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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 9 — Apr. 28, 2008
  • pp: 5983–5990

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Metallic mode confinement in microstructured fibres

Jing Hou, David Bird, Alan George, Stefan Maier, Boris Kuhlmey, and J. C. Knight  »View Author Affiliations


Optics Express, Vol. 16, Issue 9, pp. 5983-5990 (2008)
http://dx.doi.org/10.1364/OE.16.005983


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Abstract

We report the first long, uniform, optical fibers in which visible light is guided in a single mode by metallic reflection. We describe the fabrication, experiment and characterization of these metallic optical fibers and compare them with theoretical calculations.

© 2008 Optical Society of America

1. Introduction

Optical fibers formed using dielectric materials (most commonly, two types of glass) represent a mature and remarkably successful technology that constitutes one of the building blocks of our modern global telecommunications system. The use of dielectrics enables the very low optical attenuation of the guided mode required for many applications, but also limits the fiber performance in several ways [1

J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22, 475–477 (1997). [CrossRef] [PubMed]

]. Most notably, light confinement using dielectrics is limited to size scales of the order of the optical wavelength [2

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

]. Some effort has recently been put into designing optical fibers which use metallic light confinement [3–7

J. A. Sazio Pier, A. Amezcua-Correa, C. E Finlayson, J. R. Hayes, and T. J. Scheidemante, “Microstructured Optical Fibers as High-Pressure Microfluidic Reactors,” Science 311, 1583–1586 (2006). [CrossRef]

]. Several previous efforts to fabricate metal-guiding optical fibers have been based on deposition or incorporation of materials using “holey fibers” (or photonic crystal fibers, PCF) as a template [3

J. A. Sazio Pier, A. Amezcua-Correa, C. E Finlayson, J. R. Hayes, and T. J. Scheidemante, “Microstructured Optical Fibers as High-Pressure Microfluidic Reactors,” Science 311, 1583–1586 (2006). [CrossRef]

, 6

A Amezcua-Correa, J Yang, and C. E. Finlayson. “Surface-Enhanced Raman Scattering using Microstructured Optical Fiber Substrates,” Adv. Funct. Mater. 17, 2024–2030 (2007). [CrossRef]

, 8

M. A. Schmidt, L. N. Prill Sempere, H. K. Tyagi, C. G. Poulton, and P. St. J. Russell, “Waveguiding and Plasmon Resonances in Two-Dimensional Photonic Lattices of Gold and Silver Nanowires,” arXiv:0711.4553, (2007).

]. PCFs are fibers formed of silica (or another glass) with a 2-dimensional pattern of air holes running down their length [2

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

]. Infiltration of transparent material in various forms into the air holes allows for long interaction lengths between guided modes of the fiber and the inserted material, enabling complex in-fiber devices such as variable attenuators [9

C. Kerbage, A. Hale, A. Yablon, R. S. Windeler, and B. J. Eggleton. “Integrated all-fiber variable attenuator based on hybrid microstructure fiber,” Appl. Phys. Lett. 79, 3191–3193 (2001). [CrossRef]

], Mach-Zehnder interferometers [10

M. Fokine, L. Nilsson, E. Claesson, A. D. Berlemont, L. Kjellberg, L. Krummenacher, and W. Margulis. “Integrated fiber Mach-Zehnder interferometer for electro-optic switching,” Opt. Lett. 27, 1643–1645 (2002). [CrossRef]

], Raman scattering gas cells [11

F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fibers,” Science 298, 399–402 (2002). [CrossRef] [PubMed]

] and plasmon sensors [4

B. Gauvreau, A. Hassani, M. Fassi Fehri, A. Kabashin, and M. A. Skorobogatiy, “Photonic bandgap fiber-based Surface Plasmon Resonance sensors,” Opt. Express 15, 11413–11426 (2007). [CrossRef] [PubMed]

, 5

X. Zhang, R. Wang, F. M. Cox, B. T. Kuhlmey, and M. C. J. Large, “Selective coating of holes in microstructured optical fiber and its application to in-fiber absorptive polarizers,” Opt. Express 15, 16270–16278 (2007). [CrossRef] [PubMed]

]. More recently, high-pressure chemical deposition techniques have been used to deposit compact metal films along the fiber walls, and Surface-Enhanced Raman Scattering has been experimentally demonstrated [6

A Amezcua-Correa, J Yang, and C. E. Finlayson. “Surface-Enhanced Raman Scattering using Microstructured Optical Fiber Substrates,” Adv. Funct. Mater. 17, 2024–2030 (2007). [CrossRef]

]. Numerical studies of arrays of metallic nanowires embedded in a dielectric matrix have shown that light can be guided in such a structure and that both photonic band gaps and surface plasmon modes exist [7

C. G. Poulton, M. A. Schmidt, G. J. Pearce, G. Kakarantzas, and P. St. J. Russell, “Numerical study of guided modes in arrays of metallic nanowires,” Opt. Lett. 32, 1647–1649 (2007). [CrossRef] [PubMed]

]. However, filling the tiny holes (with diameters on the order of a micron) in long fiber lengths is extremely challenging, and the uniformity required along the fiber length has meant that the waveguiding properties of such metallic structures have until now hardly been reported. The nature of the fiber drawing process, in which long fibers are drawn at high temperature and speed from a preform, is unparalleled in producing long and very uniform structures, ideal for the designs being discussed. Here, we present optical fibers which rely on metallic confinement, which we fabricated using this fiber drawing. Our work is complementary to the previous works because we can draw long continuous lengths, although not yet to the same small sizes. We get the first long, uniform, optical fibers in which visible light is guided in a single mode by metal. We describe their properties and compare these with theoretical calculations. Our work represents an important step towards a new environment of strongly confining metallic waveguides, for applications in optical circuitry, fiber-integrated optoelectronic components or plasmonic sensors.

2. Fiber fabrication

Our fabrication procedure is based on incorporating the Taylor-wire process [12

I. W. Donald, “Review. Production, properties and applications of microwire and related products,” J. Mater. Sci. 22, 2661–2679 (1987). [CrossRef]

,13

I. W. Donald and B. L. Metcalfe. “The preparation, properties and applications of some glass-coated metal filaments prepared by the Taylor-wire process,” J. Mater. Sci. 31, 1139–1149 (1996). [CrossRef]

] into the well-known stack-and-draw procedure used for PCFs. To fabricate a PCF, a set of hollow fused silica capillaries are stacked around a single solid silica rod. This stack is then fed slowly into a high-temperature furnace while being rapidly drawn out of the far end, thus reducing the diameter of the structure by orders of magnitude while vastly increasing the length, and maintaining the set of air holes into the final fiber. We replaced the six capillaries immediately around the solid silica core rod with silica-coated copper rods.

The fabrication procedure consisted of etching a copper rod (length: 1 m, diameter: 3.2mm and purity: 99.99%) in dilute sulphuric acid to remove oxides, and then transferring it into a thick-walled fused-silica tube (inner diameter: 3.5mm and outer diameter: 10mm) sealed at one end, under inert atmosphere. This tube was evacuated and drawn down at a temperature of around 1880°C to an outer diameter of 1.56mm. It was then cut to suitable lengths (around 50cm) and stacked together with 114 hollow capillaries and a single solid silica rod of the same outer diameter to form the structure of interest. This stack was then inserted inside another silica tube and drawn at high temperature to fiber in two further stages. The final fiber diameter was in the range around 100–200microns.

Fig. 1. Scanning electron microscope images of metallic optical fiber with one ring of copper rods, where Λ=12µm and the core size is 21µm. a) shows a cleaved fiber end-face with six copper wires protruding from the surface. b) is detail of the six copper wires. c) is a backscattered electron image of a polished fiber sample end-face. d) shows detail of the copper rods in c).

An electron micrograph of the cross-section of a fiber sample is shown in Fig. 1(a). In the case shown, the pitch of the photonic crystal cladding is Λ=12µm, the normalized diameter of the air holes is dair/Λ=0.5 and the normalized diameter of the copper wires is dcopper/Λ≈0.35. When the metallic optical fiber is cleaved to produce an end-face for inspection, the copperwires stretch and then break, but do not necessarily break in the plane of the cleave. In Fig. 1(a), we have deliberately chosen a sample in which all six copper wires extend out of the silica surface. Figure 1(b) shows a magnified image of the six copper rods in the metallic fiber. In order to inspect the interface between the copper and the glass, we prepared polished end faces of the fiber samples, as shown in Fig. 1(c) and Fig. 1(d). The copper rods appear a lighter color in the pictures, with the darker areas being silica and air holes. All of the copper rods in these pictures have a distinct edge, and appear to be bonded tightly to the glass wall. A simple electrical conduction experiment using a 0.5m metallic optical fiber with two glasses of salty water to contact the wire ends has proven the continuity of the copper inclusions over this length scale. Although we have repeatably fabricated fibers like those shown in Fig. 1, the smallest pitch we have obtained is 6µm. We have not yet been able to further reduce the size of the fibers while maintaining the correct structure due to instabilities in our fabrication procedure. This is currently under investigation.

3. Experiments and simulations

Optical spectra transmitted through the metallic optical fibers with Λ=12µm and Λ=6µm are shown in Fig. 2(a). The excitation source is a fiber-based supercontinuum light source pumped by a Neodymium microchip laser. Broadband light is coupled into the fiber core using a 20× objective lens, and the output face was spatially filtered by imaging onto a short length of standard single-mode fiber before being recorded using an optical spectrum analyzer. The length of the metallic fiber is about 7cm and the fiber is held straight.

Fig. 2. Experimental measurements of the optical properties of guided modes of metallic optical fibers using a broadband supercontinuum as a light source. a) Measured transmitted spectra of metallic optical fibers as shown in Fig. 1. The transmission spectra are normalized to the input spectrum, so the source spectrum is compensated but the coupling efficiency of the fibers are not. b) The measured intensity distribution of the guided mode, where the metallic optical fiber is as in the SEM images with Λ=12µm and the core size is 21µm. c) The intensity distribution of the fundamental mode, where the metallic optical fiber is as in the SEM images but with Λ=6µm and the core size is 10.5µm. Near-field images at the output face of the metal photonic crystal fiber are shown both with and without the use of a bandpass filter.

Figures 2(b) and 2(c) show imaged near-field intensity patterns recorded from the output face of the metallic fiber when the input face is illuminated by the broadband source. Figure 2(b) is from the fiber with Λ=12µm while Fig. 2(c) is from the fiber with Λ=6µm. The guided light is well confined to a single core mode. The light is fully contained by the six copper wires surrounding the silica core, and the surrounding air holes are intended only to further reduce confinement loss. In each figure the image at top left was obtained without any spectral filtering and that shown top right obtained using a 10nm bandpass filter, as indicated.

We used a He-Ne laser to experimentally measure the attenuation of the metallic optical fibers by the cut-back technique. We measured attenuation of 6db/cm and 14db/cm for the fibers of Λ=12µm and Λ=6µm, respectively, at 633nm wavelength.

Using the multipole method [14–16

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. d. Sterke, and L. C Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B 19, 2322–2330 (2002). [CrossRef]

], we have calculated the effective index and attenuation of the modes in metallic optical fibers of similar design. The material dispersion of both the metal wires and the silica matrix are included in the calculations. To model the behavior of copper at optical frequencies, we used previously published experimental data [17

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phy. Rev. B 6, 4370–4378 (1972). [CrossRef]

]. One direct result of incorporating this data is that the attenuation of the fibers is expected to exhibit a minimum around 600–800nm wavelength, exactly as observed in our experiments. In order to understand the origins of the observed features, we have modeled rather smaller structures than those fabricated and studied experimentally. A structure based on that fabricated, containing one ring of copper wires and two further rings of air holes, with dair/Λ=0.5, dcopper/Λ=0.35 but with a smaller scale of Λ=2µm was simulated and the effective refractive indices of various modes are presented in Fig. 3. In the calculation, we find that the confinement loss is negligible, compared to the total attenuation which is due largely to the interaction with the copper. For example, when the wavelength is 700nm and Λ=2µm, the computed attenuation was found to be 128dB/cm, while the confinement loss was 29.9dB/km. We would expect the metallic losses to be sharply reduced at the larger size scales used in our experiments. Computations were performed with a maximum Bessel function order n=3, in order to reduce the computational time. As a result, not all the surface plasmon polariton modes are shown on the plot, on the shorter-wavelength side. The dispersion of surface plasmon polariton modes in a single copper cylinder surrounded by a dielectric of infinite extent [18

C. A. Pfeiffer and E. N. Economou, “Surface polaritons in a circularly cylindrical interface: Surface plasmons,” Phy. Rev. B 10, 3038–3051 (1974). [CrossRef]

] is also plotted. The six metal wires in our structure lead to a family of modes arising from each plasmon mode of an isolated wire, some of which are nearly degenerate and are not clearly distinguishable in our plot. The “fundamental” guided mode (i.e., the mode analogous to the guided mode in normal PCF) anti-crosses with the second- and third-order plasmon modes in the spectral range investigated. Attenuation in this range is computed to be of the order of 100dB/cm away from the anti-crossing regions in the spectral range 600–700nm, rising towards both longer and shorter wavelengths. For shorter wavelengths, or indeed for the larger fibers sizes which we have studied experimentally, we can expect that many higher order plasmon modes will anti-cross with the fundamental mode at visible and near infrared wavelengths, although we have not studied these larger structures directly due to computational constraints. In reality, although these anti-crossings must be present in our experimental fibers, they can be expected to be weak and spectrally narrow, and will therefore be sensitive to structural imperfections such as variations along the fiber length or between the different wires. While simulating the structures used in the experiment with Λ=6µm or Λ=12µm would require numerically prohibitively large orders of Bessel functions to obtain all the correct information about the anti-crossings with higher order plasmon modes in the visible wavelength range, simulations with 3 Bessel orders only still give accurate information on the fiber’s losses outside the immediate vicinity of anticrossings with plasmonic resonances. Using such simulations we calculated losses to be 0.1dB/cm for Λ=12µm and 1dB/cm for Λ=6µm at a wavelength of 700nm, in satisfactory agreement with our experiments. We intend in future work to reduce the transverse dimensions of our experimental samples down to Λ=2µm or less: while our simulations show that for that value of the pitch absorption losses will be much higher, this is also the regime in which plasmonic coupling should readily be measurable.

Fig. 3. Calculated effective refractive index of index-guided and surface plasmon modes of metallic optical fibers with one ring of copper rods and two rings of air holes. Λ=2µm, dair/Λ=0.5, dcopper/Λ≈0.35.

Figure 4(a) gives the intensity distribution of the Poynting vector (component along the fiber axis) of the core-guided mode as it transforms into the plasmonic regime through 700nm to 1400nm wavelength. It shows that the modal field pattern transforms from a “fundamental” core-guided guided mode into a surface-plasmon like mode at the anticrossing. Figure 4(b) demonstrates selected intensity distributions of the Poynting vector of the surface plasmon polariton modes, when the order n=0, 1, 2, 3.

4. Conclusion

In conclusion, metallic optical fibers have been successfully drawn on a fiber tower with a combination of the Taylor-wire and stack-and-draw fabrication processes. The fibers guide light over lengths of many centimeters using metallic confinement. Metallic optical fibers may be used both optically and electrically. Metallic optical fibers have fundamentally different characteristics to conventional fibers, opening up a new field for design of fiber sensors, surface enhanced Raman scattering sensors and plasmonic devices. One can imagine forming metallic light cages filled with air, perhaps by locally etching away the silica surrounding the wires. We plan to further reduce the size scale of the structures we can draw, enabling the observation of the surface plasmon polariton anti-crossings in a more robust environment. The unique features of metallic optical fibers make them a fascinating research topic.

Fig. 4. Field distribution of Sz of the mode in the metal photonic crystal fiber, which has the same structure as in Fig. 3. a) Mode passing through an anticrossing, following the “fundamental” mode until the n=2 anti-crossing in Fig. 3 and then follows this branch into the plasmon-like regime. Sz is normalized so that the integral over the entire cross section of the fiber is unity. b) Surface plasmon modes above the silica line.

Acknowledgments

We thank Wendy Lambson and Edwin Lambson in the Department of Physics, University of Bath for technical assistance in fiber polishing. Jing Hou wishes to thank The China Scholarship Council for financial assistance. BK acknowledges support from a Discovery grant by the Australian Research Council. Work at Bath was supported by the U.K. E.P.S.R.C.

Correspondence should be addressed to Jing Hou (e-mail:houjing25@sina.com) or J. C. Knight (e-mail: j.c.knight@bath.ac.uk).

References and links

1.

J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22, 475–477 (1997). [CrossRef] [PubMed]

2.

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

3.

J. A. Sazio Pier, A. Amezcua-Correa, C. E Finlayson, J. R. Hayes, and T. J. Scheidemante, “Microstructured Optical Fibers as High-Pressure Microfluidic Reactors,” Science 311, 1583–1586 (2006). [CrossRef]

4.

B. Gauvreau, A. Hassani, M. Fassi Fehri, A. Kabashin, and M. A. Skorobogatiy, “Photonic bandgap fiber-based Surface Plasmon Resonance sensors,” Opt. Express 15, 11413–11426 (2007). [CrossRef] [PubMed]

5.

X. Zhang, R. Wang, F. M. Cox, B. T. Kuhlmey, and M. C. J. Large, “Selective coating of holes in microstructured optical fiber and its application to in-fiber absorptive polarizers,” Opt. Express 15, 16270–16278 (2007). [CrossRef] [PubMed]

6.

A Amezcua-Correa, J Yang, and C. E. Finlayson. “Surface-Enhanced Raman Scattering using Microstructured Optical Fiber Substrates,” Adv. Funct. Mater. 17, 2024–2030 (2007). [CrossRef]

7.

C. G. Poulton, M. A. Schmidt, G. J. Pearce, G. Kakarantzas, and P. St. J. Russell, “Numerical study of guided modes in arrays of metallic nanowires,” Opt. Lett. 32, 1647–1649 (2007). [CrossRef] [PubMed]

8.

M. A. Schmidt, L. N. Prill Sempere, H. K. Tyagi, C. G. Poulton, and P. St. J. Russell, “Waveguiding and Plasmon Resonances in Two-Dimensional Photonic Lattices of Gold and Silver Nanowires,” arXiv:0711.4553, (2007).

9.

C. Kerbage, A. Hale, A. Yablon, R. S. Windeler, and B. J. Eggleton. “Integrated all-fiber variable attenuator based on hybrid microstructure fiber,” Appl. Phys. Lett. 79, 3191–3193 (2001). [CrossRef]

10.

M. Fokine, L. Nilsson, E. Claesson, A. D. Berlemont, L. Kjellberg, L. Krummenacher, and W. Margulis. “Integrated fiber Mach-Zehnder interferometer for electro-optic switching,” Opt. Lett. 27, 1643–1645 (2002). [CrossRef]

11.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fibers,” Science 298, 399–402 (2002). [CrossRef] [PubMed]

12.

I. W. Donald, “Review. Production, properties and applications of microwire and related products,” J. Mater. Sci. 22, 2661–2679 (1987). [CrossRef]

13.

I. W. Donald and B. L. Metcalfe. “The preparation, properties and applications of some glass-coated metal filaments prepared by the Taylor-wire process,” J. Mater. Sci. 31, 1139–1149 (1996). [CrossRef]

14.

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. d. Sterke, and L. C Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B 19, 2322–2330 (2002). [CrossRef]

15.

B. T. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botten, C. M. d. Sterke, and R. C. McPhedran, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am B 19, 2331–2340 (2002). [CrossRef]

16.

B. T. Kuhlmey, K. Pathmanandavel, and R. C. McPhedran, “Multipole analysis of photonic crystal fibers with coated inclusions,” Opt. Express 14, 10851–10864 (2006). [CrossRef] [PubMed]

17.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phy. Rev. B 6, 4370–4378 (1972). [CrossRef]

18.

C. A. Pfeiffer and E. N. Economou, “Surface polaritons in a circularly cylindrical interface: Surface plasmons,” Phy. Rev. B 10, 3038–3051 (1974). [CrossRef]

OCIS Codes
(060.2310) Fiber optics and optical communications : Fiber optics
(060.2400) Fiber optics and optical communications : Fiber properties
(240.6680) Optics at surfaces : Surface plasmons

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: January 22, 2008
Revised Manuscript: March 18, 2008
Manuscript Accepted: March 18, 2008
Published: April 14, 2008

Virtual Issues
Vol. 3, Iss. 5 Virtual Journal for Biomedical Optics

Citation
Jing Hou, David Bird, Alan George, Stefan Maier, Boris Kuhlmey, and J. C. Knight, "Metallic mode confinement in microstructured fibres," Opt. Express 16, 5983-5990 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-9-5983


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References

  1. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T Kobayashi, "Guiding of a one-dimensional optical beam with nanometer diameter," Opt. Lett. 22, 475-477 (1997). [CrossRef] [PubMed]
  2. J. C. Knight, "Photonic crystal fibers," Nature 424, 847-851 (2003). [CrossRef] [PubMed]
  3. J. A. Sazio Pier, A. Amezcua-Correa, C. E Finlayson, J. R. Hayes, and T. J. Scheidemante, "Microstructured Optical Fibers as High-Pressure Microfluidic Reactors," Science 311, 1583-1586 (2006). [CrossRef]
  4. B. Gauvreau, A. Hassani, M. Fassi Fehri, A. Kabashin, and M. A. Skorobogatiy, "Photonic bandgap fiber-based Surface Plasmon Resonance sensors," Opt. Express 15, 11413-11426 (2007). [CrossRef] [PubMed]
  5. X. Zhang, R. Wang, F. M. Cox, B. T. Kuhlmey, and M. C. J. Large, "Selective coating of holes in microstructured optical fiber and its application to in-fiber absorptive polarizers," Opt. Express 15, 16270-16278 (2007). [CrossRef] [PubMed]
  6. A Amezcua-Correa, J Yang, and C. E. Finlayson. "Surface-Enhanced Raman Scattering using Microstructured Optical Fiber Substrates," Adv. Funct. Mater. 17, 2024-2030 (2007). [CrossRef]
  7. C. G. Poulton, M. A. Schmidt, G. J. Pearce, G. Kakarantzas, and P. St. J. Russell, "Numerical study of guided modes in arrays of metallic nanowires," Opt. Lett. 32, 1647-1649 (2007). [CrossRef] [PubMed]
  8. M. A. Schmidt, L. N. Prill Sempere, H. K. Tyagi, C. G. Poulton, P. St. J. Russell, "Waveguiding and Plasmon Resonances in Two-Dimensional Photonic Lattices of Gold and Silver Nanowires,"arXiv:0711.4553, (2007).
  9. C. Kerbage, A. Hale, A. Yablon, R. S. Windeler, and B. J. Eggleton. "Integrated all-fiber variable attenuator based on hybrid microstructure fiber," Appl. Phys. Lett. 79, 3191-3193 (2001). [CrossRef]
  10. M. Fokine, L. Nilsson, E. Claesson, A. D. Berlemont, L. Kjellberg, L. Krummenacher, and W. Margulis. "Integrated fiber Mach-Zehnder interferometer for electro-optic switching," Opt. Lett. 27, 1643-1645 (2002). [CrossRef]
  11. F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, "Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fibers," Science 298, 399-402 (2002). [CrossRef] [PubMed]
  12. I. W. Donald, "Review. Production, properties and applications of microwire and related products," J. Mater. Sci. 22, 2661-2679 (1987). [CrossRef]
  13. I. W. Donald and B. L. Metcalfe. "The preparation, properties and applications of some glass-coated metal filaments prepared by the Taylor-wire process," J. Mater. Sci. 31, 1139-1149 (1996). [CrossRef]
  14. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. d. Sterke, and L. C Botten, "Multipole method for microstructured optical fibers. I. Formulation," J. Opt. Soc. Am. B 19, 2322-2330 (2002). [CrossRef]
  15. B. T. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botten, C. M. d. Sterke, and R. C. McPhedran, "Multipole method for microstructured optical fibers. II. Implementation and results," J. Opt. Soc. Am B 19, 2331-2340 (2002). [CrossRef]
  16. B. T. Kuhlmey, K. Pathmanandavel, and R. C. McPhedran, "Multipole analysis of photonic crystal fibers with coated inclusions," Opt. Express 14, 10851-10864 (2006). [CrossRef] [PubMed]
  17. P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phy. Rev. B 6,4370-4378 (1972). [CrossRef]
  18. C. A. Pfeiffer and E. N. Economou, "Surface polaritons in a circularly cylindrical interface: Surface plasmons," Phy. Rev. B 10, 3038-3051 (1974). [CrossRef]

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