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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 24 — Nov. 22, 2010
  • pp: 25232–25240
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Ultrafast nonlinear optofluidics in selectively liquid-filled photonic crystal fibers

M. Vieweg, T. Gissibl, S. Pricking, B. T. Kuhlmey, D. C. Wu, B. J. Eggleton, and H. Giessen  »View Author Affiliations


Optics Express, Vol. 18, Issue 24, pp. 25232-25240 (2010)
http://dx.doi.org/10.1364/OE.18.025232


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Abstract

Selective filling of photonic crystal fibers with different media enables a plethora of possibilities in linear and nonlinear optics. Using two-photon direct-laser writing we demonstrate full flexibility of individual closing of holes and subsequent filling of photonic crystal fibers with highly nonlinear liquids. We experimentally demonstrate solitonic supercontinuum generation over 600nm bandwidth using a compact femtosecond oscillator as pump source. Encapsulating our fibers at the ends we realize a compact ultrafast nonlinear optofluidic device. Our work is fundamentally important to the field of nonlinear optics as it provides a new platform for investigations of spatio-temporal nonlinear effects and underpins new applications in sensing and communications. Selective filling of different linear and nonlinear liquids, metals, gases, gain media, and liquid crystals into photonic crystal fibers will be the basis of new reconfigurable and versatile optical fiber devices with unprecedented performance. Control over both temporal and spatial dispersion as well as linear and nonlinear coupling will lead to the generation of spatial-temporal solitons, so-called optical bullets.

© 2010 Optical Society of America

1. Introduction

Since their first appearance, photonic crystal fibers (PCF) [1

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

3

3. 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, 1702–1704 (2003). [CrossRef] [PubMed]

] have entered nearly all fields of optics. They allow for tailoring the temporal and spatial dispersion of propagating light, and in combination with nonlinear effects have led to unprecedented broad supercontinua. Their nonlinear optical properties are limited by the Kerr effect in glass and fused silica which they consist of. Non-silica fibers have been developed, such as polymer-based [4

4. D. W. Garvey, K. Zimmermann, P. Young, J. Tostenrude, J. S. Townsend, Z. Zhou, M. Lobel, M. Dayton, R. Wittorf, and M.G. Kuzyk, “Single-mode nonlinear-optical polymer fibers,” J. Opt. Soc. Am. B 13, 2017–2023 (1996). [CrossRef]

] or chalcogenide-based fibers [5

5. M. Asobe, T. Kanamori, and K. Kubodera, “Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches,” IEEE J. Quantum Electron. 29, 2325–2333 (1993). [CrossRef]

], which offer striking possibilities such as an extremely high nonlinearity, but are limited in functionality and flexibility. In a different approach, first attempts have been carried out to fill the photonic structure of silica PCFs with functional media to broaden the range of their applicability even further. Up to now PCFs were filled with metals [6

6. H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, and St. P. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93, 111102 (2008). [CrossRef]

, 7

7. M. A. Schmidt, L. P. Sempere, H. K. Tyagi, C. G. Poulton, and St. P. Russell, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B 77, 033417 (2008). [CrossRef]

], gases [8

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

], semiconductors [9

9. P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, “Microstructured optical fibers as high-pressure microfluidic reactors,” Science 311, 1583–1586 (2006). [CrossRef] [PubMed]

], liquid crystals [10

10. T. T. Larsen, A. Bjarklev, D. S. Hermann, and J. Broeng, “Optical device based on liquid crystal photonic bandgap fibers,” Opt. Express 11, 2589–2596 (2003). [CrossRef] [PubMed]

], and also with different liquids [11

11. 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]

, 12

12. C. Kerbage, P. Steinvurzel, P. Reyes, P. S. Westbrook, R. S. Windeler, A. Hale, and B. J. Eggleton, “Highly tunable birefringent microstructured optical fiber,” Opt. Lett. 27, 842–844 (2002). [CrossRef]

], entering the new interdisciplinary field of optofluidics, which marries microfluidics with photonics [13

13. D. Psaltis, S. R. Quake, and C. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442, 381–386 (2006). [CrossRef] [PubMed]

, 14

14. C. Monat, P. Domachuk, and B. J. Eggleton, “Integrated optofluidics: A new river of light,” Nat. Photonics 1, 106–114 (2007). [CrossRef]

]. Example for a complete fluid-filled fiber is an ARROW-fiber presented by Fuerbach et al. [15

15. A. Fuerbach, P. Steinvurzel, J. A. Bolger, A. Nulsen, and B. J. Eggleton, “Nonlinear propagation effects in antiresonant high-index inclusion photonic crystal fibers,” Opt. Lett. 30, 830–832 (2005). [CrossRef] [PubMed]

] or by Larsen et al. [10

10. T. T. Larsen, A. Bjarklev, D. S. Hermann, and J. Broeng, “Optical device based on liquid crystal photonic bandgap fibers,” Opt. Express 11, 2589–2596 (2003). [CrossRef] [PubMed]

], where shifting of the band gap due to a change of temperature was demonstrated.

The formation of spatial solitons due to a slow thermal nonlinearity has been reported in a PCF that was completely filled with fishoil [16

16. C. R. Rosberg, F.H. Bennet, D. N. Neshev, P. D. Rasmussen, O. Bang, W. Krolikowski, A. Bjarklev, and Y. Kivshar, “Tunable diffraction and self-defocusing in liquid-filled photonic crystal fibers,” Opt. Express 15, 12145–12150 (2007). [CrossRef] [PubMed]

]. But as mentioned by the authors of [17

17. P. D. Rasmussen, A. A. Sukhorukov, D. N. Neshev, W. Krolikowski, O. Bang, J. Laegsgaard, and Y. Kivshar, “Spatiotemporal control of light by Bloch-mode dispersion in multi-core fibers,” Opt. Express 16, 5878–5891 (2008). [CrossRef] [PubMed]

] it is not possible in this case to engineer suitable spatial coupling properties in the anomalous dispersion regime which is crucial for the formation of spatio-temporal solitons.

Partially filled PCF have also been fabricated by a number of authors. Kuhlmey et al. reported a single strand filled with a liquid, which was applied to sensing [18

18. B. T. Kuhlmey, B. J. Eggleton, and D. K. C. Wu, “Fluid-filled solid-core photonic bandgap fibers,” J. Lightwave Technol. 27, 1617–1630 (2009). [CrossRef]

]. A common technique to implement this structure is to collapse the surrounding holes by the use of an electric arc [19

19. L. Xiao, W. Jin, M. S. Demokan, H. L. Ho, Y. L. Hoo, and C. Zhao, “Fabrication of selective injection microstructured optical fibers with a conventional fusion splicer,” Opt. Express 13, 9014–9022 (2005). [CrossRef] [PubMed]

] and fill the remaining core with the desired liquid. This fabrication method was used by Bethge et al. [20

20. J. Bethge, A. Husakou, F. Mitschke, F. Noack, U. Griebner, G. Steinmeyer, and J. Herrmann, “Two-octave super-continuum generation in a water-filled photonic crystal fiber,” Opt. Express 18, 6230–6240 (2010). [CrossRef] [PubMed]

] and Bozolan et al. [21

21. A. Bozolan, C. J. S. de Matos, C. M. B. Cordeiro, E. M. dos Santos, and J. Travers, “Supercontinuum in a water-core photonic crystal fiber,” Opt. Express 16, 9671–9676 (2008). [CrossRef] [PubMed]

] to generate a supercontinuum in water with very high pump powers.

All these filled devices were limited by the fabrication process resulting in either the entire structure [10

10. T. T. Larsen, A. Bjarklev, D. S. Hermann, and J. Broeng, “Optical device based on liquid crystal photonic bandgap fibers,” Opt. Express 11, 2589–2596 (2003). [CrossRef] [PubMed]

, 15

15. A. Fuerbach, P. Steinvurzel, J. A. Bolger, A. Nulsen, and B. J. Eggleton, “Nonlinear propagation effects in antiresonant high-index inclusion photonic crystal fibers,” Opt. Lett. 30, 830–832 (2005). [CrossRef] [PubMed]

, 17

17. P. D. Rasmussen, A. A. Sukhorukov, D. N. Neshev, W. Krolikowski, O. Bang, J. Laegsgaard, and Y. Kivshar, “Spatiotemporal control of light by Bloch-mode dispersion in multi-core fibers,” Opt. Express 16, 5878–5891 (2008). [CrossRef] [PubMed]

] or simple patterns consisting of a single connected area being filled [16

16. C. R. Rosberg, F.H. Bennet, D. N. Neshev, P. D. Rasmussen, O. Bang, W. Krolikowski, A. Bjarklev, and Y. Kivshar, “Tunable diffraction and self-defocusing in liquid-filled photonic crystal fibers,” Opt. Express 15, 12145–12150 (2007). [CrossRef] [PubMed]

, 18

18. B. T. Kuhlmey, B. J. Eggleton, and D. K. C. Wu, “Fluid-filled solid-core photonic bandgap fibers,” J. Lightwave Technol. 27, 1617–1630 (2009). [CrossRef]

, 20

20. J. Bethge, A. Husakou, F. Mitschke, F. Noack, U. Griebner, G. Steinmeyer, and J. Herrmann, “Two-octave super-continuum generation in a water-filled photonic crystal fiber,” Opt. Express 18, 6230–6240 (2010). [CrossRef] [PubMed]

]. Thus also the applicability of such devices is limited.

Here in this paper we demonstrate a novel and versatile optofluidic device with a high ultra-fast nonlinearity and a large degree of freedom for tailoring their optical properties. The key idea is summarized schematically in Fig. 1; we fill single strands or arbitrary patterns of a PCF selectively with the desired liquid, which then act as linear or nonlinear optofluidic waveguide embedded in the PCF. With this configuration it is possible to achieve a higher contrast between the refractive index of the core and the effective refractive index of the surrounding photonic structure, compared to a completely filled structure or waveguides written in bulk glass [22

22. M. Heinrich, Y. V. Kartashov, L. P. R. Ramirez, A. Szameit, F. Dreisow, R. Keil, S. Nolte, A. Tünnemann, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional superlattice solitons,” Opt. Lett. 34, 3701–3703 (2009). [CrossRef] [PubMed]

24

24. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21, 1729–1731 (1996). [CrossRef] [PubMed]

]. This additional freedom allows tailoring of the dispersion properties of our ultrafast nonlinear optofluidic device (UNOF) over a wide range which is of fundamental importance for the temporal control of optical pulses and crucial to the formation of supercontinuum.

Fig. 1 Schematic drawing of the ultrafast nonlinear optofluidic device. Checkerboard pattern of liquid strands embedded in a PCF acting as nonlinear waveguides. The red light is coupled in and after several centimeters of propagation spectrally broadened light leaves each liquid waveguide.

We utilize the ultrafast Kerr-nonlinearity of liquids such as carbon disulfide (CS2), toluene, carbon tetrachloride (CCl4), or chloroform. Apart from their high nonlinear refractive index n2 which is in CS2 up to 200 times higher [25

25. P. P. Ho and R. R. Alfano, “Optical Kerr effect in liquids,” Phys. Rev. A 20, 2170–2187 (1979). [CrossRef]

] than that of fused silica, these liquids are transparent in the visible and the near infrared wavelength regime [26

26. J. W. Ellis, “The near infra-red absorption spectra of some organic liquids,” Phys. Rev. 23, 48–62 (1924). [CrossRef]

]. Because of the toxicity of CS2 we have chosen toluene and CCl4 for our experiment, which enhances the nonlinearity by a factor of 60 and 6, respectively [27

27. We chose CCl4 for our nonlinear experiments because with the available photonic crystal NL-2.3-790 and our liquids, CCl4 was the only one to provide anomalous dispersion at our pump wavelength of 1030nm.

].

Our selective filling method uses the two-dimensional structure of a PCF as a scaffold for complex patterns. For instance, filling a checkerboard pattern or limited areas of the PCF with the liquid yields an ultrafast nonlinear multi-waveguide device, acting as two-dimensional discrete system embedded into a single PCF which has never been shown before. Furthermore, this concept also allows us to tailor the properties of this discrete nonlinear system to control the pulse propagation in the temporal as well as in the spatial regime, both in the linear as well as in the nonlinear domain. With this advantage the experimental demonstration of spatio-temporal solitons should become feasible [17

17. P. D. Rasmussen, A. A. Sukhorukov, D. N. Neshev, W. Krolikowski, O. Bang, J. Laegsgaard, and Y. Kivshar, “Spatiotemporal control of light by Bloch-mode dispersion in multi-core fibers,” Opt. Express 16, 5878–5891 (2008). [CrossRef] [PubMed]

, 28

28. F. Ye, Y. V. Kartashov, B. Hu, and L. Torner, “Light bullets in Bessel optical lattices with spatially modulated nonlinearity,” Opt. Express 17, 11328–11334 (2009). [CrossRef] [PubMed]

].

2. Fabrication

Commercially available PCFs are used for our UNOF device as carrier for the liquid strands. In order to selectively fill single strands of the photonic structure with a liquid, the strands which should stay empty have to be blocked individually to prevent the inflow of the liquid. To do so we use a two-photon direct laser writing technique [29

29. S. Maruo, O. Nakamura, and S. Kawata, “Three-dimensional microfabrication with two-photon-absorbed photopolymerization,” Opt. Lett. 22, 132–134 (1997). [CrossRef] [PubMed]

] that provides a very precise control of the local polymerization of an appropriate photoresist in three dimensions. To block the single strands we use the photoresist SU-8 from MicroChem [30] because it is widely used and chemically very stable after the light exposure due to its strong cross linking. Single photon polymerization using a UV laser does not provide the desired selectivity due to the lack of suitable depth resolution.

In a first step, the cleaved fiber end of a suitable PCF is completely covered with SU-8. The holes which should be blocked are then illuminated one by one with focused light of a mode-locked Ti:Sapphire femtosecond laser oscillator. Due to two-photon absorption the photoresist starts to polymerize. This procedure is schematically shown in Fig 2(a). The last step in the structuring process is the usual hardbake and developing, where the unexposed photoresist is removed. Figures 2(b)2(d) shows several examples of selectively closed holes of a PCF.

Fig. 2 (a), Scheme of the direct laser writing technique applied on the photonic structure of a PCF. (b), Name of our institute written in a NL-2.3-790 with a hole diameter of 2.5μm and a hole-to-hole distance of 2.6μm. (c), Checkerboard pattern as the most complex structure also in a NL-2.3-790. (d), Scanning electron microscope picture of the checkerboard pattern, which proves the good sealing of the strands by the cured polymer. (e), Schematic cross section of the filling setup: the structured fiber end is held in the liquid reservoir. The unblocked holes are filled by the capillary force whereas the blocked strands stay unfilled. (f), Three toluene filled rings embedded in a LMA-8 with a hole diameter of 2.7μm and a hole-to-hole distance of 5.6μm.

In order to fill the fiber with liquids we use capillary forces: The structured end of the fiber is kept in a reservoir of the desired liquid [Fig. 2(e)] so that the liquid penetrates the unblocked strands and flows along the complete length of the fiber over several centimeters. By observation of the opposite end of the fiber, one can clearly see the liquid inside the fiber strand as it is shown in Fig. 2(f).

After filling the fiber, optionally both ends can be closed by UV glue in a further step to encapsulate the liquid. Hence an easy-to-handle and compact optofluidic fiber device is achieved [Fig. 3(a)]. A disadvantage of this additional step is the fact that the coupling in and out of fluid waveguides suffers from the rougher surface at the fiber ends. Also the damage threshold is decreased due to the photoresist layers. Therefore, we used the encapsulated devices only for investigating the linear propagation properties. With the direct laser writing technique we are not limited to a single fiber type. By changing the geometry of the fiber the optical properties of our UNOF device can change dramatically, whereas the fabrication process is still the same. In contrast to [31

31. Y. Wang, C. R. Liao, and D. N. Wang, “Femtosecond laser-assisted selective infiltration of microstructured optical fibers,” Opt. Express 18, 18056–18060 (2010). [CrossRef] [PubMed]

] this is also valid for fibers with a ratio of hole diameter to hole period close to one.

Fig. 3 (a), Simple setup of our optofluidic device, with both ends closed by UV glue after liquid filling. (b), Mode image of the single strand structure in a NL-2.3-790 fiber filled with CCl4 illuminated with a cw HeNe-Laser at 633nm wavelength. It shows clearly that the light propagates in the fundamental mode. (c), Mode image of the three ring structure [Fig. 2(f)] encapsulated in a LMA-8 fiber filled with toluene and illuminated at 1064nm. The light in each waveguide is propagating in the LP11 mode. Strong coupling occurs from strand to strand within each ring and weaker coupling between the rings themselves. Apart from that, all liquid strands indeed act as waveguides. For (b) and (c) the structure of the underlying photonic crystal fiber is schematically superimposed.

3. Linear propagation

We first investigate the linear propagation properties of our UNOF device. The setup is shown in Fig. 3(a). The simplest pattern is the single strand structure. The mode image of this structure embedded in a PCF filled with CCl4 is given in Fig. 3(b) which shows the fundamental mode [32

32. In principle, we operate at this wavelength under multimode conditions, but straight incoupling and a straight fiber supports the fundamental mode.

]. The fiber chosen for this example, the NL-2.3-790, has a hole-to-hole distance of Λ = 2.6 μm and a hole diameter of d = 2.5 μm [33].

In a UNOF fiber filled with CCl4 or toluene the guiding mechanism is total internal reflection because the refractive index of CCl44 (n = 1.4503@1.03 μm [34

34. H. H. Marvin, “The selective transmission and the dispersion of the liquid chlorides,” Phys. Rev. 34, 161–186 (1912).

]) and toluene (n = 1.4816@1.03 μm [35

35. A. Samoc, “Dispersion of refractive properties of solvents: Chloroform, toluene, benzene, and carbon disulfide in ultraviolet, visible, and near-infrared,” J. Appl. Phys. 94, 6167–6174 (2003). [CrossRef]

]) is slightly higher than that of fused silica (n = 1.4497@1.03μm). The filled liquid strand acts as the core and the surrounding photonic structure as the cladding.

The same mechanism is valid for each fluid waveguide in a more complex structure. The mode image in Fig. 3(c) shows the end of an LMA-8 fiber with a toluene filled three-ring structure. In each fluid waveguide, the light is propagating in a higher order mode - this is consistent with the calculated normalized frequency V = 2.47 [36

36. N. A. Mortensen, J. R. Folkenberg, M. D. Nielsen, and K. P. Hansen, “Modal cutoff and the V parameter in photonic crystal fibers,” Opt. Lett. 28, 1879–1881 (2003). [CrossRef] [PubMed]

], which lies above the single mode criteria. The LMA-8 fiber used for this example has a hole-to-hole distance of Λ = 5.6μm and a hole diameter of d = 2.7 μm [37].

If the UNOF contains more than one liquid-filled strand, it can act as a multi-waveguide array and coupling between fluid waveguides occurs. The coupling depends on the distance between two adjacent waveguides and the refractive index difference between the strands and the surrounding. For the LMA-8 UNOF filled with toluene, the coupling length between two adjacent waveguides can be estimated for the fundamental mode by the supermode method to be Lc = 9.8mm [38

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

, 39

39. B. T. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botten, C. Martijn de 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]

]. Thus in the three ring structure filled with toluene the waveguides are mutually coupled [Fig. 3(c)]. By changing the hole-to-hole distance Λ, by variation of the hole diameter d of the used PCF, or by changing the liquid refractive index, the coupling of the waveguides in the UNOF device can be adjusted to match the requirements for a certain propagation characteristic.

By changing the filled strand medium or the geometry of the fiber, the dispersion properties of the UNOF device can be tailored. If an additional temperature change or mixtures of different liquids are allowed, another degree of freedom is added to engineer the dispersion properties almost continuously. Just by replacing the liquid in a single filled strand of the NL-2.3-790 fiber one can shift the zero-dispersion wavelength (ZDW) from 790nm for chloroform to 1270nm for CS2 over almost 500nm (see also Fig. 4c for the dispersion of a CCl4 filled UNOF). Apart from the linear propagation regime, this high degree of freedom in dispersion engineering is crucial when entering the nonlinear propagation domain, as it is well known [40

40. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006). [CrossRef]

].

Fig. 4 (a), Spectral evolution for different input powers of a 26cm long fiber with a single strand filled with CCl4 and with a core diameter of 2.5μm. The pump power was increased from 10mW to 100mW, while spectral broadening could be observed. For the highest incoupled power of 100mW a 600nm wide spectrum could be obtained. Because the fiber is pumped in the anomalous dispersion regime, solitons can form. The red shifting soliton in the near infrared wavelength regime as well as the corresponding non-solitonic radiation in the blue wavelength regime [44] could be measured. (b), Comparison between measurement and simulation of a 19cm long fiber with a single strand filled with CCl4 with a core diameter of 2.5μm and pumped with an input power of 330mW. (c), Comparison of different core media. As core medium fused silica and CCl4 in a 19cm long fiber were used. The core size for both fibers was 2.5μm and the incoupled power was 330mW. Additionally the dispersion curve for both fibers is also shown. Here one can see that the pump wavelength of 1030nm lies in the anomalous dispersion regime.

4. Nonlinear propagation

Filling our devices with highly nonlinear liquids and managing the dispersion, we demonstrate nonlinear effects including self-phase modulation (SPM), soliton formation and fission [40

40. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006). [CrossRef]

,41

41. A. V. Husakou and J. Hermann, “Supercontinuum generation of high-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001). [CrossRef] [PubMed]

] resulting in a octave-wide spectral broadening.

We pump our UNOF device (the single strand structure embedded in a NL-2.3-790 filled with CCl4) with a Yb:KGW femtosecond oscillator [42

42. F. Hoos, T. P. Meyrath, S. Li, B. Braun, and H. Giessen, “Femtosecond 5-W Yb:KGW slab laser oscillator pumped by a single broad-area diode and its application as supercontinuum source,” Appl. Phys. B 96, 5–10 (2009). [CrossRef]

] at 44MHz which provides 210fs long pulses at a center wavelength of 1030nm. The propagation takes place in the fundamental mode [Fig. 3(b)]. Numerical simulations [Fig. 4(c)] indicate that the ZDW of our device is at 900nm with a group velocity dispersion parameter at 1030nm of D = 51ps/km/nm; hence the pump wavelength of 1030nm lies in the anomalous dispersion regime, which allows soliton formation.

CCl4 is transparent in the visible as well as in the infrared and has a high nonlinear refractive index of n2 = 15 · 10−20 m2/W [25

25. P. P. Ho and R. R. Alfano, “Optical Kerr effect in liquids,” Phys. Rev. A 20, 2170–2187 (1979). [CrossRef]

], six times that of fused silica. The underlying process for this high Kerr-nonlinearity is the molecular reorientation [45

45. Y. R. Shen, Principles of Nonlinear Optics (Wiley, Hoboken, 2003).

, 46

46. R. Zhang, J. Teipel, and H. Giessen, “Theoretical design of a liquid-core photonic crystal fiber for supercontinuum generation,” Opt. Express 14, 6800–6812 (2006). [CrossRef] [PubMed]

], which takes place within several hundreds of femtoseconds, in contrast to the almost instantaneous nonlinearity of fused silica [47

47. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 2007).

, 48

48. R. V. J. Raja, A. Husakou, J. Hermann, and K. Porsezian, “Supercontinuum generation in liquid-filled photonic crystal fiber with slow nonlinear response,” J. Opt. Soc. Am. B 27, 1763–1768 (2010). [CrossRef]

]. Single strands filled with slowly responding liquids can also give rise to new propagation effects, such as the existence of so-called linearons [49

49. C. Conti, M. Schmidt, St. P. Russell, and F. Biancalana, “Linearons: highly non-instantaneous solitons in liquid-core photonic crystal fibers,” arXiv:1010.0331v1 [physics.optics], http://arxiv.org/abs/1010.0331.

].

By using toluene with a higher nonlinear refractive index of n2 = 170 · 10−20 m2/W [25

25. P. P. Ho and R. R. Alfano, “Optical Kerr effect in liquids,” Phys. Rev. A 20, 2170–2187 (1979). [CrossRef]

] the nonlinearity of our device could be increased even further. In Fig. 4(c) we show the spectrum of an ordinary PCF with a glass core. The potential of our UNOF fiber is demonstrated in comparison by replacing the core medium with CCl4, which enhances the spectral broadening substantially.

5. Simulation

The dispersion properties of the UNOF device can be simulated by solving its eigenvalue equation [47

47. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 2007).

], and the effective refractive index of the photonic structure is calculated numerically by using [50

50. M. Midrio, M. P. Singh, and C. G. Someda, “The space-filling mode of holey fibers: an analytical vectorial solution,” J. Lightwave Technol. 18, 1031–1037 (2000). [CrossRef]

]. The propagation constant β combined with the nonlinearity γ and response function R(T) as a function of time allows us to simulate the system by numerically solving the generalized nonlinear Schrödinger equation (GNLSE) [40

40. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006). [CrossRef]

, 46

46. R. Zhang, J. Teipel, and H. Giessen, “Theoretical design of a liquid-core photonic crystal fiber for supercontinuum generation,” Opt. Express 14, 6800–6812 (2006). [CrossRef] [PubMed]

]:
Azk=27ik+1k!βkkATk=iγ(1+iτschockT)(A(z,t)R(T)|A(z,TT)|2dT).
(1)
This is carried out using a split-step Fourier-method, where A is the envelope of the electric field of the pulse, βk is the kth derivative of the propagation constant β(ω) with respect to the frequency ω. Self-steepening and optical shocks are governed by τshock. γ is the nonlinearity of the device [47

47. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 2007).

] which is proportional to the nonlinear refractive index n2. For our case shown in Fig. 4(b) γ is about 370W−1km−1.

R(T) describes the delayed response function of the medium [51

51. K. Itho, Y. Toda, R. Morita, and M. Yamashita, “Coherent optical control of molecular motion using polarized sequential pulses,” Jpn. J. Appl. Phys. 43, 6448–6451 (2004). [CrossRef]

] which for the liquid is mainly given by the molecular reorientation. The vibrational molecular Raman response and the electronic contribution are also included. Figure 4(b) demonstrates the excellent agreement of measurement and simulation, which reproduces correctly the main features of the spectrum. The mismatch of the wavelength of the non-solitonic radiation arises from the uncertainty of the given refractive index of CCl4 [34

34. H. H. Marvin, “The selective transmission and the dispersion of the liquid chlorides,” Phys. Rev. 34, 161–186 (1912).

] and of the effective index calculated by [50

50. M. Midrio, M. P. Singh, and C. G. Someda, “The space-filling mode of holey fibers: an analytical vectorial solution,” J. Lightwave Technol. 18, 1031–1037 (2000). [CrossRef]

].

6. Conclusion

In conclusion, we have presented the novel fabrication method and the application of a new versatile optofluidic device with a high ultrafast nonlinearity. We have shown that the selective closing with direct laser writing and selective filling of a PCF opens a new field with complete control of the linear and nonlinear optical properties. Our approach can be extended to selectively closed PCF filled with different media such as metals, semiconductors, gasses, gain media, liquid crystals, etc. Our concept is as well applicable to photonic crystals and other photonic structures.

As examples for the versatility of our ultrafast nonlinear optofluidic devices we have demonstrated propagation in a complex shaped liquid waveguide array in a toluene filled LMA-8 fiber with a high inter-waveguide coupling, as well as nonlinear propagation in a single strand structure. We were able to manage the dispersion to demonstrate ultrafast soliton formation and fission, resulting in a 600nm wide spectral broadening with low peak powers enabled by the remarkable high nonlinearity of the liquids.

Our UNOF device allows to tailor the dispersion, spatial coupling, and spatial arrangement of a waveguide array, as well as the optical nonlinearity in a two dimensional discrete system. Such ultrafast nonlinear optofluidic devices might be at heart of future terabit photonic networks for example for novel switching, multiplexing, or mixing devices. In future our device should provide us the possibility to observe ultrafast nonlinear spatio-temporal solitons (optical bullets) in a discrete two dimensional waveguide system due to the complete control of the optical properties.

References and links

1.

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

2.

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

3.

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, 1702–1704 (2003). [CrossRef] [PubMed]

4.

D. W. Garvey, K. Zimmermann, P. Young, J. Tostenrude, J. S. Townsend, Z. Zhou, M. Lobel, M. Dayton, R. Wittorf, and M.G. Kuzyk, “Single-mode nonlinear-optical polymer fibers,” J. Opt. Soc. Am. B 13, 2017–2023 (1996). [CrossRef]

5.

M. Asobe, T. Kanamori, and K. Kubodera, “Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches,” IEEE J. Quantum Electron. 29, 2325–2333 (1993). [CrossRef]

6.

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, and St. P. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93, 111102 (2008). [CrossRef]

7.

M. A. Schmidt, L. P. Sempere, H. K. Tyagi, C. G. Poulton, and St. P. Russell, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B 77, 033417 (2008). [CrossRef]

8.

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

9.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, “Microstructured optical fibers as high-pressure microfluidic reactors,” Science 311, 1583–1586 (2006). [CrossRef] [PubMed]

10.

T. T. Larsen, A. Bjarklev, D. S. Hermann, and J. Broeng, “Optical device based on liquid crystal photonic bandgap fibers,” Opt. Express 11, 2589–2596 (2003). [CrossRef] [PubMed]

11.

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]

12.

C. Kerbage, P. Steinvurzel, P. Reyes, P. S. Westbrook, R. S. Windeler, A. Hale, and B. J. Eggleton, “Highly tunable birefringent microstructured optical fiber,” Opt. Lett. 27, 842–844 (2002). [CrossRef]

13.

D. Psaltis, S. R. Quake, and C. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442, 381–386 (2006). [CrossRef] [PubMed]

14.

C. Monat, P. Domachuk, and B. J. Eggleton, “Integrated optofluidics: A new river of light,” Nat. Photonics 1, 106–114 (2007). [CrossRef]

15.

A. Fuerbach, P. Steinvurzel, J. A. Bolger, A. Nulsen, and B. J. Eggleton, “Nonlinear propagation effects in antiresonant high-index inclusion photonic crystal fibers,” Opt. Lett. 30, 830–832 (2005). [CrossRef] [PubMed]

16.

C. R. Rosberg, F.H. Bennet, D. N. Neshev, P. D. Rasmussen, O. Bang, W. Krolikowski, A. Bjarklev, and Y. Kivshar, “Tunable diffraction and self-defocusing in liquid-filled photonic crystal fibers,” Opt. Express 15, 12145–12150 (2007). [CrossRef] [PubMed]

17.

P. D. Rasmussen, A. A. Sukhorukov, D. N. Neshev, W. Krolikowski, O. Bang, J. Laegsgaard, and Y. Kivshar, “Spatiotemporal control of light by Bloch-mode dispersion in multi-core fibers,” Opt. Express 16, 5878–5891 (2008). [CrossRef] [PubMed]

18.

B. T. Kuhlmey, B. J. Eggleton, and D. K. C. Wu, “Fluid-filled solid-core photonic bandgap fibers,” J. Lightwave Technol. 27, 1617–1630 (2009). [CrossRef]

19.

L. Xiao, W. Jin, M. S. Demokan, H. L. Ho, Y. L. Hoo, and C. Zhao, “Fabrication of selective injection microstructured optical fibers with a conventional fusion splicer,” Opt. Express 13, 9014–9022 (2005). [CrossRef] [PubMed]

20.

J. Bethge, A. Husakou, F. Mitschke, F. Noack, U. Griebner, G. Steinmeyer, and J. Herrmann, “Two-octave super-continuum generation in a water-filled photonic crystal fiber,” Opt. Express 18, 6230–6240 (2010). [CrossRef] [PubMed]

21.

A. Bozolan, C. J. S. de Matos, C. M. B. Cordeiro, E. M. dos Santos, and J. Travers, “Supercontinuum in a water-core photonic crystal fiber,” Opt. Express 16, 9671–9676 (2008). [CrossRef] [PubMed]

22.

M. Heinrich, Y. V. Kartashov, L. P. R. Ramirez, A. Szameit, F. Dreisow, R. Keil, S. Nolte, A. Tünnemann, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional superlattice solitons,” Opt. Lett. 34, 3701–3703 (2009). [CrossRef] [PubMed]

23.

M. Heinrich, Y. V. Kartashov, L. P. R. Ramirez, A. Szameit, F. Dreisow, R. Keil, S. Nolte, A. Tünnemann, V. A. Vysloukh, and L. Torner, “Two-dimensional solitons at interfaces between binary superlattices and homogeneous lattices,” Phys. Rev. A 80, 063832 (2009). [CrossRef]

24.

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21, 1729–1731 (1996). [CrossRef] [PubMed]

25.

P. P. Ho and R. R. Alfano, “Optical Kerr effect in liquids,” Phys. Rev. A 20, 2170–2187 (1979). [CrossRef]

26.

J. W. Ellis, “The near infra-red absorption spectra of some organic liquids,” Phys. Rev. 23, 48–62 (1924). [CrossRef]

27.

We chose CCl4 for our nonlinear experiments because with the available photonic crystal NL-2.3-790 and our liquids, CCl4 was the only one to provide anomalous dispersion at our pump wavelength of 1030nm.

28.

F. Ye, Y. V. Kartashov, B. Hu, and L. Torner, “Light bullets in Bessel optical lattices with spatially modulated nonlinearity,” Opt. Express 17, 11328–11334 (2009). [CrossRef] [PubMed]

29.

S. Maruo, O. Nakamura, and S. Kawata, “Three-dimensional microfabrication with two-photon-absorbed photopolymerization,” Opt. Lett. 22, 132–134 (1997). [CrossRef] [PubMed]

30.

MicroChem, http://www.microchem.com/products/su$_$eight.htm.

31.

Y. Wang, C. R. Liao, and D. N. Wang, “Femtosecond laser-assisted selective infiltration of microstructured optical fibers,” Opt. Express 18, 18056–18060 (2010). [CrossRef] [PubMed]

32.

In principle, we operate at this wavelength under multimode conditions, but straight incoupling and a straight fiber supports the fundamental mode.

33.

NKT Photonics, http://www.nktphotonics.com/files/files/NL-23-790.pdf.

34.

H. H. Marvin, “The selective transmission and the dispersion of the liquid chlorides,” Phys. Rev. 34, 161–186 (1912).

35.

A. Samoc, “Dispersion of refractive properties of solvents: Chloroform, toluene, benzene, and carbon disulfide in ultraviolet, visible, and near-infrared,” J. Appl. Phys. 94, 6167–6174 (2003). [CrossRef]

36.

N. A. Mortensen, J. R. Folkenberg, M. D. Nielsen, and K. P. Hansen, “Modal cutoff and the V parameter in photonic crystal fibers,” Opt. Lett. 28, 1879–1881 (2003). [CrossRef] [PubMed]

37.

NKT Photonics, http://www.nktphotonics.com/files/files/LMA-8-100409.pdf.

38.

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

39.

B. T. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botten, C. Martijn de 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]

40.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006). [CrossRef]

41.

A. V. Husakou and J. Hermann, “Supercontinuum generation of high-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001). [CrossRef] [PubMed]

42.

F. Hoos, T. P. Meyrath, S. Li, B. Braun, and H. Giessen, “Femtosecond 5-W Yb:KGW slab laser oscillator pumped by a single broad-area diode and its application as supercontinuum source,” Appl. Phys. B 96, 5–10 (2009). [CrossRef]

43.

A. A. Voronin, V. P. Mitrokhin, A. A. Ivanov, A. B. Fedotov, D. A. Sidorov-Biryukov, V. I. Beloglazov, M. V. Alfimov, H. Ludvigsen, and A. M. Zheltikov, “Understanding the nonlinear-optical response of a liquid-core photonic-crystal fiber,” Laser Phys. Lett. 7, 46–49 (2010). [CrossRef]

44.

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995). [CrossRef] [PubMed]

45.

Y. R. Shen, Principles of Nonlinear Optics (Wiley, Hoboken, 2003).

46.

R. Zhang, J. Teipel, and H. Giessen, “Theoretical design of a liquid-core photonic crystal fiber for supercontinuum generation,” Opt. Express 14, 6800–6812 (2006). [CrossRef] [PubMed]

47.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 2007).

48.

R. V. J. Raja, A. Husakou, J. Hermann, and K. Porsezian, “Supercontinuum generation in liquid-filled photonic crystal fiber with slow nonlinear response,” J. Opt. Soc. Am. B 27, 1763–1768 (2010). [CrossRef]

49.

C. Conti, M. Schmidt, St. P. Russell, and F. Biancalana, “Linearons: highly non-instantaneous solitons in liquid-core photonic crystal fibers,” arXiv:1010.0331v1 [physics.optics], http://arxiv.org/abs/1010.0331.

50.

M. Midrio, M. P. Singh, and C. G. Someda, “The space-filling mode of holey fibers: an analytical vectorial solution,” J. Lightwave Technol. 18, 1031–1037 (2000). [CrossRef]

51.

K. Itho, Y. Toda, R. Morita, and M. Yamashita, “Coherent optical control of molecular motion using polarized sequential pulses,” Jpn. J. Appl. Phys. 43, 6448–6451 (2004). [CrossRef]

OCIS Codes
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(320.7110) Ultrafast optics : Ultrafast nonlinear optics
(320.6629) Ultrafast optics : Supercontinuum generation

ToC Category:
Ultrafast Optics

History
Original Manuscript: October 13, 2010
Manuscript Accepted: November 2, 2010
Published: November 17, 2010

Citation
M. Vieweg, T. Gissibl, S. Pricking, B. T. Kuhlmey, D. C. Wu, B. J. Eggleton, and H. Giessen, "Ultrafast nonlinear optofluidics in selectively liquid-filled photonic crystal fibers," Opt. Express 18, 25232-25240 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-24-25232


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References

  1. J. C. Knight, "Photonic crystal fibers," Nature 424, 847-851 (2003). [CrossRef] [PubMed]
  2. C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and W. Karl, "Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003). [CrossRef] [PubMed]
  3. 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, 1702-1704 (2003). [CrossRef] [PubMed]
  4. D. W. Garvey, K. Zimmermann, P. Young, J. Tostenrude, J. S. Townsend, Z. Zhou, M. Lobel, M. Dayton, R. Wittorf, and M. G. Kuzyk, "Single-mode nonlinear-optical polymer fibers," J. Opt. Soc. Am. B 13, 2017-2023 (1996). [CrossRef]
  5. M. Asobe, T. Kanamori, and K. Kubodera, "Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches," IEEE J. Quantum Electron. 29, 2325-2333 (1993). [CrossRef]
  6. H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, and P. St. Russell, "Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber," Appl. Phys. Lett. 93, 111102 (2008). [CrossRef]
  7. M. A. Schmidt, L. P. Sempere, H. K. Tyagi, C. G. Poulton, and P. St. Russell, "Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires," Phys. Rev. B 77, 033417 (2008). [CrossRef]
  8. F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. Russell, "Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber," Science 298, 399-402 (2002). [CrossRef] [PubMed]
  9. P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured optical fibers as high-pressure microfluidic reactors," Science 311, 1583-1586 (2006). [CrossRef] [PubMed]
  10. T. T. Larsen, A. Bjarklev, D. S. Hermann, and J. Broeng, "Optical device based on liquid crystal photonic bandgap fibers," Opt. Express 11, 2589-2596 (2003). [CrossRef] [PubMed]
  11. 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]
  12. C. Kerbage, P. Steinvurzel, P. Reyes, P. S. Westbrook, R. S. Windeler, A. Hale, and B. J. Eggleton, "Highly tunable birefringent microstructured optical fiber," Opt. Lett. 27, 842-844 (2002). [CrossRef]
  13. D. Psaltis, S. R. Quake, and C. Yang, "Developing optofluidic technology through the fusion of microfluidics and optics," Nature 442, 381-386 (2006). [CrossRef] [PubMed]
  14. C. Monat, P. Domachuk, and B. J. Eggleton, "Integrated optofluidics: A new river of light," Nat. Photonics 1, 106-114 (2007). [CrossRef]
  15. A. Fuerbach, P. Steinvurzel, J. A. Bolger, A. Nulsen, and B. J. Eggleton, "Nonlinear propagation effects in antiresonant high-index inclusion photonic crystal fibers," Opt. Lett. 30, 830-832 (2005). [CrossRef] [PubMed]
  16. C. R. Rosberg, F. H. Bennet, D. N. Neshev, P. D. Rasmussen, O. Bang, W. Krolikowski, A. Bjarklev, and Y. Kivshar, "Tunable diffraction and self-defocusing in liquid-filled photonic crystal fibers," Opt. Express 15, 12145-12150 (2007). [CrossRef] [PubMed]
  17. P. D. Rasmussen, A. A. Sukhorukov, D. N. Neshev, W. Krolikowski, O. Bang, J. Laegsgaard, and Y. Kivshar, "Spatiotemporal control of light by Bloch-mode dispersion in multi-core fibers," Opt. Express 16, 5878-5891 (2008). [CrossRef] [PubMed]
  18. B. T. Kuhlmey, B. J. Eggleton, and D. K. C. Wu, "Fluid-filled solid-core photonic bandgap fibers," J. Lightwave Technol. 27, 1617-1630 (2009). [CrossRef]
  19. L. Xiao, W. Jin, M. S. Demokan, H. L. Ho, Y. L. Hoo, and C. Zhao, "Fabrication of selective injection microstructured optical fibers with a conventional fusion splicer," Opt. Express 13, 9014-9022 (2005). [CrossRef] [PubMed]
  20. J. Bethge, A. Husakou, F. Mitschke, F. Noack, U. Griebner, G. Steinmeyer, and J. Herrmann, "Two-octave supercontinuum generation in a water-filled photonic crystal fiber," Opt. Express 18, 6230-6240 (2010). [CrossRef] [PubMed]
  21. A. Bozolan, C. J. S. de Matos, C. M. B. Cordeiro, E. M. dos Santos, and J. Travers, "Supercontinuum in a water-core photonic crystal fiber," Opt. Express 16, 9671-9676 (2008). [CrossRef] [PubMed]
  22. M. Heinrich, Y. V. Kartashov, L. P. R. Ramirez, A. Szameit, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, and L. Torner, "Observation of two-dimensional superlattice solitons," Opt. Lett. 34, 3701-3703 (2009). [CrossRef] [PubMed]
  23. M. Heinrich, Y. V. Kartashov, L. P. R. Ramirez, A. Szameit, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, and L. Torner, "Two-dimensional solitons at interfaces between binary superlattices and homogeneous lattices," Phys. Rev. A 80, 063832 (2009). [CrossRef]
  24. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, "Writing waveguides in glass with a femtosecond laser," Opt. Lett. 21, 1729-1731 (1996). [CrossRef] [PubMed]
  25. P. P. Ho, and R. R. Alfano, "Optical Kerr effect in liquids," Phys. Rev. A 20, 2170-2187 (1979). [CrossRef]
  26. J. W. Ellis, "The near infra-red absorption spectra of some organic liquids," Phys. Rev. 23, 48-62 (1924). [CrossRef]
  27. We chose CCl4 for our nonlinear experiments because with the available photonic crystal NL-2.3-790 and our liquids, CCl4 was the only one to provide anomalous dispersion at our pump wavelength of 1030nm.
  28. F. Ye, Y. V. Kartashov, B. Hu, and L. Torner, "Light bullets in Bessel optical lattices with spatially modulated nonlinearity," Opt. Express 17, 11328-11334 (2009). [CrossRef] [PubMed]
  29. S. Maruo, O. Nakamura, and S. Kawata, "Three-dimensional microfabrication with two-photon-absorbed photopolymerization," Opt. Lett. 22, 132-134 (1997). [CrossRef] [PubMed]
  30. MicroChem, http://www.microchem.com/products/su$_$eight.htm.
  31. Y. Wang, C. R. Liao, and D. N. Wang, "Femtosecond laser-assisted selective infiltration of microstructured optical fibers," Opt. Express 18, 18056-18060 (2010). [CrossRef] [PubMed]
  32. In principle, we operate at this wavelength under multimode conditions, but straight in coupling and a straight fiber supports the fundamental mode.
  33. NKT Photonics, http://www.nktphotonics.com/files/files/NL-23-790.pdf.
  34. H. H. Marvin, "The selective transmission and the dispersion of the liquid chlorides," Phys. Rev. 34, 161-186 (1912).
  35. A. Samoc, "Dispersion of refractive properties of solvents: Chloroform, toluene, benzene, and carbon disulfide in ultraviolet, visible, and near-infrared," J. Appl. Phys. 94, 6167-6174 (2003). [CrossRef]
  36. N. A. Mortensen, J. R. Folkenberg, M. D. Nielsen, and K. P. Hansen, "Modal cutoff and the V parameter in photonic crystal fibers," Opt. Lett. 28, 1879-1881 (2003). [CrossRef] [PubMed]
  37. N. K. T. Photonics, http://www.nktphotonics.com/files/files/LMA-8-100409.pdf.
  38. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botten, "Multipole method for microstructured optical fibers. I. Formulation," J. Opt. Soc. Am. B 19, 2322-2330 (2002). [CrossRef]
  39. B. T. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botten, C. Martijn de 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]
  40. J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006). [CrossRef]
  41. A. V. Husakou, and J. Hermann, "Supercontinuum generation of high-order solitons by fission in photonic crystal fibers," Phys. Rev. Lett. 87, 203901 (2001). [CrossRef] [PubMed]
  42. F. Hoos, T. P. Meyrath, S. Li, B. Braun, and H. Giessen, "Femtosecond 5-W Yb:KGW slab laser oscillator pumped by a single broad-area diode and its application as supercontinuum source," Appl. Phys. B 96, 5-10 (2009). [CrossRef]
  43. A. A. Voronin, V. P. Mitrokhin, A. A. Ivanov, A. B. Fedotov, D. A. Sidorov-Biryukov, V. I. Beloglazov, M. V. Alfimov, H. Ludvigsen, and A. M. Zheltikov, "Understanding the nonlinear-optical response of a liquid-core photonic-crystal fiber," Laser Phys. Lett. 7, 46-49 (2010). [CrossRef]
  44. N. Akhmediev, and M. Karlsson, "Cherenkov radiation emitted by solitons in optical fibers," Phys. Rev. A 51, 2602-2607 (1995). [CrossRef] [PubMed]
  45. Y. R. Shen, Principles of Nonlinear Optics (Wiley, Hoboken, 2003).
  46. R. Zhang, J. Teipel, and H. Giessen, "Theoretical design of a liquid-core photonic crystal fiber for supercontinuum generation," Opt. Express 14, 6800-6812 (2006). [CrossRef] [PubMed]
  47. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 2007).
  48. R. V. J. Raja, A. Husakou, J. Hermann, and K. Porsezian, "Supercontinuum generation in liquid-filled photonic crystal fiber with slow nonlinear response," J. Opt. Soc. Am. B 27, 1763-1768 (2010). [CrossRef]
  49. C. Conti, M. Schmidt, P. St. Russell, and F. Biancalana, "Linearons: highly non-instantaneous solitons in liquidcore photonic crystal fibers," arXiv:1010.0331v1 [physics.optics], http://arxiv.org/abs/1010.0331.
  50. M. Midrio, M. P. Singh, and C. G. Someda, "The space-filling mode of holey fibers: an analytical vectorial solution," J. Lightwave Technol. 18, 1031-1037 (2000). [CrossRef]
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