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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 8 — Apr. 19, 2004
  • pp: 1477–1484
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Hollow core photonic crystal fibers for beam delivery

G. Humbert, J. C. Knight, G. Bouwmans, P. St. J. Russell, D. P. Williams, P. J. Roberts, and B. J. Mangan  »View Author Affiliations


Optics Express, Vol. 12, Issue 8, pp. 1477-1484 (2004)
http://dx.doi.org/10.1364/OPEX.12.001477


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Abstract

Hollow-core photonic crystal fibers have unusual properties which make them ideally suited to delivery of laser beams. We describe the properties of fibers with different core designs, and the observed effects of anti-crossings with interface modes. We conclude that 7-unit-cell cores are currently most suitable for transmission of femtosecond and sub-picosecond pulses, whereas larger cores (e.g. 19-cell cores) are better for delivering nanosecond pulsed and continuous-wave beams.

© 2004 Optical Society of America

1. Introduction

High power lasers (including CW, Q-switched and mode-locked configurations) are widely used in fields as diverse as marking, machining and welding, laser-Doppler velocimetry, laser surgery and THz generation. For many applications, optical fiber would be the preferred means of delivery if it were reliable and efficient, but is currently unusable. Delivery of powerful laser light (both pulsed and CW) using optical fibers is traditionally hard, because the high optical powers and energies cause fiber damage and deleterious nonlinear-optical phenomena, and also because of the group-velocity dispersion (GVD) in fibers which disperses short pulses. Our attention here is focused especially on those applications requiring fiber delivery with a high beam quality, such as micromachining or laser beams for guide stars. For such applications, fiber attenuation is generally not a limiting parameter, as the lengths involved are typically of the order of a few m. Instead, the limiting parameters are dispersion, nonlinearity and fiber damage. In this paper we describe how these parameters depend on the fiber design and which fibers are currently most useful for such applications.

2. Hollow-core photonic crystal fibers

HC-PCF’s are very different to conventional optical fibers, and can be formed in several ways using different materials. The fibers discussed in this paper are drawn from a preform created by stacking together hundreds of hollow silica capillaries, so that the final fiber has a 2-dimensional pattern of air holes running down its length. An electron micrograph of a HC-PCF is shown in Fig. 1. The periodic “holey” cladding surrounds a larger central air hole, which serves as the fiber core. Light is trapped in the core by the photonic bandgap of the cladding, which covers a finite frequency range, typically around 20% of the central frequency. Outside of the bandgap, the modes of the core are not confined, and the attenuation of the fiber is high. Within the bandgap, one or more modes are localized within the vicinity of the core, and the attenuation falls when the fundamental guided mode is most strongly peaked in the hollow core [2

2. B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. Couny, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St.J. Russell, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” postdeadline paper PDP24, OFC’04 (Los Angeles, 2004).

,6

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

]. The minimum attenuation is determined by scattering due to imperfections in the fiber and by coupling to other confined modes (interface or surface modes) which have a greater overlap with the core surround [7

7. C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Allan, and K. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003). [CrossRef] [PubMed]

,8

8. D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, P. Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibers”, in Photonic Crystal Materials and Devices, A. Adibi, A. Scherer, and S. Y. Lin, Eds. Proc. SPIE5000 (2003)

]. The properties of these interface modes are strongly dependent on the fiber design, but almost invariably influence the performance of the fiber as a whole. In particular, the lowest-loss wavelength is not necessarily determined by the center of the bandgap, but by the locations of the interface modes. Most of the fibers which have been reported have been based on 7-cell or 19-cell core designs, formed by omitting 7 or 19 central capillaries from the stack when the preform is being built (the fiber in Fig. 1 is a 7-cell design). In this paper we describe the observed effects of interface modes and other features of these two core designs that impact on their suitability for laser delivery.

Fig. 1. Scanning electron micrograph of the HC-PCF used in the experiments described in this paper

3. Guided modes

The fiber studied in this work is that shown in Fig. 1. The optical attenuation of the fiber (shown in the inset to Fig. 2) was measured with a broadband light source using the cutback technique. The attenuation minimum was found to be 78 dB/km at a wavelength of 1102 nm, and the main low-loss window is roughly 115 nm wide, centered at 1083 nm. In order to identify features in the high-loss regions surrounding the transmission window, we present in Fig. 2 the transmitted spectrum of a 5 m fiber length measured using a broadband source (tungsten-halogen lamp). On the long-wavelength edge (>1160 nm), the transmitted intensity decreases rapidly. On the short wavelength side, from 900 nm to 1000 nm, the transmission oscillates and then decreases rapidly when approaching 900 nm. This spectral transmittance is not affected by bending the fiber, as long as the bend radius is greater than a few millimeters. We believe that the region between 900 nm and 1000 nm lies within the bandgap of the cladding material, but that losses in this range are significantly increased by virtue of anti-crossings [7

7. C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Allan, and K. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003). [CrossRef] [PubMed]

,8

8. D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, P. Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibers”, in Photonic Crystal Materials and Devices, A. Adibi, A. Scherer, and S. Y. Lin, Eds. Proc. SPIE5000 (2003)

] with several interface modes, which act as an additional loss mechanism.

We have studied near-field patterns over the photonic bandgap wavelength range, including both low-loss and interface-mode regions. We used a short length (5 m) of HC-PCF and a fiber-based optical supercontinuum [11

11. W. J. Wadsworth, N. Joly, J. C. Knight, T. A. Birks, F. Biancalana, and P. St.J. Russell, “Supercontinuum and four-wave mixing with Q-switched pulses in endlessly single-mode photonic crystal fibres,” Opt. Express 12, 299–309 (2004) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-299 [CrossRef] [PubMed]

] as a light source. The supercontinuum was passed through a monochromator (3 nm bandwidth) and then coupled into the HC-PCF using an objective lens. The output end of the HC-PCF was imaged onto a digital CCD camera with high magnification, so that the output field patterns could be studied as a function of wavelength. Images were recorded at 1 nm intervals. We were unable to cover the long wavelength edge of the guiding region (beyond the supercontinuum pump wavelength of 1064 nm) because of the limited spectral response of our CCD camera. The data were corrected for the spectral profile of the supercontinuum source and the spectral response of the CCD camera.

Fig. 2. Spectrum of a broadband light source (tungsten lamp) transmitted through a 5m length of the HC-PCF. The inset shows the attenuation recorded using a cutback measurement on 85 m of the same fiber.
Fig 3. Enlarged view of the interface-mode region of the transmission curve from Fig. 2, with observed near-field intensity maps at the fiber output at wavelengths corresponding to some of the intensity mimima and maxima. The entire sequence can be viewed as a movie. (avi, 505kB)

Fig. 4. (a) Polarized near-field intensity patterns recorded using low numerical aperture excitation as a function of wavelength (log scale). (b) Near-field patterns at two different wavelengths using a higher numerical aperture excitation with the same output polarization (linear scale). One of these (1021 nm) shows interface-mode features, even though these are not apparent in the fundamental mode at this wavelength.

4. Fiber core designs for beam delivery

In traditional fibers, delivery of nanosecond pulses (or CW beams) is limited by fiber damage and nonlinear effects such as Raman generation. These limitations can be substantially relieved by using HC-PCF. The influence of the HC-PCF design manifests in two ways: the overlap of the guided mode with a Gaussian beam determines the beam launch efficiency (assuming a high-quality input beam) and thus the percentage of incident light that couples to the fundamental guided mode. Secondly, the guided mode profile sets the percentage of light guided in the air and the guided mode intensity in the silica parts of the fiber, in turn influencing the nonlinear response. In this section, we compare two designs of hollow core fiber with reference to these important criteria.

Fig. 5. 7-cell and 19-cell fiber structures and examples of computed guided-mode field patterns.

Examples of 7-cell-core and 19-cell-core fiber designs are shown in Fig. 5, along with examples of computed guided-mode field patterns in these two structures. We use a plane-wave expansion method to compute the different guided modes of these fibers for a fixed cladding structure. The chosen cladding structure has an air-fraction of 91%, and approximates the shapes of the air holes as hexagons with rounded corners. The thickness of the silica struts forming the framework of the cladding was fixed to be 0.0304 times the pitch, as was the core wall. The radii of the circles used to form the rounded hexagons was chosen so that 40% of each strut was of uniform thickness. This cladding creates a band gap for the fundamental core-guided mode extending over 24% of the central wavelength. The basic features of the observed attenuation spectra, i.e. the width and central wavelength of the band gap, are well reproduced by the computation. Modeling structures similar to that shown, we consistently find that there are interface-mode crossings on the short-wavelength side of the band gap.

In order to compare the 7-cell and 19-cell structures, the fundamental mode-field profiles are calculated for both designs at a range of wavelengths that span the entire band gap. For each structure, an optimum wavelength is chosen that maximizes the percentage of light propagating in the air parts of the fiber. At these wavelengths, the modes are not affected by anti-crossings with interface modes. Table 1 compares values for the percentage light-in-air of the fundamental modes, the peak intensity in the silica (normalized to the maximum intensity at the core center) and the optimized overlap with a Gaussian beam. The nonlinear phase shift (computed as in reference [9

9. F. Luan, J. C. Knight, P. S. J. Russell, S. Campbell, D. Xiao, D. T. Reid, B. J. Mangan, D. P. Williams, and P. J. Roberts, “Femtosecond soliton pulse delivery at 800nm wavelength in hollow-core photonic bandgap fibers,” Opt. Express 12, 835–840 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-5-835 [CrossRef] [PubMed]

]), calculated per MW of power and per m of length, is also included in the table.

The results in Table 1 show the potential advantages of using a 19-cell fiber to guide high-power lasers. The 19-cell fiber possesses a larger mode area, and since the normalized peak intensity in silica is approximately the same for both designs, the absolute peak intensity is lower in the 19-cell case, for a given power. Furthermore, the percentage of light traveling in the silica parts of the fiber is reduced from 0.8% to 0.2% by moving to the larger core. This reduced overlap with the silica combined with the increased area gives rise to a nonlinear phase shift that is significantly lower in the 19-cell design. The nonlinear phase shift due to the air in the core then dominates the nonlinear response (by a ratio 10 to 1), whereas in the 7-cell structure the contributions to the phase shift of the air and silica parts of the fiber are approximately equal. In addition to the advantage of reduced overlap with the silica, the mode overlap with a Gaussian beam is considerably better for the 19-cell structure, giving greater beam launch efficiency and decreased fraction of power incident upon the microstructured cladding. 19-cell designs are thus likely to offer superior performance for transmission of CW or ns pulsed beams, as long as the wavelength of interest is well away from an interface-mode anti-crossing.

Further experimental and numerical studies have shown that the 19-cell design has a higher density of interface modes than the 7-cell case. This must be expected due to the longer core perimeter associated with the larger core. The greater number of anti-crossings between these modes and the fundamental mode can result in a narrowing of the low-loss

Table 1. Properties of 7-cell and 19-cell fibers.

table-icon
View This Table

transmission windows in the band gap [2

2. B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. Couny, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St.J. Russell, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” postdeadline paper PDP24, OFC’04 (Los Angeles, 2004).

]. This is not a significant problem for transmission of ns pulsed or CW beams, which are intrinsically spectrally narrow, but becomes important for shorter pulse transmission.

The situation for delivery of sub-ps or fs pulses is rather different. Here, the primary limitations arise from the bandwidth of the pulse and the dispersion of the fiber. Pulses can be delivered either as high-energy solitons [4

4. D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K.W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 3011702–1704 (2003). [CrossRef] [PubMed]

,9

9. F. Luan, J. C. Knight, P. S. J. Russell, S. Campbell, D. Xiao, D. T. Reid, B. J. Mangan, D. P. Williams, and P. J. Roberts, “Femtosecond soliton pulse delivery at 800nm wavelength in hollow-core photonic bandgap fibers,” Opt. Express 12, 835–840 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-5-835 [CrossRef] [PubMed]

] or by pre-chirping the pulses (either with or without further spectral broadening) and then recompression in a length of hollow-core fiber [12

12. C. J. S. de Matos and J. R. Taylor, “Multi-kilowatt, all-fiber integrated chirped-pulse amplification system yielding 40× pulse compression using air-core fiber and conventional erbium-doped fiber amplifier,” Opt. Express 12, 405–409 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-405 [CrossRef] [PubMed]

]. In the first case, one challenge is to adjust the nonlinear phase shift to enable efficient soliton excitation with the available pulse energy, while maintaining both a low dispersion and dispersion slope. Fibers with 7-cell cores have been shown to be capable of supporting relatively long solitons (several hundred fs) when excited using amplified modelocked laser systems [4

4. D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K.W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 3011702–1704 (2003). [CrossRef] [PubMed]

,9

9. F. Luan, J. C. Knight, P. S. J. Russell, S. Campbell, D. Xiao, D. T. Reid, B. J. Mangan, D. P. Williams, and P. J. Roberts, “Femtosecond soliton pulse delivery at 800nm wavelength in hollow-core photonic bandgap fibers,” Opt. Express 12, 835–840 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-5-835 [CrossRef] [PubMed]

]. This has not yet been demonstrated using unamplified systems because the nonlinear phase shift is usually too low, even in a 7-cell defect fiber. However, the nonlinear response could be increased by using a lower air-filling-fraction cladding, a thicker core surround or by using a smaller core. A second challenge, which is relevant for linear (pre-chirped) propagation as well, is to form fibers which have the required level of second-order dispersion (GVD) but have suitably low higher-order dispersion over the bandwidth of the laser. We would expect that a larger core size – i.e. a 19-cell defect – would result in lower waveguide dispersion and hence lower dispersion slope. However, the increased density of interface modes associated with a larger core invalidates that argument, breaking up the transmission band into a number of low-loss windows within which the dispersion is adversely affected [8

8. D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, P. Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibers”, in Photonic Crystal Materials and Devices, A. Adibi, A. Scherer, and S. Y. Lin, Eds. Proc. SPIE5000 (2003)

,10

10. K. Saitoh, N. A. Mortensen, and M. Koshiba, “Air-core photonic band-gap fibers: the impact of surface modes,” Opt. Express 12, 394–400 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-394 [CrossRef] [PubMed]

]. Consequently, we believe that 7-cell-core fibers are presently more suited for the delivery of sub-picosecond or femtosecond pulses.

This conclusion may change in the future. Numerical computations show that the number and position of interface modes in a 19-cell structure are very sensitive to deformations of the core and cladding of the fiber. Improvements to the manufacture of 19-cell designs may broaden the low-loss and low-dispersion transmission windows to the extent that they become suitable for shorter pulses, allowing all the advantages of using a larger core to be realized.

5. Conclusions

As for conventional fibers, HC-PCF designs with larger cores are more suitable for transmission of high-power or high-energy laser beams, because of their increased damage threshold and reduced nonlinear response. However, the low-loss transmission bandwidth in current 19-cell fibers is significantly reduced as a result of the greater density of interface modes and their associated anti-crossings with the fundamental guided mode. We have observed the effects of interface-mode anti-crossings on the fundamental and higher-order core modes in a 7-cell fiber, and shown that the ideal properties of the guided modes are substantially destroyed in the vicinity of such a crossing. Future improvements in the manufacture of the 19-cell design may broaden the low-loss transmission windows to a level suitable for sub-ps and fs pulse delivery, but at this stage, the smaller-core fibers offer a lower interface mode density, giving fewer mode anti-crossings, more favourable dispersion characteristics and a broader bandwidth for ultra-short pulse delivery. Both 7-cell and 19-cell fiber designs will find applications in the delivery of laser beams in the future, depending on the specific application being developed.

References and links

1.

J. C. Knight, “Photonic Crystal fibers,” Nature 424, 847–851 (2003). [CrossRef] [PubMed]

2.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. Couny, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St.J. Russell, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” postdeadline paper PDP24, OFC’04 (Los Angeles, 2004).

3.

P. St.J. Russell, “Photonic crystal fibres,” Science 299, 358–362 (2003). [CrossRef] [PubMed]

4.

D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K.W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 3011702–1704 (2003). [CrossRef] [PubMed]

5.

J. D. Shephard, J. D. C. Jones, D. P. Hand, G. Bouwmans, J. C. Knight, P. St.J. Russell, and B. J. Mangan, “High energy nanosecond laser pulses delivered single-mode through hollow-core PBG fibers,” Opt. Express 12, 717–723 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-717 [CrossRef] [PubMed]

6.

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

7.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Allan, and K. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003). [CrossRef] [PubMed]

8.

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, P. Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibers”, in Photonic Crystal Materials and Devices, A. Adibi, A. Scherer, and S. Y. Lin, Eds. Proc. SPIE5000 (2003)

9.

F. Luan, J. C. Knight, P. S. J. Russell, S. Campbell, D. Xiao, D. T. Reid, B. J. Mangan, D. P. Williams, and P. J. Roberts, “Femtosecond soliton pulse delivery at 800nm wavelength in hollow-core photonic bandgap fibers,” Opt. Express 12, 835–840 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-5-835 [CrossRef] [PubMed]

10.

K. Saitoh, N. A. Mortensen, and M. Koshiba, “Air-core photonic band-gap fibers: the impact of surface modes,” Opt. Express 12, 394–400 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-394 [CrossRef] [PubMed]

11.

W. J. Wadsworth, N. Joly, J. C. Knight, T. A. Birks, F. Biancalana, and P. St.J. Russell, “Supercontinuum and four-wave mixing with Q-switched pulses in endlessly single-mode photonic crystal fibres,” Opt. Express 12, 299–309 (2004) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-299 [CrossRef] [PubMed]

12.

C. J. S. de Matos and J. R. Taylor, “Multi-kilowatt, all-fiber integrated chirped-pulse amplification system yielding 40× pulse compression using air-core fiber and conventional erbium-doped fiber amplifier,” Opt. Express 12, 405–409 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-405 [CrossRef] [PubMed]

OCIS Codes
(060.2310) Fiber optics and optical communications : Fiber optics
(160.2290) Materials : Fiber materials

ToC Category:
Focus Issue: Photonic crystals and holey fibers

History
Original Manuscript: March 3, 2004
Revised Manuscript: April 6, 2004
Published: April 19, 2004

Citation
Georges Humbert, J. Knight, G. Bouwmans, P. Russell, D. Williams, P. Roberts, and B. Mangan, "Hollow core photonic crystal fibers for beam delivery," Opt. Express 12, 1477-1484 (2004)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-8-1477


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References

  1. J. C. Knight, �??Photonic Crystal fibers,�?? Nature 424, 847-851 (2003). [CrossRef] [PubMed]
  2. B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. Couny, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, P. St.J. Russell, �??Low loss (1.7 dB/km) hollow core photonic bandgap fiber,�?? postdeadline paper PDP24, OFC�??04 (Los Angeles, 2004).
  3. P. St.J. Russell, �??Photonic crystal fibres,�?? Science 299, 358-362 (2003). [CrossRef] [PubMed]
  4. D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K.W. Koch, A. L. Gaeta, �??Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,�?? Science 301, 1702-1704 (2003). [CrossRef] [PubMed]
  5. J. D. Shephard, J. D. C. Jones, D. P. Hand, G. Bouwmans, J. C. Knight, P. St.J. Russell, B. J. Mangan, "High energy nanosecond laser pulses delivered single-mode through hollow-core PBG fibers," Opt. Express 12, 717- 723 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-717">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-717</a> [CrossRef] [PubMed]
  6. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St.J. Russell, D. Allen, P. J. Roberts, �??Single-mode photonic bandgap guidance of light in air,�?? Science 285, 1537-1539 (1999). [CrossRef] [PubMed]
  7. C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Allan, K. Koch, �??Low-loss hollow-core silica/air photonic bandgap fibre,�?? Nature 424, 657-659 (2003). [CrossRef] [PubMed]
  8. D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, P. Zhang and K. W. Koch, �??Surface modes and loss in air-core photonic band-gap fibers�??, in Photonic Crystal Materials and Devices, A. Adibi, A. Scherer, S. Y. Lin, Eds. Proc. SPIE 5000 (2003)
  9. F. Luan, J. C. Knight, P. S. J. Russell, S. Campbell, D. Xiao, D. T. Reid, B. J. Mangan, D. P. Williams, and P. J. Roberts, "Femtosecond soliton pulse delivery at 800nm wavelength in hollow-core photonic bandgap fibers," Opt. Express 12, 835-840 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-5-835">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-5-835</a> [CrossRef] [PubMed]
  10. K. Saitoh, N. A. Mortensen, and M. Koshiba, "Air-core photonic band-gap fibers: the impact of surface modes," Opt. Express 12, 394-400 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-394">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-394</a> [CrossRef] [PubMed]
  11. W. J. Wadsworth, N. Joly, J. C. Knight, T. A. Birks, F. Biancalana, and P. St.J. Russell, "Supercontinuum and four-wave mixing with Q-switched pulses in endlessly single-mode photonic crystal fibres," Opt. Express 12, 299-309 (2004) <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-299">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-299</a> [CrossRef] [PubMed]
  12. C. J. S. de Matos and J. R. Taylor, �??Multi-kilowatt, all-fiber integrated chirped-pulse amplification system yielding 40�? pulse compression using air-core fiber and conventional erbium-doped fiber amplifier,�?? Opt. Express 12, 405-409 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-405">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-405</a> [CrossRef] [PubMed]

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