The core-mode is shown only in the second bandgap for simplicity. 7×7 supercell is used for the calculation.

Figures 4(a) and (b) show the band structures of the hybrid and 2-D PBG fibers. In Fig. 4(a), neff ~1.445 corresponds to the refractive index of the F-doped low-index cladding and no bandgap exists below this line. Shown as a solid line is the fundamental core-mode in the second bandgap. The calculated transmission range is in reasonable agreement with the experiments, the difference may be attributed to the changes in the refractive index profile and shape when the preform was drawn to the fiber. When compared with the 2-D PBG structure [see Fig. 4(b)], it is seen that the hybrid structure has an additional bandgap [region surrounded by the dotted line in Fig. 4(a)] between the second and third bandgaps. Indeed, poorly confined core-modes were found within the additional bandgap in our calculation and this explains the weak transmission window observed around 1100 nm in Fig. 3. The formation of this additional bandgap is explained by considering how bands are formed by high-index regions. Bands formed from high-index regions are determined by (1) the modes of each high-index region and (2) how high-index region modes couple and form a set of supermodes [8

8. J. Lægsgaard, “Gap formation and guided modes in photonic bandgap fibres with high-index rods,” J. Opt. A 6, 798–804 (2004). [CrossRef]

]. According to this model, the set of supermodes between the second and third bandgaps is formed by the LP21 and LP02 modes of each high-index region. In the hybrid structure, high-index regions only exist in the x-direction, limiting the formation of broadband supermodes, and an additional bandgap appears between the LP21 and LP02 modes of the high-index regions. Figures 5(a) and (b) show two typical intensity profiles of the supermodes between the second and additional bandgaps; Figs. 6(a) and (b) show the intensity profiles of the supermodes between the third and additional bandgaps. In the figures, the border of the pure silica jackets and the low-index F-doped cladding is shown as solid lines. As the figures clearly show, the band of supermodes between the second and additional bandgaps is formed by the LP02-based supermodes, and that between the third and additional bandgaps is formed by the LP21-based supermodes. These additional bandgaps may be eliminated by a modified design. In our calculations, as we increased dhigh/Λ, the high-index regions became more coupled and the additional bandgap disappeared.

It should be noted that the LP11 core-mode was found in the additional bandgap in our calculation, therefore the fiber may be multi-moded in the shorter wavelength region of the second bandgap. The results presented hereafter all relate to the fundamental mode because, in the experiments, a launch fiber was spliced to the hybrid fiber to excite only the core-modes of the fiber and the launch fiber is single-mode within the wavelength range of the measurements; the fundamental core-mode of the hybrid fiber was therefore selectively excited.

Fig. 5. Typical intensity profiles of the LP02-based supermodes between the second and additional bandgaps of the hybrid structure.
Fig. 6. Typical intensity profiles of the LP21-based supermodes between the third and additional bandgaps of the hybrid structure.

Figure 7 shows the loss spectrum of the fiber in the second bandgap. A minimum loss of 8 dB/km was measured at 1300 nm using a 66 m-length fiber, which was spooled on a 160 mm-diameter bobbin. We believe that the measured loss is sufficiently low for most fiber laser applications. The loss increase around 1240 and 1380 nm originates from OH ions, as no special care was taken to reduce OH content in the fiber during fiber fabrication.

Fig. 7. Loss spectrum of the hybrid microstructured fiber.

3.2. Bend loss

The fiber should have two bend loss mechanisms, relating to each of the guidance mechanisms. To confirm this, we measured the directional dependency of bend loss of this fiber. The experimental setup is shown in Fig. 8. A half-turn bend was applied to a 1 m-length fiber using a mandrel (Radius=12.5 mm) and the bend loss was measured as a function of the bend angle θ. The results are shown in Fig. 9. When θ=0°, almost no bend loss was observed, because the dominant mechanism of bend loss is that of fibers guided by TIR and TIR is still maintained. On the other hand, when θ=90°, significant bend loss appeared at both short and long wavelength edges of the transmission range, because the dominant mechanism of bend loss is now that of all-solid PBG fibers and the bend changed the band structure of the fiber [21

21. A. Argyros, T. A. Birks, S. G. Leon-Saval, C. M. B. Cordeiro, and P. S. J. Russell, “Guidance properties of low-contrast photonic bandgap fibres,” Opt. Express 13, 2503–2511 (2005). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-13-7-2503. [CrossRef] [PubMed]

]. This property may practically be beneficial to reduce bend loss of all-solid PBG fibers, if the fiber (or its coating) has a non-circular shape which forces the fiber to be bent in the θ=0° direction.

Fig. 8. Setup for angle dependency measurement of bend loss.

Fig. 9. Measurements of angle dependency of bend loss.

3.3. Birefringence

The hybrid microstructured fiber has only twofold symmetry, so that the fiber has both form birefringence [23

23. L. Xiao, W. Jin, and M. S. Demokan, “Photonic crystal fibers confining light by both indexguiding and bandgap-guiding: hybrid PCFs,” Opt. Express 15, 15,637–15,647 (2007). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-15-24-15637. [CrossRef]

] and stress birefringence [17

17. J. K. Lyngsø, B. J. Mangan, and P. J. Roberts, “Polarization maintaining hybrid TIR/bandgap all-solid photonic crystal fiber,” in Proceedings of Conference on Lasers and Electro-Optics, and Conference on Quantum Electronics and Laser Science (Optical Society of America, 2008), paper CThV1 (2008). [PubMed]

]. The stress birefringence of the hybrid microstructured fiber arises from the one-dimensionally arranged highly Ge-doped regions, which have a higher thermal expansion coefficient compared to pure silica.

Bm(λ)=Bms(λ)+Bmf(λ).
(1)

The Bm of the fiber was measured by a cut-back method [24

24. T. Hosaka, K. Okamoto, Y. Sasaki, and T. Edahiro, “Single mode fibres with asymmetrical refractive index pits on both sides of core,” Electron. Lett. 17, 191–193 (1981). [CrossRef]

]. Linearly polarized light (polarized at 45° relative to the x-axis of the fiber) was launched into the core of the fiber. A single-mode launch fiber was spliced to the input end of the fiber to excite the fundamental core-mode. We used a short launch fiber (less than 5cm) and kept it straight so that the change of the polarization state in the launch fiber is minimized. A rotatable polarizer was positioned at the output of the fiber, and the degree of linear polarization (DOLP) at the output was determined by finding the angles where the maximum and minimum output are obtained. DOLP is defined by

DOLP=ImaxIminImax+Imin
(2)

Fig. 10. Measured DOLP as a function of removed fiber length.

We measured the group birefringence by the fixed analyzer method and the Jones matrix eigenanalysis (JME). For the fixed analyser method, broadband light from a SC source was launched into the fiber through a polarizer and the output from the fiber was detected by an OSA after another polarizer. We used a 2 m-length fiber. Two single-mode fibers with negligible birefringence were spliced to both ends of the hybrid microstructured fiber to selectively measure the fundamental core-mode. Figure 11(a) shows the measured spectrum. The measured spectrum was not normalized and the dip around 1400 nm is due to the output spectrum of the SC source. Figure 11(a) shows the measured power as a function of the wavelength; the oscillation is due to the birefringence of the fiber. This oscillation is clearly shown in the detailed spectra in Figs. 11(b) and (c). The group birefringence Bg(λ) is given by

Bg(λ)=λ2LΔλ
(3)

where L is the length of the fiber, λ is the wavelength, and Δλ is the wavelength difference between two peaks of the oscillation [26

26. X. Chen, M.-J. 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). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-12-16-3888. [CrossRef] [PubMed]

]. Interestingly, the period of the oscillation becomes very large around 1160 nm and 1540 nm. This implies that the group birefringence becomes zero and changes sign around these two wavelengths. Taking this into account, we calculated the group birefringence using Eq. (3). The result is shown in Fig. 11(d) as a blue curve. The group birefringence changes sign quite smoothly at these two wavelengths, supporting the assumption that the group birefringence becomes zero. The two red curves shown in Fig. 11(d) are the measured group birefringence by the JME using a 2 m-length fiber. The wavelength range was limited by the availability of tunable light sources. The sign of the measured group birefringence was changed accordingly, based on our assumption that the group birefringence becomes zero and changes sign around 1540 nm. These two results are in good agreement. It should be noted that the sign of the group birefringence is not determined by these experimental methods, thus the sign is arbitrary in Fig. 11(d).

Fig. 11. Measurements of the group birefringence.

Bg(λ)=Bm(λ)λdBmdλ.
(4)

Equation (4) shows that Bm and Bg can differ significantly when dBm/ is large, i.e., when Bm is highly wavelength dependent. The measured difference between Bm and Bg is therefore attributed to the relatively large wavelength dependence of Bm in the middle of the bandgap. The large wavelength dependency of Bm could be both due to stress and form birefringence. By substituting Eq. (1) into Eq. (4), we obtain

Bg(λ)=Bgs(λ)+Bgf(λ)
(5)

where

Bgs(λ)=Bms(λ)λdBmsdλ
(6)
Bgf(λ)=Bmf(λ)λdBmfdλ.
(7)

3.4. Chromatic dispersion

The chromatic dispersion of the fiber was measured by an interferometric method [30

30. H.-T. Shang, “Chromatic dispersion measurement by white-light interferometry on metre-length single-mode optical fibres,” Electron. Lett. 17, 603–605 (1981). [CrossRef]

] and the modulation phase-shift (MPS) method. We used a 27 cm-length fiber for the interferometric method. Two polarizers, which were aligned to the x-axis of the fiber, were used in the two arms of the interferometer. The measured relative group delay and chromatic dispersion are shown in Figs. 12(a) and (b). We aligned the polarizers to the y-axis and measured the chromatic dispersion, the difference was within the measurement accuracy. The measured result is shown in Fig. 12(b) as a red curve. The red curve was obtained by fitting the relative group delay to a 4th order polynomial. The fiber is highly dispersive and we were unable to fit the whole data using a single polynomial, therefore the data was divided into three sections and fitted using three different polynomials. Dots were obtained by differentiating the relative group delay. The two green curves in Fig. 12(b) are the measured chromatic dispersion by the MPS method using a 95 m-length fiber. The wavelength range was limited by the availability of tunable light sources and the input polarization was not aligned to the polarization axes of the fiber. These two results are in good agreement. Figure 12(b) shows that the chromatic dispersion is negative at the shorter edge of the bandgap, becomes zero in the bandgap, and is positive at the longer edge of the bandgap. This is a typical chromatic dispersion property of PBG fibers.

Fig. 12. Chromatic dispersion of the fiber.

4. Conclusions

Acknowledgments

The authors acknowledge the Optical Fiber Technology Group, Optics and Electronics Laboratory, Fujikura for supplying the fibers, and providing their results of the group birefringence and chromatic dispersion measurements by the JME and theMPS method. A. Docherty is acknowledged for providing the ABC-FDM code and support. A. Michie is acknowledged for useful discussions. The authors thank M. Large, M. van Eijkelenborg, A. Argyros, and S. G. Leon- Saval for access to the SC source. R. Goto acknowledges the Department of Education, Science and Training, Australia for financial support. This work was produced with the assistance of the Australian Research Council under the ARC Centre of Excellence program and the discovery project program (DP0665032). CUDOS is an ARC Centre of Excellence.

References and links

1.

F. Brechet, P. Roy, J. Marcou, and D. Pagnoux, “Single-mode propagation into depressed-core-index photonic-bandgap fibre designed for zero-dispersion propagation at short wavelengths,” Electron. Lett. 36, 514–515 (2000). [CrossRef]

2.

J. Riishede, J. Lægsgaard, J. Broeng, and A. Bjarklev, “All-silica photonic bandgap fibre with zero dispersion and a large mode area at 730 nm,” J. Opt. A 6, 667–670 (2004). [CrossRef]

3.

F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. St. J. Russell, “All-solid photonic bandgap fiber,” Opt. Lett. 29, 2369–2371 (2004). [CrossRef] [PubMed]

4.

A. Argyros, T. A. Birks, S. G. Leon-Saval, C. M. Cordeiro, F. Luan, and P. St. J. Russell, “Photonic bandgap with an index step of one percent,” Opt. Express 13, 309–314 (2005). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-13-1-309. [CrossRef] [PubMed]

5.

P. Yeh, A. Yariv, and E. Marom, “Theory of Bragg fiber,” J. Opt. Soc. Am. 68, 1196–1199 (1978). [CrossRef]

6.

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic Band Gap Guidance in Optical Fibers,” Science 282, 1476–1478 (1998). [CrossRef] [PubMed]

7.

T. A. Birks, P. J. Roberts, P. St. J. Russell, D. M. Atkin, and T. J. Shepherd, “Full 2-D photonic bandgaps in silica/air structures,” Electron. Lett. 31, 1941–1943 (1995). [CrossRef]

8.

J. Lægsgaard, “Gap formation and guided modes in photonic bandgap fibres with high-index rods,” J. Opt. A 6, 798–804 (2004). [CrossRef]

9.

T. P. White, R. C. McPhedran, C. Martjin de Sterke, N. M. Litchinitser, and B. J. Eggleton, “Resonance and scattering in microstructured optical fibers,” Opt. Lett. 27, 1977–1979 (2002). [CrossRef]

10.

N. M. Litchinitser, A. K. Abeeluck, C. Headley, and B. J. Eggleton, “Antiresonant reflecting photonic crystal optical waveguides,” Opt. Lett. 27, 1592–1594 (2002). [CrossRef]

11.

A. Wang, A. K. George, and J. C. Knight, “Three-level neodymium fiber laser incorporating photonic bandgap fiber,” Opt. Lett. 31, 1388–1390 (2006). [CrossRef] [PubMed]

12.

V. Pureur, L. Bigot, G. Bouwmans, Y. Quiquempois, M. Douay, and Y. Jaouen, “Ytterbium-doped solid core photonic bandgap fiber for laser operation around 980 nm,” Appl. Phys. Lett. 92, 061113 (2008). [CrossRef]

13.

A. Isomäki and O. G. Okhotnikov, “Femtosecond soliton mode-locked laser based on ytterbium-doped photonic bandgap fiber,” Opt. Express 14, 9238–9243 (2006). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-14-20-9238. [CrossRef] [PubMed]

14.

G. Bouwmans, L. Bigot, Y. Quiquempois, F. Lopez, L. Provino, and M. Douay, “Fabrication and characterization of an all-solid 2D photonic bandgap fiber with a low-loss region (< 20 dB/km) around 1550 nm,” Opt. Express 13, 8452–8459 (2005). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-13-21-8452. [CrossRef] [PubMed]

15.

S. Février, R. Jamier, J.-M. Blondy, S. L. Semjonov, M. E. Likhachev, M. M. Bubnov, E. M. Dianov, V. F. Khopin, M. Y. Salganskii, and A. N. Guryanov, “Low-loss singlemode large mode area all-silica photonic bandgap fiber,” Opt. Express 14, 562–569 (2006). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-14-2-562. [CrossRef] [PubMed]

16.

Y. Barannikov, A. Oussov, F. Shcherbina, R. Yagodkin, V. Gapontsev, and N. Platonov, “250W, single-mode, CW, linearly-polarized fibre source in Yb wavelength range,” in Proceedings of Conference on Lasers and Electro-Optics (Optical Society of America, 2004), paper CMS3 (2004).

17.

J. K. Lyngsø, B. J. Mangan, and P. J. Roberts, “Polarization maintaining hybrid TIR/bandgap all-solid photonic crystal fiber,” in Proceedings of Conference on Lasers and Electro-Optics, and Conference on Quantum Electronics and Laser Science (Optical Society of America, 2008), paper CThV1 (2008). [PubMed]

18.

R. Goto, K. Takenaga, K. Okada, M. Kashiwagi, T. Kitabayashi, S. Tanigawa, K. Shima, S. Matsuo, and K. Himeno, “Cladding-Pumped Yb-Doped Solid Photonic Bandgap Fiber for ASE Suppression in ShorterWavelength Region,” in Proceedings of Conference on Optical Fiber communication/National Fiber Optic Engineers Conference (Optical Society of America, 2008), paper OTuJ5 (2008). [CrossRef] [PubMed]

19.

A. Cerqueira. S. Jr., F. Luan, C. M. B. Cordeiro, A. K. George, and J. C. Knight, “Hybrid photonic crystal fiber,” Opt. Express 14, 926–931 (2006). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-14-2-926. [CrossRef] [PubMed]

20.

S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-8-3-173. [CrossRef] [PubMed]

21.

A. Argyros, T. A. Birks, S. G. Leon-Saval, C. M. B. Cordeiro, and P. S. J. Russell, “Guidance properties of low-contrast photonic bandgap fibres,” Opt. Express 13, 2503–2511 (2005). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-13-7-2503. [CrossRef] [PubMed]

22.

T. A. Birks, F. Luan, G. J. Pearce, A. Wang, J. C. Knight, and D. M. Bird, “Bend loss in all-solid bandgap fibres,” Opt. Express 14, 5688–5698 (2006). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-14-12-5688. [CrossRef] [PubMed]

23.

L. Xiao, W. Jin, and M. S. Demokan, “Photonic crystal fibers confining light by both indexguiding and bandgap-guiding: hybrid PCFs,” Opt. Express 15, 15,637–15,647 (2007). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-15-24-15637. [CrossRef]

24.

T. Hosaka, K. Okamoto, Y. Sasaki, and T. Edahiro, “Single mode fibres with asymmetrical refractive index pits on both sides of core,” Electron. Lett. 17, 191–193 (1981). [CrossRef]

25.

N. A. Issa and L. Poladian, “Vector wave expansion method for leaky modes of microstructured optical fibers,” J. Lightwave Technol. 21, 1005–1012 (2003). (Note that, in our paper, due to superior performance in most applications, a finite difference scheme is used in the radial direction instead of the basis function expansion described in the reference.) [CrossRef]

26.

X. Chen, M.-J. 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). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-12-16-3888. [CrossRef] [PubMed]

27.

W. J. Bock and W. Urbanczyk, “Measurement of polarization mode dispersion and modal birefringence in highly birefringent fibers by means of electronically scanned shearing-type inteferometry,” Appl. Opt. 32, 5841–5848 (1993). [CrossRef] [PubMed]

28.

M. S. Alam, K. Saitoh, and M. Koshiba, “High group birefringence in air-core photonic bandgap fibers,” Opt. Lett. 30, 824–826 (2005). [CrossRef] [PubMed]

29.

J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4, 1071–1089 (1983). [CrossRef]

30.

H.-T. Shang, “Chromatic dispersion measurement by white-light interferometry on metre-length single-mode optical fibres,” Electron. Lett. 17, 603–605 (1981). [CrossRef]

OCIS Codes
(060.2310) Fiber optics and optical communications : Fiber optics
(060.2400) Fiber optics and optical communications : Fiber properties

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: September 19, 2008
Revised Manuscript: October 27, 2008
Manuscript Accepted: October 27, 2008
Published: October 29, 2008

Citation
Ryuichiro Goto, Stuart D. Jackson, Simon Fleming, Boris T. Kuhlmey, Benjamin J. Eggleton, and Kuniharu Himeno, "Birefringent all-solid hybrid microstructured fiber," Opt. Express 16, 18752-18763 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-23-18752


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References

  1. F. Brechet, P. Roy, J. Marcou, and D. Pagnoux, "Single-mode propagation into depressed-core-index photonicbandgap fibre designed for zero-dispersion propagation at short wavelengths," Electron. Lett. 36, 514-515 (2000). [CrossRef]
  2. J. Riishede, J. Lægsgaard, J. Broeng, and A. Bjarklev, "All-silica photonic bandgap fibre with zero dispersion and a large mode area at 730 nm," J. Opt. A 6, 667-670 (2004). [CrossRef]
  3. F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. St. J. Russell, "All-solid photonic bandgap fiber," Opt. Lett. 29, 2369-2371 (2004). [CrossRef] [PubMed]
  4. A. Argyros, T. A. Birks, S. G. Leon-Saval, C. M. Cordeiro, F. Luan, and P. St. J. Russell, "Photonic bandgap with an index step of one percent," Opt. Express 13, 309-314 (2005), http://www.opticsexpress.org/abstract.cfm?URI=oe-13-1-309. [CrossRef] [PubMed]
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  9. T. P. White, R. C. McPhedran, C. Martjin de Sterke, N. M. Litchinitser, and B. J. Eggleton, "Resonance and scattering in microstructured optical fibers," Opt. Lett. 27, 1977-1979 (2002). [CrossRef]
  10. N. M. Litchinitser, A. K. Abeeluck, C. Headley, and B. J. Eggleton, "Antiresonant reflecting photonic crystal optical waveguides," Opt. Lett. 27, 1592-1594 (2002). [CrossRef]
  11. A. Wang, A. K. George, and J. C. Knight, "Three-level neodymium fiber laser incorporating photonic bandgap fiber," Opt. Lett. 31, 1388-1390 (2006). [CrossRef] [PubMed]
  12. V. Pureur, L. Bigot, G. Bouwmans, Y. Quiquempois, M. Douay, and Y. Jaouen, "Ytterbium-doped solid core photonic bandgap fiber for laser operation around 980 nm," Appl. Phys. Lett. 92, 061113 (2008). [CrossRef]
  13. A. Isomäki and O. G. Okhotnikov, "Femtosecond soliton mode-locked laser based on ytterbium-doped photonic bandgap fiber," Opt. Express 14, 9238-9243 (2006), http://www.opticsexpress.org/abstract.cfm?URI=oe-14-20-9238. [CrossRef] [PubMed]
  14. G. Bouwmans, L. Bigot, Y. Quiquempois, F. Lopez, L. Provino, and M. Douay, "Fabrication and characterization of an all-solid 2D photonic bandgap fiber with a low-loss region (< 20 dB/km) around 1550 nm," Opt. Express 13, 8452-8459 (2005), http://www.opticsexpress.org/abstract.cfm?URI=oe-13-21-8452. [CrossRef] [PubMed]
  15. S. Février, R. Jamier, J.-M. Blondy, S. L. Semjonov,M. E. Likhachev,M. M. Bubnov, E. M. Dianov, V. F. Khopin, M. Y. Salganskii, and A. N. Guryanov, "Low-loss singlemode large mode area all-silica photonic bandgap fiber," Opt. Express 14, 562-569 (2006), http://www.opticsexpress.org/abstract.cfm?URI=oe-14-2-562. [CrossRef] [PubMed]
  16. Y. Barannikov, A. Oussov, F. Shcherbina, R. Yagodkin, V. Gapontsev, and N. Platonov, "250W, single-mode, CW, linearly-polarized fibre source in Yb wavelength range," in Proceedings of Conference on Lasers and Electro-Optics (Optical Society of America, 2004), paper CMS3 (2004).
  17. J. K. Lyngsø, B. J. Mangan, and P. J. Roberts, "Polarization maintaining hybrid TIR / bandgap all-solid photonic crystal fiber," in Proceedings of Conference on Lasers and Electro-Optics, and Conference on Quantum Electronics and Laser Science (Optical Society of America, 2008), paper CThV1 (2008). [PubMed]
  18. R. Goto, K. Takenaga, K. Okada, M. Kashiwagi, T. Kitabayashi, S. Tanigawa, K. Shima, S. Matsuo, and K. Himeno, "Cladding-Pumped Yb-Doped Solid Photonic Bandgap Fiber for ASE Suppression in ShorterWavelength Region," in Proceedings of Conference on Optical Fiber communication/National Fiber Optic Engineers Conference (Optical Society of America, 2008), paper OTuJ5 (2008). [CrossRef] [PubMed]
  19. A. Cerqueira. S. Jr., F. Luan, C. M. B. Cordeiro, A. K. George, and J. C. Knight, "Hybrid photonic crystal fiber," Opt. Express 14, 926-931 (2006), http://www.opticsexpress.org/abstract.cfm?URI=oe-14-2-926. [CrossRef] [PubMed]
  20. S. Johnson and J. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8, 173-190 (2001), http://www.opticsexpress.org/abstract.cfm?URI=oe-8-3-173. [CrossRef] [PubMed]
  21. A. Argyros, T. A. Birks, S. G. Leon-Saval, C. M. B. Cordeiro, and P. S. J. Russell, "Guidance properties of low-contrast photonic bandgap fibres," Opt. Express 13, 2503-2511 (2005), http://www.opticsexpress.org/abstract.cfm?URI=oe-13-7-2503. [CrossRef] [PubMed]
  22. T. A. Birks, F. Luan, G. J. Pearce, A. Wang, J. C. Knight, and D. M. Bird, "Bend loss in all-solid bandgap fibres," Opt. Express 14, 5688-5698 (2006), http://www.opticsexpress.org/abstract.cfm?URI=oe-14-12-5688. [CrossRef] [PubMed]
  23. L. Xiao, W. Jin, and M. S. Demokan, "Photonic crystal fibers confining light by both indexguiding and bandgap-guiding: hybrid PCFs," Opt. Express 15, 15637-15647 (2007), http://www.opticsexpress.org/abstract.cfm?URI=oe-15-24-15637. [CrossRef]
  24. T. Hosaka, K. Okamoto, Y. Sasaki, and T. Edahiro, "Single mode fibres with asymmetrical refractive index pits on both sides of core," Electron. Lett. 17, 191-193 (1981). [CrossRef]
  25. N. A. Issa and L. Poladian, "Vector wave expansion method for leaky modes of microstructured optical fibers," J. Lightwave Technol. 21, 1005-1012 (2003). (Note that, in our paper, due to superior performance in most applications, a finite difference scheme is used in the radial direction instead of the basis function expansion described in the reference.) [CrossRef]
  26. X. Chen, M.-J. 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=oe-12-16-3888. [CrossRef] [PubMed]
  27. W. J. Bock and W. Urbanczyk, "Measurement of polarization mode dispersion and modal birefringence in highly birefringent fibers by means of electronically scanned shearing-type inteferometry," Appl. Opt. 32, 5841-5848 (1993). [CrossRef] [PubMed]
  28. M. S. Alam, K. Saitoh, and M. Koshiba, "High group birefringence in air-core photonic bandgap fibers," Opt. Lett. 30, 824-826 (2005). [CrossRef] [PubMed]
  29. J. Noda, K. Okamoto, and Y. Sasaki, "Polarization-maintaining fibers and their applications," J. Lightwave Technol. 4, 1071-1089 (1983). [CrossRef]
  30. H.-T. Shang, "Chromatic dispersion measurement by white-light interferometry on metre-length single-mode optical fibres," Electron. Lett. 17, 603-605 (1981). [CrossRef]

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