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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 8 — Apr. 22, 2013
  • pp: 9514–9519
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Light transmission in negative curvature hollow core fiber in extremely high material loss region

Anton N. Kolyadin, Alexey F. Kosolapov, Andrey D. Pryamikov, Alexander S. Biriukov, Victor G. Plotnichenko, and Evgeny M. Dianov  »View Author Affiliations


Optics Express, Vol. 21, Issue 8, pp. 9514-9519 (2013)
http://dx.doi.org/10.1364/OE.21.009514


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Abstract

In this paper we demonstrate the light transmission in a spectral range of 2.5 to 7.9 µm through a silica negative curvature hollow core fiber (NCHCF) with a cladding consisting of eight capillaries. A separation between the cladding capillaries was introduced to remove the additional resonances in the transmission bands. The measured optical loss at 3.39 µm was about 50 dB/km under a few modes waveguide regime.

© 2013 OSA

1. Introduction

The hollow core microstructured optical fibers (HC MOFs) are a special kind of optical fibers [1

1. P. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003). [CrossRef] [PubMed]

] which confine the electromagnetic field inside a hollow core surrounded by a microstructured cladding. Such HC MOFs as hollow core photonic crystal fibers (HC PCFs) or Kagome lattice HC MOFs now have a wide range of applications such as light-gas interactions [2

2. F. Benabid, P. J. Roberts, F. Couny, and P. S. Light, “Light and gas confinement in hollow-core photonic crystal fibre based photonic microcells,” J. European Opt. Soc. 4, 09004 (2009), https://www.jeos.org/index.php/jeos_rp/article/view/09004. [CrossRef]

], high power and ultra short pulse delivery [3

3. A. Urich, R. R. J. Maier, B. J. Mangan, S. Renshaw, J. C. Knight, D. P. Hand, and J. D. Shephard, “Delivery of high energy Er:YAG pulsed laser light at 2.94 µm through a silica hollow core photonic crystal fibre,” Opt. Express 20(6), 6677–6684 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-6-6677. [CrossRef] [PubMed]

], terahertz applications [4

4. J. Anthony, R. Leonhardt, S. G. Leon-Saval, and A. Argyros, “THz propagation in kagome hollow-core microstructured fibers,” Opt. Express 19(19), 18470–18478 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-19-18470. [CrossRef] [PubMed]

] and others. The key advantage of HC MOFs is that the radiation propagates mostly in the air core and the optical damage threshold is raised. HC PCFs usually have a circular core-cladding boundary and a complicated photonic crystal cladding with a triangular arrangement of air holes. The localization of light occurs due to the presence of a full photonic bandgap over appropriate optical frequencies. The light guidance occurs when the photonic band gap coincides with a core resonance. Kagome lattice HC MOFs guide the light due to inhibited coupling mechanism [5

5. F. Benabid and P. J. Roberts, “Linear and nonlinear optical properties of hollow core photonic crystal fiber,” J. Mod. Opt. 58(2), 87–124 (2011). [CrossRef]

]. Furthermore, it was shown that single-layer cladding is an efficient way to simplify the kagome lattice HC MOFs [6

6. S. Février, B. Beaudou, and P. Viale, “Understanding origin of loss in large pitch hollow-core photonic crystal fibers and their design simplification,” Opt. Express 18(5), 5142–5150 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-5-5142. [CrossRef] [PubMed]

].

Recently, a new type of HC MOFs with a negative curvature of the core-cladding boundary and a simplified cladding has been proposed [7

7. Y. Wang, F. Couny, P. J. Roberts, and F. Benabid, “Low loss broadband transmission in optimized core–shaped Kagome Hollow-Core PCF,” CLEO 2010, paper CPDB4.

, 8

8. A. D. Pryamikov, A. S. Biriukov, A. F. Kosolapov, V. G. Plotnichenko, S. L. Semjonov, and E. M. Dianov, “Demonstration of a waveguide regime for a silica hollow--core microstructured optical fiber with a negative curvature of the core boundary in the spectral region > 3.5 μm,” Opt. Express 19(2), 1441–1448 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-2-1441. [CrossRef] [PubMed]

]. The advantage of using the negative curvature of the core boundary for decreasing the optical loss was first demonstrated in [7

7. Y. Wang, F. Couny, P. J. Roberts, and F. Benabid, “Low loss broadband transmission in optimized core–shaped Kagome Hollow-Core PCF,” CLEO 2010, paper CPDB4.

], where the core boundary had the form of a hypocycloid. In [8

8. A. D. Pryamikov, A. S. Biriukov, A. F. Kosolapov, V. G. Plotnichenko, S. L. Semjonov, and E. M. Dianov, “Demonstration of a waveguide regime for a silica hollow--core microstructured optical fiber with a negative curvature of the core boundary in the spectral region > 3.5 μm,” Opt. Express 19(2), 1441–1448 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-2-1441. [CrossRef] [PubMed]

] the term “negative curvature” was introduced and it was demonstrated that in the case of a silica negative curvature hollow core fiber (NCHCF) it was possible to guide the light in the mid infrared spectral range (> 3.5 μm) where the material loss of silica glass is very high. Such constructions led to a complication of the boundary conditions for the core modes and strengthened their localization in the air core [8

8. A. D. Pryamikov, A. S. Biriukov, A. F. Kosolapov, V. G. Plotnichenko, S. L. Semjonov, and E. M. Dianov, “Demonstration of a waveguide regime for a silica hollow--core microstructured optical fiber with a negative curvature of the core boundary in the spectral region > 3.5 μm,” Opt. Express 19(2), 1441–1448 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-2-1441. [CrossRef] [PubMed]

]. In [9

9. A. F. Kosolapov, A. D. Pryamikov, A. S. Biriukov, V. S. Shiryaev, M. S. Astapovich, G. E. Snopatin, V. G. Plotnichenko, M. F. Churbanov, and E. M. Dianov, “Demonstration of CO2-laser power delivery through chalcogenide-glass fiber with negative-curvature hollow core,” Opt. Express 19(25), 25723–25728 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-25-25723. [CrossRef] [PubMed]

] CO2 laser power delivery was demonstrated at a wavelength of 10.6 μm using a fiber with the same cross section design but made of chalcogenide glass. In [10

10. F. Y. Yu, W. J. Wadsworth, and J. C. Knight, “Low loss silica hollow core fibers for 3-4 μm spectral region,” Opt. Express 20(10), 11153–11158 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-10-11153. [CrossRef] [PubMed]

] the authors demonstrated silica NCHCF for a transmission in the mid IR with a minimum attenuation of 34 dB/km at wavelength of 3.05 μm. It was also shown that the NCHCF had a transmission band above the wavelength of 4 μm. The authors of [11

11. A. Urich, R. R. J. Maier, F. Yu, J. C. Knight, D. P. Hand, and J. D. Shephard, “Flexible delivery of Er:YAG radiation at 2.94 µm with negative curvature silica glass fibers: a new solution for minimally invasive surgical procedures,” Biomed. Opt. Express 4(2), 193–205 (2013), http://www.opticsinfobase.org/boe/abstract.cfm?uri=boe-4-2-193. [CrossRef] [PubMed]

] demonstrated the delivery of high energy microsecond pulses through NCHCF described in [10

10. F. Y. Yu, W. J. Wadsworth, and J. C. Knight, “Low loss silica hollow core fibers for 3-4 μm spectral region,” Opt. Express 20(10), 11153–11158 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-10-11153. [CrossRef] [PubMed]

] at 2.94 μm. In authors’ opinion the delivery system can be useful for minimally invasive surgical laser procedures. In work [12

12. V. Setti, L. Vincetti, and A. Argyros, “Flexible tube lattice fibers for terahertz applications,” Opt. Express 21(3), 3388–3399 (2013), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-3-3388. [CrossRef] [PubMed]

] it was demonstrated that a flexible NCHCF with capillaries in the cladding made of polymethylmethacrylate could be used for THz guidance.

It should be also noted that a negative curvature of core-cladding boundary is a necessary but not sufficient condition for a low optical loss [13

13. A. D. Pryamikov and A. S. Biriukov, “Excitation of cyclic Sommerfeld waves and Wood anomalies under plane wave scattering from dielectric cylinder at oblique incidence,” Phys.- Usp. (to be published).

]. Moreover, it is known that the cladding elements in HC PCFs such as interstitial apexes or struts are optical resonators that form the lower or upper frequency band gap edges [5

5. F. Benabid and P. J. Roberts, “Linear and nonlinear optical properties of hollow core photonic crystal fiber,” J. Mod. Opt. 58(2), 87–124 (2011). [CrossRef]

]. In this paper we show that the touching points between the cladding capillaries can be considered as additional optical resonators that cause optical loss increase in the transmission bands. It is shown that it is possible to achieve a low-loss light transmission under extremely high material loss in the mid infrared spectral range > 5 μm using silica NCHCF by removing the touching points between the cladding capillaries. The paper has four sections. In Section 2 we show the impact that touching points of cladding capillaries have on the optical loss inside the transmission bands by using numerical simulations as well as describe the fiber fabrication process. In Section 3 the optical loss measurements are described. Section 4 contains the conclusions.

2. Fiber development

In this section we demonstrate the impact that optical resonators occurred at the touching points between the cladding capillaries have on the optical loss level. The numerical simulation was carried out using the Femlab 3.1 commercial packet. Two silica NCHCFs with the same cross-section were analyzed. Each fiber had eight capillaries in the cladding, the outer diameter of the capillaries was 63 μm and the inner diameter was 51 μm. The distance between the capillaries was 1.3 μm. The difference between the considered fibers was that in the first sample the capillaries in the cladding didn’t touch while in the second sample the capillaries were in contact with each other Fig. 1
Fig. 1 The analyzed fiber geometries; a) NCHCF with non touching capillaries; b) NCHCF with touching capillaries in the cladding.
. The loss spectrums were calculated for both structures in the spectral range of 3 – 6.5 μm Fig. 2(a)
Fig. 2 (a) the calculated fundamental mode loss for a silica NCHCF with capillaries touching and not touching in the cladding; (b) the output end of the NCHCF with touching capillaries excited by visible light.
. The presence of additional optical resonators in the cladding led to an increase in the density of electromagnetic states in the cladding Fig. 2(b) and, consequently, to an increase in total optical losses in the transmission bands Fig. 2(a).

In terms of production it is much more difficult to fabricate a NCHCF with touching capillaries in the cladding because the high temperature reduces the silica glass viscosity and the surface tension forces straighten the capillary walls. In this case, it is much more difficult to obtain a negative curvature of the core boundary. In the case of a NCHCF with non touching capillaries in the cladding it is possible to keep the negative curvature of the core boundary even at high drawing temperature.

To demonstrate the possibility of the fabrication of a NCHCF with capillaries not touching in the cladding, a fiber was made by the stack and draw technique. Eight identical capillaries were drawn from a silica tube (Suprasil F300, Heraeus) and were installed into a tube with a larger diameter and soldered to it. The resulting preform was drawn on a standard drawing tower into a fiber with a core diameter of 119 µm and with a capillary wall thickness of 6 µm Fig. 3
Fig. 3 Cross section of a NCHCF with non touching capillaries.
.

3. Measurements and numerical simulations

It is seen in Fig. 4 that there are three transmission bands in the spectral range of 2.5 – 5 μm with a minimum loss level of 4 – 5 dB/m. The average losses measured in the spectral bands at 5.8 and 7.7 µm were 30 and 50 dB/m, respectively. The bands at 3.3 and 4.3 µm have a number of absorption peaks. The location of the peaks in the band at 3.3 µm Fig. 4 (inset) can be explained by the presence of HCl in the core and they are identical to the peaks observed in [10

10. F. Y. Yu, W. J. Wadsworth, and J. C. Knight, “Low loss silica hollow core fibers for 3-4 μm spectral region,” Opt. Express 20(10), 11153–11158 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-10-11153. [CrossRef] [PubMed]

]. The peaks in the band at 4.3 µm correspond to absorption peaks of CO2 in the atmosphere.

As one can see from Fig. 4, the simulated and experimental band edges superpose very well. Note that the transmission band at 7.7 µm is especially interesting as the silica glass refractive index becomes equal to one and enters the anomalous region (n<1) at 7.3 µm [15]. Thus, the light transmission in the transmission band at 7.7 µm occurs due to a superposition of two guiding mechanisms, namely, total internal reflection and the ARROW [16

16. T. P. White, R. C. McPhedran, C. M de Sterke, N. M. Litchinitser, and B. J. Eggleton, “Resonance and scattering in microstructured optical fibers,” Opt. Lett. 27(22), 1977–1979 (2002), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-27-22-1977. [CrossRef] [PubMed]

]. For example, similar light guidance was demonstrated in hollow core oxide-glass cladding optical fibers [17

17. T. Hidaka, T. Morikawa, and J. Shimada, “Hollow‐core oxide‐glass cladding optical fibers for middle‐infrared region,” J. Appl. Phys. 52(7), 4467–4471 (1981), http://jap.aip.org/resource/1/japiau/v52/i7/p4467_s1. [CrossRef]

]. In the case of NCHCFs the nature of light localization in the anomalous region requires further investigations.

The discrepancy between the measured loss level and the calculated one for the fundamental mode Fig. 4 in the wavelength range < 5 µm is mainly due to the presence of multimode waveguide regime. The imperfect launching conditions leads to an excitation of high-aperture modes which can propagate along the fiber length at some distance. Moreover, as the wavelength decreases the values of Re(neff) Fig. 4 become closer to each other and an intermodal interaction occurs. All this leads to an increase in the total loss. Thus, the measurements defined only the upper limit of the loss values. To find the lower limit of the loss values it is necessary to improve the excitation conditions, for example, by using of a high-bright source and larger fiber lengths.

To confirm this finding we carried out several experiments with a few-mode He-Ne laser at a wavelength of 3.39 µm. The loss was measured by cut-back method with a fiber length from 11 to 1 meter. The bend radius of the fiber was 20 cm. The He-Ne laser radiation intensity versus fiber length is shown in Fig. 5
Fig. 5 The He-Ne laser radiation intensity versus fiber length. The straight line is an approximation of the exponential curve. The insets show the intensity distribution in the near field at the fiber length of 1 and 11 m.
. The intensity distributions in the near field in the case of different lengths of the fiber are shown in the insets of Fig. 5. These pictures were obtained with Electrophysics PV320 thermal imaging camera. The striped structure of the images Fig. 5 (insets) is due to an interference of coherent laser radiation on the entrance window of the camera. There are two different ranges of the fiber length which are clearly seen in Fig. 5. The first range of the fiber length is up to 2 m and in this range the multimode waveguide regime still exists. The second range of the fiber length > 3 m and in this range the signal decreases exponentially. As one can see from Fig. 5, the mode structure of the fiber is stabilized at the fiber lengths over 3 m and only the first several modes are present in the fiber. The part of the signal dependence from 3 to 11 m was approximated by an exponential curve. The value of the optical loss estimated with this curve at a wavelength of 3.39 µm was 50 ± 8 dB/km Fig. 4 (red asterisk).

It should be noted, that the level of the transmitted signal and the mode structure are strongly dependent on the local tensions. Therefore, the stress was not applied to the fixing input and output ends of the fiber. In our opinion, the tension created the micro bends which strongly increased the loss level.

4. Conclusion

The light propagation through silica NCHCF in transmission bands at 4.5, 5.8 and 7.7 µm in extremely high material loss region was demonstrated. The total loss was at least three orders of magnitude lower than the material loss of silica glass. It confirms a very weak coupling of the air core modes with the cladding structure. The NCHCFs with non touching capillaries in the cladding allow to decrease the loss level in the transmission bands due to an absence of additional optical resonators in the cladding. It should be noted that the considered NCHCF has a great potential for different applications and for the light guidance from UV to mid IR spectral regions. To decrease the loss level in the required spectral range it is necessary to carry out an optimization of the NCHCF structure. The main parameters of the considered NCHCFs to optimize are the air core diameter, the number of capillaries in the cladding, the outer and the inner diameters of the capillaries.

Acknowledgments

The authors thank Dr. S.L. Semjonov and Dr. V.V. Vel’miskin for their help in developing the fiber technology. This work was supported by the AI “Technopark Mordovia”, project No 24/2011.

References and links

1.

P. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003). [CrossRef] [PubMed]

2.

F. Benabid, P. J. Roberts, F. Couny, and P. S. Light, “Light and gas confinement in hollow-core photonic crystal fibre based photonic microcells,” J. European Opt. Soc. 4, 09004 (2009), https://www.jeos.org/index.php/jeos_rp/article/view/09004. [CrossRef]

3.

A. Urich, R. R. J. Maier, B. J. Mangan, S. Renshaw, J. C. Knight, D. P. Hand, and J. D. Shephard, “Delivery of high energy Er:YAG pulsed laser light at 2.94 µm through a silica hollow core photonic crystal fibre,” Opt. Express 20(6), 6677–6684 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-6-6677. [CrossRef] [PubMed]

4.

J. Anthony, R. Leonhardt, S. G. Leon-Saval, and A. Argyros, “THz propagation in kagome hollow-core microstructured fibers,” Opt. Express 19(19), 18470–18478 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-19-18470. [CrossRef] [PubMed]

5.

F. Benabid and P. J. Roberts, “Linear and nonlinear optical properties of hollow core photonic crystal fiber,” J. Mod. Opt. 58(2), 87–124 (2011). [CrossRef]

6.

S. Février, B. Beaudou, and P. Viale, “Understanding origin of loss in large pitch hollow-core photonic crystal fibers and their design simplification,” Opt. Express 18(5), 5142–5150 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-5-5142. [CrossRef] [PubMed]

7.

Y. Wang, F. Couny, P. J. Roberts, and F. Benabid, “Low loss broadband transmission in optimized core–shaped Kagome Hollow-Core PCF,” CLEO 2010, paper CPDB4.

8.

A. D. Pryamikov, A. S. Biriukov, A. F. Kosolapov, V. G. Plotnichenko, S. L. Semjonov, and E. M. Dianov, “Demonstration of a waveguide regime for a silica hollow--core microstructured optical fiber with a negative curvature of the core boundary in the spectral region > 3.5 μm,” Opt. Express 19(2), 1441–1448 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-2-1441. [CrossRef] [PubMed]

9.

A. F. Kosolapov, A. D. Pryamikov, A. S. Biriukov, V. S. Shiryaev, M. S. Astapovich, G. E. Snopatin, V. G. Plotnichenko, M. F. Churbanov, and E. M. Dianov, “Demonstration of CO2-laser power delivery through chalcogenide-glass fiber with negative-curvature hollow core,” Opt. Express 19(25), 25723–25728 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-25-25723. [CrossRef] [PubMed]

10.

F. Y. Yu, W. J. Wadsworth, and J. C. Knight, “Low loss silica hollow core fibers for 3-4 μm spectral region,” Opt. Express 20(10), 11153–11158 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-10-11153. [CrossRef] [PubMed]

11.

A. Urich, R. R. J. Maier, F. Yu, J. C. Knight, D. P. Hand, and J. D. Shephard, “Flexible delivery of Er:YAG radiation at 2.94 µm with negative curvature silica glass fibers: a new solution for minimally invasive surgical procedures,” Biomed. Opt. Express 4(2), 193–205 (2013), http://www.opticsinfobase.org/boe/abstract.cfm?uri=boe-4-2-193. [CrossRef] [PubMed]

12.

V. Setti, L. Vincetti, and A. Argyros, “Flexible tube lattice fibers for terahertz applications,” Opt. Express 21(3), 3388–3399 (2013), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-3-3388. [CrossRef] [PubMed]

13.

A. D. Pryamikov and A. S. Biriukov, “Excitation of cyclic Sommerfeld waves and Wood anomalies under plane wave scattering from dielectric cylinder at oblique incidence,” Phys.- Usp. (to be published).

14.

E. B. Kryukova, V. G. Plotnichenko, and E. M. Dianov, “IR absorption spectra in high-purity silica glasses fabricated by different technologies,” Proc. SPIE 4083, 71–80 (2000). [CrossRef]

15.

Optical constants of FUSED SILICA, http://refractiveindex.info/?group=GLASSES&material=F_SILICA

16.

T. P. White, R. C. McPhedran, C. M de Sterke, N. M. Litchinitser, and B. J. Eggleton, “Resonance and scattering in microstructured optical fibers,” Opt. Lett. 27(22), 1977–1979 (2002), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-27-22-1977. [CrossRef] [PubMed]

17.

T. Hidaka, T. Morikawa, and J. Shimada, “Hollow‐core oxide‐glass cladding optical fibers for middle‐infrared region,” J. Appl. Phys. 52(7), 4467–4471 (1981), http://jap.aip.org/resource/1/japiau/v52/i7/p4467_s1. [CrossRef]

OCIS Codes
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(060.2390) Fiber optics and optical communications : Fiber optics, infrared
(060.4005) Fiber optics and optical communications : Microstructured fibers

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: February 22, 2013
Revised Manuscript: April 5, 2013
Manuscript Accepted: April 6, 2013
Published: April 10, 2013

Citation
Anton N. Kolyadin, Alexey F. Kosolapov, Andrey D. Pryamikov, Alexander S. Biriukov, Victor G. Plotnichenko, and Evgeny M. Dianov, "Light transmission in negative curvature hollow core fiber in extremely high material loss region," Opt. Express 21, 9514-9519 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-8-9514


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References

  1. P. Russell, “Photonic crystal fibers,” Science299(5605), 358–362 (2003). [CrossRef] [PubMed]
  2. F. Benabid, P. J. Roberts, F. Couny, and P. S. Light, “Light and gas confinement in hollow-core photonic crystal fibre based photonic microcells,” J. European Opt. Soc.4, 09004 (2009), https://www.jeos.org/index.php/jeos_rp/article/view/09004 . [CrossRef]
  3. A. Urich, R. R. J. Maier, B. J. Mangan, S. Renshaw, J. C. Knight, D. P. Hand, and J. D. Shephard, “Delivery of high energy Er:YAG pulsed laser light at 2.94 µm through a silica hollow core photonic crystal fibre,” Opt. Express20(6), 6677–6684 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-6-6677 . [CrossRef] [PubMed]
  4. J. Anthony, R. Leonhardt, S. G. Leon-Saval, and A. Argyros, “THz propagation in kagome hollow-core microstructured fibers,” Opt. Express19(19), 18470–18478 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-19-18470 . [CrossRef] [PubMed]
  5. F. Benabid and P. J. Roberts, “Linear and nonlinear optical properties of hollow core photonic crystal fiber,” J. Mod. Opt.58(2), 87–124 (2011). [CrossRef]
  6. S. Février, B. Beaudou, and P. Viale, “Understanding origin of loss in large pitch hollow-core photonic crystal fibers and their design simplification,” Opt. Express18(5), 5142–5150 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-5-5142 . [CrossRef] [PubMed]
  7. Y. Wang, F. Couny, P. J. Roberts, and F. Benabid, “Low loss broadband transmission in optimized core–shaped Kagome Hollow-Core PCF,” CLEO 2010, paper CPDB4.
  8. A. D. Pryamikov, A. S. Biriukov, A. F. Kosolapov, V. G. Plotnichenko, S. L. Semjonov, and E. M. Dianov, “Demonstration of a waveguide regime for a silica hollow--core microstructured optical fiber with a negative curvature of the core boundary in the spectral region > 3.5 μm,” Opt. Express19(2), 1441–1448 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-2-1441 . [CrossRef] [PubMed]
  9. A. F. Kosolapov, A. D. Pryamikov, A. S. Biriukov, V. S. Shiryaev, M. S. Astapovich, G. E. Snopatin, V. G. Plotnichenko, M. F. Churbanov, and E. M. Dianov, “Demonstration of CO2-laser power delivery through chalcogenide-glass fiber with negative-curvature hollow core,” Opt. Express19(25), 25723–25728 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-25-25723 . [CrossRef] [PubMed]
  10. F. Y. Yu, W. J. Wadsworth, and J. C. Knight, “Low loss silica hollow core fibers for 3-4 μm spectral region,” Opt. Express20(10), 11153–11158 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-10-11153 . [CrossRef] [PubMed]
  11. A. Urich, R. R. J. Maier, F. Yu, J. C. Knight, D. P. Hand, and J. D. Shephard, “Flexible delivery of Er:YAG radiation at 2.94 µm with negative curvature silica glass fibers: a new solution for minimally invasive surgical procedures,” Biomed. Opt. Express4(2), 193–205 (2013), http://www.opticsinfobase.org/boe/abstract.cfm?uri=boe-4-2-193 . [CrossRef] [PubMed]
  12. V. Setti, L. Vincetti, and A. Argyros, “Flexible tube lattice fibers for terahertz applications,” Opt. Express21(3), 3388–3399 (2013), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-3-3388 . [CrossRef] [PubMed]
  13. A. D. Pryamikov and A. S. Biriukov, “Excitation of cyclic Sommerfeld waves and Wood anomalies under plane wave scattering from dielectric cylinder at oblique incidence,” Phys.- Usp. (to be published).
  14. E. B. Kryukova, V. G. Plotnichenko, and E. M. Dianov, “IR absorption spectra in high-purity silica glasses fabricated by different technologies,” Proc. SPIE4083, 71–80 (2000). [CrossRef]
  15. Optical constants of FUSED SILICA, http://refractiveindex.info/?group=GLASSES&material=F_SILICA
  16. T. P. White, R. C. McPhedran, C. M de Sterke, N. M. Litchinitser, and B. J. Eggleton, “Resonance and scattering in microstructured optical fibers,” Opt. Lett.27(22), 1977–1979 (2002), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-27-22-1977 . [CrossRef] [PubMed]
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