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An efficient and tunable 176-550 nm source based on the emission of resonant dispersive radiation from ultrafast solitons at 800 nm is demonstrated in a gas-filled hollow-core photonic crystal fiber (PCF). By careful optimization and appropriate choice of gas, informed by detailed numerical simulations, we show that bright, high quality, localized bands of UV light (relative widths of a few percent) can be generated at all wavelengths across this range. Pulse energies of more than 75 nJ in the deep-UV, with relative bandwidths of ~3%, are generated from pump pulses of a few μJ. Excellent agreement is obtained between numerical and experimental results. The effects of positive and negative axial pressure gradients are also experimentally studied, and the coherence of the deep-UV dispersive wave radiation numerically investigated.
©2013 Optical Society of America
1. Introduction
Mature, tunable, solid-state lasers emitting ultrashort (fs) pulses of coherent ultraviolet (UV) and visible light do not so far exist, despite being much sought after in applications such as ultrafast spectroscopy, multiphoton microscopy and remote sensing. Available pulsed UV light sources are mostly based on frequency conversion, in nonlinear crystals, of 800 nm pulses generated in a Ti-sapphire laser [1]. Such systems tend to be complicated to set up and use, which is undesirable in many applications [2]. An alternative is to generate a bright supercontinuum using solid-core photonic crystal fiber (PCF) [3,4], from which one can subsequently filter and select a desired wavelength. In practice, however, the ultra-broadband nature of the supercontinuum reduces the spectral brightness, and furthermore the shortest supercontinuum wavelength generated in solid-core PCF is limited to ~280 nm [5]. An alternative method for concentrating the emitted energy into a narrower bandwidth is to use phase-matched dispersive wave emission [6,7]. In solid-core optical fibers, although dispersive wave emission has often been investigated in the context of supercontinuum generation [8–12], it has also been demonstrated alone as a practical method of frequency conversion to the visible and IR [6,7,13–15]. Although the phase-match wavelength of the dispersive wave can be adjusted over a small range by varying the input pulse energy, significant tunability is not possible since the dispersion landscape in solid-core PCF is fixed. Furthermore, material absorption in solid-core fiber at UV wavelengths fundamentally limits the shortest transmitted wavelength and achievable pulse energy.
Recently, the emission of dispersive waves in gas-filled kagomé-style hollow-core photonic crystal fiber (HC-PCF) has been investigated [16], showing high conversion efficiency and signals detectable down to the deep-UV (200 nm) [17]. These fibers offer broadband transmission and weak anomalous dispersion from the UV to the near-IR (Fig. 1(a)), the dispersion being accurately modeled using hollow capillary waveguide theory [18–20].
Fig. 1 (a) Measured loss (solid curve) and calculated dispersion characteristics (dashed curves) of a kagomé fiber with 27 µm core diameter and filled with Ar at three different pressures. (b) Calculated wavelength of dispersive waves for different gases and at different filling pressure.
These properties not only help support ultrafast soliton dynamics, but also allow the guidance of any UV light that is subsequently generated at a relatively low loss of ~3 dB/m [17]. The ability to quickly adjust the gas species and gas pressure inside the fiber core also offers a new degree of freedom over conventional fibers, enabling pump-independent dispersion landscape tuning (Fig. 1(a)). It should be noted that although the dispersion follows that of a simple capillary, the large losses in capillary fibers (associated with the small core sizes required to achieve anomalous dispersion while maintaining a usable level of nonlinearity) rule out their use for UV dispersive wave emission. In this paper, we continue our earlier study on such emission [17], showing how the emission characteristics can be further optimized with the aid of accurate numerical simulations. We demonstrate significant enhancement to the output tunability, both to the vacuum UV and the visible spectrum. The enhanced vacuum UV emission in particular is of significance to many applications and cannot be easily accessed by conventional techniques. We also investigate the additional degree of freedom that comes from creating a pressure gradient within the fiber.
2. Phase-matched resonant dispersive wave emission
Also known as non-solitonic or Čerenkov radiation, resonant dispersive-wave emission was originally understood to occur when a soliton is perturbed by higher-order dispersion [21–24]. Briefly, an extremely short soliton – usually obtained by self-compression of a high-order soliton – can have sufficient bandwidth to overlap with a spectral region where the phase velocity of linear (i.e., dispersive) waves matches that of the soliton. In this case, energy is resonantly transferred from the soliton to the dispersive wave at the phase-match frequency, with very high efficiency. It has recently been suggested that this phenomenon can be better explained as arising from cascaded four-wave-mixing [25], without any reference to soliton dynamics. In both descriptions the phase-matching condition is, however, the same:
where β is the frequency-dependent modal propagation constant along the fiber axis and βNL is the nonlinear propagation constant, including the Kerr effect [12]. While a more generalized representation of βNL does exist [26], for rapid estimation of the phase-match wavelength without going through full numerical simulations, it is often replaced by the more simple nonlinear soliton propagation constant βsol:where ω0 is the soliton center frequency, γ is the nonlinear coefficient [27], and P0 its peak power. Substituting this representation of βsol, which implicitly neglects the self-steepening effect, for βNL in Eq. (1) then leads to the phase-matching condition:Note that whereas Eq. (2) includes the soliton peak power P0, Eq. (3) is based on calculating the Kerr contribution using the compressed peak power Pc, which can be significantly higher than P0. This leads to better agreement with numerical simulations and experiment. It has previously been stated in the literature [15] that one should take the peak power of the most intense individual soliton emerging from the fission of the input high order soliton in Eq. (3). This is however inaccurate, since the nonlinear refractive index shift is caused by the total field intensity, not just by the most intense soliton. The exact peak power of the compressed pulse is only fully determined by the dynamics in the fiber including the full dispersion landscape. One approximation that improves the usefulness of Eq. (3) involves taking simple empirical relations for soliton effect compression [28,29], and using them to replace the last term on the left hand side with , where N is the input soliton order.In solid-core fibers the phase-matching is dominated by the linear terms, whereas the low dispersion slope in gas-filled kagomé fibers means that, even though the material nonlinearity is relatively weak, the nonlinear contribution to the phase-matching is significant. The calculated phase-match wavelengths (based on Eq. (3)) in a kagomé-style HC-PCF with core diameter 27 μm are plotted against pressure in Fig. 1(b) for Ar, Kr, and Xe. Phase-matching is achievable from 150 nm to beyond 550 nm.
Clean dispersive wave pulses are generated only when the point of maximum compression is very close to the end of the fiber, which occurs for particular combinations of input pulse energy and gas pressure. If the point of maximum compression is far from the end-face, the residual pump pulse can undergo several recompression events, resulting in the emission of further dispersive waves and spectral interference. Additionally, the dynamics associated with pump pulse compression, such as shock-wave formation via self-steepening, strongly determine the strength of the emitted dispersive wave. These are also determined by the input energy and the properties of the gas-filled fiber. In order to select the best sets of parameters, we conducted numerical simulations, based on a unidirectional full-field equation that includes the optical shock effect, full higher order dispersion, third harmonic generation, and ionization [30–32], and scanned for the optimal combinations of pressure, input energy and fiber length. Four different signal wavelengths (200 nm, 225 nm, 250 nm and 275 nm) were chosen and optimizations carried out for the highest conversion efficiency and the narrowest dispersive wave spectral bandwidth. For this initial simulation, an ideal Gaussian input pulse was used, while fiber loss was excluded.
3. Experiment
The kagomé HC-PCF used in most of the experiments had a core diameter of 27 μm and 5 rows of unit cells in the cladding (inset of Fig. 1(a)). For generating dispersive waves in the vacuum UV, a three-row kagomé HC-PCF with 37 μm core diameter was used. The two fiber ends were sealed inside two separate gas cells, as shown in Fig. 2, independently connected to the gas control system, enabling independent control of pressure at each end.
Fig. 2 Schematic of the experimental set-up. Chirped mirrors were employed at the input to compensate for the material dispersion due to the lens and glass window.
Linearly polarized pulses of FWHM duration ~38 fs, generated by an amplified Ti:sapphire laser system (Coherent Mantis, Legend) and centered at 805 nm, were focused into the fiber using a suitable achromatic lens placed outside the gas cells. Located at the entrance and exit end of the gas cells are 1 mm thick MgF2 windows, whose dimension and material were chosen to minimize unwanted dispersion, nonlinearity and absorption on the in-coming and out-going beam (the intensity at the window can reach several GW/cm2). The second-order dispersion of the lens and window was pre-compensated with matching chirped-mirror pairs. The diagnostic equipment included a power meter (Ophir PD-300UV) and two spectrometers. In the visible to deep-UV range a CCD-array spectrometer (OceanOptics MAYA2000Pro) with an attached optical fiber was used, the wavelength-dependent sensitivity of the combination being carefully calibrated. For the vacuum UV measurements a monochromator (McPherson 234/302) purged with Ar gas was used. Approximately wavelength-independent attenuation of the output beam was achieved by multiple reflections at fused-silica glass surfaces.
In preparation for the experiments the gas system and fiber were evacuated and purged with the target gas to ensure purity of the final sample. Changes in gas species and pressure were found to have an almost immediate effect on the output spectrum, which stabilizes within seconds, while the coupling efficiency and output energy remained unchanged. Nevertheless, data were taken at least 20 seconds after any change of gas pressure to ensure that the system had fully settled down to the new equilibrium.
For optimal dispersive waves at 250 nm, the numerical simulations suggested that 10 cm of fiber, 9 bar of Ar and 1.22 µJ of input energy would be required. The corresponding experimental UV outputs, taken at four different input energies around the predicted value, are plotted in Fig. 3.
Fig. 3 Measured output spectra of the kagomé HC-PCF (core diameter 27 μm, 9 bar Ar) at various input energies, showing the range of different spectral shapes obtainable in the UV.
It is clear from the graph that, for a particular fiber filling pressure, there exists an input energy level that provides the best UV generation, both in terms of bandwidth and spectral shape. Furthermore, an increase in input energy also influences the power-dependent phase-matching condition, shifting the emission peak towards shorter wavelengths, in agreement with previous experiments [9,13]. The input energy required for optimal conversion in the experiment is approximately 10% higher than that predicted by initial simulations (1.31 μJ compared to 1.22 μJ). We attribute this small disparity to the fiber loss, which was not included in the numerical modeling.
The full experimental input-energy tuning dynamics for the four pressures chosen by the optimization routine are illustrated in Fig. 4 (top row). Corresponding simulations that include fiber loss, and where experimentally measured input pulse were used, are also illustrated (bottom row). As the input energy is increased, for example from 0.2 to 1.5 µJ at 5 bar (Fig. 4(a)), the full potential of soliton self-compression, indicated by dramatic spectral broadening, can be appreciated. This permits the soliton spectrum to overlap with the resonant wavelength, facilitating the emission of dispersive waves. Further increase in input energy does not enhance the output UV spectrum, but rather can lead to degradation in quality due to cross-phase modulation with the residual pump light at 800 nm.
Fig. 4 Experimental (top row) and simulated (bottom row) output spectra of a 10 cm Ar-filled kagomé HC-PCF at various input energies and pressures of (a,e) 5 bar, (b,f) 6.9 bar, (c,g) 9 bar and (d,h) 13.5 bar. The zero-dispersion wavelength is indicated by the dashed black-white line. An additional signal from a HOM dispersive wave can be seen in (d).
At 13.5 bar the measured spectra (Fig. 4(d)) show an additional signal at wavelengths just shorter than the main dispersive wave. By modeling the dispersion and phase-matching condition between pump (in the fundamental mode) and dispersive waves in higher-order modes (HOMs), we identified this signal as a dispersive wave generated in the HE12 HOM [33]. Such HOM dispersive waves have also been detected at pressures other than 13.5 bar, but they are much weaker than those generated in the fundamental mode. This is because (a) the modal overlap with the fundamental pump mode is smaller and (b) the phase-match wavelength lies deeper in the UV, where the broadened soliton spectrum is much weaker.
The experimentally measured relative bandwidths vary between 1.8 and 3.1%, in good agreement with the simulations. A slight disparity between the measured and predicted UV wavelength was however apparent (204 nm versus 226 nm in Fig. 4(a) and 4(e), for a pressure of 5 bar). This disparity was found to vary in an unsystematic manner as the pressure was increased. Inaccuracies in the model used to calculate the dispersion [18] cannot fully explain the discrepancies, since one would expect any such errors to be systematic and less significant at shorter wavelengths. Additionally, the agreement between simulation and experiment around 800 nm is extremely close, which indicates that the values used for material nonlinearity and total dispersion are reliable in that spectral region. A more likely reason is uncertainties in the phase-matching condition, which is highly sensitive to small errors in the Ar dispersion curve, its reliability being reduced in the UV. Additionally, two-photon resonances can play a significant role when generating light so deep in the UV, with the result that the gas nonlinearity can become strongly frequency dependent.
The pulse energies in the UV band were measured by multiple reflections of the output beam at filtering mirrors, which were specifically selected for the four target wavelengths mentioned above, with reflections up to 99% within approximately ± 10 nm of the target wavelength, and below 10% for other regions. Experimental measurements, summarized in Table 1, indicate that up to 6.6% of the total output power lies within the narrow UV band, which translates to a pulse energy of 75 nJ.
Table 1. Experimental Parameters for Optimized Dispersive Wave Generation at Various Wavelengths
While higher dispersive wave conversion efficiencies from the IR to the visible have been reported [6,15,34], the frequency shifts were substantially smaller than reported here. Furthermore, the signal energies were spread over a much larger bandwidth than in our experiments, which specifically aim for the narrow spectral bandwidths useful in applications such as the seeding of free-electron lasers [35]. The change in total energy transmission ratio for the four cases in Table 1 can be explained by the wavelength-dependent loss of the fiber and the differing spectral dynamics.
Figure 5 illustrates the wide tuning capability of the system, showing that the dispersive wave can be continuously tuned from 200 nm to 275 nm in Ar gas, and further extended to beyond 550 nm using Kr or Xe.
Fig. 5 Experimental generation of coherent ultrashort pulses through resonant dispersive wave emission in gas-filled kagomé HC-PCF. Each peak is the individual normalized spectrum for a specific gas, pressure and pump energy. All the tuning was carried out in an identical length of kagomé HC-PCF (27 µm core diameter), except in the case of neon, where the core diameter was 37 µm.
The maximum pressure of 14 bar was constrained only by the mechanical strength of the MgF2 window used in the system, and could be substantially increased, thus further enhancing the tuning range. The tuning range can easily exceed 600 nm if broader-bandwidth dispersive waves, generated at lower pump energies, are included. The generation of dispersive waves below 200 nm presents a challenge, as the broader compressed soliton spectrum necessitates higher peak intensity, leading to undesirable ionization in the core [36]. Using Ne gas, however, together with a kagomé HC-PCF with a larger 37 µm diameter, one can achieve phase-matching in the 200 nm region. Since the ionization threshold in Ne is higher than in Ar, significant dispersive wave signals can be generated in the vacuum-UV (VUV). In the experiment, strong signals were detected with the monochromator at wavelengths down to 176 nm. In principle, the generated dispersive waves could be shifted further into the VUV region by pumping at 400 nm using a frequency doubled Ti:sapphire laser.
Although the dispersive wave emission is widely tunable (Fig. 5), some wavelength bands (most notably at ~420 nm) coincide with high fiber loss, which suppresses the emission. These loss bands stem from resonances in the glass cladding structure that become phase-matched to the core light, and are unique to the geometry of the fiber. The wavelength of these loss bands can be shifted by altering the cladding structure.
4. Dispersive wave emission in a pressure gradient
Independent pressure control over the input and output ends of the fiber makes it easy to produce a pressure gradient along the fiber. In doing so we can explore how an axially-varying dispersion affects dispersive wave generation. The stationary pressure distribution along the fiber, can be written as [37]:
where p0 and p1 are the pressures at the input and output end of the fiber, z is the position along the fiber, and L is the total fiber length. The green dotted curve in Fig. 6 shows the pressure distribution when one end of the fiber is held at 0 bar and the other at 12 bar. Also plotted are the corresponding zero-dispersion wavelengths (ZDW) (Fig. 6, blue solid line) and the phase-match wavelength for the dispersive wave (Fig. 6, red dashed line).Fig. 6 Calculated pressures (green dotted line), ZDWs (blue solid line) and wavelengths of the dispersive wave (red dashed line) in a Kr-filled kagomé PCF with core diameter 27 µm with a pressure gradient between input and output.
When the input energy is increased, the nonlinearity is strengthened, which has the effect of slightly shifting the phase-match wavelength to higher frequencies (Fig. 7(a)). Changing the input energy also shifts the position of maximum self-compression, which in a fiber with a pressure gradient causes the dispersion experienced by the compressed pulse to vary. Compared to energy tuning in the absence of any pressure gradient, this leads to a more dramatic change in phase-match wavelength.
Fig. 7 (a) Experimental output spectra with Kr at constant pressure of 12 bar in 90 cm of kagomé fiber with 27 μm core diameter pumped at 800 nm with a pulse FWHM of ~50 fs; (b) positive pressure gradient of 0 to 12 bar; (c) negative pressure gradient of 12 to 0 bar.
This is illustrated in Fig. 7 for a 90 cm long fiber. For constant pressure (12 bar in Fig. 7(a)) the dispersive wave is observed to shift to higher frequencies for higher energies, whereas when the pressure is fixed at 0 bar at the input and 12 bar at the output (positive gradient, Fig. 7(b)), the dispersive wave shifts more strongly to higher frequency as the pulse energy is increased.
On the other hand, when a negative gradient is applied (Fig. 7(c)), the nonlinear and pressure-gradient contributions compete against each other, resulting in reduced tunability and a dispersive wave frequency that is almost independent of pump energy. Note that the threshold for dispersive wave emission slightly increases as one goes from constant pressure to a negative pressure gradient, and to a positive pressure gradient (Fig. 7(a-c)), as would be expected from the decreasing effective nonlinearity during the compression stage at the beginning of the fiber. Note also that for low energies the compression point is nearer the output end of the fiber, so that the compressed pulse will experience a higher pressure for a positive pressure gradient than for a negative, and therefore will emit a dispersive wave at longer wavelength (compare Figs. 7(b) and 7(c) at energies below ~250 nJ).
5. Temporal dynamics and coherence
Additional insight can be gained by studying the numerically simulated temporal evolution. Plotted in Fig. 8(a) are the results of one such simulation for a 10 cm long fiber at a constant Ar pressure of 9 bar and a launched pump pulse energy of 1.4 µJ – parameters similar to those used in [17].
Fig. 8 (a) Evolution of the squared electric field (green line) and field envelope (blue line) for 9 bar Ar and 1.4 µJ input energy, plotted on a normalized linear scale. The red line represents the high frequency component (200 to 300 nm) of the electric field, with its intensity doubled for better contrast. (b) Simulated spectrograms of the pulse at different stages for the same parameters in (a), obtained with a 10 fs Gaussian gating-pulse, with the ZDW indicated by the red dashed line.
The green line represents the squared electric field, while the blue line denotes the pulse envelope. The red line represents the high frequency component of the electric field, obtained by bandpass filtering between 200 and 300 nm (the spectral intensity relative to the pump has been doubled for better contrast). At the point of maximum self-compression (z ~7 cm), where the pulse duration is ~2 fs, a clear shock front is formed and UV frequency components begin to emerge from it. The dispersive wave, initially overlapping with the pump in time, induces interference in the envelope. Having a slower group velocity compared to the pump, it gradually lags behind the main pulse, at which point interference between the two ceases. Figure 8(b) shows the corresponding XFROG traces, obtained with a 10 fs Gaussian gating-pulse. Since the gas pressure and energy were deliberately chosen for maximum UV generation near the fiber end, the walk-off between pump and dispersive wave is not dramatic. From Fig. 8(a) it can be seen that the duration of the UV pulse at the output is some 10s of fs. During the early stages of generation it has a duration of only a few fs (8 cm in Fig. 8(a)).
The temporal coherence of the generated dispersive wave pulse was also explored by examining the modulus of the complex degree of first-order coherence in the numerical simulations, which can be simplified to [38]:
where the angle brackets denote an ensemble average over multiple numerically simulated electric fields that differ from each other by the initial seed noise. If the independently generated electric fields had perfectly equal phase and intensity, the value of gpq would be 1, whereas a gpq of 0 indicates completely random phases between different shots.Figure 9(a) shows the simulated propagation of a 1.5 µJ input pulse (core diameter 27 µm, Ar pressure 13.5 bar). Figure 9(c) plots the corresponding coherence, showing that the dispersive wave is coherently generated for these parameters.
Fig. 9 (a,b) Simulated pulse evolution and coherence at different point of propagation for 1.5 µJ and 3 µJ of input energy, in a fiber filled with 13.5 bar of Ar. (c, d) Normalized coherence parameter gpq along propagation for the two different energies, with a value of 1 indicating perfect coherence.
On the other hand, for an input energy of 3 µJ, plotted in Fig. 9(b,d), there are substantial shot-to-shot fluctuations over a large spectral range, especially in the later stages of propagation. While the dispersive waves, once generated, remain largely coherent while they propagate, the visible band experiences progressive de-coherence as the pulse propagates. This may be attributed to the generation of additional incoherent light from various sources, including but not limited to modulational instability [39]. This incoherent light is much more prominent when ionization terms are included in the simulations, providing possible evidence for the recently reported ionization-induced modulational instability [40].
5. Conclusions
Excellent agreement can be obtained between the experimental and numerically simulated dynamics of short pulses in gas-filled kagomé-style HC-PCF, allowing relatively accurate optimization and prediction of the parameters needed for efficient, spectrally-localized resonant dispersive wave emission. Conversion efficiencies of several percent to a wavelength band a few nm wide, tunable over 1 PHz from 176 to 550 nm, can be obtained using few-μJ 38 fs pulses at 800 nm. The tunability can be further controlled by introducing a gas pressure gradient. Numerical simulations show that the generated dispersive wave pulses are highly coherent, independent of the input pulse energy, while their durations are of the order of tens of fs. The gas-filled kagomé HC-PCF system fulfills for the first time the demands of applications where a simple, compact and widely tunable UV source is required.
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