1. Introduction

Photonic crystal fiber (PCF), including photonic bandgap (PBG) fiber, has proved invaluable for linear and nonlinear optics because of its designable spectral guidance window and dispersion properties over large wavelength ranges [1]. Standard solid-core PCFs guide light in a fused-silica core, limiting study to silica-photon interactions. In contrast, hollow-core photonic bandgap (HC-PBG) fiber, which guides light in a low-refractive index hollow core, allows guidance in a wide variety of media [2]. By filling the hollow channels within the fiber with a gas or liquid, composite systems can be created to study nonlinear effects mediated by the filling fluid while maintaining the tailorability of the HC-PBG fiber [2]. For example, noble-gas-filled HC-PBG fibers have allowed study of soliton propagation beyond peak power limits associated with solid fibers [3], and gas-filled HC-PBG fibers have been used to enable stimulated Raman scattering at unprecedentedly low threshold intensities [4], and saturated-absorption spectroscopy [5].

Here we demonstrate that supercritical xenon at room temperature is a promising medium for filling such fibers because of its highly variable density and unique combination of gaseous and liquid qualities, which allow post-production control over the guidance of the HC-PBG fiber. Because we work near the critical point, where the fluid compressibility is high, a small change of gas pressure leads to a large change of density, and subsequently a large index change, allowing us to tune the guidance band edge over 100 nm in wavelength by changing the gas pressure only 11% [6]. The linear refractive index of Xe in this regime is in the range 1.09 - 1.18, which is remarkably high for a pure atomic gas, and we point out that its nonlinear refractive index is expected to approach that of fused silica. This suggests several applications for such a system, in both linear and nonlinear optics, which we discuss.

2. Theory

Optical guidance in HC-PBG fiber derives not from total internal reflection, but from the formation of an out-of-plane optical bandgap in the 2-D photonic crystal lattice of high-refractive-index silica struts and low-index gas-filled holes, surrounding the low-index hollow core (Fig. 1). The spectral width and location of this bandgap are dependent on the geometry of the lattice and the ratio of the refractive indices of the holes and struts [2]. When wavelengths of light within this bandgap are coupled into the core, the bandgap prevents leakage through the lattice, and the light is transmitted in the core with low loss.

 

Fig. 1 An SEM image of the face of a HC-PBG fiber, similar to those used in this study, showing the central hollow core and surrounding lattice of silica struts and holes.

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As the ratio of the refractive indices of the holes and struts is increased, for example by increasing the density of the filling fluid, the guidance window of the fiber shifts toward shorter wavelengths, as described by a model developed by [7]. In a scalar-wave model for propagating in a fiber consisting of two materials with indices $n$ and $n_s$, there are two constants, $\nu$ and $w$, defined in terms of the free-space wavelength $\lambda$ of the light, the longitudinal component $\beta$ of the optical wave vector in the fiber, the uniform transverse spatial length scale $\Lambda$ of the fiber structure, and the high and low refractive indices of the lattice, $n_s$ and $n$ respectively:

To account for the change of wavelength-dependent refractive index with varying xenon density, we use a Lorentz-Lorenz equation developed by modifying the dilute-gas Sellmeier equation [9]:

We repeated the above process for a range of pressures and temperatures to model the guidance window shift as the xenon is varied from the low-density gas phase into the high-density supercritical phase. As illustrated in Fig. 2, the supercritical phase occupies the region of a phase diagram above the critical point, where gas and liquid become indistinguishable. Near the critical point (which for Xe occurs at 57.6 atm and 16.6 C), attractive interatomic forces cause a high fluid compressibility, so that density increases rapidly when the pressure rises. Figure 3 illustrates this high compressibility for supercritical Xe at room temperature (21 C). It shows a region of rapidly increasing density for small pressure increases, leading to densities significantly higher than predicted by the ideal-gas law. For example, the density at 21 C and 80 atm is ~4 times higher than the ideal-gas prediction [10].

 

Fig. 2 Sketch of phase diagram of Xe, with the critical point highlighted in blue.

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Fig. 3 Density vs. pressure for Xe, taken from NIST data for the equation of state [10], and for the ideal-gas law prediction, at temperature 21 C.

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Xenon makes an excellent choice as a supercritical fluid for filling HC-PBG fiber. Its easily accessible critical point makes it convenient to create supercritical xenon with a density several hundred times that at STP while working at room temperature. The procedure described above using Eqs. (2) and (3) predicts that at 21 C, an increase in pressure from 1 atm to 80 atm leads to a refractive index change from 1.0007 to 1.21. Working several degrees above critical temperature, we bypass the liquid phase, avoiding possible formation of liquid xenon droplets within the fiber, and any critical opalescence created by working extremely close to the unstable critical point. By using a supercritical fluid, we combine the tunability of gases with the large index of liquids. This is a versatile medium, enabling control over the guidance window of the fiber using a single fluid but only small pressure changes.

3. Experimental

To demonstrate experimentally the shifting of the guidance window in the Xe supercritical regime, we coupled the fundamental mode of a fiber-laser-based white-light source into a meter long section of Xe-filled HC-PBG fiber, with core diameter of 10 micrometers and guidance window centered at 1064 nm when filled to one atmosphere. The open fiber ends were contained in high-pressure cells, which were connected to a Xe gas system to allow control of the common pressure within the core and cladding holes of the fiber. The method we use for creating a high pressure of Xe from a lower-pressure source is detailed in the Appendix. Optical windows on the cells allowed coupling of light into and out of the fiber, while graphite ferrules compressed around the fiber inhibited xenon leakage out of the cells at the fiber entry points.

The spectrum of the light transmitted by the fiber was spatially filtered to ensure detection of only light emerging from the core and measured with a spectrometer, with results shown in Fig. 4. Due to the low sensitivity of the spectrometer at longer wavelengths, only the short-wavelength edge of the guidance window was measured. As the pressure of Xe was varied, the transmission spectrum demarked the shifting guidance window of the fiber, allowing us to observe the transition to supercritical fluid.

 

Fig. 4 (a) Four transmission spectra on a normalized intensity scale from the same fiber under different pressures of Xe, demonstrating the shift of the short-wavelength edge of the guidance window. Note the white light source’s pump laser line at 1064 nm and, that due to loss of sensitivity of the spectrometer, the long-wavelength edge was not measured. (b) The spectrum of the source before being coupled into the fiber, on a different vertical scale.

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The short-wavelength portions of the transmission spectra show several dips, which are typical signatures of surface-mode overlap with the core-guided modes [11]. This coupling reduces the transmitted intensity and, because the surface modes do not follow the same pressure dependence as does the guidance window, also causes the spectral pattern to slowly change with pressure. This leads to some uncertainty in determining the edge of the guidance window. In order to compare the predictions of the simple scaling theory above to the experiments, we arbitrarily defined the guidance window edge to be at 5% of the maximum transmitted intensity, excluding the white light source’s pump laser peak at 1064 nm. Such a definition allows for comparison between spectra with different absolute intensities. When we adopted various alternative definitions of window edge, the results were found to be similar.

4. Results

The measured guidance window edge for this fiber is plotted vs. pressure in Fig. 5, where we compare it to the theoretical prediction obtained using Eqs. (2) and (3) at the measured temperature 21 C (accurate to within 1 C). The results show a shift in the guidance window by over 200 nm as the pressure is varied from 6.6 atm to 72.4 atm. Also plotted is the predicted edge wavelength for an ideal gas under similar pressures. Clear evidence of the supercritical transition is seen, in good agreement with the simple scaling theory using no free parameters, other than the guidance window edge measured at 6.6 atm. The good agreement between the experimental data and the model gives strong evidence that the change in the transmission spectrum is caused by the changing refractive index of xenon, which alters the fiber’s bandgap.

 

Fig. 5 Theoretical predictions and experimental results for the shift in the guidance window short-wavelength edge of a HC-PBG fiber filled with Xe, showing the transition to supercritical fluid. The prediction of the ideal gas law is shown for comparison.

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To illustrate the versatility and practicality of the bandgap-shifting technique, we also show in Fig. 6 the results of xenon filling a HC-PBG fiber whose guidance window centers at 1550 nm at one atmosphere. Both guidance window edges are shown in this case. The band edges are found to shift to shorter wavelengths as predicted by Eqs. (2) and (3). Observe the surface mode structure that occurs at the short-wavelength edge, which gradually changes with pressure of xenon.

 

Fig. 6 Six transmission spectra from a 17 m piece of 1550 nm HC-PBG fiber under different pressures of Xe.

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5. Summary

Supercritical fluids combine some of the most useful features of gases and liquids for work in HC-PBG fiber, allowing for control over the guidance window of the composite system with control of the fluid density. We have successfully demonstrated the use of supercritical xenon to shift the guidance window edge of a HC-PBG fiber by over 200 nm. Because of the large density variation with pressure associated with working near the critical point of xenon, we anticipate that the dispersion and nonlinear refractive index of the HC-PBG system will also be tunable over large ranges.

Very recently a study using high-pressure argon in hollow-core Kagome PCF showed tuning of the zero-dispersion wavelength with changing gas pressure as well as optical nonlinearity with values approaching that of solid fused silica [12]. At 150 atm of argon they measured a value of nonlinear refractive index $n_2$equal to $1.2\times {10}^{-17}{\text{cm}}^2/\text{W}$ near 800 nm wavelength. For our new supercritical xenon system, we predict, using the known value of $n_2=6.4\times {\text{10}}^{-19}{\text{cm}}^2/\text{W}$ at STP [13], the Xe equation of state used to successfully model the data in Fig. 5, and assuming a linear relationship of $n_2$ with density, that at 80 atm of xenon and room temperature the nonlinear refractive index has a value $n_2\approx 2.0\times {\text{10}}^{-16}{\text{cm}}^2/\text{W}$ at 800 nm. This is around 70% the value for fused silica, $n_2\approx 2.8\times {10}^{-16}{\text{cm}}^2/\text{W}$ [14], remarkable for a pure atomic fluid. As an added positive feature, demonstrated in argon [12], such noble gases lack Raman scattering, which offers advantages for certain studies, such as entangled photon-pair generation [15], soliton propagation [3], and quantum-noise squeezing [16].

Appendix – Supercritical Xe Filling System

To reach supercritical pressures with a minimum amount of xenon, we designed a system to transfer xenon from commercially purchased, moderate-pressure tanks to a high-pressure containment apparatus (Fig. 7). Liquid nitrogen (LN2) is sufficient to freeze the Xe gas into a solid, making it a useful method for moving xenon within the apparatus [17]. The apparatus was first evacuated with a vacuum pump (at G) before transferring xenon. The LN2 trap (F) then drew xenon from the tank (A), freezing it in the trap. Two valves (B₁, B₂) and a small fillable volume (D) allowed us to transfer volumetric units of xenon to the LN2 trap. This gave us precise control over the amount of xenon added to the high-pressure apparatus, while a pressure gauge (C) was used to monitor the pressure of each transferred unit of xenon as the pressure in the tank decreased.

 

Fig. 7 An apparatus for compressing gaseous xenon into a supercritical fluid.

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After a desired amount of xenon had been transferred, the containment apparatus could be sealed and the LN2 removed. An emergency release valve (E) kept pressures of xenon from reaching dangerous levels. A volume was wrapped with heat tape (H), to provide an option for small pressure adjustments without transferring additional xenon out of the tank (not used in this paper’s work). PEEK™ tubing (J) then connected the apparatus to containment cells that housed the ends of the HC-PBG fiber. A pressure transducer (I) measured the xenon pressure within the fiber while additional valves (B₃-B₅) allowed for controlled flow of xenon to the fiber to minimize pressure differentials and the possibility of strut-rupture within the fiber, and for pressure to be maintained in the fiber while additional xenon was loaded from the tank with LN2.

Acknowledgments

We acknowledge support from NSF Physics (USA), ANR and la région limousine (France), and would like to thank John Hardwick at the University of Oregon for his valuable insights on this experiment.

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