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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 16 — Aug. 8, 2005
  • pp: 6039–6050
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New defect design in index guiding holey fiber for uniform birefringence and negative flat dispersion over a wide spectral range

Soan Kim, U. C. Paek, and Kyunghwan Oh  »View Author Affiliations


Optics Express, Vol. 13, Issue 16, pp. 6039-6050 (2005)
http://dx.doi.org/10.1364/OPEX.13.006039


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Abstract

A novel silica index guiding holey fiber (IGHF) design is proposed utilizing a new defect structure that is composed of an elliptic high index ring structure and an elliptic air-hole at the center with triangular lattice structure. The proposed IGHF showed unique modal properties such as uniform and high birefringence over a wide spectral range and single polarization single mode (SPSM) guidance along with a flat negative chromatic dispersion. Optical waveguide properties were numerically analyzed using the plane wave expansion method in terms of mode intensity distribution, modal birefringence, chromatic dispersion for the new defect structural parameters.

© 2005 Optical Society of America

1. Introduction

In recent years, the authors have introduced a new type of optical fiber, hollow optical fiber (HOF), with a triple layered structure, a central air hole, germanosilicate ring core, and silica cladding for the versatile photonic device applications [13–15

13. K. Oh, S. Choi, Y. Jung, and Jhang. W. Lee, “Novel hollow optical fibers and eir applications in photonic devices for optical communications,” J. Lightwave Technol. 23, 524–532 (2005). [CrossRef]

]. Birefringece in elliptic HOF has been also investigated [16

16. I. K. Hwang, Y. H. Lee, K. Oh, and D. N. Payne, “High birefringence in elliptic hollow optical fiber,” Opt. Express 12, 1916–1923 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1916. [CrossRef] [PubMed]

].

In this paper, we present a novel defect design based on HOF structure embedded in IGHF, for the first time to the best knowledge of the authors, and its structure is schematically shown in Fig. 1(a). Based on the already established fabrication techniques of HOFs and the elliptical hole IGHFs, the proposed structure is believed to be attainable with a high feasibility.

In the Fig. 1(a), the defect consists of germanosilicate high index elliptic ring surrounding the elliptic air hole inside, which can endow a new degree of freedom in defect engineering for IGHFs such as hole diameter, (Dx, Dy), ring width (Wring_x, Wring_y), and the ring index (Δ), to control the birefringence and chromatic dispersion simultaneously. We numerically investigated the effects of the proposed defect designs on the bound mode intensity distributions, dispersion relations, the birefringence characteristics, and chromatic dispersion property.

2. Defect parameters and analysis of optical properties

2.1 Impacts of defect parameters over modal birefringence

In the prior elliptic hole IGHFs, the major design parameters were the air hole diameter D, its pitch Λ, and the ellipticity η (the ratio of major to minor axis for the air holes) as in Fig. 1(b) introduced by Steel et al [10

10. M. J. Steel and P. M. Osgood Jr., “Elliptic-hole photonic crystal fibers,” Opt. Lett. 26, 229–231 (2001). [CrossRef]

,11

11. M. J. Steel and R. M. Osgood, “Polarization and dispersive properties of elliptical-hole photonic crystal fibers,” J. Lightwave Technol. 19, 495–503 (2001). [CrossRef]

] and one more defect parameter Dc in Fig. 1(c) introduced by Broeng et al [12

12. J. Broeng, D. Mogilevtsev, S. E. B. Libori, and A. Bjarklev, “Polarization-preserving holey fibers,” Optical Fiber Communications, technical digest, paperMA1.3, 6–7, Anaheim, California. (2001).

]. For the sake of convenience, we will assume the regime η > 1 with the major axis oriented along the y-direction. In contrast to these prior structures, the optical properties of the proposed IGHF with new defect design can be further tailored by three more defect parameters; the width of germanosilicate ring (Wring_x and Wring_y), the diameter of central elliptic hole (Dcx and Dcy) and the index difference between high index doped ring and pure silica Δ = nGe-doped-nsilica as illustrated in Fig. 1(a), which can provide flexible and versatile defect engineering.

The calculation accuracy in the plane wave expansion method is influenced by several parameters such as the number of plane waves, the size and shape of supercell, and the tolerance [19

19. In-Kag Hwang, Yong-Jae Lee, and Yong-Hee Lee, “Birefringence induced by irregular structure in photonic crystal fiber,” Opt. Express 11, 2799–2806 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2799. [CrossRef] [PubMed]

]. In our calculations, the optimum parameters were chosen such as; supercell size of 7Λ×4√3Λ as a rectangular shape, the tolenrance of 10-7 and the resolution of 256, which corresponds to the number of plane waves of (7Λ×4√3Λ) × (7×256). The error due to the finite number of the plane waves in calculation of the birefringence was to be less than 5% [16

16. I. K. Hwang, Y. H. Lee, K. Oh, and D. N. Payne, “High birefringence in elliptic hollow optical fiber,” Opt. Express 12, 1916–1923 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1916. [CrossRef] [PubMed]

, 19

19. In-Kag Hwang, Yong-Jae Lee, and Yong-Hee Lee, “Birefringence induced by irregular structure in photonic crystal fiber,” Opt. Express 11, 2799–2806 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2799. [CrossRef] [PubMed]

].

Fig. 1. (a) Schematic diagram of the proposed defect structure of the elliptic hole IGHF. The defect structures of (b) the conventional elliptic hole IGHF [10, 11] and (c) the prior elliptic hole IGHF with smaller elliptic hole at the center Dc [12]. The new defect structures of (d) the elliptic hole IGHF with high index ring Wring, and (e) the elliptic hole IGHF with high index ring, Wring and central airhole defect, Dc. The shaded region represents the raised index ring by doping GeO2.

To illustrate the mode field distributions in the proposed elliptic hole IGHF with new defect design, we show two fundamental modes with orthogonal polarizations at wavelength λ= 1.31μm, parallel to the major axis (y-axis) in Fig. 2(a), and minor axis (x-axis) in Fig. 2(b), where Λ = 2.2 μm, D/Λ = 0.7, Dc/Λ=0.2, Wring = 2Λ, Δ= 0.013 and ellipticity, η= 4. The effective indices of y-polarization and x-polarization mode are 1.4214 and 1.4150 with a birefringence B = neffy - neffx = 6.4×10-3, respectively. The y-polarization mode is more bound to the central core region compared to x polarization, which can be directly inferred from the effective indices of two polarization modes in reference to the effective cladding index nclad = 1.4144. From the intensity distribution of the modes along the major and minor axes, we could also find that the bound modes are linearly polarized and transverse, similar to prior polarization maintaining fibers. In elliptical hollow optical fiber (E-HOF), high birefringence was found to originate from the boundary conditions for electromagnetic fields at the elliptical air and silica ring core interface [16

16. I. K. Hwang, Y. H. Lee, K. Oh, and D. N. Payne, “High birefringence in elliptic hollow optical fiber,” Opt. Express 12, 1916–1923 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1916. [CrossRef] [PubMed]

].

The electric field intensity distribution directly modifies the effective index of the guided mode. Similar patterns were also observed in our studies with prominent intensity suppression around the hole in x polarization as shown in Fig. 2(b) to result in a lower effective index than the y polarization mode. Due to this polarization dependent disparity in the intensity distribution near the central elliptic hole defect, the difference of effective index between the slow axis and fast axis can be enhanced by optimizing defect parameters, Dc [16

16. I. K. Hwang, Y. H. Lee, K. Oh, and D. N. Payne, “High birefringence in elliptic hollow optical fiber,” Opt. Express 12, 1916–1923 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1916. [CrossRef] [PubMed]

], along with hollow ring defects to further tailor polarization properties.

Fig. 2. Intensity profiles for bound modes of the proposed IGHF with Λ=2.2μm, D/Λ=0.7, ellipticity, η = 4, Δ=0.013, Dc=0.2Λ and Wring=2Λ at λ=1310nm (< Λcutoff). (a) y-polarization and (b) x-polarization (see Fig. 1(e)). 1D line profiles show the mode intensities along x and y directions in each polarization mode profile.

To compare the polarization mode dispersion of the proposed IGHF with newly introduced defect design (Fig. 1(d), (e)) with the prior elliptic hole IGHF (Fig. 1(b), (c)) the effective indices of the core-guided modes and cladding were calculated as a function of wavelength. The results are summarized in Fig. 3. In calculations, we have assumed the same structural parameters, Λ=2.2μm, D/Λ=0.7, and η=4. The open and solid symbols represent the x, and y polarization modes, respectively. As indicated the electric field intensity distribution in Fig. 2, the y-polarization modes consistently showed a higher effective index than the x-polarization modes..

Fig. 3. Dispersion relations of the fundamental modes and effective cladding mode for the fibers in Fig. 1(b) and (d) which do not have central air hole defect, Dc=0 (a) and for the fibers in Fig. 1(c) and (e) which have smaller elliptic air hole at the center, Dc=0.2Λ. Solid:HE11y, Open:HEx 11.

The effect of the presence of high index ring (Wring≠0) on the dispersion relation is shown in Fig. 3(a) and those of the central elliptic hole (Dc≠0) are shown in Fig. 3(b). The high index ring defect along the minor axis was found to increase birefringence as indicated by solid and open triangle symbols in Fig. 3(a). It is also noteworthy that the cut-off wavelength of x-polarization mode shifted significantly to longer wavelength by more than 50nm. With the high index ring defects, the single polarization single mode (SPSM) operation can be achieved in the wavelength range over 1.7μm and below this cut-off the fiber retains a high birefringence. When the central elliptic hole is furthermore introduced (Dc=0.2Λ), the birefringence was found to further enhanced as indicated by solid and open star symbols in Fig. 3(b). The cut-off wavelength for SPSM condition was found to be shifted to 1.42 μm, which could be of high importance for optical communication and sensing in C, L band.

Based on calculations of the effective indices in Fig. 3, the birefriengence, Δn=∣nx-ny, ∣, was plotted as a function of wavelength in Fig. 4. With the proposed defect structure consisted of both high index rings along the minor axis and central elliptic hole, it is found that the IGHF showed high and uniform birefringence over a very broad wavelength range, λ=1.15 to λ=1.42μm, as shown in solid star symbols in Fig. 4. The similar behavior could be also achieved with a lower birefringence for the case only with central elliptic hole by optimizing the defect parameters, Dc and ellipticity η, which is represented by solid circles.

Fig. 4. Modal birefringence for four fibers in Fig. 1: λcutoff_1 =1.42μm for the fibers in Fig. 1(c) and (e), λcutoff_2 =1.64μm for the fiber in Fig. 1(b), and λcutoff_3 =1.7μm for the fiber in Fig. 1(d) where Λ=2.2μm, D/Λ=0.7, η=4, Dc=0.2Λ, Λ=0.013, and Wring=2Λ.

For other parameters, Wring and Δ, we found that the cut-off wavelength did not change, fixed at 1.42 μm, yet only the maginitude of birefringence increased for larger Wring and higher Δ as shown in Fig. 5(b) and (c), respectively. It is observed that these two parameters did not significantly change the spectral uniformity of birefringence over the wavelength range. It is also noteworthy the hollow index ring with depressed refractive index, Δ<0, could also work as a defect as good as raised refractive index case, Δ>0. Depressed refractive index can be realized by doping Fluorine instead GeO2.

Fig. 5. Dependence of modal birefringence on defect parameters for the proposed fiber in Fig. 1(e) where Λ=2.2μm, D/Λ=0.7, and Dc=0.2Λ: (a) ellipticity, η (λcutoff_l =1. 42μm when η = 4, λcutoff_2 =1.54μm when η = 3). (b)Wring (c) index difference, Δ. Inset in (a) is the enlarged figure for the circular IGHF with two orders magnitude lower than that of elliptic IGHF.

2.2 Impacts of defect parameters over chromatic dispersion

Fig. 6. Chromatic dispersion for four fibers in Fig.: λcutoff_1 =1.42μm for the fibers Fig.1(c) and (e), λcutoff_2 =1.64μm for the fiber in Fig. 1(b), and λcutoff_3 =1.7μm for the fiber in Fig. 1(d) where Λ=2.2μm, D/Λ=0.7, η=4, Dc=0.2λ, Δ=0.013, and Wring=Λ.

In the case of Dc=0 as in Fig. 1(b) and (d), monotonically decreasing dispersion was obtained over S, C, L band in the range of ±3ps/km.nm2 with dispersion slope range of -0.02ps/km.nm2 at 1.55μm as shown in the upper plots in Fig. 6, which is comparable to prior reports with circular holes [10–11

10. M. J. Steel and P. M. Osgood Jr., “Elliptic-hole photonic crystal fibers,” Opt. Lett. 26, 229–231 (2001). [CrossRef]

, 20–22

20. A. Ferrando, E. Silvestre, and P. Andres, “Designing the properties of dispersion-flattened photonic crystal fibers,” Opt. Express 9, 687–697 (2001). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-687. [CrossRef] [PubMed]

]. It is noted that the proposed hollow ring defect can significantly alter the dispersion slope to enable detailed dispersion tailoring. In the case of Dc=0.2Λ as in Fig. 1(c) and (e), we could obtain a negative and flat dispersion of D ~-5.5ps/km.nm over a wide wavelength range of 1.42 to 1.65μm and very low dispersion slope less than 0.001ps/km.nm2 at λ=1.55μm as shown in the lower plots of Fig. 6.

Considering the single mode single polarization operation in these conditions as illustrated in Fig. 3(b), the negative flat dispersion,in addition, will make this fiber almost ideal transmission medium for high capacity WDM systems. Impacts of the other defect parameters such as ellipticity η, Wring, and Δ over the dispersion and its slope, have been numerically investigated and the results are summarized in Fig. 7.

Fig. 7. Dependence of the dispersion curves on defect parameters for the proposed fiber in Fig. 1(e) where Λ=2.2μm, D/Λ=0.7, and Dc= 0.2Λ: (a) ellipticity, η (λcutoff_1 =1.42 and λcutoff_2=1.54μm when η = 4 and 3, respectively). (b) Wringcutoff =1.42μm independent of Wring). (c) index difference, Δ (λcutoff=l.42μm independent of Δ).

As the ellipticity change from η=1 to 4, the overall dispersion value monotonically decrease from +36.5 to -5.07ps/km.nm at 1.55μm, changing the dispersion characteristics from anomalous to normal in S, C, and L band as shown in Fig. 7(a). The proposed fiber with η=3, showed interesting characteristics with a small non-zero dispersion value of 4.06ps/km.nm along with a very low negative dispersion slope of -0.001ps/km.nm2 at λ= 1.55μm. For higher ellipticity η=4, the dispersion properties change their signs such that dispersion and its slope are -5.07ps/km.nm and 0.002ps/km.nm2 , respectively at 1.55μm.

Fixing the ellipticity η=4, we then further investigated the impacts of hollow ring width, Wring, and the results are summarized in Fig. 7(b), As Wring varies from l.0Λto 2.0Λ, the dispersion slope monotonically increases and flat-negative dispersion was attainable only near Wring=Λ. Having η=4, and Wring=Λ, the impacts of the relative index difference, Δ, was also analyzed and the results are shown in Fig. 7(c). As Δ decreases from 0.02 to -0.015, both the chromatic dispersion and its slope decrease. Especially for the depressed refractive index ring defects with Δ=-0.015, dispersion and its slope are -5.57ps/km.nm and 0.0007ps/km.nm2, respectively. Note that in this case of Δ=-0.015, the dispersion is extremely flat over entire C, and L band, which can be directly utilized in WDM transmission dispersion control [26–27

26. I. Tomkos, D. Chowdhury, J. Conradi, D. Culverhouse, K. Ennser, C. Giroux, B. Hallock, T. Kennedy, A. Kruse, S. Kumar, N. Lascar, I. Roudas, M. Sharma, R. S. Vodhanel, and C.-C. Wang, “Demonstration of negative dispersion fibers for DWDM metropolitan area networks,” IEEE J. Sel. Top. Quantum Electron. 7, 439–453 (2001). [CrossRef]

].

From these numerical analyses, we confirmed the potential and flexibility of the proposed defect structures in IGHF such that they could provide unique waveguide properties to obtain uniform high birefringence over the wide wavelength region, and a negative flat dispersion over the single polarization single mode operation region, simultaneously.

3. Conclusion

Acknowledgments

This work was partially supported by KOSEF through UFON, and ERC program, by MOE-BK21.

References and Links

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

2.

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

6.

K. Suzuki, H. Kubota, S. Kawanishi, M. Tanaka, and M. Fujita, “Highl-speed bi-directional polarization division multiplexed optical transmission in ultra-low-loss (1.3dB/km).polarization-maintaining photonic crystal fiber,” Electron. Lett. 37, 1399–1401 (2001). [CrossRef]

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J. Ju, W. Jin, and M. S. Demokan, “Properties of a Highly Birefringent Photonic Crystal Fiber,” IEEE Photonics. Technol. Lett . 15, 1375–1377 (2003). [CrossRef]

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T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knuders, A. Bjarklev, J. R. Jensen, and H. Simonsen, “Highly birefringent index-guiding photonic crystal fibers,” IEEE Photonics. Technol. Lett. 13, 588–590 (2001). [CrossRef]

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12.

J. Broeng, D. Mogilevtsev, S. E. B. Libori, and A. Bjarklev, “Polarization-preserving holey fibers,” Optical Fiber Communications, technical digest, paperMA1.3, 6–7, Anaheim, California. (2001).

13.

K. Oh, S. Choi, Y. Jung, and Jhang. W. Lee, “Novel hollow optical fibers and eir applications in photonic devices for optical communications,” J. Lightwave Technol. 23, 524–532 (2005). [CrossRef]

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S. Choi, W. Shin, and K. Oh, “Higher-order-mode dispersion compensation technique based on mode converter using hollow optical fiber,” In Optical Fiber Comminication Conf. , 177–178 (2002).

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S. Choi, T. J. Eom, J. W. Yu, B. H. Lee, and K. Oh, “Novel all-fiber bandpass filter based on hollow optical fiber,” IEEE Photonics. Technol. Lett. 14, 1701–1703 (2002). [CrossRef]

16.

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

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20.

A. Ferrando, E. Silvestre, and P. Andres, “Designing the properties of dispersion-flattened photonic crystal fibers,” Opt. Express 9, 687–697 (2001). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-687. [CrossRef] [PubMed]

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A. Ferrando, E. Silvestre, J. J. Miret, and P. Andres, “Nearly zero ultraflattened dispersion in photonic crystal fibers,” Opt. Lett. 25, 790–792 (2000). [CrossRef]

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W. Zhi, R. Guobin, and L. Shuqin, “A novel supercell overlapping method for different photonic crystal fibers,” J. Lightwave Technol. 22, 903–916 (2004). [CrossRef]

26.

I. Tomkos, D. Chowdhury, J. Conradi, D. Culverhouse, K. Ennser, C. Giroux, B. Hallock, T. Kennedy, A. Kruse, S. Kumar, N. Lascar, I. Roudas, M. Sharma, R. S. Vodhanel, and C.-C. Wang, “Demonstration of negative dispersion fibers for DWDM metropolitan area networks,” IEEE J. Sel. Top. Quantum Electron. 7, 439–453 (2001). [CrossRef]

27.

Jose A. P. Morgado and Adolfo V. T. Cartaxo, “Directly modulated laser parameters optimization for metropolitan area networks utilizing negative dispersion fibers,” IEEE J. Sel. Top. Quantum Electron. 9, 1315–1324 (2003). [CrossRef]

28.

Nader A. Issa, Martijn A. van Eijkelenborg, Matthew Fellew, Felcity Cox, Geoff Henry, and Maryanne C. J. Large, “Fabrication and study of microstructured optical fibers with elliptical holes,” Opt. Lett. 29, 1336–1338 (2004). [CrossRef] [PubMed]

29.

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OCIS Codes
(000.4430) General : Numerical approximation and analysis
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(060.2420) Fiber optics and optical communications : Fibers, polarization-maintaining
(230.3990) Optical devices : Micro-optical devices

ToC Category:
Research Papers

History
Original Manuscript: June 14, 2005
Revised Manuscript: July 21, 2005
Published: August 8, 2005

Citation
Soan Kim, U. Paek, and Kyunghwan Oh, "New defect design in index guiding holey fiber for uniform birefringence and negative flat dispersion over a wide spectral range," Opt. Express 13, 6039-6050 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-16-6039


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References

  1. T. A. Birks, J. C. Knight, and P. S. J. Russell, �??Endlessly single-mode photonic crystal fiber,�?? Opt. Lett. 22, 961-963 (1997). [CrossRef] [PubMed]
  2. J. K. Ranka, R. S. Windeler, and A. J. Stenz, �??Optical properties of high-delta air-silica microstructure optical fibers,�?? Opt. Lett. 25, 796-798 (2000). [CrossRef]
  3. D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, �??Group-velocity dispersion in photonic crystal fibers,�?? Opt. Lett. 23, 1662-1664 (1998). [CrossRef]
  4. T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, �??Holey optical fibers: An efficient modal model,�?? J. Lightwave Technol. 17, 1093-1102 (1999). [CrossRef]
  5. A. Ortigosa-Blanch, J. C. Knight, W. J. Wadsworth, J. Arriaga, B. J. Mangan, T. A. Birks, and P. S. J. Russell, �??Highly birefringent photonic crystal fibers,�?? Opt. Lett. 25, 1325-1327 (2000). [CrossRef]
  6. K. Suzuki, H. Kubota, S. Kawanishi, M. Tanaka, and M. Fujita, �??Highl-speed bi-directional polarization division multiplexed optical transmission in ultra-low-loss (1.3dB/km).polarization-maintaining photonic crystal fiber,�?? Electron. Lett. 37, 1399-1401 (2001). [CrossRef]
  7. J. Ju, W. Jin, M. S. Demokan, �??Properties of a Highly Birefringent Photonic Crystal Fiber,�?? IEEE Photonics. Technol. Lett. 15, 1375-1377 (2003). [CrossRef]
  8. T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knuders, A. Bjarklev, J. R. Jensen, and H. Simonsen, �??Highly birefringent index-guiding photonic crystal fibers,�?? IEEE Photonics. Technol. Lett. 13, 588-590 (2001). [CrossRef]
  9. J. Noda, K. Okamoto, and Y. Sasaki, �??Polarization-maintaining fibers and their applications,�?? J. Lightwave Technol. 4, 1071-1089 (1986). [CrossRef]
  10. M. J. Steel, P. M. Osgood. Jr, �??Elliptic-hole photonic crystal fibers,�?? Opt. Lett. 26, 229-231 (2001). [CrossRef]
  11. M. J. Steel and R. M. Osgood, �??Polarization and dispersive properties of elliptical-hole photonic crystal fibers,�?? J. Lightwave Technol. 19, 495-503 (2001). [CrossRef]
  12. J. Broeng, D. Mogilevtsev, S. E. B. Libori, and A. Bjarklev, �??Polarization-preserving holey fibers,�?? Optical Fiber Communications, technical digest, paper MA1.3, 6-7, Anaheim, California. (2001).
  13. K. Oh, S. Choi, Y. Jung, and Jhang. W. Lee, �??Novel hollow optical fibers and eir applications in photonic devices for optical communications,�?? J. Lightwave Technol. 23, 524-532 (2005). [CrossRef]
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