1. Introduction

The last two decades have triggered dramatic progress in controlling and confining light at the micrometre and nanometre scales through the development of a myriad of micro- and nano-structured photonic devices and materials such as photonic crystals [1] and photonic crystal fibers [2], thus enabling highly integrated photonic functionalities. However, the active material phase-states of these devices are either in solid-phase or in gas-phase [3]. Subsequently, their band-gap energies limit their operational optical spectral-range to below those of near UV [4], and their refractive indices to values higher than 1. One route that could extend these to ranges that no other solid-state or gas-phase materials would allow is to incorporate plasma-phase in their active materials. The plasma-state features can be used, for example to laser-emit in the range of UV to the soft x-ray where electrical discharge-induced plasma is hitherto the sole material for laser-action at wavelengths shorter than 300 nm [5,6]. One of the existing photonic structures that could be a candidate for plasma micro-confinement is hollow-core photonic crystal fiber (HC-PCF) [3] and its integrated form photonic microcells [7]. The ability of HC-PCF in confining light and gas together over a micrometric modal area and a meter-scale interaction length enabled the demonstration in gas-phase media of several coherent and nonlinear optical phenomena [8]. It would thus be desirable to extend gas-filled HC-PCF performances to ionised gases, as it would trigger, for example, the advent of the long hoped for compact and integrated UV-XUV laser sources and would provide a photonic platform whereby micro-plasmas could be generated and harnessed with the same degree of control which we currently have with the other matter phases.

This in turn, requires the vision and development of a system that could generate and micro-confine stable gas-plasma within a photonic structure without any damage or intrusion, whilst exhibiting both high electron density (>10¹¹ cm⁻³) and high power-density coupled to the plasma (>10 kW.cm⁻³). Recent attempts using conventional electrode excitation schemes [9,10] illustrate the challenge of such an endeavour and the need for an alternative excitation approach. Indeed, Shi et al. [9] placed electrodes inside hollow capillaries to produce a longitudinal direct-current (DC) excitation, but failed to produce stable DC breakdown at tube diameter smaller than 60 μm. On the other hand, Ji et al. [10] successfully generated atmospheric-pressure dielectric barrier discharges (DBD) in polymer vapour-filled capillaries with diameters as small as 30 μm. However, the non-homogeneous spatial-concentration of the DBD on the inner surface, and the low power density involved (estimated to kW.cm⁻³) disqualifies it as a viable technique to generate and sustain uniform micro-plasmas that preserve the integrity of the host structure [11] whilst sufficiently sustaining high power density to efficiently ionise inert gases. Finally, it is noteworthy that none of these works produces plasma within a real photonic structure.

Here we report on a new means of generating microwave plasma in a photonic dielectric structure based on HC-PCF that combines stability, high ionization rate and unprecedentedly large microwave power densities. The results show a rather counter-intuitive situation whereby a high level of power densities (~0.1 MW.cm⁻³) and electron densities (~10¹⁴ cm⁻³) co-exist with a relatively low plasma gas-temperature. The temperature level, however, is sufficiently high to be comparable to the transformation temperature of HC-PCF silica material, yet exhibits a steep transverse distribution that preserves the structural integrity of the HC-PCF. In this novel scheme a 6 cm-long argon-plasma column is generated and confined using low power (~10s W) microwave source in the ~100 μm diameter core of a Kagome-lattice HC-PCF. The plasma generation scheme is electrode-free and relies on exciting a self-guiding microwave surface-wave (SW) whose maximum electric-field intensity, in a similar manner to a plasmonic wave, is localised at the interface between the argon-filled HC-PCF core and the nanometric thick silica core-surround. The configuration exhibits an ultra-large electrostatic space-charge field, which enables the confinement of micro-plasma (~1300 K gas temperature, and more than 10 eV electron energy) within a cross area as small as 60 μm diameter, with no damage to the HC-PCF. This in turn, and despite a relatively low microwave pump power, favours unprecedentedly strong emission of several Ar⁺ lines in the visible and near UV and their guidance within the fiber-core.

2. Experiments on microplasma ignition in Kagome-latticed HC-PCF

The principle of the experiment is schematically illustrated in Fig. 1. An inert gas (here argon) filled HC-PCF [12] is inserted in a non-intrusive fashion into a microwave cavity called surfatron [13]. The surfatron is a microwave cavity comprising two co-axial metallic cylindrical tubes. This cavity exhibits a gap at a position where the field is at its maximum, and which acts as an impedance-matching coupler between the cavity field and the one that propagates along the optical fiber (Fig. 1(b)). Under these conditions, the scenario of the generation of stable plasma within the fiber core is as follows. The high intensity of the electromagnetic wave-field at the gap of the cavity creates gas breakdown in the fiber section residing in the gap. The subsequent plasma creates the necessary conditions for the formation of a tandem of a sub-diffraction self-guided surface-microwave and self-sustained extended plasma whereby the field intensity is highly localised at the core-surround interface between the plasma-filled core and the fiber cladding [14].

 

Fig. 1 (a) Schematics of the overall set-up and of the generation of the microwave surface-wave at the interface of HC-PCF core and its cladding. (b) Surfatron: principle of operation and schematic of the field lines. (c) Zoom inside optical waveguide core depicting the transverse profile of the plasma constituents and the forces involved in the creation of the space-charge sheath and the plasma neutral region.

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Figure 1(c) schematically shows the typical transverse distribution of the plasma particles. As observed, the neutral plasma region (NPR) is confined within a central area surrounded by a positively-charged layer termed the space-charge sheath [15]. The layer results from a charge separation between the highly-mobile electrons and the slower positive ions as both species move towards the wall. The net positive charge within this layer creates an electrostatic potential that decelerates the electrons and accelerates the ions beyond the Bohm sound speed [15]. This dynamic turns the space-charge sheath into an electrical gap barrier that self-consistently confines the NPR with respect to the dielectric wall. Unlike previous work [16], we will show that the sheath-layer and subsequently the fluid-dynamics of the plasma are strongly affected by the highly reduced HC-PCF core-radius. Furthermore, to our knowledge, there is no report of SW microwave plasma generated in a capillary with a diameter less than 500 μm or in a HC-PCF [17]. The HC-PCF used in our experiments is a 19-cell core defect with a Kagome-lattice cladding (see SEM picture on Fig. 2(a)). This fiber exhibits a 100 µm core diameter and has been fabricated by the well-known stack and draw process. Such a large fiber-core facilitates the ignition and maintenance of the microwave plasma. The fiber guides via inhibiting coupling (IC) mechanism [18]. Unlike the photonic bandgap guiding HC-PCF, IC guiding HC-PCF can exhibit fiber-core sizes as large as 100 μm, and secondly, it guides over a spectral range that spans from UV to mid-IR [18]. The transmission spectrum has been measured using a white-light source (see Fig. 2(b)). Several low-loss transmission bands are identified going from 400 nm to 1700 nm. One notes that the UV low-loss spectral windows have not been measured due to the limitation of our optical spectrum analyser.

 

Fig. 2 (a) SEM image of the cross-section of the fiber (b) Measured transmission spectrum through a 50 cm-long piece of HC-PCF under test.

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Figures 3 and 4 summarise theoretical and experimental results of the SW generation of a ~6 cm-long argon-plasma column inside a ~100 μm core diameter HC-PCF, with no damage to the dielectric structure of the fiber and with a high ionisation rate (~10⁻²). Figure 3(a) shows the 3D electromagnetic finite-element-method (FEM) simulation results of the overall field distribution for a constant electron density of 4 × 10¹⁴ cm⁻³ and a constant electron-neutral collisional rate of 2.4 × 10⁹ s⁻¹ estimated at the experimental pressure of 1 mbar. The surfatron cavity is being excited at 2.45 GHz with a continuous microwave power of 45 W. This cavity was designed through an iterative process between FEM simulations and experimental results. Similarly, the value of n_e has been chosen to be close to the one deduced from the experimental conditions. The field distribution readily shows the vacuum resonant mode in the surfatron cavity and the SW mode that extends outside the cavity. Figure 3(b1) shows a close-up of the SW field-magnitude distribution. The field maximum intensity is localised at the interface between the fiber-core and the cladding, with a propagation constant β ~300 m⁻¹ and an attenuation coefficient α ~20 m⁻¹. The SW exhibits similar properties to those of plasmonic waves with the salient difference that in addition to a transverse field component, whose intensity is localised at the interface core-cladding (Fig. 3(b2)). The field comprises also a longitudinal component with phase-shift relative to the transverse components, and whose maximum intensity is in the plasma region (Fig. 3(b3)). The latter is the necessary field that maintains the plasma along the SW propagation length, whilst the transverse component (with magnitude ~10 times larger) enables the SW propagation and subsequently the plasma column formation. Hence, most of the total intensity of microwave is localised at the interface being carried by the transverse component of the field. This is illustrated in Fig. 3(c), which shows the transverse profile of the field magnitude at z = 3.15 mm (Fig. 3(c1)) and z = 7.32 mm (Fig. 3(c2)) (origin position at the gap). Furthermore, we use the propagative model described in [19] to deduce the evolution of n_e, and subsequently of the propagation constant β and the attenuation coefficient α, as a function of the propagation length over the whole plasma column [19]. Experimentally, the plasma length that extends outside the cavity away from the gap was measured to be 4 cm (see Fig. 4(a)). In turn, using the above-mentioned propagative model, and an electron-neutral collisional rate of 2.4x10⁹ collision/s estimated for the experimental pressure of 1 mbar, the evolution of n_e, β and α along the plasma column is deduced (see Fig. 3(d)), giving the electron density at the gap position (z = 0) to be n_e(0) = 4 × 10¹⁴ cm⁻³. The 10¹⁴ cm⁻³ electron density-level obtained here with the CW microwave excitation at 1 mbar gas pressure confirms a very effective power-transfer to the plasma, yielding an ionization degree of ~10⁻² assuming a gas temperature of 1000 K, which is close to the experimentally measured value (see below). Such an ionization rate is several orders of magnitude higher than the ~10⁻⁶ in a DC excitation [20,21] (taking n_e ~10¹² cm⁻³ for gas at 33 mbar pressure and room temperature) and the ~10⁻⁵ in the micro-DBD (taking n_e ~10¹⁴ cm⁻³ for gas at atmospheric pressure and room temperature) [22].

 

Fig. 3 (a) Overall distribution of the calculated E-field. (b) (1) Close-up on the SW field magnitude; (2) transverse and (3) longitudinal field components. See (Media 1) for an animated version of the SW field. (c) Transverse profile of the field magnitude at a peak position (z = 3.15 mm from the gap) (1) and minimum field position (z = 7.32 mm) (2). (d) Evolution along the propagation axis z of the SW attenuation coefficient α and propagation constant β (rhs), and of the electron density n_e (lhs). The horizontal dotted line indicates the critical electron density n_c below which the plasma extinguishes.

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Fig. 4 (a) Picture of a section of the plasma column. (b) Optical emission spectrum of the plasma recorded longitudinally at one end of the HC-PCF (40 cm away from the surfatron). Insets: Scanning Electron Micrograph of the fiber after use and output profile of the transmitted emission at 750 nm.

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Figure 4(a) shows a photograph capturing the fluorescence of the plasma column outside the cavity and scattered off the side of the HC-PCF. The fiber is ~80 cm long with its end-tips being attached to two twin chambers for gas loading and flow-control. The argon pressure near the surfatron gap is set to 1 mbar. The surfatron is placed at mid-position of the fiber length and is driven by a CW microwave generator. The surfatron has a tunable cavity length to adjust its resonance frequency, and a gap-distance of 2 mm. On resonance the microwave power coupling efficiency exceeds 90%. This allowed the minimisation of the microwave field mismatch induced heating, which causes fiber damage. Figure 4(b) shows the recorded spectrum as it is transmitted through the HC-PCF. The output profile of the transmitted emission at 750 nm (Fig. 4(b) right-hand-side inset) exhibits a Bessel-like profile indicating that the spectrum is guided dominantly in a single mode fashion. A distinctive feature of this spectrum compared to those generated in conventional capillaries with a much higher microwave power [23] is its strong emission of Argon ion (Ar II) in the range of 350 nm to 500 nm. The unusually large ratio of the Ar II line intensities over those of Ar I lines (range: ~700–800 nm) is indicative of a very strong ionisation rate and/or a large microwave power density [24]. In particular, our excitation system yields power densities of ~0.1 MW.cm⁻³ (45 W applied to a 100 μm fiber-diameter to produce a 6 cm-long plasma). Furthermore, the plasma remains stably running over hours with no measurable damage on the fiber.

The successful confinement of such extreme levels in power and electron densities with no damage to the host structure raises questions about the gas temperature level and profile.

The gas temperature of the NPR was deduced using spectroscopic diagnostics [25] by fitting the measured ro-vibrational OH band, coming from traces of water adsorbed on the fiber core inner-wall to calibrated spectra. The wall temperature (i.e. the temperature at the HC-PCF outer-jacket) was measured with a thermal probe. The measurements near the gap give a gas temperature of 1300 ± 200 K in the plasma center, and a wall temperature of 500 ± 20 K. This high NPR gas temperature and strong gradient is explained in Fig. 5 which summarises the results obtained numerically using a self-consistent fluid-type model and describes the dynamics of the plasma charged particles and the energy transfer from the SW field to the electrons and to the neutral gas in our experimental conditions [26,27].

 

Fig. 5 Calculated transverse profiles of (a) the plasma potential (black) and the electron mean energy (red), and (b) the normalized densities for the electrons (black) and the ions (red), for average electron density of 1.3x10¹⁴ cm⁻³ and r₀ = 50 μm. The insets show the evolution with the radius of (a) the maximum plasma potential and (b) the space-charge sheath thickness, defined from a reference position that corresponds to 1% of relative charge separation. (c) Gas temperature transverse profiles for different radii and average electron densities. (d) Gas power-density associated with ion acceleration (dashed lines) and electron-neutral elastic collisions (solid lines), obtained at 1.3x10¹⁴ cm⁻³ average electron density for radii of 1000 μm (black) and 50 μm (red). The dotted vertical red line in (b) and (d) shows the axial position of the sheath beginning for 50 μm core-size case. All simulations were performed at 1 mbar pressure, 2.45 GHz frequency and 500 K wall gas temperature.

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3. Dynamics and confinement of surface-wave microplasmas discharges

Figures 5(a) and 5(b) show the transverse profiles, when the core-radius is 50 μm, for the electron mean energy and its associated plasma potential (Fig. 5(a)), and for the charge particle densities (Fig. 5(b)). The results reveal the electron mean-energy reaching a staggering figure of ~10.5 eV, consistent with an axis-to-wall potential difference of ~45 V [21], and associated with a space-charge field which is found to be 100 times higher than the microwave electric field. Concomitantly, the results show that the plasma effective region (i.e. the NPR) is localised within ~60 μm diameter area in the center of the 100 μm diameter fiber-core, thus surrounded by a very wide space-charge sheath relative to the host-structure size. These distinctive features are mainly a direct result of the micro-scaled fiber-core as is illustrated in the exponential-like increase of the plasma potential maximum (Fig. 5(a) inset) and the sheath-width (Fig. 5(b) inset) with the radius decrease. For example, the sheath-width increases from less than 1% of the core radius to ~40% when the radius is dropped from 1 mm to 50 μm respectively (Fig. 5(b) inset). As a consequence, most of the highly-mobile electrons are confined within the NPR whereas the ions are strongly accelerated towards the core-surround. This dynamic explains both the strong ionization implied by the experimentally observed enhanced Ar II line intensities and the gas-temperature gradient between the center of the fiber and its wall. The latter is corroborated by the calculated gas temperature transverse profiles for different representative combinations of radius and electron density (Fig. 5(c)). Firstly, the figure shows NPR gas-temperatures in the range ~950 K to ~1600 K, when n_e is in the range of 1.3x10¹⁴ cm⁻³ to 5x10¹⁴ cm⁻³, which is in qualitative agreement with the spectrally measured value of ~1300 ± 200 K at 4x10¹⁴ cm⁻³. Secondly, the on-axis gas temperature increases with the electron density as confirmed by results obtained at r₀ = 1 mm for n_e = 2.2x10¹³ cm⁻³ (at 0.9 W.cm⁻¹ power per unit length transferred from the plasma to the gas) and n_e = 1.3x10¹⁴ cm⁻³ (at 8.2 W.cm⁻¹). However, the on-axis gas temperature decreases with the core-radius, as shown by results obtained at n_e = 1.3x10¹⁴ cm⁻³ for r₀ = 1 mm (at 8.2 W.cm⁻¹ power per unit length) and r₀ = 50 μm (at 1.4 W.cm⁻¹). The implied decrease of thermal plasma-to-gas power transfer upon core-radius reduction is explained in Fig. 5(d). The figure compares the transverse profiles of the gas power-density gain associated with ion acceleration (and subsequent collisions with neutrals) and electron-neutral collisions, calculated for n_e = 1.3x10¹⁴ cm⁻³. Unlike in conventional SW discharges where electron-neutral collisions control the plasma-to-gas power transfer [26,27], here the results show that the power transfer is overpowered by ion acceleration. The latter exhibits a 200-fold enhancement in power density when the radius is decreased from 1000 μm to 50 μm to reach several 10 kW.cm⁻³ in the NPR, (see Fig. 5(d)). Furthermore, because of the large mean free paths of the ions (typically ~100 μm), this ion-acceleration-induced collisional ion-to-neutral heat transfer is sensibly reduced, which explains the smaller on-axis gas temperature at 50 μm core-radius. Finally, it is noteworthy to highlight that because of the mean-free path of one the plasma constituents (here the ions) exceeds the geometrical transverse dimensions of the hosting structure, the fluid model provides a qualitative picture, and that in order to take into account the complicity of the plasma dynamics in such a highly confined geometry a full kinematics model is required.

4. Conclusion

In conclusion, generation and confinement of stable microwave gas-plasma in photonic dielectric microstructure such as HC-PCF has been demonstrated. This original and compact platform could in particular trigger the emergence of highly compact lasers in the UV-XUV spectral range or of plasma-state photonic crystal structures. Finally, the unique combination of extremely high microwave power densities and ionization degrees with relatively low temperatures indicates that the present plasma could host novel fundamental phenomena both in nonlinear optics and plasma physics.