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Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 16 — Aug. 11, 2003
  • pp: 1900–1905
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Strong resonance and a highly compact long-period grating in a large-mode-area photonic crystal fiber

Yinian Zhu, Ping Shum, Hin-Joo Chong, M. K. Rao, and Chao Lu  »View Author Affiliations


Optics Express, Vol. 11, Issue 16, pp. 1900-1905 (2003)
http://dx.doi.org/10.1364/OE.11.001900


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Abstract

A strong resonance and extremely short length long-period grating (LPG) has been fabricated in a large-mode-area photonic crystal fiber (PCF) by use of a CO2 laser heat source. We believe that such a long-period grating in pure silica PCF is the first example of a point-by-point technique. The fabrication method is simple and repeatable. The resulting LPG has been developed with eight periodic collapses within a 2.8-mm-long period of the fiber, which gives the strong resonance of core-cladding mode coupling. The lowest mode of LP01 is at a 1529.2-nm wavelength with a full width at half-maximum of ~0.7 nm and a resonance strength of -31.5 dB. The principal advantages of this LPG are that (1) it is temperature insensitive and stable, (2) the device is compact when it is packaged, and (3) it provides practical, low-cost all-fiber filters and PCF-based devices for optical fiber communications and sensing systems.

© 2003 Optical Society of America

1. Introduction

Since the first pure silica photonic crystal fiber (PCF) was achieved for practical use in 1996 [1

1. J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996). [CrossRef] [PubMed]

], most research efforts have focused on the development of the fibers themselves. A PCF consists of regularly spaced air holes along the fiber cladding. The core of the PCF is formed by the introduction of a defect or a missed hole at the center of the fiber. According to the distinct mechanisms of light propagation in the core region, PCFs fall into two general categories: (1) microstructure fiber or holey fiber in which the light is guided by the total internal reflection as in conventional optical fiber, and (2) photonic bandgap fiber or Bragg fiber in which the core of the fiber is hollow, and the light is guided by the photonic bandgap effects [2

2. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic bandgap guidance of light in air,” Science 285, 1537–1539 (1999). [CrossRef] [PubMed]

]. The advantages of PCFs over conventional optical fibers include the endless single-mode operation [3

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

], a large-mode area up to hundreds of square micrometers [4

4. J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J.-P. de Sandro, “Large mode area photonic crystal fiber,” Electron. Lett. 13, 1347–1348 (1998). [CrossRef]

], dispersion flattening with a dispersion slope of 0.002 ps/nm2 at 1.3–1.5 µm, high dispersion with 2000 ps/nm/km for specially designed structures [5

5. T. A. Birks, D. Mogilevstev, J. C. Knight, and P. St. J. Russell, “Dispersion compensation using single-material fibers,” IEEE Photon. Technol. Lett. 11, 674–676 (1999). [CrossRef]

], anomalous and zero dispersion below 1.3 µm or in the visible region, and controllable field localization [6

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

]. Now, however, the emphasis has shifted toward the potential applications in optical communications, optical fiber-based sensing [7

7. T. M. Monro, W. Belardi, K. Furusawa, J. C. Bagget, N. G. R. Broderick, and D. J. Richardson, “Sensing with microstructured optical fibers,” Meas. Sci. Technol. 12, 854–858 (2001). [CrossRef]

], frequency metrology, and optical coherence tomography [8

8. R. Holzwarth, M. Zimmermann, T. Udem, T. W. Hansch, P. Russbuldt, K. Gabel, R. Poprawe, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “White-light frequency comb generation with a diode-pumped Cr:LiSAF laser,” Opt. Lett. 26, 1376–1378 (2001). [CrossRef]

]. The methodology that is applied in the fabrication of PCF-based devices is post-processing by use of a CO2 laser as the heat-treatment source. This technique involves heating the fiber with a CO2 laser until it softens, then the holes are collapsed in a controlled manner to create various all-fiber telecom-related components.

Long-period gratings (LPGs) typically have pitches in the 200–800-µm range based on the coupling between the fundamental mode and the co-propagating cladding modes when the inter-modal beat period equals the grating pitch [9

9. A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996). [CrossRef]

]. In general, a LPG can be described by four parameters: n core, the effective refractive index of the fundamental mode; ncladdingi , the effective refractive index of the i order cladding mode; Λ, the pitch of the grating; and λi, the resonance wavelength of LP0i. Their transmission spectra are characterized by dips at wavelengths that satisfy the resonance condition, which is given by

λi=(ncorencladdingi)Λ
(1)

LPGs have a wide range of application in optical fiber communications and sensing systems, such as dispersion compensators [10

10. C. Y. Lin and L. A. Wang, “A wavelength- and loss- tunable band-rejection filter based on corrugated long-period fiber grating,” IEEE Photon. Technol. Lett. 13, 332–334 (2001). [CrossRef]

], gain equalizers in erbium-doped fiber amplifiers (EDFAs) [11

11. A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, and P. J. Lemaire, “Long-period fiber-grating-based gain equalizers,” Opt. Lett. 21, 336–338 (1996). [CrossRef] [PubMed]

], and as sensors for temperature, strain, vibration, and chemical measurements [12

12. V. Bhatia, “Applications of long-period gratings to single and multi-parameter sensing,” Opt. Express 4, 457–466 (1999), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-11-457 [CrossRef] [PubMed]

]. LPGs are usually fabricated by periodic modulation of the refractive index of a photosensitive fiber core that is exposed to an UV beam. With such a method, a LPG written in a PCF, which is doped with germanium in the core, was first reported in 1999 [13

13. B. J. Eggleton, P. S. Westbrook, R. S. Windeler, S. Spalter, and T. A. Strasser, “Grating resonances in air-silica microstructured optical fibers,” Opt. Lett. 24, 1460–1462 (1999). [CrossRef]

]. Other fabrication methods of LPGs and structural rocking filters in PCF were subsequently demonstrated by use of CO2 lasers [14

14. G. Kakarantzas, T. A. Birks, and P. St. J. Russell, “Structural long-period gratings in photonic crystal fibers,” Opt. Lett. 27, 1013–1015 (2002). [CrossRef]

18

18. G. Humbert, A. Malki, S. Fevrier, P. Roy, and D. Pagnoux, “Electric arc-induced long-period gratings in Ge-free air-silica microstructure fiber,” Electron. Lett. 4, 349–350 (2003). [CrossRef]

]. In contrast with the LPGs written by UV light, which become unstable over time, CO2 laser-induced LPGs are temperature insensitive because of their structural perturbation along the fiber.

To simplify and obtain a cost-effective method, we propose what we believe is the first point-by-point demonstration of an extremely short-length LPG with strong resonance in a large-mode-area PCF in a CO2 laser beam. The resulting LPG with unique optical properties in the PCF has the potential to be used as a conventional fiber-optic device.

2. Fabrication of a long-period grating in large-mode-area photonic crystal fiber

The large-mode-area PCF used in our experiments was fabricated at Crystal Fibre A/S by the stack-and-draw process for which we employed an array of silica capillaries and rods. A scanning electron micrograph (SEM) image of the PCF is shown in Fig. 1. The PCF was 3 m long and had a center-to-center distance between air holes of Λ ~ 6.1 µm as well as an average air-hole diameter of d ~ 1.8 µm, so the value of d/Λ was 0.295. The holes were arranged in a hexagonal pattern that extended to a diameter of 65 µm. Defining the core diameter (D core) yields the relation of D core=Λ(2-d/Λ) and the value of 10.4 µm. The outer diameter of the PCF matches the standard value of 125 µm.

Fig. 1. Scanning electron micrograph (SEM) of a cross-section of the large-mode-area PCF used in the fabrication of the LPG.

The LPGs in the large-mode-area PCF were fabricated with a CO2 laser system. The experimental setup is shown in Fig. 2, which includes the CO2 laser (Synrad J48-1, 2.5-W full power) with a galvanometer that directs and focuses the laser beam diameter to an approximately 180-µm Gaussian focal spot; a fiber holder whose movement can be controlled by use of translation stages attached to it; and two CCD cameras, each mounted at a 45° angle to capture the fiber image and display it through an optical graph (OG) monitor. An optical spectrum analyzer (OSA) with a 1450–1650-nm wavelength region was employed to analyze the transmission spectrum profile of a LPG in situ. The point-by-point technique was used to localize the heating at periodic intervals on the large-mode-area PCF. A 4.2-g weight was attached to the PCF over the fiber holder to provide constant tension. As the fiber was moved to each new position by the translation stage, the CO2 laser was turned on and the light beam was incident on the PCF. This procedure causes period decreases on the cladding diameter of the PCF because of the holes in the cladding that collapse in size rather than in the immediate neighboring sections. The time and power of the PCF determine the number of collapsed holes. The neck diameter in which the cladding is mostly collapsed is approximately 101.4 µm, which is shown in Fig. 3. The resulting grating has eight periods with Λ=350 µm for each period, and the laser power was 0.57 W with a laser-focused spot of 100 µm FWHM. The laser beam stop time for each period was 450 ms.

Fig. 2. Schematic diagram of the experimental setup: CO2, laser; PCF, photonic crystal fiber; CCD, camera; OM, optical micrograph; SLD, super-luminescent diode; OSA, optical spectrum analyzer.
Fig. 3. Optical micrograph of a section of LPG after the PCF is treated by the heat source of a CO2 laser, Λ is 350 µm of the spacing of one period.

3. Experimental results and discussion

The resonance that appeared in the transmission spectrum of a LPG in a large-mode-area PCF is due to coupling from the fundamental core mode to cladding modes that are then radiated away through the coating. Figure 4 shows the transmission spectra of the LPG with 6, 7, and 8 periods. The resonance wavelength of the LPG with 8 periods is located at 1529.2 nm with a FWHM of ~0.7 nm, and the strongest resonance is approximately -31.5 dB. The total length of the LPG is 2.8 mm, which is a highly compact LPG. The transmission spectra also show that the mode-coupling efficiency increases quickly when the grating period increases. The insertion loss (loss of background) increased because deformation of the fiber cladding increased after each period was written. At each period of the grating, the fundamental mode is no longer guided by the long wavelength. It should be noted that there are no side-lobes on two sides of the resonance.

Fig. 4. Transmission spectra of the LPG in large-mode-area PCF with 6, 7, and 8 periods.

A CO2 laser-written LPG is typically rectangular with a 50% duty cycle and creates the index modulation. The Fourier series of the rectangular index modulation with the given period is given by

δn(z)=Δn[12+2πm=11msin(2)cos(2πmΛz)]
(2)

where Λ is the period, Δn is the peak index change, and m is an integer, and order of interactions for coupling to all cladding modes. For LPGs, the index modulation during the writing process makes the coupling coefficient, a function of the transmittance, and the peak index change. Meanwhile, the definition of the effective refractive index is described in the cladding of the PCF. If the fiber cladding is substantially homogeneous, then the effective refractive index of the cladding is the same as the refractive index of pure silica. If, however, the cladding is inhomogeneous, for example, a cladding region that comprises holes filled with air and distributed in silica, then the effective refractive index of the cladding will differ from both the refractive index of the silica and the refractive index of air. For a close approximation, the effective index of an inhomogeneous material can be considered to be a weighted average of the refractive indices of the constituents of the material. From the above statement we learned that the effective refractive index n eff of a two-component material of silica air could be given by

(nsilicanair)fsilicanair2+fairnsilica2nefffsilicansilica2+fairnair2
(3)

where n silica and n air are the refractive indices of silica and air, respectively, and f silica and f air are silica and air volume fractions. For a material consisting of 50% silica and 50% air, the effective refractive index is approximately 1.205, so that the refractive index between core and cladding of PCF can be 2 orders of magnitude larger than that for conventional fiber.

4. Conclusion

In conclusion, we have demonstrated a point-by-point technique for the fabrication of deeply notched and highly compact LPGs in a large-mode-area PCF with a CO2 laser. Strong coupling efficiencies, as high as -31.5 dB at 1529.2-nm wavelength with a FWHM of ~0.7 nm, and a LPG as short as 2.8 mm were achieved for a compactly packaged fiber-based device. Compared with the lengths of all the previously reported LPGs in PCFs, which had a range of several centimeters, this is, to our knowledge, the strongest resonance and shortest LPG ever reported. There are major advantages for the use of such LPGs in optical telecommunications and sensors including (1) temperature insensitivity and stability, (2) a compact device when it is packaged, and (3) practical, low-cost all-fiber filters and PCF-based devices.

Acknowledgments

Funding for this project was provided by the Nanyang Technological University and the Agency for Science, Technology, and Research (A*STAR) in Singapore.

References and links

1.

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996). [CrossRef] [PubMed]

2.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic bandgap guidance of light in air,” Science 285, 1537–1539 (1999). [CrossRef] [PubMed]

3.

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

4.

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J.-P. de Sandro, “Large mode area photonic crystal fiber,” Electron. Lett. 13, 1347–1348 (1998). [CrossRef]

5.

T. A. Birks, D. Mogilevstev, J. C. Knight, and P. St. J. Russell, “Dispersion compensation using single-material fibers,” IEEE Photon. Technol. Lett. 11, 674–676 (1999). [CrossRef]

6.

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

7.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Bagget, N. G. R. Broderick, and D. J. Richardson, “Sensing with microstructured optical fibers,” Meas. Sci. Technol. 12, 854–858 (2001). [CrossRef]

8.

R. Holzwarth, M. Zimmermann, T. Udem, T. W. Hansch, P. Russbuldt, K. Gabel, R. Poprawe, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “White-light frequency comb generation with a diode-pumped Cr:LiSAF laser,” Opt. Lett. 26, 1376–1378 (2001). [CrossRef]

9.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996). [CrossRef]

10.

C. Y. Lin and L. A. Wang, “A wavelength- and loss- tunable band-rejection filter based on corrugated long-period fiber grating,” IEEE Photon. Technol. Lett. 13, 332–334 (2001). [CrossRef]

11.

A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, and P. J. Lemaire, “Long-period fiber-grating-based gain equalizers,” Opt. Lett. 21, 336–338 (1996). [CrossRef] [PubMed]

12.

V. Bhatia, “Applications of long-period gratings to single and multi-parameter sensing,” Opt. Express 4, 457–466 (1999), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-11-457 [CrossRef] [PubMed]

13.

B. J. Eggleton, P. S. Westbrook, R. S. Windeler, S. Spalter, and T. A. Strasser, “Grating resonances in air-silica microstructured optical fibers,” Opt. Lett. 24, 1460–1462 (1999). [CrossRef]

14.

G. Kakarantzas, T. A. Birks, and P. St. J. Russell, “Structural long-period gratings in photonic crystal fibers,” Opt. Lett. 27, 1013–1015 (2002). [CrossRef]

15.

G. Kakarantzas, A. Ortigosa-Mlanch, T. A. Birks, P. St. J. Russell, L. Farr, F. Couny, and B. J. Mangan, “Structural rocking filters in highly birefringent photonic crystal fiber,” Opt. Lett. 28, 158–160 (2003). [CrossRef] [PubMed]

16.

N. Groothoff, J. Canning, E. Buckley, K. Lyttikainen, and J. Zagari, “Bragg gratings in air-silica structured fibers,” Opt. Lett. 28, 233–235 (2003). [CrossRef] [PubMed]

17.

M. D. Nielsen, G. Vienne, and J. R. Folkenberg, “Investigation of microdeformation-induced attenuation spectra in a photonic crystal fiber,” Opt. Lett. 28, 236–238 (2003). [CrossRef] [PubMed]

18.

G. Humbert, A. Malki, S. Fevrier, P. Roy, and D. Pagnoux, “Electric arc-induced long-period gratings in Ge-free air-silica microstructure fiber,” Electron. Lett. 4, 349–350 (2003). [CrossRef]

19.

B. J. Eggleton, P. S. Westbrook, C. A. White, C. Kerbage, R. S. Windelar, and G. L. Burdge, “Cladding mode resonances in air-silica microstructure fiber,” J. Lightwave Tech. 18, 1084–1100 (2000). [CrossRef]

20.

B. J. Eggleton, C. Kerbage, P. S. Westbrook, R. S. Windeler, and A. Hale, “Microstructured optical fiber devices,” Opt. Express 9, 698–713 (2001),http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-698 [CrossRef] [PubMed]

21.

C. Kerbage, B. J. Eggleton, P. S. Westbrook, and R. S. Windeler, “Experimental and scalar beam propagation analysis of an air-silica microstructure fiber,” Opt. Express 7, 113–123 (2000), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-3-113 [CrossRef] [PubMed]

OCIS Codes
(060.2310) Fiber optics and optical communications : Fiber optics
(230.0230) Optical devices : Optical devices
(230.1480) Optical devices : Bragg reflectors
(230.3990) Optical devices : Micro-optical devices

ToC Category:
Research Papers

History
Original Manuscript: July 1, 2003
Revised Manuscript: July 31, 2003
Published: August 11, 2003

Citation
Yinian Zhu, Ping Shum, Hin-Joo Chong, M. Rao, and Chao Lu, "Strong resonance and a highly compact longperiod grating in a large-mode-area photonic crystal fiber," Opt. Express 11, 1900-1905 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-16-1900


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References

  1. J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, �??All-silica single-mode optical fiber with photonic crystal cladding,�?? Opt. Lett. 21, 1547�??1549 (1996). [CrossRef] [PubMed]
  2. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, �??Single-mode photonic bandgap guidance of light in air,�?? Science 285, 1537�??1539 (1999). [CrossRef] [PubMed]
  3. T. A. Birks, J. C. Knight, and P. St. J. Russell, �??Endlessly single-mode photonic crystal fiber,�?? Opt. Lett. 22, 961�??963 (1997). [CrossRef] [PubMed]
  4. J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J.�??P. de Sandro, �??Large mode area photonic crystal fiber,�?? Electron. Lett. 13, 1347�??1348 (1998). [CrossRef]
  5. T. A. Birks, D. Mogilevstev, J. C. Knight, and P. St. J. Russell, �??Dispersion compensation using singlematerial fibers,�?? IEEE Photon. Technol. Lett. 11, 674�??676 (1999). [CrossRef]
  6. J. K. Ranka, R. S. Windeler, and A. J. Stentz, �??Optical properties of high-delta air�??silica microstructure optical fiber,�?? Opt. Lett. 25, 796�??798 (2000). [CrossRef]
  7. T. M. Monro, W. Belardi, K. Furusawa, J. C. Bagget, N. G. R. Broderick, and D. J. Richardson, �??Sensing with microstructured optical fibers,�?? Meas. Sci. Technol. 12, 854�??858 (2001). [CrossRef]
  8. R. Holzwarth, M. Zimmermann, T. Udem, T. W. Hansch, P. Russbuldt, K. Gabel, R. Poprawe, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, �??White-light frequency comb generation with a diode-pumped Cr:LiSAF laser,�?? Opt. Lett. 26, 1376�??1378 (2001). [CrossRef]
  9. A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, �??Long-period fiber gratings as band-rejection filters,�?? J. Lightwave Technol. 14, 58�??65 (1996). [CrossRef]
  10. C. Y. Lin and L. A. Wang, �??A wavelength- and loss- tunable band-rejection filter based on corrugated longperiod fiber grating,�?? IEEE Photon. Technol. Lett. 13, 332�??334 (2001). [CrossRef]
  11. A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, and P. J. Lemaire, �??Long-period fiber-grating-based gain equalizers,�?? Opt. Lett. 21, 336�??338 (1996). [CrossRef] [PubMed]
  12. V. Bhatia, �??Applications of long-period gratings to single and multi-parameter sensing,�?? Opt. Express 4, 457-466 (1999), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-11-457">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-11-457</a> [CrossRef] [PubMed]
  13. B. J. Eggleton, P. S. Westbrook, R. S. Windeler, S. Spalter, and T. A. Strasser, �??Grating resonances in air�??silica microstructured optical fibers,�?? Opt. Lett. 24, 1460�??1462 (1999). [CrossRef]
  14. G. Kakarantzas, T. A. Birks, and P. St. J. Russell, �??Structural long-period gratings in photonic crystal fibers,�?? Opt. Lett. 27, 1013�??1015 (2002). [CrossRef]
  15. G. Kakarantzas, A. Ortigosa-Mlanch, T. A. Birks, P. St. J. Russell, L. Farr, F. Couny, and B. J. Mangan, �??Structural rocking filters in highly birefringent photonic crystal fiber,�?? Opt. Lett. 28, 158�??160 (2003). [CrossRef] [PubMed]
  16. N. Groothoff, J. Canning, E. Buckley, K. Lyttikainen, and J. Zagari, �??Bragg gratings in air�??silica structured fibers,�?? Opt. Lett. 28, 233�??235 (2003). [CrossRef] [PubMed]
  17. M. D. Nielsen, G. Vienne, and J. R. Folkenberg, �??Investigation of microdeformation-induced attenuation spectra in a photonic crystal fiber,�?? Opt. Lett. 28, 236�??238 (2003). [CrossRef] [PubMed]
  18. G. Humbert, A. Malki, S. Fevrier, P. Roy, and D. Pagnoux, �??Electric arc-induced long-period gratings in Ge-free air�??silica microstructure fiber,�?? Electron. Lett. 4, 349�??350 (2003). [CrossRef]
  19. B. J. Eggleton, P. S. Westbrook, C. A. White, C. Kerbage, R. S. Windelar, and G. L. Burdge, �??Cladding mode resonances in air�??silica microstructure fiber,�?? J. Lightwave Tech. 18, 1084�??1100 (2000). [CrossRef]
  20. B. J. Eggleton, C. Kerbage, P. S. Westbrook, R. S. Windeler, and A. Hale, �??Microstructured optical fiber devices,�?? Opt. Express 9, 698�??713 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-698">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-698</a> [CrossRef] [PubMed]
  21. C. Kerbage, B. J. Eggleton, P. S. Westbrook, and R. S. Windeler, �??Experimental and scalar beam propagation analysis of an air-silica microstructure fiber,�?? Opt. Express 7, 113�??123 (2000), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-3-113">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-3-113</a> [CrossRef] [PubMed]

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