Gas-filled hollow-core fibers present an interesting means for realizing femtosecond ultraviolet (UV) light sources [1–3]. The technique capitalizes on the unique dispersion landscape of hollow-core fibers, which permits phase-matched conversion of the pump in the near-infrared to UV through dispersive wave generation. This coupled with solarization-free guidance of UV in hollow-core fibers has led to multiple demonstrations of the UV generation process, achieving wavelengths as short as 110 nm [4].

For the onset of UV in the gas-filled hollow-core fiber, the pump must accumulate sufficient nonlinear phase shifts along the propagation. One common drawback of the gas-based system in this respect is its relatively small nonlinear index. For instance, the third-order susceptibility of argon at its standard pressure and temperature is about 4 orders of magnitude lower than that of fused silica. While this shortfall can be compensated to some degree by increasing the gas pressure or choosing heavier gas, doing so also largely affects the dispersion, shifting the phase-matching point toward a longer wavelength, which may not be desirable in many applications. Alternatively, one can use longer propagation distance or higher pump peak power to produce enough nonlinear phase shifts. However, the former is subject to transmission and bending losses in the hollow-core fiber, and the latter raises the bar on the pump source requirement.

One simple approach to mitigate the issue is to come up with a hollow-core fiber that tightly confines light into very small mode area. In the small-mode-area hollow-core fiber (SMA-HCF), much higher intensity is achieved for given peak power, allowing large nonlinear effects to be induced from relatively small pulse energy. It exploits the universal energy scaling in gas-based nonlinear optics [5]. Up-scaling of the process demonstrated recently in a large-core capillary led to generating microjoule-level UV pulses [4]. The down-scaling has also been tested in a kagomé-type hollow-core photonic-crystal fiber with flat-to-flat core diameter of 22 μm, achieving the UV radiation by launching a 800 nJ pump, which is the lowest reported until now [6]. We note, by confining the beam further into <50μm2, the pulse energy requirement for the UV emission can be reduced to sub-hundred nanojoules—to a level that is accessible by modern compact femtosecond oscillators operating at multi-megahertz repetition rates [7]. This opens a potential pathway to develop a compact and robust UV frequency comb source.

In this work, we report low-energy-threshold onset of the wavelength-tunable deep-UV pulses in an argon-filled hollow-core fiber. This is achieved in a short piece of SMA-HCF, which is obtained by scaling down a tubular hollow-core fiber through tapering. We demonstrate that with the effective fundamental mode area of 51.3μm2, the energy threshold for triggering the UV radiation can be as low as 125 nJ.

The transmission loss is the main point of concern when a small-scale hollow-core fiber is considered. In both a simple dielectric capillary and an antiresonant-guiding hollow-core fiber, the loss increases rapidly with reduction in the core size [8,9]. We note, on the other hand, a remarkable recent progress in low-loss antiresonant-guiding hollow-core fibers [10,11]. Studies have shown substantial suppression of the loss when negative curvatures are introduced at the core-cladding interface. This has promoted a simple fiber design that consists only of several non-touching cylindrical cladding tubes surrounding the central hollow core [12,13]. The geometry of SMA-HCF is based on this nodeless tubular hollow-core fiber structure.

Fabricating a small-scale low-loss hollow-core fiber directly from the drawing tower is challenging. This is because, without a careful control, the cladding elements tend to stick to each other due to surface tension, forming dielectric nodes that substantially degrade light guidance [14]. Among the tubular-type hollow-core fibers, the smallest core diameter achieved straight from the thermal drawing so far is 15 μm intended to guide light at 355 nm [15]. One attractive approach to overcome this difficulty is to post-process the fiber in a tapering rig to gently stretch it under heat in a well-controlled manner [16]. This technique has been demonstrated for down-scaling a tubular hollow-core fiber to finally arrive at a core diameter as small as 5.8 μm [17].

For the fabrication of SMA-HCF, a tubular hollow-core fiber with the original core diameter of 25.6 μm is used. The tapering produces a down- and an up-transition regions, and between the two, there is a taper waist where the reduced dimension is maintained along its length. This part can serve as SMA-HCF. In our setup, we can produce the taper waist of up to 15 cm in length, which is sufficiently long for the experiment to follow.

The transmission spectra of the original fiber and SMA-HCF obtained using a high-power xenon lamp are plotted in Figs. 1(b) and 1(c), respectively. The gray shaded regions are the high-loss bands that appear due to the cladding element wall thickness [18]. A reduction in the wall thickness from 415 nm in the original fiber to 186 nm in SMA-HCF blueshifts these loss bands correspondingly. That is, the first high-loss band is moved from 800–960 to 380–420 nm, and the second one is pushed from 440–490 to, supposedly, 200–220 nm, which is outside the coverage of our xenon lamp. In Fig. 1(c), light guidance in the core is not supported beyond 970 nm in SMA-HCF. This cutoff shifts to shorter wavelength with further reduction in the cross-sectional structure, placing an ultimate limit on the applicable scaling-down factor for a given pump wavelength. The loss at 800 nm measured using cut-back method is 16dB⋅m−1. The oscillations seen in the transmission spectra in Figs. 1(b) and 1(c) are attributed to the outer jacket thickness-induced resonances. They appear because of the incoherent xenon lamp exciting modes of the overall structure. Here, the outer jacket acts as an additional antiresonant reflection layer, resulting in the high-loss regions that are uniformly separated at a frequency governed by its thickness. This effect is comprehensively studied in thin-wall dielectric capillaries of different wall thicknesses [19]. The jacket thicknesses in the original fiber and SMA-HCF are 7 and 2.9 μm, amounting to the separations of 14.8 and 35.7 THz, respectively. These values are in good agreement with the fringe patterns in Figs. 1(b) and 1(c). Nonetheless, the jacket thickness-induced resonances have negligible impact on the fundamental core mode due to small spatial overlap between the core and dielectric jacket modes. With the use of a laser beam, the light can be coupled predominantly into the fundamental core mode and avoid the jacket thickness-induced resonances.

The loss spectrum of SMA-HCF calculated using finite-element modeling is presented in Fig. 1(c) as reference. Here, a uniform tubular hollow-core fiber that has a 10.6-μm-diameter core surrounded by six cladding tubes of diameter 4.45 μm and wall thickness 186 nm is assumed. Figure 1(c) shows also the expected normalized transmission of the 5-cm-long SMA-HCF, which is obtained from the calculated loss and source spectrum. The cutoff wavelength and locations of the high-loss bands in the calculation are in excellent agreement with the measured values. From the modeling, the loss is 11dB⋅m−1 at 800 nm, which is close to the measured value.

Within the simple six-tube geometry, the lowest loss is achieved when the ratio of cladding tube diameter to core diameter is 0.6–0.8 [20]. Considering that this ratio is 0.42 in SMA-HCF, there still is room for further reduction in loss that can be realized by controlling the cladding tube size during the fabrication. For better improvement, we can adopt a fiber design that is optimized for ultra-low-loss transmission, such as the nested antiresonant nodeless hollow-core fiber [21]. Alternatively, the system can be pumped at a shorter wavelength, e.g., at the second harmonic, to increase the core diameter to wavelength ratio, which is the dominant factor influencing loss in hollow-core fibers [22].

The effective mode area of SMA-HCF is calculated to be 51.3μm2 at 800 nm. The small mode area presents an ideal observe broadening of the platform for hosting nonlinear experiments at low pulse energies.

For the measurement of output spectrum, the exiting beam emerging from the output window of the gas chamber is collected directly using a fiber patch cable attached to the spectrometer. This raw measurement is intensity calibrated by applying spectral response functions of the diagnostic instruments. Further to that, rather low average power at the output of SMA-HCF makes it impractical to use an integrating sphere to collect the entire beam into the spectrometer. Hence, when taking measurements, the end face of the patch cable is placed at the center of the output beam. Since the divergence angle of the beam depends on the wavelength, the recorded spectrum needs to be scaled by the square of the wavelength to obtain true spectral composition of the total output. We affirm that the measured spectra presented in the subsequent sections have this correction factor applied.

The UV radiation weakens as the pump energy is decreased, and it disappears into the noise when the observed output pulse energy is below 100 nJ. This amounts to the pump energy of 125 nJ. At this point, there is only a small peak that is approximately 30 dB down from the pump at 239 nm as shown in Fig. 3(b). We highlight that the demonstrated pump energy threshold is the lowest reported so far, and it is at the level that can be delivered by modern high-repetition-rate femtosecond laser oscillators. One major limiting factor in this regard is the poor coupling efficiency, which we believe can be improved with further engineering of the gas chamber and fiber coupling optics.

We examine our observations numerically by solving the unidirectional field propagation equation. It is given by [24] $$\begin{gathered} ∂zE(z,ω)=i(β−ωv+iα2)E(z,ω)+iω2μ02βF{ϵ0χ(3)E(z,t)3} \\ −ωμ02βF{∂tn(z,t)IPE(z,t)+e2me∫−∞tn(z,t′)E(z,t′)dt′}, \end{gathered}$$(1)where t is the time frame moving at a reference velocity, v, and z is the propagation length. E(z,ω) is the optical field in the frequency domain with ω denoting angular frequency. This is obtained by taking the Fourier transformation of the fast oscillating electric field, i.e., E(z,ω)=F{E(z,t)}. We assume propagation only in the fundamental mode of SMA-HCF. Its linear dispersion is accounted for in β, where pressure dependent contribution from the gas is obtained using a Sellmeier equation [25]. The waveguide portion of β and transmission loss α are calculated using finite-element modeling. The term containing χ(3) is responsible for the third-order nonlinearity of the pressurized argon [26]. The last term is accountable for photoionization, which has negligible effect for the cases studied in this work, but it is nevertheless included for the sake of completeness. Here, IP is the first ionization energy, and e and me are the electron charge and mass, respectively. For the calculation of local free-electron density, n(z,t), we use a model developed by Ammosov et al. [27].

The UV is generated in the form of a dispersive wave [28]. The spectral evolution along SMA-HCF leading to this output is presented in Fig. 4(b). After the launch, the 150 nJ pump, which amounts to a higher-order soliton of order 4.7, undergoes temporal compression and spectral broadening due to interplay between the anomalous dispersion and nonlinearity. Eventually, the low-intensity spectral tail of the pump reaches the phase-matching point indicated with a red vertical dashed line in Fig. 4, and conversion from the pump to this wavelength takes place. The phase-matching condition is obtained using Δβ=β−β0−β1(ω−ω0)−3ω2ϵ0μ08βχ(3)|E0|2=0,(2)where β0 and β1 are the zeroth and first Taylor series expansion coefficients of β at the pump, ω0, linked to its phase and group velocities, respectively, and E0 is the peak electric field strength of the input pulse. Figure 4(c) shows the plot of the phase mismatch featuring a zero mismatch at 238 nm. We observe another peak that appears at 400 nm, which originates from rapid variation in the dispersion near the resonant band [29]. Here, the wavelength is determined solely by, and is highly sensitive to, the wall thickness of the dielectric cladding elements. Hence, the much broader emission band observed near 400 nm in the experiment can be attributed to variations in the thickness of the cladding element walls in SMA-HCF.

The shot-to-shot coherence of the output is quantified numerically and presented in Fig. 4(d). It is obtained by running 50 simulations with random shot-noise added in the input pulse and calculating the degree of first-order coherence between them, such that 1 denotes complete preservation of the shot-to-shot coherence and 0 otherwise [30]. The entire output maintains a high degree of coherence, meaning that the phase relation between the spectral components in the pump and UV band is well-maintained.

Again, we notice a similar spectral feature at 400 nm as observed in Fig. 3, which is caused by the band edge effect. Its location is neither affected by the pulse energy nor gas pressure as is apparent in Figs. 3 and 5.

We demonstrate low-energy-threshold onset of the wavelength-tunable deep-UV emission in SMA-HCF through dispersive wave generation. The fiber is obtained by post-processing a nodeless tubular hollow-core fiber on a tapering rig. It confines light tightly into a small mode area allowing accumulation of nonlinear phase shift that is sufficient for the frequency conversion process with relatively small pump pulse energy. The energy scaling down is achieved alongside the reduction in the length requirement. This not only mitigates the issue of having high attenuation per unit length in SMA-HCF, but it is also advantageous for building a compact system. It opens a promising avenue for a compact wavelength-tunable UV frequency comb source driven directly by a femtosecond oscillator operating at a multi-megahertz repetition rate.

Acknowledgment. The authors thank J. C. Travers for valuable discussion.