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Double photonic bandgap hollow-core photonic crystal fiber
Optics Express, Vol. 17, Issue 18, pp. 16238-16243 (2009)
http://dx.doi.org/10.1364/OE.17.016238
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– Abstract
1. Introduction
2. Cladding design
3. Fabrication and optical characterization
4. Conclusion
– References and links
– Abstract
1. Introduction
2. Cladding design
3. Fabrication and optical characterization
4. Conclusion
– References and links
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Abstract
We report on the design, fabrication and characterization of hollow-core photonic crystal fiber with two robust bandgaps that bridge the benchmark laser wavelengths of 1064nm and 1550nm. The higher-order bandgap arises due to the extremely thin struts of the silica cladding and their fine-tuning relative to the apex size. The optimum strut thickness was found to be approximately one hundredth of the cladding pitch.
© 2009 OSA
1. Introduction
Advances in the design and fabrication of photonic-bandgap (PBG) hollow-core photonic crystal fiber (HC-PCF) with claddings of high air-filling fraction, have resulted in the advent of triangular-lattice HC-PCF whose optical attenuation is as low as 1.2 dB/km at 1550nm [1]. Efforts are now concentrating on speeding up the fiber fabrication process [2] and tailoring the core for polarization maintaining purposes [3], or on the removal of unwanted surface modes from the bandgap [2,4]. The latter aspect enables loss reduction together with an enhanced useable spectral bandwidth and lowered chromatic dispersion. Progress has also been made in finding PBG air-guidance in fibers with cladding structures other than the above-mentioned triangular-lattice [5].
P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, and P. St J Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express 13(1), 236–244 (2005). [CrossRef] [PubMed]
R. Amezcua-Correa, F. Gèrôme, S. G. Leon-Saval, N. G. R. Broderick, T. A. Birks, and J. C. Knight, “Control of surface modes in low loss hollow-core photonic bandgap fibers,” Opt. Express 16(2), 1142–1149 (2008). [CrossRef] [PubMed]
R. Amezcua-Correa, F. Gèrôme, S. G. Leon-Saval, N. G. R. Broderick, T. A. Birks, and J. C. Knight, “Control of surface modes in low loss hollow-core photonic bandgap fibers,” Opt. Express 16(2), 1142–1149 (2008). [CrossRef] [PubMed]
Y. Y. Wang, P. S. Light, and F. Benabid, “Core-Surround Shaping of Hollow-Core Photonic Crystal Fiber Via HF Etching,” IEEE Photon. Technol. Lett. 20(12), 1018–1020 (2008). [CrossRef]
F. Poletti and D. J. Richardson, “Hollow-core photonic bandgap fibers based on a square lattice cladding,” Opt. Lett. 32(16), 2282–2284 (2007). [CrossRef] [PubMed]
The high efficiency resulting from the confined geometry of low loss HC-PCF has been exploited in many applications including soliton delivery [6], electromagnetically induced transparency [7,8] and Raman scattering [9] to mention a few. Nevertheless, the narrow transmission bandwidth offered by PBG fiber has hindered the extension of its benefits to areas requiring the simultaneous guidance of optical frequencies spaced by more than 70 THz. For example, it would be desirable to bridge the wavelength ranges of Nd:YAG and Yb lasers at ~1 µm with that of the Ti:Sapphire (~800 nm) or Er-doped lasers used in telecommunications (~1.5 µm). Large pitch hollow core fibers [10,11] address this issue by offering an ultra-broadband guidance and a chromatic dispersion figure below 2ps/nm/km [11]. This is achieved, however, at the expense of a generally higher loss than that offered by PBG fibers.
D. G. Ouzounov, F. R. Ahmad, D. Müller, 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 301(5640), 1702–1704 (2003). [CrossRef] [PubMed]
S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94(9), 093902 (2005). [CrossRef] [PubMed]
F. Benabid, P. S. Light, F. Couny, and P. S. J. Russell, “Electromagnetically-induced transparency grid in acetylene-filled hollow-core PCF,” Opt. Express 13(15), 5694–5703 (2005). [CrossRef] [PubMed]
F. Benabid, G. Bouwmans, J. C. Knight, P. S. J. Russell, and F. Couny, “Ultrahigh efficiency laser wavelength conversion in a gas-filled hollow core photonic crystal fiber by pure stimulated rotational Raman scattering in molecular hydrogen,” Phys. Rev. Lett. 93(12), 123903 (2004). [CrossRef] [PubMed]
F. Couny, F. Benabid, and P. S. Light, “Large-pitch kagome-structured hollow-core photonic crystal fiber,” Opt. Lett. 31(24), 3574–3576 (2006). [CrossRef] [PubMed]
F. Couny, P. J. Roberts, T. A. Birks, and F. Benabid, “Square-lattice large-pitch hollow-core photonic crystal fiber,” Opt. Express 16(25), 20626–20636 (2008). [CrossRef] [PubMed]
F. Couny, P. J. Roberts, T. A. Birks, and F. Benabid, “Square-lattice large-pitch hollow-core photonic crystal fiber,” Opt. Express 16(25), 20626–20636 (2008). [CrossRef] [PubMed]
In parallel to these experimental endeavors, a powerful and intuitive tool explaining bandgap formation in HC-PCF, akin to the tight binding model in solid-state physics, has been developed [12]. This photonic tight binding model (PTBM) gives an intuitive physical picture of the guidance mechanism based on the nature of the modes present in the photonic cladding and their associated structural features.
In this paper, we use the PTBM framework in designing and fabricating a PBG HC-PCF that provides two robust bandgaps, and thus two spectral windows of low-loss guidance, centered around 1064nm and 1550nm, bridging telecoms wavelengths with those of Nd:YAG and Yb lasers. The scaling of the fiber structure would allow simultaneous guidance of other benchmark laser wavelength doublets, such as 1μm and 800nm, or 800nm and 633nm.
2. Cladding design
The PTBM model has previously been used to identify the waveguiding features (or resonators) present in the cladding of HC-PCF and responsible for photonic band formation [13]. The results of this analysis are summarized in Fig. 1
. Figure 1a shows the calculated density of photonic states (DOPS) for a typical triangular-lattice PBG HC-PCF cladding-structure (air-filling fraction ~93%, see top-left inset). The DOPS was calculated using a variational plane wave method [13] and illustrates the density of supported cladding modes as a function of effective index and normalized frequency kΛ. Here k is the wavenumber and Λ is the photonic structure pitch. Bandgaps appear white, representing zero density of states, with the grayscale representing an increasing cladding state density.
S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001). [CrossRef] [PubMed]
S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001). [CrossRef] [PubMed]
Fig. 1 (a) Density of photonic states for the cladding structure illustrated inset top-left, with a strut thickness of t = 0.04Λ and apex meniscus curvature r = 0.24Λ as defined in the lower-right inset. White represents zero density, and black the greatest. (b) - (d): Mode profiles calculated at the bandgap edge at the positions indicated in the DOPS plot.
The photonic allowed bands (i.e. cladding modes) are formed by identifiable resonators within the cladding structure; the band at lowest normalized frequency is associated with the silica apexes, as illustrated by the cladding mode in Fig. 1b calculated at the point illustrated on the DOPS plot. Similarly, the photonic band forming the high-frequency edge of the bandgap is due to the struts of the cladding (Fig. 1c) at effective indices above 0.98, and by the air-holes (Fig. 1d) for effective indices below 0.98 [12].
Intriguingly, Fig. 1a predicts a narrow second bandgap around kΛ = 23. However, as this small bandgap barely extends below the air-line, its use for guidance in an air core is expected to be characterized by high optical attenuation. This is in agreement with experimental measurement made on HC-PCF with such a structure, where no transmission is observed in this spectral region even through just a few centimeters of fiber. Nonetheless, the presence of this second bandgap so close to the air-line raises the question of whether its spectral width and depth can be increased sufficiently to achieve low-loss guidance through tailoring of the cladding resonator geometry. By virtue of the PTBM, changes to the resonator geometries alter their dispersion curves, and if done appropriately, the second PBG would open-up sufficiently below the air-line.
This was investigated numerically by making changes to the size of the struts and the apexes of a triangular-lattice that exhibits a very high-air-filling fraction (~97%). Figure 2
plots the effective indices of cladding modes against normalized frequency kΛ for five cladding structures of varying strut width and apex size. The modes are calculated using the finite-element method. As all band-edges of the PBGs are defined by high-symmetry points of the reciprocal lattice [12], computational speed can be greatly improved by calculating the cladding modes only at these points. Conversely, not all symmetry point modes lie at a band edge and so, for clarity, in Fig. 2 bandgaps that cross the air-line are shaded. The fundamental core mode of a 7-cell core fiber in the first bandgap has a typical effective index of ~0.996, and in the second bandgap of ~0.999. The key characteristics of the two bandgaps are their relative spectral width and central frequency, as detailed in Table 1
for each of the cladding structures with varying strut thickness and apex meniscus curvature presented in Fig. 2.
Fig. 2 Effective indices of cladding modes calculated at high symmetry points for six structures. Left: constant strut thickness t = 0.05Λ and varying apex curvature radius r (top) r = 0.10Λ, (middle) rc = 0.15Λ and (bottom) r = 0.20Λ. Right: constant apex curvature r = 0.15Λ and varying strut thickness t (top) t = 0.005Λ, (middle) t = 0.010Λ and (bottom) t = 0.015Λ. The locations of bandgaps that cross the air-line are shaded. The horizontal line represents the air light line at neff = 1.
Table 1 Fundamental and second bandgap widths for the modeled structures. The parameters of the fabricated structure are highlighted in bold type.
It is important to note that the air-filling fraction, often quoted as the sole defining parameter for a HC-PCF cladding structure, is not sufficient for the study of PBG; indeed for all considered structures the air-filling fraction is between 96.5% and 97.5%. From Fig. 2, one notices that the position and depth of the bandgaps strongly depend on both strut width and apex size. It is clear that the width of the first (lower normalized frequency) bandgap benefits from relatively large apexes and extremely thin struts. For example, decreasing the strut width from t = 0.015Λ to t = 0.005Λ dramatically increases the bandgap width from 21.3% to 49.3% of its central frequency. In contrast, the second bandgap has a weaker dependence on strut thickness, with nearly no changes to the bandgap width as the strut thickness is tripled. The second bandgap, however, favors a smaller apex, with the bandgap-width nearly doubling as the apex curvature is decreased from r = 0.15Λ to r = 0.10Λ. As expected, a similar apex curvature to that of state-of-the-art HC-PCF (i.e. >0.20Λ) results in the complete closure of the second bandgap (Fig. 2, lower-left graph).
Interestingly, the spacing between the central frequencies of the two bandgaps in the structures studied is largely independent of the strut and apex sizes. Set around 1.39, this ratio does not allow for guidance of lasers separated by an octave frequency-spacing, but it is however conveniently spaced for simultaneous guidance of many benchmarks laser pairs, such as telecoms/Nd:YAG (1310/1550nm and 1064nm), Nd:YAG/Ti:Sapph (1064nm and 800nm), and Ti:Sapph/HeNe (800nm and 633nm).
These results also highlight the compromise between achieving two robust bandgaps, and maximizing their respective widths. Maximum spectral coverage across both bandgaps is therefore achieved using narrow struts and by limiting the size of the apex to 0.15Λ. Due to such small strut and apex dimensions, these bandgaps are positioned at higher normalized frequency than conventional PBG fibres. This is an advantage from an engineering point of view, as they can be fabricated more easily, having a pitch Λ nearly twice as large as their single bandgap counterpart.
The full DOPS calculated for the cladding structure chosen for fabrication (indicated in bold in Table 1) is shown in Fig. 3
. The fundamental (HE11-like) core-guided mode calculated for a 7-cell core fiber with this cladding structure is shown by the thick grey lines crossing each bandgap and clearly indicates that guidance via the fundamental mode is indeed possible in both bandgaps.
Fig. 3 Calculated density of photonic states for the structure illustrated inset top-left, with a strut thickness of t = 0.01Λ and apex meniscus curvature of r = 0.15Λ. The colored lines trace the cladding modes that form the edges of the two bandgaps. The grey line crossing each bandgap shows the effective index of the fundamental core-guided mode of a 7-cell core fiber with the modeled cladding structure. Inset bottom-right: cladding modes of apexes alone (red) and struts alone (blue). The shaded regions indicate the extent of each band.
The bottom-right inset in Fig. 3 plots the effective indices of modes in a cladding consisting of only apexes (red) and only struts (blue) that together form the selected cladding structure. The full photonic bands are shaded such that overlap between the bands is clearly visible. It is the repulsive interaction (due to a strong symmetry overlap) between these modes in the full structure that leads to the opening of the two bandgaps at the air-line. A full theoretical discussion, based on the PTBM, of this interaction and the opening of the two bandgaps at the air light line will be given in a future publication.
3. Fabrication and optical characterization
Based on the above results, we fabricated several HC-PCFs using the standard stack-and-draw technique with a structure optimized to achieve two robust bandgaps. In order to obtain sufficiently large apex sizes, relatively thick capillaries were stacked, each with a normalized wall thickness greater than the required normalized strut thickness in the final fiber (capillary ID/OD = 0.76). Pressurization was used during the fiber drawing process to reduce the thickness of the struts and increase the relative size of the apexes from those of the initial stack. A thin-wall core tube (ID/OD = 0.93) was used such that the fiber core wall thickness is ~60% of the strut thickness. Vacuum was applied during the cane during process to reduce the size of the interstitial holed. While drawing to fiber from a 3.3mm cane in a 10mm jacket, pressures of 29 kPa and 22 kPa were applied to the cladding holes and core hole respectively.
Figure 4b
shows scanning electron micrographs of the fiber cross-section and detail of the cladding structure. The pressurization of the stack during the cane pulling and fiber drawing stages allowed an air-filling-fraction of ~97% to be obtained in the fiber cladding, with the strut thickness and apex curvature close to those modeled in Fig. 3. The pitch of the fabricated fiber shows some variation across the cladding due to the high pressurization, being between 5.8 µm and 6.3 µm for the inner six rings, with an average over this region of 6.0 µm.
Fig. 4 (a) Transmission spectra of 5 m lengths of the fabricated HC-PCF with varying pitch, offset vertically for clarity. (b) SEMs showing the fiber cross-section and the cladding structure (c) Attenuation measured by cutback of a 25 m length of fibre. (d) Measured group delay (squares), and dispersion (solid lines) calculated based on fourth order polynomial fit to group delay data (dashed lines).
The transmission and loss spectra of the fiber shown in Fig. 4b are given by the black curve in Fig. 4a and Fig. 4c, respectively. The first band gap extends from 1335 nm to above 1750 nm (the detection limit of the optical spectrum analyzer), and the second bandgap extends from 1080 nm to 1140 nm. These correspond to normalized widths of 30% and 5.5% respectively. These figures compare reasonably well with the theoretical relative frequency spacing of 1.39 and spectral widths (see Table 1) of 32.7% and 13.3% respectively. It is expected that the discrepancy in width is due to the observed fluctuation in pitch across the fiber cladding, and the fact that the core surround shape and thickness have not been optimized leading to surface modes existing towards the edge of the bandgaps. The expected blue-shift in both bandgaps with smaller cladding pitch is illustrated by three further transmission spectra of fibers fabricated with differing pitch, shown by dashed lines in Fig. 4a.
The attenuation of the fiber (Fig. 4c) was measured using a cutback technique on a 25 m fibre sample cut to 5 m. The first order bandgap has a loss of 80 dB km−1 which is typical for a non-optimized draw process due to the non-uniformity of the cladding. The second bandgap has a loss of 500 dB km−1, greater than that of the fundamental bandgap. In part this is due to scattering losses due to surface roughness being greater at shorter wavelengths [14], but mostly it is due to a higher confinement loss which manifests because of the narrower PBG region below the air-line. It is expected that both of these loss figures can be significantly lowered by improving the uniformity of the cladding structure through better control of pressurization during the fiber drawing process. It is interesting to add that the fiber has the typical dispersion characteristic of bandgap HC-PCF, with large normal dispersion near the low wavelength edge of each bandgap and large anomalous dispersion towards the high wavelength edge (Fig. 4d). The magnitude of the dispersion toward the edges of the second bandgap is observed to be several times greater than that of the fundamental bandgap.
4. Conclusion
We have fabricated a PBG HC-PCF that guides in two wavelength regions, allowing simultaneous guidance of both Nd:YAG/Yb radiation at 1µm and all telecommunication bands at 1.5-1.6µm in a single fiber. Scaling of the fiber should allow dual-guidance of 1µm and 800nm light, or both 800nm and 633nm. Such fiber has applications including the delivery of laser pairs, which are often too separated in frequency to guide in a conventional HC-PCF. Furthermore, it should be possible to tailor the zero-GVD of each bandgap to allow high-fidelity transmission of laser pulses at two separate wavelengths.
It is also worth noting that the presence of two bandgaps is not limited to the triangular structure considered here. Similar control of the apex size and strut thickness in a square lattice cladding also leads to the opening of a second bandgap.
References and links
P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, and P. St J Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express 13(1), 236–244 (2005). [CrossRef] [PubMed] | |
R. Amezcua-Correa, F. Gèrôme, S. G. Leon-Saval, N. G. R. Broderick, T. A. Birks, and J. C. Knight, “Control of surface modes in low loss hollow-core photonic bandgap fibers,” Opt. Express 16(2), 1142–1149 (2008). [CrossRef] [PubMed] | |
B. J. Mangan, J. K. Lyngso, and P. J. Roberts, “Realization of low loss and polarization maintaining hollow core photonic crystal fibers,” 2008 Conference on Lasers and Electro-Optics 2016–2017 (2008). | |
Y. Y. Wang, P. S. Light, and F. Benabid, “Core-Surround Shaping of Hollow-Core Photonic Crystal Fiber Via HF Etching,” IEEE Photon. Technol. Lett. 20(12), 1018–1020 (2008). [CrossRef] | |
F. Poletti and D. J. Richardson, “Hollow-core photonic bandgap fibers based on a square lattice cladding,” Opt. Lett. 32(16), 2282–2284 (2007). [CrossRef] [PubMed] | |
D. G. Ouzounov, F. R. Ahmad, D. Müller, 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 301(5640), 1702–1704 (2003). [CrossRef] [PubMed] | |
S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94(9), 093902 (2005). [CrossRef] [PubMed] | |
F. Benabid, P. S. Light, F. Couny, and P. S. J. Russell, “Electromagnetically-induced transparency grid in acetylene-filled hollow-core PCF,” Opt. Express 13(15), 5694–5703 (2005). [CrossRef] [PubMed] | |
F. Benabid, G. Bouwmans, J. C. Knight, P. S. J. Russell, and F. Couny, “Ultrahigh efficiency laser wavelength conversion in a gas-filled hollow core photonic crystal fiber by pure stimulated rotational Raman scattering in molecular hydrogen,” Phys. Rev. Lett. 93(12), 123903 (2004). [CrossRef] [PubMed] | |
F. Couny, F. Benabid, and P. S. Light, “Large-pitch kagome-structured hollow-core photonic crystal fiber,” Opt. Lett. 31(24), 3574–3576 (2006). [CrossRef] [PubMed] | |
F. Couny, P. J. Roberts, T. A. Birks, and F. Benabid, “Square-lattice large-pitch hollow-core photonic crystal fiber,” Opt. Express 16(25), 20626–20636 (2008). [CrossRef] [PubMed] | |
F. Couny, F. Benabid, P. J. Roberts, M. T. Burnett, and S. A. Maier, “Identification of Bloch-modes in hollow-core photonic crystal fiber cladding,” Opt. Express 32, 2282–2284 (2007). | |
S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001). [CrossRef] [PubMed] | |
T. A. Birks, P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, J. C. Knight and P. St. J. Russell, “The Fundamental Limits to the Attenuation of Hollow-Core Photonic Crystal Fibres,” ICTON (2005) Paper Mo.B2.1. |
OCIS Codes
(060.2270) Fiber optics and optical communications : Fiber characterization
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(060.5295) Fiber optics and optical communications : Photonic crystal fibers
ToC Category:
Photonic Crystal Fibers
History
Original Manuscript: July 16, 2009
Revised Manuscript: July 30, 2009
Manuscript Accepted: August 3, 2009
Published: August 27, 2009
Virtual Issues
August 28, 2009 Spotlight on Optics
Citation
Philip S. Light, François Couny, Ying Ying Wang, Natalie V. Wheeler, P. John Roberts, and Fetah Benabid, "Double photonic bandgap hollow-core photonic crystal fiber," Opt. Express 17, 16238-16243 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-18-16238
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References
- P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express 13(1), 236–244 (2005). [CrossRef] [PubMed]
- R. Amezcua-Correa, F. Gèrôme, S. G. Leon-Saval, N. G. R. Broderick, T. A. Birks, and J. C. Knight, “Control of surface modes in low loss hollow-core photonic bandgap fibers,” Opt. Express 16(2), 1142–1149 (2008). [CrossRef] [PubMed]
- B. J. Mangan, J. K. Lyngso, and P. J. Roberts, “Realization of low loss and polarization maintaining hollow core photonic crystal fibers,” 2008 Conference on Lasers and Electro-Optics 2016–2017 (2008).
- Y. Y. Wang, P. S. Light, and F. Benabid, “Core-Surround Shaping of Hollow-Core Photonic Crystal Fiber Via HF Etching,” IEEE Photon. Technol. Lett. 20(12), 1018–1020 (2008). [CrossRef]
- F. Poletti and D. J. Richardson, “Hollow-core photonic bandgap fibers based on a square lattice cladding,” Opt. Lett. 32(16), 2282–2284 (2007). [CrossRef] [PubMed]
- D. G. Ouzounov, F. R. Ahmad, D. Müller, 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 301(5640), 1702–1704 (2003). [CrossRef] [PubMed]
- S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94(9), 093902 (2005). [CrossRef] [PubMed]
- F. Benabid, P. S. Light, F. Couny, and P. S. J. Russell, “Electromagnetically-induced transparency grid in acetylene-filled hollow-core PCF,” Opt. Express 13(15), 5694–5703 (2005). [CrossRef] [PubMed]
- F. Benabid, G. Bouwmans, J. C. Knight, P. S. J. Russell, and F. Couny, “Ultrahigh efficiency laser wavelength conversion in a gas-filled hollow core photonic crystal fiber by pure stimulated rotational Raman scattering in molecular hydrogen,” Phys. Rev. Lett. 93(12), 123903 (2004). [CrossRef] [PubMed]
- F. Couny, F. Benabid, and P. S. Light, “Large-pitch kagome-structured hollow-core photonic crystal fiber,” Opt. Lett. 31(24), 3574–3576 (2006). [CrossRef] [PubMed]
- F. Couny, P. J. Roberts, T. A. Birks, and F. Benabid, “Square-lattice large-pitch hollow-core photonic crystal fiber,” Opt. Express 16(25), 20626–20636 (2008). [CrossRef] [PubMed]
- F. Couny, F. Benabid, P. J. Roberts, M. T. Burnett, and S. A. Maier, “Identification of Bloch-modes in hollow-core photonic crystal fiber cladding,” Opt. Express 32, 2282–2284 (2007).
- S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001). [CrossRef] [PubMed]
- T. A. Birks, P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, J. C. Knight and P. St. J. Russell, “The Fundamental Limits to the Attenuation of Hollow-Core Photonic Crystal Fibres,” ICTON (2005) Paper Mo.B2.1.
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