Abstract

We analyze the properties of HE2 surface plasmon polaritons on fiber-integrated gold, silver and copper nanowires and find a systematic blue-shift of the measured resonance wavelengths which we attribute to the emergence of a narrow nanometer-sized gap between the nanowire surface and the surrounding silica cladding. Our analysis relies on the determination of the nanogap width from the experimentally measured phase-matching wavelength by comparison with numerical simulations, revealing that these gaps are much smaller than expected from the bulk material considerations. This implies a diminished coefficient of thermal expansion along the radial direction that we believe results from the domination of interfacial van der Waals forces at high temperatures. These results are important for future fiber designs involving nanowires fabricated by pressure-assisted melt filling.

© 2017 Optical Society of America

1. Introduction

The excitation of surface plasmon polaritons (SPPs) on gold nanowires (NWs) has been observed in various types of hybrid optical fibers (HOFs) [1–3]. The guided NW-SPPs are closely related to their planar counterparts, traveling on helical trajectories with discrete helix angles along the wire surface and experiencing curvature-induced geometric momenta [4,5]. It was also shown that arrays of metal NWs impose plasmonic hybridization, leading to plasmonic supermodes and plasmonic band gaps [6–8]. So far, research has mostly targeted gold as the plasmonic metal to be integrated into optical fiber, with only minor effort being invested for investigating other metals such as silver [1], copper [9] or platinum [10]. One issue that has been regularly observed in experiments but has not been rigorously addressed so far is the systematic blue-shift of the measured phase-matching wavelength of the SPP and the fiber core mode [1,2,6,11]. This spectral blue-shift appears in all systems fabricated by either direct drawing or pressure-assisted melt filling and is typically associated with a nanometer-sized air gap (nanogap) between the capillary wall and the surface of the wire, imposed by the mismatch of the thermal expansion coefficients of silica and metals. The blue-shift originates from the partial location of the evanescent field of the SPP mode inside the air nanogap surrounding the nanowire. Since the relative permittivity of air is much smaller than that of silica (air: 1.0, silica: 2.1), the SPP mode experiences a smaller effective refractive index, which overall blue-shifts the plasmon dispersion curve and thus the crossing point of SPP and HE11-like mode.

Here, we present a detailed analysis of these nanogaps and their influence on the plasmonic properties of the hybrid fiber, with a focus on the HE2 SPP mode. This study will play an important role for novel HOF materials [12] and designs including fiber-integrated polarizers and polarization converters [13] and directional couplers [14,15].

2. Fiber design and sample preparation

The HOF geometries considered here consist of a dielectric core and a parallel metal NW (see Fig. 1), which are prepared by fiber drawing and subsequent post-processing. The pristine silica fibers possess a GeO2-doped parabolic graded-index core (diameter D, maximum doping level: 9.5 mol %) with a parallel cylindrical hole (center-to-center distance Λ, diameter dhole). Two different types of such modified graded index fibers (MGIFs) were fabricated (MGIF1: D = 1.7 µm, Λ = 3.8 µm; MGIF2: D = 2.9 µm, Λ = 4.9 µm), exhibiting different light guiding characteristics (e.g., cutoff wavelength). The hole diameter was adjusted during fiber drawing in the range of 0.3 µm < dhole < 2.0 µm by changing the applied air pressure.

 figure: Fig. 1

Fig. 1 Sketch of hybrid fiber being composed of a metallic nanowire (yellow) and a parallel-running graded-index core (blue) separated by a center-to-center distance Λ. The green area highlights the nanogap which is formed due to thermal contraction of the NW during fabrication.

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2.1. Nanowire fabrication

Pressure-assisted melt filling (PAMF) [6] was used to press liquid gold, silver or copper into the empty hole of the MGIFs at appropriate temperatures (see Table 1). The sample fabrication procedure involves (i) placing a few millimeter long bulk metal wire (diameter: 50 µm) into a capillary (inner diameter ≈ 80 µm), (ii) splicing this arrangement to an intermediate capillary (inner diameter ≈ 20 µm), (iii) splicing this combination to the MGIF and (iv) heating it in order to melt the metal and pressing it into the empty hole via Argon gas. The additional step (ii) yields mechanically stable splices through better matching of the hole diameters since a direct splice of the 80 µm capillary to the MGIF can yield weak connections. Oxidation or other chemical reactions were prevented by collapsing the hole of the MGIF at its open side and evacuating the system between step (iii) and (iv) for several hours at 600 °C.

Tables Icon

Table 1. Viscosity, surface tension and contact angle for gold, silver and copper at the filling temperature Tfill.

The filling dynamics within PAMF are governed by the Washburn equation, allowing to determine the filling time [16]

tfill4ηdholeγcos(θ)+dhole2p/4L2,
required to fill a hole of diameter dholeover a length L at pressure p (gravity effects are negligible). The viscosity η, surface tension γ and contact angle θ of gold, silver and copper are summarized in Table 1. For typical hole diameters of 1 µm and a pressure of 200 bar, the time to fill a 30 cm sample is of the order of a few minutes.

2.2. Formation of nanogaps

The linear coefficient of thermal expansion (CTE) of fused silica is comparably small and can be assumed to be constant between room and filling temperature Tfill, with an average value of αSiO2 = 0.5 × 10−6 K−1 [26]. However, metals like gold, silver and copper typically exhibit CTEs more than one order of magnitude larger than that of silica. This mismatch of the CTEs suggests the formation of a nanogap between the surfaces of the wire and the hole during cooling to ambient temperature (293 K) after PAMF. The width w of this nanogap can be calculated by [27]

w=dhole2([A1αSiO2][Tm293K]+A2[Tm293K]2).
Here, A1 and A2 are fit parameters (Table 2) and Tm is the melting temperature (in Kelvin). The resulting relative gap width w/dhole is listed in Table 2, suggesting the emergence of gap widths in the magnitude of 10 nm per micrometer of hole diameter.

Tables Icon

Table 2. Fit parameters A1 and A2 in Eq. (2) for gold, silver and copper [27] as well as the resulting relative gap width for a cooling from the melting temperature Tm to room temperature.

3. Experiments

In order to investigate the existence and the spectral influence of a possible nanogap around the metal NW, the attenuation spectra of several gold-, silver- and copper-filled MGIFs with different hole diameters were measured. It is well-known from experiments and numerical simulation that the attenuation of the fundamental core mode drastically increases around the phase-matching wavelength. In this study we want to focus on the interaction of the HE11 core mode with the HE2 NW-SPP.

3.1. Experimental setup

The optical characterization of the MGIFs relies on measuring the phase-matching wavelength between the fundamental fiber core mode and the HE2 SPP using the cutback technique (setup shown in Fig. 2). The input side of the transmission setup is composed of an unpolarized supercontinuum source (NKT Photonics SuperK COMPACT) and a combination of mirrors (M1, M2), a linear polarizer (LP) and a half-wave plate (HWP) for beam and polarization control. Efficient light coupling into the sample was ensured by a 40× objective (O1, NA=0.65). Typical sample lengths were about 40 cm, with an unfilled part at the input side (length: ~20 cm) in order to strip off undesired cladding light by applying mode-stripping gel. The output light is collimated using a 60× microscope objective (O2, NA=0.90) and directed into a multimode fiber (MMF) via another objective (O3, NA=0.25). An aperture (I1) is inserted into the beam path to spatially block the light propagating in the cladding, which is excited at the sample input in addition to the dielectric core mode. The collected light is finally analyzed by an optical spectrum analyzer (OSA).

 figure: Fig. 2

Fig. 2 Setup for measureming the spectral distribution of the transmission of the fiber samples. The spectral attenuation was determined using a cutback technique. Details of the experimental setup and experimental methods are given in the main text.

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3.2. Experimental results

In this work we investigated eight samples filled with gold, silver and copper. Fig. 3(b) shows an example polarization-resolved attenuation spectrum of a silver-filled MGIF1 (hole diameter: 380 nm). A distinct increase of the attenuation at around 614 nm is observed for both polarization states. This attenuation peak originates from a coupling of the fundamental core mode and the HE2 SPP on the silver NW, as confirmed by finite-element method (FEM) simulations. As Fig. 3(a) shows, it is found that if no nanogap between the silica wall and the wire is considered, the simulated attenuation peak is located around 630 nm, being 16 nm longer than observed in the experiment. A narrow air gap of constant width w = 0.8 nm around the wire shifts the phase-matching position towards shorter wavelengths and matches well with the experimental results. It is important to note that the centered alignment of the NW inside the hole is an idealized approximation since the NW necessarily touches the wall. The position of the NW strongly affects the magnitude of the attenuation but, has only negligible influence on the phase-matching wavelength.

 figure: Fig. 3

Fig. 3 Comparison of simulations and measurements of a silver-filled MGIF including a NW of diameter of 380 nm. (a) Spectral distribution of real parts of the calculated effective indices of the shifted and non-shifted HE2 SPP (green lines) and the HE11-like fundamental core modes (blue solid lines). The difference between both polarizations is smaller than 10−5 in the investigated spectral window. The solid black line represents the refractive index of bulk silica. (b) Attenuation spectra of the x-polarized (blue lines) and y-polarized (red lines) core modes. Solid lines represent simulations, while the dotted lines refer to the measurements. The vertical dashed line corresponds to the quasi-cutoff wavelength using Eq. 5 from [5].

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Using FEM simulations we identified two origins of the different loss magnitudes of the experimental data compared to calculations: First, discontinuities of the NW along the fiber reduce the total amount of metal the optical mode interacts with during propagation. Secondly, the transverse position of the nanowire inside the hole changes randomly along the sample length. To analyze the influence of the transverse NW position we performed example FEM simulations (geometry MGIF1, inset of Fig. 3) for the situation of a centered NW with a azimuthally uniform nanogap width (4.3 nm, case i), a NW touching the wall at the location facing the fiber core (case ii) and a NW touching the wall opposite to the core (case iii). All three cases have their resonance at around the same wavelength (resonance wavelength difference is less than 1 nm) but with different loss magnitudes. Our simulations also showed that the transverse alignment of the wire inside the hole has no influence on the spectral bandwidth of the resonance peak, as verified by calculating the average of the three above-mentioned cases of wire location inside the hole. The partial filling along the fiber axis (i.e., the junctions between the filled and unfilled parts) was not included into the simulations, as preliminary simulations revealed that the overlap of the dielectric-type modes in the filled and unfilled sections is >90 %, indicating that an excitation of the plasmonic-like mode in the wire section can be neglected [6].

4. Determination of the nanogap width

For all simulations the permittivities of pure silica and Germanium-doped silica were obtained from a Sellmeier equation [28,29], while the permittivity of the metals has been modeled using a Drude plus two critical points (D2CP) model [30]:

ε=ε1λp2(1/λ2+i/γpλ)+k=12Akλk[eiϕk1/λk1/λiγk+eiϕk1/λk+1/λ+i/γk].
While the model parameters for gold and silver can be found in the literature [31, 32], the corresponding values for the permittivity of copper have been fitted to experimental data [33] in this work, yielding an well matching analytic expression for the dielectric function of copper for the first time. The D2CP parameters for all three metals are listed in Table 3.

Tables Icon

Table 3. Fit parameters for the D2CP model of the permittivity for gold, silver and copper.

In order to determine the actual width of the nanogap inside a fiber sample, a full-vectorial transfer-matrix method was utilized [34], treating the fiber core and the metal wire as two independent waveguides. In a first step, the effective index of the fundamental dielectric core mode nHE11 was calculated at the experimentally observed resonance wavelength λr by a discretization of the parabolic refractive index profile (Fig. 1(c)) into 15 concentric layers. Secondly, the coaxially wire/nanogap/silica system was solved at the phase-matching condition Re(neffSPP,λr)=Re(neffHE11,λr) as a function of w and Im(neffSPP) in order to find the gap width matching the measured blue-shift. Secondly, the coaxially wire/nanogap/silica system was solved at the phase-matching condition Re(neffSPP,λr)=Re(neffHE11,λr) as a function of the gap width w and Im(neffSPP) in order to find the gap width matching the measured blue-shift, where neffSPP and neffHE11 is the effective refractive index of the SPP and the fundamental core mode, respectively. The resulting absolute and relative nanogap widths for all fiber samples are listed in Table 4. Because w naturally vanishes for dhole → 0, an offset-free linear function was fitted to the estimated gap width, yielding values w/dhole of 4.3(3.6, 4.8) nm/µm, 3.3(2.7, 3.8) nm/µm and 4.4(3.6, 5.2) nm/µm for gold, silver and copper, respectively (last column in Table 4).

Tables Icon

Table 4. Overview of measured resonance wavelengths λr and the resulting calculated gap widths w for all investigated hole diameters dhole. The shaded row corresponds to the sample analyzed in Fig. 3

The error of the determined gap width was estimated by repeating the calculations at the lower and upper limit of the error interval of dhole and λr. Based on these values the phase-matching wavelengths for all hole diameters between 300 nm and 1400 nm were calculated and are shown in Fig. 4. The minimum and maximum values for the phase-matching wavelength correspond to simulations assuming a gap width obtained from Eq. (2) (dahsed lines in Fig. 4) and the absence of a gap (dotted lines in Fig. 4), respectively. The experimentally observed phase-matching wavelengths consistently show excellent agreement match with the simulations when the appropriate nanogaps are considered. However, it is important to note that the experimentally observed phase-matching wavelengths are shorter than those calculated neglecting the air gap but longer than those assuming the CTE of the bulk metal. This indirectly proves the existence of a narrow nanogap around the NW but also implies that its width must be smaller than predicted by the bulk CTE. It needs to be pointed out that to our knowledge there is no approach to study nanogaps of these dimensions directly, as cleaving fibers with incorporated NWs leads to the formation of nanotips that typically start tapering at a position inside the capillary, so that the nanogap dimensions cannot be visually discerned [15,35].

 figure: Fig. 4

Fig. 4 Dependence of phase-matching wavelength on hole diameter ((a) gold, (b) silver and (c) copper). The blue solid lines correspond to simulations using the fitted relative gap width w/dhole based on determined values shown in Table 4. The shaded areas cover the range between the minimum and maximum values of the fitted parameters. The broken lines represent the phase-matching wavelengths assuming no gap (red dotted) and the values from Table 2 (green dashed). In all plots the blue circles refer to the measured phase-matching wavelengths.

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A possible explanation for this phenomenon is the very small roughness of the inner surface of the hole which is caused by frozen-in surface capillary waves, typically of the order of a few hundred picometers [36]. Since the capillary was filled with liquid metal at high pressure, it can be assumed that the average distance h between the surfaces of the hole and NW is of the order of the surface roughness (see Fig. 5). The attracting van der Waals force (per unit area) between the two surfaces can be estimated by FW = A/6πh3, with A being the material-dependent Hamaker constant (typically in the magnitude of 10−19 J for solids [37]). Assuming an average distance h ≈ 0.2 nm, the van der Waals force per unit area FW (which attracts the two surfaces) is ∼ 109 N/m2. However, a counteracting thermal-contraction-induced force Fc at a given temperature T also exists, and can be roughly estimated to be Fc = E(TmT)(ααSiO2) [38] and is assumed to vanish at the melting temperature of the metal. Here, E is Young’s modulus and α is the linear CTE of the nanowire material. Literature values of E for gold, silver and copper are 78 GPa, 83 GPa and 130 GPa [39] respectively, yielding contraction forces of the same magnitude as the van der Waals force for a complete cooling to room temperature. Therefore, the cooling process can be divided into two phases as follows: (i) The NW cools from the melting temperature to a threshold temperature Ttr without detaching from the silica wall because Fc < FW. In this phase the contraction of the NW is constrained and it is shrinking solely along its axial direction (see Fig. 5(a)). (ii) During cooling the temperature T drops below Ttr where Fc > FW. Below this temperature the NW detaches from the silica wall and contracts in both the axial and radial direction (see Fig. 5(b)). As a result, the NW is not shrinking radially during the entire cooling period, but only below the threshold temperature. This leads to an effectively smaller gap width than predicted by Eq. (2) which may also be affected by other process conditions, e.g., cooling rate.

 figure: Fig. 5

Fig. 5 Illustration of the NW contraction (a) above and (b) below the threshold temperature. The solid horizontal lines correspond to an mean level of the rough surfaces of the hole and NW, respectively, separated by the average distance h.

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5. Conclusion

In conclusion, we have analyzed the properties of gold, silver and copper nanowires in MGIFs and determined the spectral attenuation of the fundamental core mode, showing a blue-shift of the resonance wavelength compared to finite-element simulations. We attribute this discrepancy to the emergence of an nano-sized air gap between wire surface and silica wall, which is caused by the mismatch of the CTE between metals and silica. Our simulations showed that the spectral blue-shift can indeed be explained by this nanogaps. However, using a detailed analysis procedure it was found that their width is smaller by approximately 50 % to what is expected from the literature values of the CTE in order to fit the experiments. We explained this effect by the interaction of van der Waals and contraction forces at the metal-silica interface, constraining the radial contraction of the metal during cooling and resulting in an effectively smaller gap width. Future studies will aim to analysis other filling metals using our nanogap analysis procedure with one goal being the integration of a plasmonically relevant metal or alloy with a negligible air gap width.

References and links

1. M. A. Schmidt, L. 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,” Phys. Rev. B 77(3), 033417 (2008). [CrossRef]  

2. H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. Prill Sempere, and P. St. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93(11), 111102 (2008). [CrossRef]  

3. M. A. Schmidt, A. Argyros, and F. Sorin, “Hybrid Optical Fibers – An Innovative Platform for In-Fiber Photonic Devices,” Adv. Opt. Mater. 4(1), 13–36 (2016). [CrossRef]  

4. M. A. Schmidt and P. St. J. Russell, “Long-range spiralling surface plasmon modes on metallic nanowires,” Opt. Express 16(18), 13617–13623 (2008). [CrossRef]   [PubMed]  

5. R. Spittel, P. Uebel, H. Bartelt, and M. A. Schmidt, “Curvature-induced geometric momenta: the origin of waveguide dispersion of surface plasmons on metallic wires,” Opt. Express 23(9), 12174–12188 (2015). [CrossRef]   [PubMed]  

6. H. W. Lee, M. A. Schmidt, R. F. Russell, N. Y. Joly, H. K. Tyagi, P. Uebel, and P. St. J. Russell, “Pressure-assisted melt-filling and optical characterization of Au nano-wires in microstructured fibers,” Opt. Express 19(13), 12180–12189 (2011). [CrossRef]   [PubMed]  

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(12), 1647–1649 (2007). [CrossRef]   [PubMed]  

8. R. Spittel, H. Bartelt, and M. A. Schmidt, “A semi-analytical model for the approximation of plasmonic bands in arrays of metal wires in photonic crystal fibers,” Opt. Express 22(10), 11741–11753 (2014). [CrossRef]   [PubMed]  

9. J. Hou, D. Bird, A. George, S. Maier, B. T. Kuhlmey, and J. C. Knight, “Metallic mode confinement in microstructured fibres,” Opt. Express 16(9), 5983–5990 (2008). [CrossRef]   [PubMed]  

10. R. He, P. J. A. Sazio, A. C. Peacock, N. Healy, J. R. Sparks, M. Krishnamurthi, V. Gopalan, and J. V. Badding, “Integration of gigahertz-bandwidth semiconductor devices inside microstructured optical fibres,” Nat. Photon. 6(3), 174–179 (2012). [CrossRef]  

11. H. W. Lee, M. A. Schmidt, and P. St. J. Russell, “Excitation of a nanowire “molecule” in gold-filled photonic crystal fiber,” Opt. Lett. 37(14), 2946–2948 (2012). [CrossRef]   [PubMed]  

12. C. Jain, A. Tuniz, K. Reuther, T. Wieduwilt, M. Rettenmayr, and M. A. Schmidt, “Micron-sized gold-nickel alloy wire integrated silica optical fibers,” Opt. Mat. Express 6(6), 1790–1799 (2016). [CrossRef]  

13. A. Tuniz, C. Jain, S. Weidlich, and M. A. Schmidt, “Broadband azimuthal polarization conversion using gold nanowire enhanced step-index fiber,” Opt. Lett. 41(3), 448–451 (2016). [CrossRef]   [PubMed]  

14. A. Tuniz and M. A. Schmidt, “Broadband efficient directional coupling to short-range plasmons: towards hybrid fiber nanotips,” Opt. Express 24(7), 7507–7524 (2016). [CrossRef]   [PubMed]  

15. A. Tuniz, M. Chemnitz, J. Delith, S. Weidlich, and M. A. Schmidt, “Hybrid-mode-assisted long-distance excitation of short-range surface plasmons in a nanotip-enhanced step-index fiber,” Nano Lett. 17(2), 631–637 (2017). [CrossRef]  .

16. E. W. Washburn, “The dynamics of capillary flow,” Phys. Rev. 17(3), 273–283 (1921). [CrossRef]  

17. D. Ofte, “The viscosities of liquid uranium, gold and lead,” J. Nucl. Mater. 22(1), 28–32 (1967). [CrossRef]  

18. I. Egry, G. Lohoefer, and G. Jacobs, “Surface tension of liquid metals: results from measurements on ground and in space,” Phys. Rev. Lett. 75(22), 4043 (1995). [CrossRef]   [PubMed]  

19. R. Sangiorgi, M. L. Muolo, D. Chatain, and N. Eustathopoulos, “Wettability and work of adhesion of nonreactive liquid metals on silica,” J. Am. Ceram. Soc. 71(9), 742–748 (1988). [CrossRef]  

20. K. Gering and F. Sauerwald, “Über die innere Reibung geschmolzener Metalle und Legierungen. VI. Die innere Reibung von Pb, Cd, Zn, Ag, Sn, K, Na und die Frage der Strukturviskosität von Amalgamen,” Z. Anorg. Allg. Chem. 223(2), 204–208 (1935). [CrossRef]  

21. G. Bernard and C. H. P. Lupis, “The surface tension of liquid silver alloys: Part I. silver-gold alloys,” Metall. Trans. 2(2), 555–559 (1971). [CrossRef]  

22. R. Sangiorgi, M. L. Muolo, and A. Passerone, “Reactivity of vitreous silica in contact with liquid metals,” Rev. Int. Hautes Temp. Refract. 22, 175–184 (1985).

23. M. J. Assael, A. E. Kalyva, K. D. Antoniadis, R. M. Banish, I. Egry, J. Wu, E. Kaschnitz, and W. A. Wakeham, “Reference data for the density and viscosity of liquid copper and liquid tin,” J. Phys. Chem. Ref. Data 39(3), 033105 (2010). [CrossRef]  

24. D. A. Harrison, D. Yan, and S. Blair, “The surface tension of liquid copper,” J. Chem. Thermodyn. 9(12), 1111–1119 (1977). [CrossRef]  

25. J. V. Naidich, “The wettability of solids by liquid metals,” in Progress in surface and membrane science Vol. 14 (Academic, 1981), pp. 353–484. [CrossRef]  

26. N. P. Bansal and R. H. Doremus, Handbook of Glass Properties (Academic, 1986).

27. I. Suh, H. Ohta, and Y. Waseda, “High-temperature thermal expansion of six metallic elements measured by dilatation method and X-ray diffraction,” J. Mater. Sci. 23(2), 757–760 (1988). [CrossRef]  

28. I. H. Malitson, “Interspecimen Comparison of the Refractive Index of Fused Silica,” J. Opt. Soc. Am. A 55(10), 1205–1209 (1965). [CrossRef]  

29. J. W. Fleming, “Dispersion in GeO2–SiO2 glasses,” Appl. Opt. 23(24), 4486–4493 (1984). [CrossRef]   [PubMed]  

30. P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125(16), 164705 (2006). [CrossRef]   [PubMed]  

31. P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “Erratum: An analytic model for the optical properties of gold,” J. Chem. Phys. 127(18), 9901 (2007). [CrossRef]  

32. A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, “A new model of dispersion for metals leading to a more accurate modeling of plasmonic structures using the FDTD method,” Appl. Phys. A 103(3), 849–853 (2011). [CrossRef]  

33. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370 (1972). [CrossRef]  

34. T. Grujic, B. T. Kuhlmey, C. M. de Sterke, and C. G. Poulton, “Modelling of photonic crystal fiber based on layered inclusions,” J. Opt. Soc. Am. B 26(10), 1852–1861 (2009). [CrossRef]  

35. P. Uebel, S. T. Bauerschmidt, M. A. Schmidt, and P. St. J. Russell, “A gold-nanotip optical fiber for plasmon-enhanced near-field detection,” Appl. Phys. Lett. 103(2), 021101 (2013). [CrossRef]  

36. C. Brun, X. Buet, B. Bresson, M. S. Capelle, M. Ciccotti, A. Ghomari, P. Lecomte, J. P. Roger, M. N. Petrovich, F. Poletti, D. J. Richardson, D. Vandembroucq, and G. Tessier, “Picometer-scale surface roughness measurements inside hollow glass fibres,” Opt. Express 22(24), 29554–29567 (2014).

37. J. N. Israelachvili, Intermolecular and Surface Forces (Academic, 2011), Chap. 13.

38. B. Harris, “Shrinkage stresses in glass/resin composites,” J. Mater. Sci. 13(1), 173–177 (1978). [CrossRef]  

39. G. Kaye and T. Laby, Tables of Physical and Chemical Constants (Longman, 1995).

References

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  1. M. A. Schmidt, L. 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,” Phys. Rev. B 77(3), 033417 (2008).
    [Crossref]
  2. H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. Prill Sempere, and P. St. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93(11), 111102 (2008).
    [Crossref]
  3. M. A. Schmidt, A. Argyros, and F. Sorin, “Hybrid Optical Fibers – An Innovative Platform for In-Fiber Photonic Devices,” Adv. Opt. Mater. 4(1), 13–36 (2016).
    [Crossref]
  4. M. A. Schmidt and P. St. J. Russell, “Long-range spiralling surface plasmon modes on metallic nanowires,” Opt. Express 16(18), 13617–13623 (2008).
    [Crossref] [PubMed]
  5. R. Spittel, P. Uebel, H. Bartelt, and M. A. Schmidt, “Curvature-induced geometric momenta: the origin of waveguide dispersion of surface plasmons on metallic wires,” Opt. Express 23(9), 12174–12188 (2015).
    [Crossref] [PubMed]
  6. H. W. Lee, M. A. Schmidt, R. F. Russell, N. Y. Joly, H. K. Tyagi, P. Uebel, and P. St. J. Russell, “Pressure-assisted melt-filling and optical characterization of Au nano-wires in microstructured fibers,” Opt. Express 19(13), 12180–12189 (2011).
    [Crossref] [PubMed]
  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(12), 1647–1649 (2007).
    [Crossref] [PubMed]
  8. R. Spittel, H. Bartelt, and M. A. Schmidt, “A semi-analytical model for the approximation of plasmonic bands in arrays of metal wires in photonic crystal fibers,” Opt. Express 22(10), 11741–11753 (2014).
    [Crossref] [PubMed]
  9. J. Hou, D. Bird, A. George, S. Maier, B. T. Kuhlmey, and J. C. Knight, “Metallic mode confinement in microstructured fibres,” Opt. Express 16(9), 5983–5990 (2008).
    [Crossref] [PubMed]
  10. R. He, P. J. A. Sazio, A. C. Peacock, N. Healy, J. R. Sparks, M. Krishnamurthi, V. Gopalan, and J. V. Badding, “Integration of gigahertz-bandwidth semiconductor devices inside microstructured optical fibres,” Nat. Photon. 6(3), 174–179 (2012).
    [Crossref]
  11. H. W. Lee, M. A. Schmidt, and P. St. J. Russell, “Excitation of a nanowire “molecule” in gold-filled photonic crystal fiber,” Opt. Lett. 37(14), 2946–2948 (2012).
    [Crossref] [PubMed]
  12. C. Jain, A. Tuniz, K. Reuther, T. Wieduwilt, M. Rettenmayr, and M. A. Schmidt, “Micron-sized gold-nickel alloy wire integrated silica optical fibers,” Opt. Mat. Express 6(6), 1790–1799 (2016).
    [Crossref]
  13. A. Tuniz, C. Jain, S. Weidlich, and M. A. Schmidt, “Broadband azimuthal polarization conversion using gold nanowire enhanced step-index fiber,” Opt. Lett. 41(3), 448–451 (2016).
    [Crossref] [PubMed]
  14. A. Tuniz and M. A. Schmidt, “Broadband efficient directional coupling to short-range plasmons: towards hybrid fiber nanotips,” Opt. Express 24(7), 7507–7524 (2016).
    [Crossref] [PubMed]
  15. A. Tuniz, M. Chemnitz, J. Delith, S. Weidlich, and M. A. Schmidt, “Hybrid-mode-assisted long-distance excitation of short-range surface plasmons in a nanotip-enhanced step-index fiber,” Nano Lett. 17(2), 631–637 (2017). .
    [Crossref]
  16. E. W. Washburn, “The dynamics of capillary flow,” Phys. Rev. 17(3), 273–283 (1921).
    [Crossref]
  17. D. Ofte, “The viscosities of liquid uranium, gold and lead,” J. Nucl. Mater. 22(1), 28–32 (1967).
    [Crossref]
  18. I. Egry, G. Lohoefer, and G. Jacobs, “Surface tension of liquid metals: results from measurements on ground and in space,” Phys. Rev. Lett. 75(22), 4043 (1995).
    [Crossref] [PubMed]
  19. R. Sangiorgi, M. L. Muolo, D. Chatain, and N. Eustathopoulos, “Wettability and work of adhesion of nonreactive liquid metals on silica,” J. Am. Ceram. Soc. 71(9), 742–748 (1988).
    [Crossref]
  20. K. Gering and F. Sauerwald, “Über die innere Reibung geschmolzener Metalle und Legierungen. VI. Die innere Reibung von Pb, Cd, Zn, Ag, Sn, K, Na und die Frage der Strukturviskosität von Amalgamen,” Z. Anorg. Allg. Chem. 223(2), 204–208 (1935).
    [Crossref]
  21. G. Bernard and C. H. P. Lupis, “The surface tension of liquid silver alloys: Part I. silver-gold alloys,” Metall. Trans. 2(2), 555–559 (1971).
    [Crossref]
  22. R. Sangiorgi, M. L. Muolo, and A. Passerone, “Reactivity of vitreous silica in contact with liquid metals,” Rev. Int. Hautes Temp. Refract. 22, 175–184 (1985).
  23. M. J. Assael, A. E. Kalyva, K. D. Antoniadis, R. M. Banish, I. Egry, J. Wu, E. Kaschnitz, and W. A. Wakeham, “Reference data for the density and viscosity of liquid copper and liquid tin,” J. Phys. Chem. Ref. Data 39(3), 033105 (2010).
    [Crossref]
  24. D. A. Harrison, D. Yan, and S. Blair, “The surface tension of liquid copper,” J. Chem. Thermodyn. 9(12), 1111–1119 (1977).
    [Crossref]
  25. J. V. Naidich, “The wettability of solids by liquid metals,” in Progress in surface and membrane science Vol. 14 (Academic, 1981), pp. 353–484.
    [Crossref]
  26. N. P. Bansal and R. H. Doremus, Handbook of Glass Properties (Academic, 1986).
  27. I. Suh, H. Ohta, and Y. Waseda, “High-temperature thermal expansion of six metallic elements measured by dilatation method and X-ray diffraction,” J. Mater. Sci. 23(2), 757–760 (1988).
    [Crossref]
  28. I. H. Malitson, “Interspecimen Comparison of the Refractive Index of Fused Silica,” J. Opt. Soc. Am. A 55(10), 1205–1209 (1965).
    [Crossref]
  29. J. W. Fleming, “Dispersion in GeO2–SiO2 glasses,” Appl. Opt. 23(24), 4486–4493 (1984).
    [Crossref] [PubMed]
  30. P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125(16), 164705 (2006).
    [Crossref] [PubMed]
  31. P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “Erratum: An analytic model for the optical properties of gold,” J. Chem. Phys. 127(18), 9901 (2007).
    [Crossref]
  32. A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, “A new model of dispersion for metals leading to a more accurate modeling of plasmonic structures using the FDTD method,” Appl. Phys. A 103(3), 849–853 (2011).
    [Crossref]
  33. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370 (1972).
    [Crossref]
  34. T. Grujic, B. T. Kuhlmey, C. M. de Sterke, and C. G. Poulton, “Modelling of photonic crystal fiber based on layered inclusions,” J. Opt. Soc. Am. B 26(10), 1852–1861 (2009).
    [Crossref]
  35. P. Uebel, S. T. Bauerschmidt, M. A. Schmidt, and P. St. J. Russell, “A gold-nanotip optical fiber for plasmon-enhanced near-field detection,” Appl. Phys. Lett. 103(2), 021101 (2013).
    [Crossref]
  36. C. Brun, X. Buet, B. Bresson, M. S. Capelle, M. Ciccotti, A. Ghomari, P. Lecomte, J. P. Roger, M. N. Petrovich, F. Poletti, D. J. Richardson, D. Vandembroucq, and G. Tessier, “Picometer-scale surface roughness measurements inside hollow glass fibres,” Opt. Express 22(24), 29554–29567 (2014).
  37. J. N. Israelachvili, Intermolecular and Surface Forces (Academic, 2011), Chap. 13.
  38. B. Harris, “Shrinkage stresses in glass/resin composites,” J. Mater. Sci. 13(1), 173–177 (1978).
    [Crossref]
  39. G. Kaye and T. Laby, Tables of Physical and Chemical Constants (Longman, 1995).

2017 (1)

A. Tuniz, M. Chemnitz, J. Delith, S. Weidlich, and M. A. Schmidt, “Hybrid-mode-assisted long-distance excitation of short-range surface plasmons in a nanotip-enhanced step-index fiber,” Nano Lett. 17(2), 631–637 (2017). .
[Crossref]

2016 (4)

C. Jain, A. Tuniz, K. Reuther, T. Wieduwilt, M. Rettenmayr, and M. A. Schmidt, “Micron-sized gold-nickel alloy wire integrated silica optical fibers,” Opt. Mat. Express 6(6), 1790–1799 (2016).
[Crossref]

A. Tuniz, C. Jain, S. Weidlich, and M. A. Schmidt, “Broadband azimuthal polarization conversion using gold nanowire enhanced step-index fiber,” Opt. Lett. 41(3), 448–451 (2016).
[Crossref] [PubMed]

A. Tuniz and M. A. Schmidt, “Broadband efficient directional coupling to short-range plasmons: towards hybrid fiber nanotips,” Opt. Express 24(7), 7507–7524 (2016).
[Crossref] [PubMed]

M. A. Schmidt, A. Argyros, and F. Sorin, “Hybrid Optical Fibers – An Innovative Platform for In-Fiber Photonic Devices,” Adv. Opt. Mater. 4(1), 13–36 (2016).
[Crossref]

2015 (1)

2014 (2)

2013 (1)

P. Uebel, S. T. Bauerschmidt, M. A. Schmidt, and P. St. J. Russell, “A gold-nanotip optical fiber for plasmon-enhanced near-field detection,” Appl. Phys. Lett. 103(2), 021101 (2013).
[Crossref]

2012 (2)

R. He, P. J. A. Sazio, A. C. Peacock, N. Healy, J. R. Sparks, M. Krishnamurthi, V. Gopalan, and J. V. Badding, “Integration of gigahertz-bandwidth semiconductor devices inside microstructured optical fibres,” Nat. Photon. 6(3), 174–179 (2012).
[Crossref]

H. W. Lee, M. A. Schmidt, and P. St. J. Russell, “Excitation of a nanowire “molecule” in gold-filled photonic crystal fiber,” Opt. Lett. 37(14), 2946–2948 (2012).
[Crossref] [PubMed]

2011 (2)

H. W. Lee, M. A. Schmidt, R. F. Russell, N. Y. Joly, H. K. Tyagi, P. Uebel, and P. St. J. Russell, “Pressure-assisted melt-filling and optical characterization of Au nano-wires in microstructured fibers,” Opt. Express 19(13), 12180–12189 (2011).
[Crossref] [PubMed]

A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, “A new model of dispersion for metals leading to a more accurate modeling of plasmonic structures using the FDTD method,” Appl. Phys. A 103(3), 849–853 (2011).
[Crossref]

2010 (1)

M. J. Assael, A. E. Kalyva, K. D. Antoniadis, R. M. Banish, I. Egry, J. Wu, E. Kaschnitz, and W. A. Wakeham, “Reference data for the density and viscosity of liquid copper and liquid tin,” J. Phys. Chem. Ref. Data 39(3), 033105 (2010).
[Crossref]

2009 (1)

2008 (4)

J. Hou, D. Bird, A. George, S. Maier, B. T. Kuhlmey, and J. C. Knight, “Metallic mode confinement in microstructured fibres,” Opt. Express 16(9), 5983–5990 (2008).
[Crossref] [PubMed]

M. A. Schmidt and P. St. J. Russell, “Long-range spiralling surface plasmon modes on metallic nanowires,” Opt. Express 16(18), 13617–13623 (2008).
[Crossref] [PubMed]

M. A. Schmidt, L. 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,” Phys. Rev. B 77(3), 033417 (2008).
[Crossref]

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. Prill Sempere, and P. St. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93(11), 111102 (2008).
[Crossref]

2007 (2)

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(12), 1647–1649 (2007).
[Crossref] [PubMed]

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “Erratum: An analytic model for the optical properties of gold,” J. Chem. Phys. 127(18), 9901 (2007).
[Crossref]

2006 (1)

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125(16), 164705 (2006).
[Crossref] [PubMed]

1995 (1)

I. Egry, G. Lohoefer, and G. Jacobs, “Surface tension of liquid metals: results from measurements on ground and in space,” Phys. Rev. Lett. 75(22), 4043 (1995).
[Crossref] [PubMed]

1988 (2)

R. Sangiorgi, M. L. Muolo, D. Chatain, and N. Eustathopoulos, “Wettability and work of adhesion of nonreactive liquid metals on silica,” J. Am. Ceram. Soc. 71(9), 742–748 (1988).
[Crossref]

I. Suh, H. Ohta, and Y. Waseda, “High-temperature thermal expansion of six metallic elements measured by dilatation method and X-ray diffraction,” J. Mater. Sci. 23(2), 757–760 (1988).
[Crossref]

1985 (1)

R. Sangiorgi, M. L. Muolo, and A. Passerone, “Reactivity of vitreous silica in contact with liquid metals,” Rev. Int. Hautes Temp. Refract. 22, 175–184 (1985).

1984 (1)

1978 (1)

B. Harris, “Shrinkage stresses in glass/resin composites,” J. Mater. Sci. 13(1), 173–177 (1978).
[Crossref]

1977 (1)

D. A. Harrison, D. Yan, and S. Blair, “The surface tension of liquid copper,” J. Chem. Thermodyn. 9(12), 1111–1119 (1977).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370 (1972).
[Crossref]

1971 (1)

G. Bernard and C. H. P. Lupis, “The surface tension of liquid silver alloys: Part I. silver-gold alloys,” Metall. Trans. 2(2), 555–559 (1971).
[Crossref]

1967 (1)

D. Ofte, “The viscosities of liquid uranium, gold and lead,” J. Nucl. Mater. 22(1), 28–32 (1967).
[Crossref]

1965 (1)

I. H. Malitson, “Interspecimen Comparison of the Refractive Index of Fused Silica,” J. Opt. Soc. Am. A 55(10), 1205–1209 (1965).
[Crossref]

1935 (1)

K. Gering and F. Sauerwald, “Über die innere Reibung geschmolzener Metalle und Legierungen. VI. Die innere Reibung von Pb, Cd, Zn, Ag, Sn, K, Na und die Frage der Strukturviskosität von Amalgamen,” Z. Anorg. Allg. Chem. 223(2), 204–208 (1935).
[Crossref]

1921 (1)

E. W. Washburn, “The dynamics of capillary flow,” Phys. Rev. 17(3), 273–283 (1921).
[Crossref]

Antoniadis, K. D.

M. J. Assael, A. E. Kalyva, K. D. Antoniadis, R. M. Banish, I. Egry, J. Wu, E. Kaschnitz, and W. A. Wakeham, “Reference data for the density and viscosity of liquid copper and liquid tin,” J. Phys. Chem. Ref. Data 39(3), 033105 (2010).
[Crossref]

Argyros, A.

M. A. Schmidt, A. Argyros, and F. Sorin, “Hybrid Optical Fibers – An Innovative Platform for In-Fiber Photonic Devices,” Adv. Opt. Mater. 4(1), 13–36 (2016).
[Crossref]

Assael, M. J.

M. J. Assael, A. E. Kalyva, K. D. Antoniadis, R. M. Banish, I. Egry, J. Wu, E. Kaschnitz, and W. A. Wakeham, “Reference data for the density and viscosity of liquid copper and liquid tin,” J. Phys. Chem. Ref. Data 39(3), 033105 (2010).
[Crossref]

Badding, J. V.

R. He, P. J. A. Sazio, A. C. Peacock, N. Healy, J. R. Sparks, M. Krishnamurthi, V. Gopalan, and J. V. Badding, “Integration of gigahertz-bandwidth semiconductor devices inside microstructured optical fibres,” Nat. Photon. 6(3), 174–179 (2012).
[Crossref]

Banish, R. M.

M. J. Assael, A. E. Kalyva, K. D. Antoniadis, R. M. Banish, I. Egry, J. Wu, E. Kaschnitz, and W. A. Wakeham, “Reference data for the density and viscosity of liquid copper and liquid tin,” J. Phys. Chem. Ref. Data 39(3), 033105 (2010).
[Crossref]

Bansal, N. P.

N. P. Bansal and R. H. Doremus, Handbook of Glass Properties (Academic, 1986).

Bartelt, H.

Bauerschmidt, S. T.

P. Uebel, S. T. Bauerschmidt, M. A. Schmidt, and P. St. J. Russell, “A gold-nanotip optical fiber for plasmon-enhanced near-field detection,” Appl. Phys. Lett. 103(2), 021101 (2013).
[Crossref]

Bernard, G.

G. Bernard and C. H. P. Lupis, “The surface tension of liquid silver alloys: Part I. silver-gold alloys,” Metall. Trans. 2(2), 555–559 (1971).
[Crossref]

Bird, D.

Blair, S.

D. A. Harrison, D. Yan, and S. Blair, “The surface tension of liquid copper,” J. Chem. Thermodyn. 9(12), 1111–1119 (1977).
[Crossref]

Bresson, B.

Brun, C.

Buet, X.

Capelle, M. S.

Chatain, D.

R. Sangiorgi, M. L. Muolo, D. Chatain, and N. Eustathopoulos, “Wettability and work of adhesion of nonreactive liquid metals on silica,” J. Am. Ceram. Soc. 71(9), 742–748 (1988).
[Crossref]

Chemnitz, M.

A. Tuniz, M. Chemnitz, J. Delith, S. Weidlich, and M. A. Schmidt, “Hybrid-mode-assisted long-distance excitation of short-range surface plasmons in a nanotip-enhanced step-index fiber,” Nano Lett. 17(2), 631–637 (2017). .
[Crossref]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370 (1972).
[Crossref]

Ciccotti, M.

Cunff, L. Le

A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, “A new model of dispersion for metals leading to a more accurate modeling of plasmonic structures using the FDTD method,” Appl. Phys. A 103(3), 849–853 (2011).
[Crossref]

de Sterke, C. M.

Delith, J.

A. Tuniz, M. Chemnitz, J. Delith, S. Weidlich, and M. A. Schmidt, “Hybrid-mode-assisted long-distance excitation of short-range surface plasmons in a nanotip-enhanced step-index fiber,” Nano Lett. 17(2), 631–637 (2017). .
[Crossref]

Doremus, R. H.

N. P. Bansal and R. H. Doremus, Handbook of Glass Properties (Academic, 1986).

Dridi, M.

A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, “A new model of dispersion for metals leading to a more accurate modeling of plasmonic structures using the FDTD method,” Appl. Phys. A 103(3), 849–853 (2011).
[Crossref]

Egry, I.

M. J. Assael, A. E. Kalyva, K. D. Antoniadis, R. M. Banish, I. Egry, J. Wu, E. Kaschnitz, and W. A. Wakeham, “Reference data for the density and viscosity of liquid copper and liquid tin,” J. Phys. Chem. Ref. Data 39(3), 033105 (2010).
[Crossref]

I. Egry, G. Lohoefer, and G. Jacobs, “Surface tension of liquid metals: results from measurements on ground and in space,” Phys. Rev. Lett. 75(22), 4043 (1995).
[Crossref] [PubMed]

Etchegoin, P. G.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “Erratum: An analytic model for the optical properties of gold,” J. Chem. Phys. 127(18), 9901 (2007).
[Crossref]

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125(16), 164705 (2006).
[Crossref] [PubMed]

Eustathopoulos, N.

R. Sangiorgi, M. L. Muolo, D. Chatain, and N. Eustathopoulos, “Wettability and work of adhesion of nonreactive liquid metals on silica,” J. Am. Ceram. Soc. 71(9), 742–748 (1988).
[Crossref]

Fleming, J. W.

George, A.

Gering, K.

K. Gering and F. Sauerwald, “Über die innere Reibung geschmolzener Metalle und Legierungen. VI. Die innere Reibung von Pb, Cd, Zn, Ag, Sn, K, Na und die Frage der Strukturviskosität von Amalgamen,” Z. Anorg. Allg. Chem. 223(2), 204–208 (1935).
[Crossref]

Ghomari, A.

Gopalan, V.

R. He, P. J. A. Sazio, A. C. Peacock, N. Healy, J. R. Sparks, M. Krishnamurthi, V. Gopalan, and J. V. Badding, “Integration of gigahertz-bandwidth semiconductor devices inside microstructured optical fibres,” Nat. Photon. 6(3), 174–179 (2012).
[Crossref]

Grujic, T.

Harris, B.

B. Harris, “Shrinkage stresses in glass/resin composites,” J. Mater. Sci. 13(1), 173–177 (1978).
[Crossref]

Harrison, D. A.

D. A. Harrison, D. Yan, and S. Blair, “The surface tension of liquid copper,” J. Chem. Thermodyn. 9(12), 1111–1119 (1977).
[Crossref]

He, R.

R. He, P. J. A. Sazio, A. C. Peacock, N. Healy, J. R. Sparks, M. Krishnamurthi, V. Gopalan, and J. V. Badding, “Integration of gigahertz-bandwidth semiconductor devices inside microstructured optical fibres,” Nat. Photon. 6(3), 174–179 (2012).
[Crossref]

Healy, N.

R. He, P. J. A. Sazio, A. C. Peacock, N. Healy, J. R. Sparks, M. Krishnamurthi, V. Gopalan, and J. V. Badding, “Integration of gigahertz-bandwidth semiconductor devices inside microstructured optical fibres,” Nat. Photon. 6(3), 174–179 (2012).
[Crossref]

Hou, J.

Israelachvili, J. N.

J. N. Israelachvili, Intermolecular and Surface Forces (Academic, 2011), Chap. 13.

Jacobs, G.

I. Egry, G. Lohoefer, and G. Jacobs, “Surface tension of liquid metals: results from measurements on ground and in space,” Phys. Rev. Lett. 75(22), 4043 (1995).
[Crossref] [PubMed]

Jain, C.

A. Tuniz, C. Jain, S. Weidlich, and M. A. Schmidt, “Broadband azimuthal polarization conversion using gold nanowire enhanced step-index fiber,” Opt. Lett. 41(3), 448–451 (2016).
[Crossref] [PubMed]

C. Jain, A. Tuniz, K. Reuther, T. Wieduwilt, M. Rettenmayr, and M. A. Schmidt, “Micron-sized gold-nickel alloy wire integrated silica optical fibers,” Opt. Mat. Express 6(6), 1790–1799 (2016).
[Crossref]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370 (1972).
[Crossref]

Joly, N. Y.

Kakarantzas, G.

Kalyva, A. E.

M. J. Assael, A. E. Kalyva, K. D. Antoniadis, R. M. Banish, I. Egry, J. Wu, E. Kaschnitz, and W. A. Wakeham, “Reference data for the density and viscosity of liquid copper and liquid tin,” J. Phys. Chem. Ref. Data 39(3), 033105 (2010).
[Crossref]

Kaschnitz, E.

M. J. Assael, A. E. Kalyva, K. D. Antoniadis, R. M. Banish, I. Egry, J. Wu, E. Kaschnitz, and W. A. Wakeham, “Reference data for the density and viscosity of liquid copper and liquid tin,” J. Phys. Chem. Ref. Data 39(3), 033105 (2010).
[Crossref]

Kaye, G.

G. Kaye and T. Laby, Tables of Physical and Chemical Constants (Longman, 1995).

Knight, J. C.

Krishnamurthi, M.

R. He, P. J. A. Sazio, A. C. Peacock, N. Healy, J. R. Sparks, M. Krishnamurthi, V. Gopalan, and J. V. Badding, “Integration of gigahertz-bandwidth semiconductor devices inside microstructured optical fibres,” Nat. Photon. 6(3), 174–179 (2012).
[Crossref]

Kuhlmey, B. T.

Laby, T.

G. Kaye and T. Laby, Tables of Physical and Chemical Constants (Longman, 1995).

Laroche, T.

A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, “A new model of dispersion for metals leading to a more accurate modeling of plasmonic structures using the FDTD method,” Appl. Phys. A 103(3), 849–853 (2011).
[Crossref]

Le Ru, E. C.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “Erratum: An analytic model for the optical properties of gold,” J. Chem. Phys. 127(18), 9901 (2007).
[Crossref]

Lecomte, P.

Lee, H. W.

Lohoefer, G.

I. Egry, G. Lohoefer, and G. Jacobs, “Surface tension of liquid metals: results from measurements on ground and in space,” Phys. Rev. Lett. 75(22), 4043 (1995).
[Crossref] [PubMed]

Lupis, C. H. P.

G. Bernard and C. H. P. Lupis, “The surface tension of liquid silver alloys: Part I. silver-gold alloys,” Metall. Trans. 2(2), 555–559 (1971).
[Crossref]

Maier, S.

Malitson, I. H.

I. H. Malitson, “Interspecimen Comparison of the Refractive Index of Fused Silica,” J. Opt. Soc. Am. A 55(10), 1205–1209 (1965).
[Crossref]

Meyer, M.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “Erratum: An analytic model for the optical properties of gold,” J. Chem. Phys. 127(18), 9901 (2007).
[Crossref]

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125(16), 164705 (2006).
[Crossref] [PubMed]

Muolo, M. L.

R. Sangiorgi, M. L. Muolo, D. Chatain, and N. Eustathopoulos, “Wettability and work of adhesion of nonreactive liquid metals on silica,” J. Am. Ceram. Soc. 71(9), 742–748 (1988).
[Crossref]

R. Sangiorgi, M. L. Muolo, and A. Passerone, “Reactivity of vitreous silica in contact with liquid metals,” Rev. Int. Hautes Temp. Refract. 22, 175–184 (1985).

Naidich, J. V.

J. V. Naidich, “The wettability of solids by liquid metals,” in Progress in surface and membrane science Vol. 14 (Academic, 1981), pp. 353–484.
[Crossref]

Ofte, D.

D. Ofte, “The viscosities of liquid uranium, gold and lead,” J. Nucl. Mater. 22(1), 28–32 (1967).
[Crossref]

Ohta, H.

I. Suh, H. Ohta, and Y. Waseda, “High-temperature thermal expansion of six metallic elements measured by dilatation method and X-ray diffraction,” J. Mater. Sci. 23(2), 757–760 (1988).
[Crossref]

Passerone, A.

R. Sangiorgi, M. L. Muolo, and A. Passerone, “Reactivity of vitreous silica in contact with liquid metals,” Rev. Int. Hautes Temp. Refract. 22, 175–184 (1985).

Peacock, A. C.

R. He, P. J. A. Sazio, A. C. Peacock, N. Healy, J. R. Sparks, M. Krishnamurthi, V. Gopalan, and J. V. Badding, “Integration of gigahertz-bandwidth semiconductor devices inside microstructured optical fibres,” Nat. Photon. 6(3), 174–179 (2012).
[Crossref]

Pearce, G. J.

Petrovich, M. N.

Poletti, F.

Poulton, C. G.

Prill Sempere, L.

M. A. Schmidt, L. 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,” Phys. Rev. B 77(3), 033417 (2008).
[Crossref]

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. Prill Sempere, and P. St. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93(11), 111102 (2008).
[Crossref]

Rettenmayr, M.

C. Jain, A. Tuniz, K. Reuther, T. Wieduwilt, M. Rettenmayr, and M. A. Schmidt, “Micron-sized gold-nickel alloy wire integrated silica optical fibers,” Opt. Mat. Express 6(6), 1790–1799 (2016).
[Crossref]

Reuther, K.

C. Jain, A. Tuniz, K. Reuther, T. Wieduwilt, M. Rettenmayr, and M. A. Schmidt, “Micron-sized gold-nickel alloy wire integrated silica optical fibers,” Opt. Mat. Express 6(6), 1790–1799 (2016).
[Crossref]

Richardson, D. J.

Roger, J. P.

Ru, E. C. Le

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125(16), 164705 (2006).
[Crossref] [PubMed]

Russell, P. St. J.

P. Uebel, S. T. Bauerschmidt, M. A. Schmidt, and P. St. J. Russell, “A gold-nanotip optical fiber for plasmon-enhanced near-field detection,” Appl. Phys. Lett. 103(2), 021101 (2013).
[Crossref]

H. W. Lee, M. A. Schmidt, and P. St. J. Russell, “Excitation of a nanowire “molecule” in gold-filled photonic crystal fiber,” Opt. Lett. 37(14), 2946–2948 (2012).
[Crossref] [PubMed]

H. W. Lee, M. A. Schmidt, R. F. Russell, N. Y. Joly, H. K. Tyagi, P. Uebel, and P. St. J. Russell, “Pressure-assisted melt-filling and optical characterization of Au nano-wires in microstructured fibers,” Opt. Express 19(13), 12180–12189 (2011).
[Crossref] [PubMed]

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. Prill Sempere, and P. St. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93(11), 111102 (2008).
[Crossref]

M. A. Schmidt, L. 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,” Phys. Rev. B 77(3), 033417 (2008).
[Crossref]

M. A. Schmidt and P. St. J. Russell, “Long-range spiralling surface plasmon modes on metallic nanowires,” Opt. Express 16(18), 13617–13623 (2008).
[Crossref] [PubMed]

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(12), 1647–1649 (2007).
[Crossref] [PubMed]

Russell, R. F.

Sangiorgi, R.

R. Sangiorgi, M. L. Muolo, D. Chatain, and N. Eustathopoulos, “Wettability and work of adhesion of nonreactive liquid metals on silica,” J. Am. Ceram. Soc. 71(9), 742–748 (1988).
[Crossref]

R. Sangiorgi, M. L. Muolo, and A. Passerone, “Reactivity of vitreous silica in contact with liquid metals,” Rev. Int. Hautes Temp. Refract. 22, 175–184 (1985).

Sauerwald, F.

K. Gering and F. Sauerwald, “Über die innere Reibung geschmolzener Metalle und Legierungen. VI. Die innere Reibung von Pb, Cd, Zn, Ag, Sn, K, Na und die Frage der Strukturviskosität von Amalgamen,” Z. Anorg. Allg. Chem. 223(2), 204–208 (1935).
[Crossref]

Sazio, P. J. A.

R. He, P. J. A. Sazio, A. C. Peacock, N. Healy, J. R. Sparks, M. Krishnamurthi, V. Gopalan, and J. V. Badding, “Integration of gigahertz-bandwidth semiconductor devices inside microstructured optical fibres,” Nat. Photon. 6(3), 174–179 (2012).
[Crossref]

Schmidt, M. A.

A. Tuniz, M. Chemnitz, J. Delith, S. Weidlich, and M. A. Schmidt, “Hybrid-mode-assisted long-distance excitation of short-range surface plasmons in a nanotip-enhanced step-index fiber,” Nano Lett. 17(2), 631–637 (2017). .
[Crossref]

C. Jain, A. Tuniz, K. Reuther, T. Wieduwilt, M. Rettenmayr, and M. A. Schmidt, “Micron-sized gold-nickel alloy wire integrated silica optical fibers,” Opt. Mat. Express 6(6), 1790–1799 (2016).
[Crossref]

A. Tuniz, C. Jain, S. Weidlich, and M. A. Schmidt, “Broadband azimuthal polarization conversion using gold nanowire enhanced step-index fiber,” Opt. Lett. 41(3), 448–451 (2016).
[Crossref] [PubMed]

A. Tuniz and M. A. Schmidt, “Broadband efficient directional coupling to short-range plasmons: towards hybrid fiber nanotips,” Opt. Express 24(7), 7507–7524 (2016).
[Crossref] [PubMed]

M. A. Schmidt, A. Argyros, and F. Sorin, “Hybrid Optical Fibers – An Innovative Platform for In-Fiber Photonic Devices,” Adv. Opt. Mater. 4(1), 13–36 (2016).
[Crossref]

R. Spittel, P. Uebel, H. Bartelt, and M. A. Schmidt, “Curvature-induced geometric momenta: the origin of waveguide dispersion of surface plasmons on metallic wires,” Opt. Express 23(9), 12174–12188 (2015).
[Crossref] [PubMed]

R. Spittel, H. Bartelt, and M. A. Schmidt, “A semi-analytical model for the approximation of plasmonic bands in arrays of metal wires in photonic crystal fibers,” Opt. Express 22(10), 11741–11753 (2014).
[Crossref] [PubMed]

P. Uebel, S. T. Bauerschmidt, M. A. Schmidt, and P. St. J. Russell, “A gold-nanotip optical fiber for plasmon-enhanced near-field detection,” Appl. Phys. Lett. 103(2), 021101 (2013).
[Crossref]

H. W. Lee, M. A. Schmidt, and P. St. J. Russell, “Excitation of a nanowire “molecule” in gold-filled photonic crystal fiber,” Opt. Lett. 37(14), 2946–2948 (2012).
[Crossref] [PubMed]

H. W. Lee, M. A. Schmidt, R. F. Russell, N. Y. Joly, H. K. Tyagi, P. Uebel, and P. St. J. Russell, “Pressure-assisted melt-filling and optical characterization of Au nano-wires in microstructured fibers,” Opt. Express 19(13), 12180–12189 (2011).
[Crossref] [PubMed]

M. A. Schmidt, L. 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,” Phys. Rev. B 77(3), 033417 (2008).
[Crossref]

M. A. Schmidt and P. St. J. Russell, “Long-range spiralling surface plasmon modes on metallic nanowires,” Opt. Express 16(18), 13617–13623 (2008).
[Crossref] [PubMed]

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. Prill Sempere, and P. St. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93(11), 111102 (2008).
[Crossref]

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(12), 1647–1649 (2007).
[Crossref] [PubMed]

Sorin, F.

M. A. Schmidt, A. Argyros, and F. Sorin, “Hybrid Optical Fibers – An Innovative Platform for In-Fiber Photonic Devices,” Adv. Opt. Mater. 4(1), 13–36 (2016).
[Crossref]

Sparks, J. R.

R. He, P. J. A. Sazio, A. C. Peacock, N. Healy, J. R. Sparks, M. Krishnamurthi, V. Gopalan, and J. V. Badding, “Integration of gigahertz-bandwidth semiconductor devices inside microstructured optical fibres,” Nat. Photon. 6(3), 174–179 (2012).
[Crossref]

Spittel, R.

Suh, I.

I. Suh, H. Ohta, and Y. Waseda, “High-temperature thermal expansion of six metallic elements measured by dilatation method and X-ray diffraction,” J. Mater. Sci. 23(2), 757–760 (1988).
[Crossref]

Tessier, G.

Tuniz, A.

A. Tuniz, M. Chemnitz, J. Delith, S. Weidlich, and M. A. Schmidt, “Hybrid-mode-assisted long-distance excitation of short-range surface plasmons in a nanotip-enhanced step-index fiber,” Nano Lett. 17(2), 631–637 (2017). .
[Crossref]

A. Tuniz and M. A. Schmidt, “Broadband efficient directional coupling to short-range plasmons: towards hybrid fiber nanotips,” Opt. Express 24(7), 7507–7524 (2016).
[Crossref] [PubMed]

A. Tuniz, C. Jain, S. Weidlich, and M. A. Schmidt, “Broadband azimuthal polarization conversion using gold nanowire enhanced step-index fiber,” Opt. Lett. 41(3), 448–451 (2016).
[Crossref] [PubMed]

C. Jain, A. Tuniz, K. Reuther, T. Wieduwilt, M. Rettenmayr, and M. A. Schmidt, “Micron-sized gold-nickel alloy wire integrated silica optical fibers,” Opt. Mat. Express 6(6), 1790–1799 (2016).
[Crossref]

Tyagi, H. K.

H. W. Lee, M. A. Schmidt, R. F. Russell, N. Y. Joly, H. K. Tyagi, P. Uebel, and P. St. J. Russell, “Pressure-assisted melt-filling and optical characterization of Au nano-wires in microstructured fibers,” Opt. Express 19(13), 12180–12189 (2011).
[Crossref] [PubMed]

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. Prill Sempere, and P. St. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93(11), 111102 (2008).
[Crossref]

M. A. Schmidt, L. 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,” Phys. Rev. B 77(3), 033417 (2008).
[Crossref]

Uebel, P.

Vandembroucq, D.

Vial, A.

A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, “A new model of dispersion for metals leading to a more accurate modeling of plasmonic structures using the FDTD method,” Appl. Phys. A 103(3), 849–853 (2011).
[Crossref]

Wakeham, W. A.

M. J. Assael, A. E. Kalyva, K. D. Antoniadis, R. M. Banish, I. Egry, J. Wu, E. Kaschnitz, and W. A. Wakeham, “Reference data for the density and viscosity of liquid copper and liquid tin,” J. Phys. Chem. Ref. Data 39(3), 033105 (2010).
[Crossref]

Waseda, Y.

I. Suh, H. Ohta, and Y. Waseda, “High-temperature thermal expansion of six metallic elements measured by dilatation method and X-ray diffraction,” J. Mater. Sci. 23(2), 757–760 (1988).
[Crossref]

Washburn, E. W.

E. W. Washburn, “The dynamics of capillary flow,” Phys. Rev. 17(3), 273–283 (1921).
[Crossref]

Weidlich, S.

A. Tuniz, M. Chemnitz, J. Delith, S. Weidlich, and M. A. Schmidt, “Hybrid-mode-assisted long-distance excitation of short-range surface plasmons in a nanotip-enhanced step-index fiber,” Nano Lett. 17(2), 631–637 (2017). .
[Crossref]

A. Tuniz, C. Jain, S. Weidlich, and M. A. Schmidt, “Broadband azimuthal polarization conversion using gold nanowire enhanced step-index fiber,” Opt. Lett. 41(3), 448–451 (2016).
[Crossref] [PubMed]

Wieduwilt, T.

C. Jain, A. Tuniz, K. Reuther, T. Wieduwilt, M. Rettenmayr, and M. A. Schmidt, “Micron-sized gold-nickel alloy wire integrated silica optical fibers,” Opt. Mat. Express 6(6), 1790–1799 (2016).
[Crossref]

Wu, J.

M. J. Assael, A. E. Kalyva, K. D. Antoniadis, R. M. Banish, I. Egry, J. Wu, E. Kaschnitz, and W. A. Wakeham, “Reference data for the density and viscosity of liquid copper and liquid tin,” J. Phys. Chem. Ref. Data 39(3), 033105 (2010).
[Crossref]

Yan, D.

D. A. Harrison, D. Yan, and S. Blair, “The surface tension of liquid copper,” J. Chem. Thermodyn. 9(12), 1111–1119 (1977).
[Crossref]

Adv. Opt. Mater. (1)

M. A. Schmidt, A. Argyros, and F. Sorin, “Hybrid Optical Fibers – An Innovative Platform for In-Fiber Photonic Devices,” Adv. Opt. Mater. 4(1), 13–36 (2016).
[Crossref]

Appl. Opt. (1)

Appl. Phys. A (1)

A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, “A new model of dispersion for metals leading to a more accurate modeling of plasmonic structures using the FDTD method,” Appl. Phys. A 103(3), 849–853 (2011).
[Crossref]

Appl. Phys. Lett. (2)

P. Uebel, S. T. Bauerschmidt, M. A. Schmidt, and P. St. J. Russell, “A gold-nanotip optical fiber for plasmon-enhanced near-field detection,” Appl. Phys. Lett. 103(2), 021101 (2013).
[Crossref]

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. Prill Sempere, and P. St. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93(11), 111102 (2008).
[Crossref]

J. Am. Ceram. Soc. (1)

R. Sangiorgi, M. L. Muolo, D. Chatain, and N. Eustathopoulos, “Wettability and work of adhesion of nonreactive liquid metals on silica,” J. Am. Ceram. Soc. 71(9), 742–748 (1988).
[Crossref]

J. Chem. Phys. (2)

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125(16), 164705 (2006).
[Crossref] [PubMed]

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “Erratum: An analytic model for the optical properties of gold,” J. Chem. Phys. 127(18), 9901 (2007).
[Crossref]

J. Chem. Thermodyn. (1)

D. A. Harrison, D. Yan, and S. Blair, “The surface tension of liquid copper,” J. Chem. Thermodyn. 9(12), 1111–1119 (1977).
[Crossref]

J. Mater. Sci. (2)

I. Suh, H. Ohta, and Y. Waseda, “High-temperature thermal expansion of six metallic elements measured by dilatation method and X-ray diffraction,” J. Mater. Sci. 23(2), 757–760 (1988).
[Crossref]

B. Harris, “Shrinkage stresses in glass/resin composites,” J. Mater. Sci. 13(1), 173–177 (1978).
[Crossref]

J. Nucl. Mater. (1)

D. Ofte, “The viscosities of liquid uranium, gold and lead,” J. Nucl. Mater. 22(1), 28–32 (1967).
[Crossref]

J. Opt. Soc. Am. A (1)

I. H. Malitson, “Interspecimen Comparison of the Refractive Index of Fused Silica,” J. Opt. Soc. Am. A 55(10), 1205–1209 (1965).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys. Chem. Ref. Data (1)

M. J. Assael, A. E. Kalyva, K. D. Antoniadis, R. M. Banish, I. Egry, J. Wu, E. Kaschnitz, and W. A. Wakeham, “Reference data for the density and viscosity of liquid copper and liquid tin,” J. Phys. Chem. Ref. Data 39(3), 033105 (2010).
[Crossref]

Metall. Trans. (1)

G. Bernard and C. H. P. Lupis, “The surface tension of liquid silver alloys: Part I. silver-gold alloys,” Metall. Trans. 2(2), 555–559 (1971).
[Crossref]

Nano Lett. (1)

A. Tuniz, M. Chemnitz, J. Delith, S. Weidlich, and M. A. Schmidt, “Hybrid-mode-assisted long-distance excitation of short-range surface plasmons in a nanotip-enhanced step-index fiber,” Nano Lett. 17(2), 631–637 (2017). .
[Crossref]

Nat. Photon. (1)

R. He, P. J. A. Sazio, A. C. Peacock, N. Healy, J. R. Sparks, M. Krishnamurthi, V. Gopalan, and J. V. Badding, “Integration of gigahertz-bandwidth semiconductor devices inside microstructured optical fibres,” Nat. Photon. 6(3), 174–179 (2012).
[Crossref]

Opt. Express (7)

A. Tuniz and M. A. Schmidt, “Broadband efficient directional coupling to short-range plasmons: towards hybrid fiber nanotips,” Opt. Express 24(7), 7507–7524 (2016).
[Crossref] [PubMed]

R. Spittel, H. Bartelt, and M. A. Schmidt, “A semi-analytical model for the approximation of plasmonic bands in arrays of metal wires in photonic crystal fibers,” Opt. Express 22(10), 11741–11753 (2014).
[Crossref] [PubMed]

J. Hou, D. Bird, A. George, S. Maier, B. T. Kuhlmey, and J. C. Knight, “Metallic mode confinement in microstructured fibres,” Opt. Express 16(9), 5983–5990 (2008).
[Crossref] [PubMed]

M. A. Schmidt and P. St. J. Russell, “Long-range spiralling surface plasmon modes on metallic nanowires,” Opt. Express 16(18), 13617–13623 (2008).
[Crossref] [PubMed]

R. Spittel, P. Uebel, H. Bartelt, and M. A. Schmidt, “Curvature-induced geometric momenta: the origin of waveguide dispersion of surface plasmons on metallic wires,” Opt. Express 23(9), 12174–12188 (2015).
[Crossref] [PubMed]

H. W. Lee, M. A. Schmidt, R. F. Russell, N. Y. Joly, H. K. Tyagi, P. Uebel, and P. St. J. Russell, “Pressure-assisted melt-filling and optical characterization of Au nano-wires in microstructured fibers,” Opt. Express 19(13), 12180–12189 (2011).
[Crossref] [PubMed]

C. Brun, X. Buet, B. Bresson, M. S. Capelle, M. Ciccotti, A. Ghomari, P. Lecomte, J. P. Roger, M. N. Petrovich, F. Poletti, D. J. Richardson, D. Vandembroucq, and G. Tessier, “Picometer-scale surface roughness measurements inside hollow glass fibres,” Opt. Express 22(24), 29554–29567 (2014).

Opt. Lett. (3)

Opt. Mat. Express (1)

C. Jain, A. Tuniz, K. Reuther, T. Wieduwilt, M. Rettenmayr, and M. A. Schmidt, “Micron-sized gold-nickel alloy wire integrated silica optical fibers,” Opt. Mat. Express 6(6), 1790–1799 (2016).
[Crossref]

Phys. Rev. (1)

E. W. Washburn, “The dynamics of capillary flow,” Phys. Rev. 17(3), 273–283 (1921).
[Crossref]

Phys. Rev. B (2)

M. A. Schmidt, L. 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,” Phys. Rev. B 77(3), 033417 (2008).
[Crossref]

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370 (1972).
[Crossref]

Phys. Rev. Lett. (1)

I. Egry, G. Lohoefer, and G. Jacobs, “Surface tension of liquid metals: results from measurements on ground and in space,” Phys. Rev. Lett. 75(22), 4043 (1995).
[Crossref] [PubMed]

Rev. Int. Hautes Temp. Refract. (1)

R. Sangiorgi, M. L. Muolo, and A. Passerone, “Reactivity of vitreous silica in contact with liquid metals,” Rev. Int. Hautes Temp. Refract. 22, 175–184 (1985).

Z. Anorg. Allg. Chem. (1)

K. Gering and F. Sauerwald, “Über die innere Reibung geschmolzener Metalle und Legierungen. VI. Die innere Reibung von Pb, Cd, Zn, Ag, Sn, K, Na und die Frage der Strukturviskosität von Amalgamen,” Z. Anorg. Allg. Chem. 223(2), 204–208 (1935).
[Crossref]

Other (4)

J. V. Naidich, “The wettability of solids by liquid metals,” in Progress in surface and membrane science Vol. 14 (Academic, 1981), pp. 353–484.
[Crossref]

N. P. Bansal and R. H. Doremus, Handbook of Glass Properties (Academic, 1986).

J. N. Israelachvili, Intermolecular and Surface Forces (Academic, 2011), Chap. 13.

G. Kaye and T. Laby, Tables of Physical and Chemical Constants (Longman, 1995).

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Figures (5)

Fig. 1
Fig. 1 Sketch of hybrid fiber being composed of a metallic nanowire (yellow) and a parallel-running graded-index core (blue) separated by a center-to-center distance Λ. The green area highlights the nanogap which is formed due to thermal contraction of the NW during fabrication.
Fig. 2
Fig. 2 Setup for measureming the spectral distribution of the transmission of the fiber samples. The spectral attenuation was determined using a cutback technique. Details of the experimental setup and experimental methods are given in the main text.
Fig. 3
Fig. 3 Comparison of simulations and measurements of a silver-filled MGIF including a NW of diameter of 380 nm. (a) Spectral distribution of real parts of the calculated effective indices of the shifted and non-shifted HE2 SPP (green lines) and the HE11-like fundamental core modes (blue solid lines). The difference between both polarizations is smaller than 10−5 in the investigated spectral window. The solid black line represents the refractive index of bulk silica. (b) Attenuation spectra of the x-polarized (blue lines) and y-polarized (red lines) core modes. Solid lines represent simulations, while the dotted lines refer to the measurements. The vertical dashed line corresponds to the quasi-cutoff wavelength using Eq. 5 from [5].
Fig. 4
Fig. 4 Dependence of phase-matching wavelength on hole diameter ((a) gold, (b) silver and (c) copper). The blue solid lines correspond to simulations using the fitted relative gap width w/dhole based on determined values shown in Table 4. The shaded areas cover the range between the minimum and maximum values of the fitted parameters. The broken lines represent the phase-matching wavelengths assuming no gap (red dotted) and the values from Table 2 (green dashed). In all plots the blue circles refer to the measured phase-matching wavelengths.
Fig. 5
Fig. 5 Illustration of the NW contraction (a) above and (b) below the threshold temperature. The solid horizontal lines correspond to an mean level of the rough surfaces of the hole and NW, respectively, separated by the average distance h.

Tables (4)

Tables Icon

Table 1 Viscosity, surface tension and contact angle for gold, silver and copper at the filling temperature Tfill.

Tables Icon

Table 2 Fit parameters A1 and A2 in Eq. (2) for gold, silver and copper [27] as well as the resulting relative gap width for a cooling from the melting temperature Tm to room temperature.

Tables Icon

Table 3 Fit parameters for the D2CP model of the permittivity for gold, silver and copper.

Tables Icon

Table 4 Overview of measured resonance wavelengths λr and the resulting calculated gap widths w for all investigated hole diameters dhole. The shaded row corresponds to the sample analyzed in Fig. 3

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

t fill 4 η d hole γ cos ( θ ) + d hole 2 p / 4 L 2 ,
w = d hole 2 ( [ A 1 α SiO 2 ] [ T m 293 K ] + A 2 [ T m 293 K ] 2 ) .
ε = ε 1 λ p 2 ( 1 / λ 2 + i / γ p λ ) + k = 1 2 A k λ k [ e i ϕ k 1 / λ k 1 / λ i γ k + e i ϕ k 1 / λ k + 1 / λ + i / γ k ] .

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