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  • Editor: Xi-Cheng Zhang
  • Vol. 39, Iss. 2 — Jan. 15, 2014
  • pp: 295–298
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Low-loss and low-bend-sensitivity mid-infrared guidance in a hollow-core–photonic-bandgap fiber

Natalie V. Wheeler, Alexander M. Heidt, Naveen K. Baddela, Eric Numkam Fokoua, John R. Hayes, Seyed R. Sandoghchi, Francesco Poletti, Marco N. Petrovich, and David J. Richardson  »View Author Affiliations


Optics Letters, Vol. 39, Issue 2, pp. 295-298 (2014)
http://dx.doi.org/10.1364/OL.39.000295


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Abstract

Hollow-core–photonic-bandgap fiber, fabricated from high-purity synthetic silica, with a wide operating bandwidth between 3.1 and 3.7 μm, is reported. A minimum attenuation of 0.13dB/m is achieved through a 19-cell core design with a thin core wall surround. The loss is reduced further to 0.05dB/m following a purging process to remove hydrogen chloride gas from the fiber—representing more than an order of magnitude loss reduction as compared to previously reported bandgap-guiding fibers operating in the mid-infrared. The fiber also offers a low bend sensitivity of <0.25dB per 5 cm diameter turn over a 300 nm bandwidth. Simulations are in good agreement with the achieved losses and indicate that a further loss reduction of more than a factor of 2 should be possible by enlarging the core using a 37-cell design.

© 2014 Optical Society of America

Conventional all-solid optical fibers have revolutionized many fields, starting with telecommunications and branching to areas as diverse as fiber optic gyroscopes and other sensors, high-power fiber lasers, and endoscopes for medical applications [1

1. B. Culshaw and A. Kersey, J. Lightwave Technol. 26, 1064 (2008). [CrossRef]

,2

2. D. J. Richardson, J. Nilsson, and W. A. Clarkson, J. Opt. Soc. Am. B 27, B63 (2010). [CrossRef]

]. The spectral range where conventional fibers have made the greatest impact has been largely defined by the transparency window of silica glass, which is usually the main constituent of these fibers. High-purity, dry synthetic silica (e.g., Suprasil F300 from Heraeus) is transparent (<10dB/km [3

3. O. Humbach, H. Fabian, U. Grzesik, U. Haken, and W. Heitmann, J. Non-Cryst. Solids 203, 19 (1996). [CrossRef]

]) between 500 and 2000 nm, and limited at short wavelengths by electronic absorption and at longer wavelengths by multiphonon absorption. The fabrication of low-loss, durable, and bend-insensitive fibers at wavelengths extending to longer wavelengths and into the mid-infrared (mid-IR) is desirable for applications including high-power laser beam delivery, gas sensing, gas lasers, and surgery.

Hollow-core–photonic-bandgap fibers (HC-PBGFs) provide an alternative mechanism for light confinement in an air-core fiber. Until now, the lowest reported loss in this spectral region was 1dB/m [12

12. A. Urich, R. R. J. Maier, B. J. Mangan, S. Renshaw, J. C. Knight, D. P. Hand, and J. D. Shephard, Opt. Express 20, 6677 (2012). [CrossRef]

] in a seven-cell fiber operating at wavelengths up to 3.4 μm. Here we report a 19-cell HC-PBGF that demonstrates an order of magnitude reduction in loss (0.13dB/m at 3.33 μm) in combination with a wide operating bandwidth, extending from 3.1 to 3.7 μm, and that also exhibits very low bend sensitivity. Furthermore, we show, for the first time, to the best of our knowledge, experimental results confirming that unwanted absorption features due to HCl in the hollow core can be successfully removed through gas purging. Transmission loss measurements in the near-IR show that in addition to the fundamental bandgap guidance in the mid-IR, several further low-loss spectral regions exist with losses as low as 1.2dB/m. The origin of this guidance is discussed. Finally, we present simulations of the fiber characteristics based on the structure of the fabricated fiber that are in good agreement with the achieved minimum loss.

The HC-PBGF has a 19-cell core design and was fabricated using the conventional two-step stack and draw technique. The differential pressure between the core and cladding regions of the structure was carefully controlled during the fiber drawing process to maintain an optimum core surround and to minimize the overlap between the core guided modes and the silica core surround. This approach, combined with a thin-walled core surround, is necessary to enable a wide, surface mode free operating bandwidth [13

13. F. Poletti, N. V. Wheeler, M. N. Petrovich, N. Baddela, E. N. Fokoua, J. R. Hayes, D. R. Gray, and D. J. Richardson, Nat. Photonics 7, 279 (2013). [CrossRef]

]. A scanning electron microscope (SEM) image of the fabricated fiber is shown in Fig. 1(a); the average core diameter is 50 μm, the average hole-to-hole distance is 9.3 μm, and the relative hole size [14

14. N. A. Mortensen and M. D. Nielsen, Opt. Lett. 29349, (2004). [CrossRef]

] is 0.965.

Fig. 1. (a) SEM of fabricated fiber. (b) Transmission through 5 m (purple line) and 58 m (red line) and corresponding attenuation calculated from cutback measurement (black line).

The fiber transmission in the mid-IR [Fig. 1(b)] was recorded using a custom built supercontinuum source that generates a broad spectrum spanning from 0.75 to 4 μm by pumping a ZBLAN fiber with a diode-seeded picosecond thulium-doped fiber amplifier system at 2 μm [15

15. A. M. Heidt, J. H. V. Price, C. Baskiotis, J. S. Feehan, Z. Li, S. U. Alam, and D. J. Richardson, Opt. Express 21, 24281 (2013). [CrossRef]

]. A monochromator with 5nm resolution was used for detection of the signal transmitted through the PBGF. The measurement over a 5 m fiber length [purple line in Fig. 1(b)] shows that the bandgap extends from 3.1 to 3.8 μm and a cutback loss measurement (58 to 5 m) shows a minimum loss of 0.13(±0.05)dB/m at 3.33 μm and <1dB/m transmission loss over >500nm bandwidth despite the high bulk silica attenuation. The uncertainty associated with this measurement arises from a combination of source instability [15

15. A. M. Heidt, J. H. V. Price, C. Baskiotis, J. S. Feehan, Z. Li, S. U. Alam, and D. J. Richardson, Opt. Express 21, 24281 (2013). [CrossRef]

] and variations in the fiber cleave. This low-loss value indicates that the average overlap between the core guided modes and the silica surround is less than 0.3%.

At the short wavelength edge of the bandgap, there are several loss peaks that we believe are due to surface modes, while between 3.3 and 3.6 μm many gas absorption lines are visible. These can be attributed to HCl absorption; this gas is present in the fiber due to the use of chlorine to dehydrate the bulk silica glass that is used as the raw material in fabrication [16

16. J. K. Lyngso, B. J. Mangan, C. Jakobsen, and P. J. Roberts, Opt. Express 17, 23468 (2009). [CrossRef]

]. Figure 2(a) shows the theoretical HCl absorption lines in this spectral region [17

17. L. S. Rothman, I. E. Gordon, A. Barbe, D. C. Benner, P. E. Bernath, M. Birk, V. Boudon, L. R. Brown, A. Campargue, J. P. Champion, K. Chance, L. H. Coudert, V. Dana, V. M. Devi, S. Fally, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, I. Kleiner, N. Lacome, W. J. Lafferty, J. Y. Mandin, S. T. Massie, S. N. Mikhailenko, C. E. Miller, N. Moazzen-Ahmadi, O. V. Naumenko, A. V. Nikitin, J. Orphal, V. I. Perevalov, A. Perrin, A. Predoi-Cross, C. P. Rinsland, M. Rotger, M. Simeckova, M. A. H. Smith, K. Sung, S. A. Tashkun, J. Tennyson, R. A. Toth, A. C. Vandaele, and J. Vander Auwera, J. Quantum Spectrosc. Radiat. Transfer 110, 533 (2009). [CrossRef]

]; the excellent agreement between this data and the observed loss peaks in experimental loss measurement confirms that their origin is HCl absorption. The measured minimum loss lies between two such absorption lines, and it is likely that the loss value would be lower if the gas was eliminated from the fiber. Note that the loss measurement shown in Fig. 1(b) is limited by the 5 nm resolution of the monochromator. Furthermore, due to the large mismatch between the launch ZBLAN fiber (9 μm core diameter) and the HC-PBGF, excitation of higher-order modes in the latter is almost inevitable, which will most likely lead to a loss overestimate.

Fig. 2. (a) HCl absorption spectrum taken from HITRAN database. (b) High-resolution attenuation measurements (0.2 nm) measured by cutback technique before and after purging the HC-PBGF with argon for five days (red and green lines, respectively). Cutback lengths were from 53 to 5 m and 48 to 5 m, respectively.

Fig. 3. Bend loss: transmission of 5 m of the HC-PBGF was recorded with five coils of 5 cm diameter in the fiber (red line) and with the fiber loosely coiled (purple line). The bend loss per turn (blue line) is <0.25dB over a 300 nm bandwidth.

Several low-loss guidance windows were also observed in the visible and near-IR, with a minimum transmission loss of 1.2dB/m at 1690 nm and several similar low-loss regions between 800 and 1000 nm, as shown by the cutback measurement in Fig. 4. This opens up the possibility of simultaneous guidance of both near and mid-IR light in this fiber. The presence of resonant loss features within this band is indicative of AR guidance, although it is possible that these low-loss regions could be attributed to narrow, higher-order bandgaps. AR guidance bands have been previously observed in the visible region in HC-PBGFs designed to operate at 1550 nm [18

18. R. E. P. de Oliveira, C. J. S. de Matos, G. E. Nunes, and I. H. Bechtold, J. Opt. Soc. Am. B 29, 977 (2012). [CrossRef]

], with losses of the order of dB/cm, two orders of magnitude higher than the losses reported here. However, for a fair comparison it is important to note that those results were recorded at wavelengths around 600 nm in a fiber with a smaller core diameter (11.4 μm), so scattering due to surface roughness would have a much larger impact on attenuation than in the fiber reported here. From the SEM image shown in Fig. 1(a), the core surround thickness was estimated as 180±30nm. From these measurements, resonance with the core surround would be expected at 370nm, with a broad AR region at longer wavelengths.

Fig. 4. (a) Transmission through 10 m of HC-PBGF recorded using a commercial supercontinuum source; the mode image shown in the inset was recorded at 1.1μm. (b) Attenuation of the HC-PBGF in the near-IR calculated by cutback to 5 m length. Blacked out regions correspond to effectively zero transmission.

To gain further insight into this guidance mechanism, the bend loss in this spectral region was also recorded. In the low-loss regions of the near-IR guidance, the bend loss was 0.8dB per 8 cm diameter turn. For a fundamental bandgap operating in this spectral region, the bend losses are expected to be negligible [19

19. T. P. Hansen, J. B. J. Broeng, C. Jakobsen, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, J. Lightwave Technol. 22, 11 (2004). [CrossRef]

], so this could support an AR guidance mechanism; however, the transmission properties of higher-order bandgaps in HC-PBGFs have not been extensively examined and studies in all-solid PBGFs have revealed complex bend sensitivity that does indeed increase with bandgap number [20

20. T. A. Birks, F. Luan, G. J. Pearce, A. Wang, J. C. Knight, and D. M. Bird, Opt. Express 14, 5688 (2006). [CrossRef]

]. Further work is underway to confirm the nature of the guidance mechanism that is appropriate here.

In order to assess the potential of improving this fiber design for lower loss operation in the mid-IR we first simulated the fabricated fiber to determine the agreement between the minimum attenuation achieved in the fabricated fiber and that expected theoretically. Fiber parameters, such as average cladding strut thickness and hole separation, were extracted from the SEM shown in Fig. 1(a) and used in a model based on the finite element method. The wavelength dependence of the attenuation of Suprasil F300 in this spectral range was extracted from [3

3. O. Humbach, H. Fabian, U. Grzesik, U. Haken, and W. Heitmann, J. Non-Cryst. Solids 203, 19 (1996). [CrossRef]

]. The simulated fiber transmission is shown in Fig. 5(a); the minimum attenuation was found to be 0.07dB/m for a core mode overlap with the silica structure of 0.1%. This is in good agreement, to within the associated uncertainty of the experimental minimum loss post purging. In contrast to HC-PBGFs operating in the near-IR, the loss is limited by the silica absorption instead of scattering due to surface roughness [21

21. 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. S. J. Russell, Opt. Express 13, 236 (2005). [CrossRef]

]. The dominance of silica absorption in defining the fiber attenuation is highlighted in Fig. 5(b), where confinement loss is plotted and compared with the total attenuation. From this figure it is clear that confinement loss is negligible compared to silica absorption for the fiber design operating in the mid-IR. Furthermore, two surface modes are indicated in the simulation, toward the short wavelength edge of the bandgap; the presence of these indicates that the loss peaks observed in this region of the bandgap in the experimental transmission are also due to surface modes.

Fig. 5. (a) Simulated attenuation (blue line) is in good agreement with measured attenuation before and after purging (black and green lines with 5 and 0.2 nm resolution, respectively). (b) Breakdown of loss contribution; simulated confinement loss (purple line) is compared to total simulated loss (red line).

To achieve lower losses using a bandgap fiber design, it will be necessary to reduce the overlap with the silica fiber cladding. The use of a 37-cell defect core to increase the core radius, which has already been demonstrated for data transmission applications [22

22. N. K. Baddela, M. N. Petrovich, Y. Jung, J. R. Hayes, N. V. Wheeler, D. R. Gray, N. Wong, F. Parmigiani, E. Numkam, J. P. Wooler, F. Poletti, and D. J. Richardson, in CLEO/QELS (2013), paper CTu2K.3.

], is expected to reduce the overlap by an additional 60%, indicating that losses can be reduced to achieve a level comparable with or in fact lower than state-of-the-art AR fibers operating in this spectral region [9

9. A. N. Kolyadin, A. F. Kosolapov, A. D. Pryamikov, A. S. Biriukov, V. G. Plotnichenko, and E. M. Dianov, Opt. Express 21, 9514 (2013). [CrossRef]

,10

10. F. Yu, W. J. Wadsworth, and J. C. Knight, Opt. Express 20, 11153 (2012). [CrossRef]

], without compromising on bend sensitivity.

In conclusion, we have fabricated and characterized a 19-cell HC-PBGF that provides low-loss (<1dB/m) guidance between 3.1 and 3.6 μm. The fiber has a record minimum attenuation of 0.13dB/m at 3.33 μm for a HC-PBGF operating in the mid-IR, which reduced to 0.05dB/m after purging to remove HCl gas. This low-loss operation is combined with an extremely low bend loss for this spectral region of <0.25dB per 5 cm diameter turn over a 300 nm bandwidth making this fiber suitable for applications such as gas sensing and surgery, which may require a device with a small footprint and/or high flexibility. In particular, it is expected that a fiber with the same design but scaled to operate at 2.94 μm would be highly suited for Er:YAG laser delivery for high-precision medical applications, such as cutting through hard biological tissue [12

12. A. Urich, R. R. J. Maier, B. J. Mangan, S. Renshaw, J. C. Knight, D. P. Hand, and J. D. Shephard, Opt. Express 20, 6677 (2012). [CrossRef]

]. Interestingly, low-loss guidance (1.2dB/m) in the near-IR was also recorded in this fiber, the nature of which is yet to be confirmed, but an initial investigation indicates the possibility of antiresonant guidance. Due to this near-IR transmission, this fiber may be a suitable host for a hollow optical fiber gas laser that is pumped in the near-IR and lases in the mid-IR [23

23. A. M. Jones, A. V. V. Nampoothiri, A. Ratanavis, T. Fiedler, N. V. Wheeler, F. Couny, R. Kadel, F. Benabid, B. R. Washburn, K. L. Corwin, and W. Rudolph, Opt. Express 19, 2309 (2011). [CrossRef]

]. By enlarging the core to a 37-cell defect, in order to reduce the overlap of the core guided mode with the silica cladding, it is anticipated that losses can be reduced further without increasing the bend sensitivity.

This work was supported by the UK EPSRC through grants EP/I01196X/1 (HYPERHIGHWAY) and EP/H02607X/1. A. M. H. acknowledges funding from the EU 7th Framework Program (Marie Curie Actions) under grant agreement 300859 (ADMIRATION). F. P. gratefully acknowledges support from the Royal Society.

References

1.

B. Culshaw and A. Kersey, J. Lightwave Technol. 26, 1064 (2008). [CrossRef]

2.

D. J. Richardson, J. Nilsson, and W. A. Clarkson, J. Opt. Soc. Am. B 27, B63 (2010). [CrossRef]

3.

O. Humbach, H. Fabian, U. Grzesik, U. Haken, and W. Heitmann, J. Non-Cryst. Solids 203, 19 (1996). [CrossRef]

4.

J. A. Harrington, Infrared Fibers and Their Applications (SPIE, 2004).

5.

P. W. Carter, S. F. Moore, M. W. Szebesta, D. Williams, J. R. Ranson, and D. France, Electron. Lett. 26, 2115 (1990). [CrossRef]

6.

J. M. Kriesel, N. Gat, B. E. Bernacki, R. L. Erikson, B. D. Cannon, T. L. Myers, C. M. Bledt, and J. A. Harrington, Proc SPIE 8018, 80180V (2011).

7.

F. Benabid, P. J. Roberts, F. Couny, and P. S. Light, J. Eur. Opt. Soc. Rapid Publ. 4, 09004 (2009). [CrossRef]

8.

T. Ritari, J. Tuominen, H. Ludvigsen, J. H. Petersen, T. Sorensen, T. Hansen, and H. Simonsen, Opt. Express 12, 4080 (2004). [CrossRef]

9.

A. N. Kolyadin, A. F. Kosolapov, A. D. Pryamikov, A. S. Biriukov, V. G. Plotnichenko, and E. M. Dianov, Opt. Express 21, 9514 (2013). [CrossRef]

10.

F. Yu, W. J. Wadsworth, and J. C. Knight, Opt. Express 20, 11153 (2012). [CrossRef]

11.

Y. Y. Wang, N. V. Wheeler, F. Couny, P. J. Roberts, and F. Benabid, Opt. Lett. 36, 669 (2011). [CrossRef]

12.

A. Urich, R. R. J. Maier, B. J. Mangan, S. Renshaw, J. C. Knight, D. P. Hand, and J. D. Shephard, Opt. Express 20, 6677 (2012). [CrossRef]

13.

F. Poletti, N. V. Wheeler, M. N. Petrovich, N. Baddela, E. N. Fokoua, J. R. Hayes, D. R. Gray, and D. J. Richardson, Nat. Photonics 7, 279 (2013). [CrossRef]

14.

N. A. Mortensen and M. D. Nielsen, Opt. Lett. 29349, (2004). [CrossRef]

15.

A. M. Heidt, J. H. V. Price, C. Baskiotis, J. S. Feehan, Z. Li, S. U. Alam, and D. J. Richardson, Opt. Express 21, 24281 (2013). [CrossRef]

16.

J. K. Lyngso, B. J. Mangan, C. Jakobsen, and P. J. Roberts, Opt. Express 17, 23468 (2009). [CrossRef]

17.

L. S. Rothman, I. E. Gordon, A. Barbe, D. C. Benner, P. E. Bernath, M. Birk, V. Boudon, L. R. Brown, A. Campargue, J. P. Champion, K. Chance, L. H. Coudert, V. Dana, V. M. Devi, S. Fally, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, I. Kleiner, N. Lacome, W. J. Lafferty, J. Y. Mandin, S. T. Massie, S. N. Mikhailenko, C. E. Miller, N. Moazzen-Ahmadi, O. V. Naumenko, A. V. Nikitin, J. Orphal, V. I. Perevalov, A. Perrin, A. Predoi-Cross, C. P. Rinsland, M. Rotger, M. Simeckova, M. A. H. Smith, K. Sung, S. A. Tashkun, J. Tennyson, R. A. Toth, A. C. Vandaele, and J. Vander Auwera, J. Quantum Spectrosc. Radiat. Transfer 110, 533 (2009). [CrossRef]

18.

R. E. P. de Oliveira, C. J. S. de Matos, G. E. Nunes, and I. H. Bechtold, J. Opt. Soc. Am. B 29, 977 (2012). [CrossRef]

19.

T. P. Hansen, J. B. J. Broeng, C. Jakobsen, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, J. Lightwave Technol. 22, 11 (2004). [CrossRef]

20.

T. A. Birks, F. Luan, G. J. Pearce, A. Wang, J. C. Knight, and D. M. Bird, Opt. Express 14, 5688 (2006). [CrossRef]

21.

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. S. J. Russell, Opt. Express 13, 236 (2005). [CrossRef]

22.

N. K. Baddela, M. N. Petrovich, Y. Jung, J. R. Hayes, N. V. Wheeler, D. R. Gray, N. Wong, F. Parmigiani, E. Numkam, J. P. Wooler, F. Poletti, and D. J. Richardson, in CLEO/QELS (2013), paper CTu2K.3.

23.

A. M. Jones, A. V. V. Nampoothiri, A. Ratanavis, T. Fiedler, N. V. Wheeler, F. Couny, R. Kadel, F. Benabid, B. R. Washburn, K. L. Corwin, and W. Rudolph, Opt. Express 19, 2309 (2011). [CrossRef]

OCIS Codes
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(060.5295) Fiber optics and optical communications : Photonic crystal fibers

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: October 10, 2013
Revised Manuscript: November 21, 2013
Manuscript Accepted: November 22, 2013
Published: January 8, 2014

Virtual Issues
January 14, 2014 Spotlight on Optics

Citation
Natalie V. Wheeler, Alexander M. Heidt, Naveen K. Baddela, Eric Numkam Fokoua, John R. Hayes, Seyed R. Sandoghchi, Francesco Poletti, Marco N. Petrovich, and David J. Richardson, "Low-loss and low-bend-sensitivity mid-infrared guidance in a hollow-core–photonic-bandgap fiber," Opt. Lett. 39, 295-298 (2014)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-39-2-295


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References

  1. B. Culshaw and A. Kersey, J. Lightwave Technol. 26, 1064 (2008). [CrossRef]
  2. D. J. Richardson, J. Nilsson, and W. A. Clarkson, J. Opt. Soc. Am. B 27, B63 (2010). [CrossRef]
  3. O. Humbach, H. Fabian, U. Grzesik, U. Haken, and W. Heitmann, J. Non-Cryst. Solids 203, 19 (1996). [CrossRef]
  4. J. A. Harrington, Infrared Fibers and Their Applications (SPIE, 2004).
  5. P. W. Carter, S. F. Moore, M. W. Szebesta, D. Williams, J. R. Ranson, and D. France, Electron. Lett. 26, 2115 (1990). [CrossRef]
  6. J. M. Kriesel, N. Gat, B. E. Bernacki, R. L. Erikson, B. D. Cannon, T. L. Myers, C. M. Bledt, and J. A. Harrington, Proc SPIE 8018, 80180V (2011).
  7. F. Benabid, P. J. Roberts, F. Couny, and P. S. Light, J. Eur. Opt. Soc. Rapid Publ. 4, 09004 (2009). [CrossRef]
  8. T. Ritari, J. Tuominen, H. Ludvigsen, J. H. Petersen, T. Sorensen, T. Hansen, and H. Simonsen, Opt. Express 12, 4080 (2004). [CrossRef]
  9. A. N. Kolyadin, A. F. Kosolapov, A. D. Pryamikov, A. S. Biriukov, V. G. Plotnichenko, and E. M. Dianov, Opt. Express 21, 9514 (2013). [CrossRef]
  10. F. Yu, W. J. Wadsworth, and J. C. Knight, Opt. Express 20, 11153 (2012). [CrossRef]
  11. Y. Y. Wang, N. V. Wheeler, F. Couny, P. J. Roberts, and F. Benabid, Opt. Lett. 36, 669 (2011). [CrossRef]
  12. A. Urich, R. R. J. Maier, B. J. Mangan, S. Renshaw, J. C. Knight, D. P. Hand, and J. D. Shephard, Opt. Express 20, 6677 (2012). [CrossRef]
  13. F. Poletti, N. V. Wheeler, M. N. Petrovich, N. Baddela, E. N. Fokoua, J. R. Hayes, D. R. Gray, and D. J. Richardson, Nat. Photonics 7, 279 (2013). [CrossRef]
  14. N. A. Mortensen and M. D. Nielsen, Opt. Lett. 29349, (2004). [CrossRef]
  15. A. M. Heidt, J. H. V. Price, C. Baskiotis, J. S. Feehan, Z. Li, S. U. Alam, and D. J. Richardson, Opt. Express 21, 24281 (2013). [CrossRef]
  16. J. K. Lyngso, B. J. Mangan, C. Jakobsen, and P. J. Roberts, Opt. Express 17, 23468 (2009). [CrossRef]
  17. L. S. Rothman, I. E. Gordon, A. Barbe, D. C. Benner, P. E. Bernath, M. Birk, V. Boudon, L. R. Brown, A. Campargue, J. P. Champion, K. Chance, L. H. Coudert, V. Dana, V. M. Devi, S. Fally, J. M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, I. Kleiner, N. Lacome, W. J. Lafferty, J. Y. Mandin, S. T. Massie, S. N. Mikhailenko, C. E. Miller, N. Moazzen-Ahmadi, O. V. Naumenko, A. V. Nikitin, J. Orphal, V. I. Perevalov, A. Perrin, A. Predoi-Cross, C. P. Rinsland, M. Rotger, M. Simeckova, M. A. H. Smith, K. Sung, S. A. Tashkun, J. Tennyson, R. A. Toth, A. C. Vandaele, and J. Vander Auwera, J. Quantum Spectrosc. Radiat. Transfer 110, 533 (2009). [CrossRef]
  18. R. E. P. de Oliveira, C. J. S. de Matos, G. E. Nunes, and I. H. Bechtold, J. Opt. Soc. Am. B 29, 977 (2012). [CrossRef]
  19. T. P. Hansen, J. B. J. Broeng, C. Jakobsen, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, J. Lightwave Technol. 22, 11 (2004). [CrossRef]
  20. T. A. Birks, F. Luan, G. J. Pearce, A. Wang, J. C. Knight, and D. M. Bird, Opt. Express 14, 5688 (2006). [CrossRef]
  21. 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. S. J. Russell, Opt. Express 13, 236 (2005). [CrossRef]
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