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Abstract
The possibility to perform time-resolved spectroscopic studies in the molecular fingerprinting region or extending the cutoff wavelength of high-harmonic generation has recently boosted the development of efficient mid-infrared (mid-IR) ultrafast lasers. In particular, fiber lasers based on active media such as thulium or holmium are a very active area of research since they are robust, compact, and can operate at high repetition rates. These systems, however, are still complex, are unable to deliver pulses shorter than 100 fs, and are not yet as mature as their near-infrared counterparts. Here, we report the generation of sub-40 fs pulses at 1.8 µm, with quantum efficiencies of 50% and without the need for post-compression, in hydrogen-filled, hollow-core photonic crystal fiber pumped by a commercial high-repetition-rate 300 fs fiber laser at 1030 nm. This is achieved by pressure-tuning the dispersion and avoiding Raman gain suppression by adjusting the chirp of the pump pulses and the proportion of higher-order modes launched into the fiber. The system is optimized using a physical model that incorporates the main linear and nonlinear contributions to the optical response. The approach is average power-scalable, permits adjustment of the pulse shape, and can potentially allow access to much longer wavelengths.
© 2020 Optical Society of America
1. INTRODUCTION
Lasers emitting ultrashort pulses in the 2 µm range have attracted much interest over the past decade, as they provide an entry point into the mid-infrared (mid-IR) (2–5 µm) [1]. For example, high-repetition-rate thulium-doped (Tm-doped) fiber lasers [2] are being used to produce high-flux soft X-rays by high-harmonic generation in gases [3]. These complex systems have a relatively narrow gain bandwidth, so that they cannot yet offer pulse durations below 100 fs, unless external spectral broadening and compression is used [4].
Stimulated Raman scattering (SRS) in gases can be used to red shift the wavelength of a near-IR pump source, offering an alternative approach to generate 2 µm light [5] using, for example, gas cells [6–8] or gas-filled capillaries [9]. In these systems, linearly chirped pump pulses have been used to decrease the peak power and reduce spectral broadening caused by self-phase modulation (SPM) [10]. As a consequence, the red-shifted Stokes pulses must be recompressed to reach transform-limited durations, commonly measured by simple intensity autocorrelation, which does not reveal the complex amplitude of the Stokes pulse shape.
The efficiency of gas-based SRS has been dramatically improved with the advent of hollow core photonic crystal fiber (HC-PCF) guiding light by antiresonant reflection [11]. Offering low transmission loss, tight field confinement, and pressure-tunable dispersion, these fibers are extremely advantageous for boosting the nonlinear effects in gases [12,13]. HC-PCFs filled with hydrogen have been shown to be highly efficient for downshifting laser light by 18 THz (rotational SRS) [14] or 125 THz (vibrational) [15], in the latter case allowing access to the 1.8–2 µm region with commonly available 1 µm pump lasers. Recent studies have reported the generation of subpicosecond Stokes pulses in gas-filled HC-PCF [16,17]. By studying in detail the ultrafast nonlinear dynamics that governs the evolution of chirped and unchirped pulses in the gas-filled fiber, we show here how these results can be extended into the femtosecond regime. We pay particular attention to the detailed measurements of the phase and amplitude of the carrier-wave below the pulse envelope, which are vital in many applications.
In the experiments reported here, 300 fs pulses at 1030 nm from a commercial Yb-based fiber laser are downshifted to 1.8 µm by vibrational SRS in a ${{\rm{H}}_2}$-filled single-ring HC-PCF. Because the pump pulse duration is less than the lifetime of the Raman coherence, the system operates in the so-called “transient” SRS regime [18], yielding quantum efficiencies in excess of 50%. Moreover, strong interactions with Raman coherence waves, along with nonlinear effects such as SPM, enable temporal compression of the 1.8 µm Stokes pulses to durations of 39 fs [measured using second-harmonic generation frequency-resolved optical gating (SHG-FROG)], without the need for post-compression. Using numerical modeling to optimize the conversion dynamics, we unveil the key roles played by pump chirp, intermodal walk-off, and higher-order modes in the observed dynamics.
2. RAMAN CONVERSION IN HYDROGEN
In SRS, the Raman coherence manifests itself as a wave of synchronized internal molecular motion that is driven by the beat note between the pump and Stokes light, which travels at a phase velocity ${\Omega _R}c/({\omega _P}{n_P} - {\omega _S}{n_S})$, where ${\omega _P}$, ${\omega _R}$, and ${\Omega _R}$ are the angular frequencies of the pump, the Stokes and the Raman coherence; ${n_P}$ and ${n_S}$ are the refractive indices of the pump and Stokes; and $c$ is the vacuum velocity of light. The coherence lifetime ranges from $ps$ to $ns$, depending on the gas pressure [19]. In this work, we use linearly polarized pump pulses, which favors vibrational SRS, although rotational SRS turns out to play a significant role in the observed dynamics, as explained below. In the transient regime, the pump, Stokes, and coherence waves are able to exchange energy coherently, causing the Stokes light to be generated predominantly toward the trailing edge of the pulse [18]. Interestingly, in this regime the SRS gain does not saturate with increasing gas pressure, in contrast to the steady-state regime.
Raman gain suppression, normally associated with systems pumped by narrowband lasers, arises when the coherence wave for pump-to-Stokes generation is identical to the coherence wave for pump-to-anti-Stokes generation [20,21], i.e., when
where $\beta _{{\rm AS}}^{01}$, $\beta _S^{01}$, and $\beta _P^{01}$ are the wave vectors of the ${{\rm{LP}}_{01}}$-like (from this point on we shall abbreviate “${{\rm{LP}}_{\textit{mn}}}$-like” to “${{\rm{LP}}_{\textit{mn}}}$”) mode at the anti-Stokes, Stokes, and pump frequencies. Under these circumstances the probabilities of pump-to-Stokes phonon creation and pump-to-anti-Stokes phonon annihilation are equal, bringing the intramodal Raman gain to zero irrespective of pump power, and favoring the emergence of intermodal SRS, which normally sees much lower gain.We report that 1.8 µm light can be efficiently generated in the ${{\rm{LP}}_{01}}$ mode by launching a small proportion of pump light into higher-order modes (HOMs) and linearly chirping the pump pulses. The chirp reduces extreme nonlinear spectral broadening, while group velocity walk-off inhibits intermodal SRS. Together, they frustrate gain suppression.
In the absence of loss-inducing anti-crossings between the core mode and resonances in the glass walls surrounding the core [22], the modal wave vectors in single-ring HC-PCF are given to good accuracy by [13]
A further attractive feature of the system is that the second vibrational Stokes band at ${\sim}{{7}}\;\unicode{x00B5}{\rm m}$ is effectively suppressed by loss of guidance, high glass absorption, and low Raman gain, permitting highly efficient conversion solely to the first Stokes band.
3. EXPERIMENTAL RESULTS
We used a 60-cm length of single-ring HC-PCF with a core diameter of 60 µm and a capillary wall thickness of ${{310}} \pm {{40}}\;{\rm{nm}}$ (see Fig. 1 inset). By finite-element modeling, we verified that the first anti-crossing occurs at ${\sim}{{650}}\;{\rm{nm}}$, i.e., sufficiently far away from the first anti-Stokes band (${\lambda _{{\rm AS}}}\sim{{721}}\;{\rm{nm}}$) to avoid high loss, while close enough to distort the shallow dispersion and hence to affect the gain suppression condition in Eq. (1).
Fig. 1. (a) Experimental setup. The linear chirp and duration of the pump pulses were precisely controlled using a stretcher inside the fiber laser. A combination of half-wave plate (HWP) and thin-film polarizer (TFP) were used to adjust the input power. Achromatic lenses L1 and L2 were used to launch and collimate the light. A long-pass filter (LPF) with a cut-on wavelength of 1.2 µm separated the Stokes pulses from the residual pump light. (b) Autocorrelation trace of transform-limited pulses. The dashed red curve is a FWHM ${\sim}{{310}}\;{\rm{fs}}$ Gaussian fit. (c) Scanning electron micrograph of the fiber cross-section.
The fiber was mounted between two gas cells equipped with anti-reflection-coated silica windows to allow evacuation or filling with hydrogen to a controllable pressure, as shown in Fig. 1. The repetition rate of the fiber laser was adjustable, and most experiments were conducted at 151 kHz. The pump energy was controlled using a half-wave plate and a thin-film polarizer and the chirp was adjusted inside the laser. The generated signals were collimated, spectrally separated using a long-pass filter with a cut-on wavelength of 1200 nm and delivered to diagnostic systems including an optical spectrum analyzer in the visible/near-infrared, an InGaAs spectrometer for longer wavelengths, and a dispersion-free SHG-FROG system for temporal characterization of the 1.8 µm pulses. The power and mode profiles were measured with a thermal power meter and a thermal camera. The input chirp of the pump pulses was precisely controlled by fine-tuning the stretcher before the main amplification stage of the fiber laser.
Fig. 2. Mid-IR Stokes power (1.8 µm) as a function of launched pump power (1030 nm) at three different pressures. The laser pulses (300 fs when transform-limited) were chirped to a duration of ${\sim}{{600}}\;{\rm{fs}}$ by adding ${0.055}\;{\rm{p}}{{\rm{s}}^2}$ of GDD. The inset is a near-field image of the generated ${{\rm{LP}}_{01}}$ mode. The quantum efficiencies (%) of Stokes conversion are marked on the right next to each curve.
Fig. 3. Stokes pulses generated by pump pulses chirped to durations of (a) ${\sim}{{600}}\;{\rm{fs}}$ (${0.055}\;{\rm{p}}{{\rm{s}}^2}$ of added GDD) and (b) ${\sim}{{1}}\;{\rm{ps}}$ (${0.105}\;{\rm{p}}{{\rm{s}}^2}$ of added GDD). In panel (a), the shortest feature in the experimental retrieved pulse (undershaded) is already transform-limited because the output gas-cell window and collimating lens provide the required small negative chirp. (b) Experimentally retrieved pulse is shown with a solid dark blue line, yielding after compression the undershaded curve. The undershaded pulses are compared with simulations (dotted red lines) compressed by adding GDDs of (a) ${-}{{400}}\;{\rm{f}}{{\rm{s}}^2}$ and (b) ${-}{0.014}\;{\rm{p}}{{\rm{s}}^2}$. Note that the pump chirp is the same in both experiment and simulations.
In the experiment, the highest efficiency of conversion to the ${{\rm{LP}}_{01}}$ Stokes signal was obtained when the pump pulse duration (300 fs when transform-limited) was frequency-chirped to 600 fs by adding ${0.055}\;{\rm{p}}{{\rm{s}}^2}$ of group delay dispersion (GDD), as shown in Fig. 2. As expected in transient SRS [18], the quantum efficiencies (QE) increased with pressure, reaching 50% (${\gt}{1.2}\;{\rm{W}}$) at the 35 bar. While the SRS threshold decreased with increasing pressure, the slope efficiency remained unaltered at ${\sim}{{40}}\%$. These results were obtained at a 151 kHz repetition rate, and the performance of the system remained steady up to ${\sim}{{1}}\;{\rm{MHz}}$. At higher repetition rates, the output power became unstable and ultimately dropped as a consequence of the increasing thermal load.
These results make clear that SRS conversion in a gas-filled HC-PCF can be highly efficient, even in the ultrafast regime. There is, however, a surprise hidden in the temporal dynamics. Fig. 3(a) shows the experimental 1.8 µm Stokes pulse retrieved using SHG-FROG when the pump pulse (chirped to 600 fs) energy was 23 µJ. The 1.8 µm pulses unexpectedly show a transform-limited feature, with a duration of 39 fs (full width at half-maximum) and containing 40% of the total energy, followed by a long pedestal.
Figure 3(b) shows the result when the pump pulse is further chirped, to a duration of 1 ps. In this case, the short feature in the generated Stokes pulse is 140 fs long.
We found in the experiment that the conversion efficiency increased by a factor of ${\sim}{{2}}$ when the incoupling was slightly misaligned from optimal ${{\rm{LP}}_{01}}$ injection so as to increase the HOM content (see below).
4. NUMERICAL MODELING
To gain insight into the dynamics of simultaneous Stokes generation and temporal compression we numerically modeled the system using a multimode unidirectional full-field propagation equation [27]. The model includes full waveguide dispersion, instantaneous third-order nonlinear effects such as Kerr effect, third-harmonic generation, four-wave mixing, and the temporally nonlocal contributions of both rotational and vibrational SRS to the nonlinear polarization [28]. Based on experimental observations, only the ${{\rm{LP}}_{01}}$ and ${{\rm{LP}}_{02}}$ modes were included, and the intermodal overlap integrals were calculated using the modal fields obtained from finite-element modeling of a perfect single-ring HC-PCF with the same structural parameters as the fiber used. Although SRS plays a major role, instantaneous nonlinear effects such as SPM, combined with the anomalous mid-IR dispersion of the fiber, contribute to the self-compression of the Stokes pulses after they have been generated. The best agreement with the experiment was found when the pump consisted of a mixture of ${{\rm{LP}}_{01}}$ and ${{\rm{LP}}_{02}}$ modes, confirming that imperfect launching conditions play a key role in the efficient generation of Stokes light.
For pump pulses chirped to ${\sim}{{600}}\;{\rm{fs}}$, the ultrashort feature in the Stokes signal, as shown in Fig. 3(a), matches very well in simulations and experiment, showing a transform-limited feature ${\sim}{{39}}\;{\rm{fs}}$ in duration. Note that the output gas cell window and collimating lens provided the small GDD required to reach the minimum duration.
When the pump pulse was chirped to a duration of ${\sim}{{1}}\;{\rm{ps}}$, pump, Stokes and coherence waves exchange energy coherently, resulting in a series of Stokes peaks on the trailing edge of the pulse, as seen in Fig. 3(b), where dispersion-compensated versions of experimental (undershaded) and simulated (red dotted line) pulses are compared. The GDD required to compress these pulses is ${\sim}\; - {0.01}\;{\rm{p}}{{\rm{s}}^2}$, which is easily achievable with standard grating compressors. Note that the duration of the transform-limited ultrashort feature in Fig. 3(b) is longer (${\sim}{{140}}\;{\rm{fs}}$) than in Fig. 3(a) as a result of the lower peak intensity and weaker nonlinear response. In any case, the 1.8 µm pulse is always shorter than the pump pulse, even immediately after the fiber. As a result, its shape can be widely tuned by varying the pressure and the chirp, in response to requirements.
Figure 4 shows the simulated behavior of both pump and Stokes signals for pump pulses with 28 µJ pump energy, positively chirped to ${\sim}{{600}}\;{\rm{fs}}$. The transient behavior is clear: The pump is depleted on its trailing edge, giving rise to a delayed Stokes pulse. Moreover, since the initial pump duration is longer than a half-cycle at ${\sim}{{125}}\;{\rm{THz}}$, vibrational coherence is not impulsively excited but takes some time to build up. Once sufficient coherence is present, the Stokes signal is rapidly amplified at the trailing edge of the pump pulse. Combined with the strong remaining pump power, this creates an ultrashort feature on the leading edge of the Stokes pulse, followed by a pedestal, as seen in the lower panels of Fig. 4. At higher pump energies, further Stokes peaks appear after the main one, as also seen in the numerical curve in Fig. 3(b).
Fig. 4. Simulated dynamics of ${{\rm{LP}}_{01}}$ signals at the pump and Stokes frequencies (top panels). The 600 fs chirped pump pulse (top-left panel) contains 28 µJ energy with modal content 80% ${{\rm{LP}}_{01}}$ and 20% ${{\rm{LP}}_{02}}$. In the bottom panels, we display the temporal profiles of the pump and Stokes pulses, the latter multiplied by 2 for clarity, at (a) 25 cm, (b) 40 cm, and (c) 60 cm, indicated in the upper plots. The dashed red curves in the lower plots show the launched pump pulse at $z = {{0}}\;{\rm{cm}}$.
Fig. 5. Measured (diamonds) pressure dependence of the quantum efficiency (QE) of Raman conversion to the 1.8 µm vibrational Stokes band for a 30 µJ pump pulse of chirped duration ${\sim}{{600}}\;{\rm{fs}}$ (${0.055}\;{\rm{p}}{{\rm{s}}^2}$ of GDD added to the laser pulses). The open circles (dashed lines) mark the values calculated numerically for a perfect gas-filled PCF with different proportions of pump energy in the ${{\rm{LP}}_{02}}$ mode.
Fig. 6. (a) Dispersion diagram for the ${{\rm{LP}}_{01}}$ and ${{\rm{LP}}_{02}}$ modes at the gain suppression pressure of ${\sim}{{34}}\;{\rm{bar}}$. To bring out the weak underlying ${\rm{S}}$-shaped dispersion, the quantity ${\beta _{{\rm ref}}} - \beta$ is plotted, where $\beta$ is the modal propagation constant and ${\beta _{{\rm{ref}}}} = 1.004\;{k_0}$. The arrows mark the different coherence waves that can be generated by pump-to-Stokes conversion; note that 25% of the pump energy is in the ${{\rm{LP}}_{02}}$ mode (indicated by the shaded circles). Under these conditions, some Stokes light is generated in the ${{\rm{LP}}_{02}}$ mode, resulting in a coherence wave (red) that can be used, over a coherence length of $\pi /\Delta \beta = {{8}}\;{\rm{mm}}$, to create anti-Stokes photons in the fundamental mode. (b) Simulations of the quantum efficiency for the generation of Stokes (${\rm{S}}$, blue) and anti-Stokes (AS, red) photons in the ${{\rm{LP}}_{01}}$ (upper plot) and ${{\rm{LP}}_{02}}$ (lower plot) modes. Two different cases are compared, the first (full curves) for 25% of the pump energy in the ${{\rm{LP}}_02}$ mode, and the second (dashed curves) for 100% of the energy in the ${{\rm{LP}}_{01}}$ mode. In the lower plot, the anti-Stokes signal is weaker than ${-}{{120}}\;{\rm{dB}}$.
5. COHERENT GAIN SUPPRESSION
As already mentioned, intramodal gain is suppressed when the coherence waves for pump-to-Stokes and pump-to-anti-Stokes conversion are identical [29]. These coherence waves are represented by blue arrows in Fig. 6(a), where their vertical and horizontal projections correspond to the Raman frequency shift and propagation constant, respectively. Using narrowband, nanosecond pump pulses [20], the gain suppression pressure was measured to be ${\sim}{{34}}\;{\rm{bar}}$, in good agreement with the predictions of Eq. (1). This was further confirmed in the femtosecond regime by full-field numerical simulations of the generated Stokes signal with increasing pressure, shown by the blue dashed line in Fig. 5.
In the experiments, however, we observed no noticeable reduction in Stokes conversion at this pressure, as shown by the full orange line in Fig. 5. Although SPM and four-wave mixing can alter the Stokes/anti-Stokes balance and partially frustrate gain suppression, for best agreement it was found necessary in the modeling to launch a proportion of pump energy in the ${{\rm{LP}}_{02}}$ mode. Since intermodal SRS (normally weaker than its intramodal counterpart) is strongly enhanced close to the gain suppression point [20,29], a significant Stokes signal is generated in the ${{\rm{LP}}_{02}}$ mode by the intermodal coherence wave represented by the black arrow in Fig. 6(a). This Stokes signal then seeds down-conversion of photons from the pump light in the ${{\rm{LP}}_{02}}$ mode, resulting in the creation of the intramodal coherence wave represented by the lower red arrow in the figure. This coherence wave is then able to break the Stokes/anti-Stokes balance by scattering pump photons into anti-Stokes photons via the intermodal SRS [upper red arrow in Fig. 6(a)] over a dephasing length of $\pi /\Delta \beta = {{8}}\;{\rm{mm}}$—significantly longer than the effective gain length, meaning that a few mm of propagation is sufficient to upset the fragile balance needed for coherent gain suppression [see Fig. 6(b)].
6. EFFECT OF PUMP PULSE CHIRP: THEORY
Remarkably, despite the relatively high ${{\rm{LP}}_{02}}$ mode content used in the simulations in Fig. 5, ${\sim}{{99}}\%$ of the Stokes energy emerges in the ${{\rm{LP}}_{01}}$ mode [Fig. 6(b)]. We attribute this to rapid group velocity walk-off of the ${{\rm{LP}}_{01}}$ pump and the ${{\rm{LP}}_{02}}$ Stokes pulses, together with the presence of a linear frequency chirp in the pump pulse that is enhanced by SPM during propagation. During walk-off, the instantaneous beat frequency between the chirped ${{\rm{LP}}_{01}}$ pump and ${{\rm{LP}}_{02}}$ Stokes pulses gradually detunes from the Raman frequency, resulting in effective suppression of intermodal Raman gain. This means that a coherence wave created toward the leading edge of the pump pulse is no longer driven resonantly at the trailing edge by the beat-note between the Stokes and pump pulses.
This effect can be modeled by considering that the intermodal coherence wave formed by the pump and noise-seeded Stokes light forms an effective gain region at the trailing edge of the pump pulse (blue undershaded in Fig. 7). The growth in the Stokes field $E_s^{02}$ during propagation can then be modeled by integrating over the moving gain region. Assuming that $E_s^{02}$ starts to grow from a very weak signal at $z = {{0}}$, its value at $z = L$ can be written (see Supplement 1 for details) as
Fig. 7. Pump (${{\rm{LP}}_{01}}$) and Stokes (${{\rm{LP}}_{02}}$) pulses after 1 m of propagation. Full-field numerical simulations (Stokes signal is undershaded in light red) are compared to the analytical model in Eq. (3). The simulation was performed using laser pulses carrying 20 µJ of energy entirely in the ${{\rm{LP}}_{01}}$ mode and chirped to a duration of 600 fs by adding ${0.055}\;{\rm{p}}{{\rm{s}}^2}$ of GDD. Both the amplitude of the Raman coherence (which will not decay on the time-scale of the plot) and the effective gain region (blue undershaded) are represented schematically. The gas pressure was 34 bar and the intramodal SRS was switched off to reduce pump depletion. Both pump and Stokes pulses are normalized to their peak values.
7. EFFECT OF PUMP PULSE CHIRP: EXPERIMENT
As seen in the upper panel in Fig. 8(a), transform-limited pump pulses (${\sim}{{300}}\;{\rm{fs}}$) broaden to a supercontinuum in the fiber and very little 1.8 µm Stokes light is emitted. Although the low conversion efficiency for a zero chirp meant that the modal content at 1.8 µm could not be directly measured, at all wavelengths longer than 1200 nm the Stokes light was found to be in the ${{\rm{LP}}_{02}}$ mode [see the far-field profile in the inset of Fig. 8(a), upper]. In contrast, when the input pulses were sufficiently chirped, the SRS threshold dropped and the efficiency increased strongly, as seen in Figs. 8(a) (lower panel) and 8(b). Under these circumstances the 1.8 µm signal was always in the ${{\rm{LP}}_{01}}$ mode, while the spectrum consisted of relatively narrowband Stokes and anti-Stokes signals, as seen in the lower panel of Fig. 8(a).
Fig. 8. (a) Measured spectral evolution for different input energies at 34 bar for (upper) transform-limited pump pulses (${\sim}{{300}}\;{\rm{fs}}$, GDD = 0) and (lower) chirped pump pulses (${\sim}{{600}}\;{\rm{fs}}$, ${\rm{GDD}} = {0.055}\;{\rm{p}}{{\rm{s}}^2}$). The inset shows the far-field beam profile of the signals with wavelengths $\gt \sim 1170\,\,{\rm nm}$. (b) Stokes quantum efficiency measured at 34 bar for different pump pulse energies and input pulse durations, adjusted by adding GDD (right-hand axis) to the 300 fs pulses from the laser. The data points correspond to the total integrated spectral power above 1600 nm. All measurements with efficiencies above 10% (i.e., the detection limit of the thermal camera used) are emitted in a clean fundamental mode.
The behavior for unchirped pump pulses has its origins in the combination of rotational SRS, the reduction in vibrational Raman gain due to pump broadening, and coherent gain suppression. Indeed, in full-field propagation simulations involving both ${{\rm{LP}}_{01}}$ and ${{\rm{LP}}_{02}}$ modes the spectral broadening is caused mainly by rotational SRS, seeded by SPM broadening. This is particularly pronounced in the ${{\rm{LP}}_{02}}$ Stokes signal [left column in Fig. 9(b)] owing to its higher central intensity and stronger dispersion. Under these circumstances the Stokes signal in the ${{\rm{LP}}_{01}}$ mode remains very weak everywhere because (a) it competes with the much stronger rotational SRS, which is now coherently seeded in the ${{\rm{LP}}_{02}}$-mode, and (b) the Raman gain falls due to pump broadening.
Fig. 9. Simulated evolution of the spectral intensities in (a) the ${{\rm{LP}}_{01}}$ and (b) the ${{\rm{LP}}_{02}}$ modes when 15 µJ pump pulses (75% ${{\rm{LP}}_{01}}$ and 25% ${{\rm{LP}}_{02}}$) are launched into a HC-PCF filled with 34 bar of hydrogen. The left-hand panels are for unchirped ${\sim}{{300}}\;{\rm{fs}}$ pump pulses, including both rotational and vibrational SRS. In the middle panels, the rotational SRS is switched off, but otherwise the parameters are the same as in (a). In the right-hand panels, the pump pulse is chirped to ${\sim}{{600}}\;{\rm{fs}}$ duration, and both the rotational and vibrational SRS are included. Simulations using only the ${{\rm{LP}}_{01}}$ mode yield mid-IR Stokes conversion efficiencies $\ll 1\%$ under all conditions.
The key role played by the rotational SRS is further confirmed by turning off the rotational Raman gain in the simulations. In this hypothetical case (central column in Fig. 9), the ${{\rm{LP}}_{02}}$ mode is only slightly broadened, whereas the ${{\rm{LP}}_{01}}$ Stokes is much more efficiently generated. The situation is radically different when the input pulses are chirped to durations longer than ${\sim}{{600}}\;{\rm{fs}}$ [Fig. 8(b)], when the overall SPM broadening (right-hand column in Fig. 9) is reduced so that the spectrum cannot reach the rotational bands except by noise-seeding, conditions which facilitate vibrational pump-Stokes interactions and favour efficient amplification of the 1.8 µm signal in the ${{\rm{LP}}_{01}}$ mode.
Even in the unrealistic case when the rotational SRS is switched off, pumping with a chirped pulse is slightly more efficient (34% quantum efficiency in Fig. 9) than chirp-free pumping (28% quantum efficiency).
8. CONCLUSIONS
Ultrashort pulses at 1.8 µm can be efficiently generated by pumping hydrogen-filled HC-PCF with pulses at 1.03 µm from a commercial high-repetition-rate fiber laser. Quantum efficiencies as high as 50% and 1.8 µm Stokes pulse durations of ${\sim}{{39}}\;{\rm{fs}}$ can be achieved. To understand the underlying physics, ultrafast SRS must be analyzed alongside competing nonlinear effects such as SPM, rotational SRS, and coherent Raman gain suppression (observed in the ultrafast regime for the first time, to the best of our knowledge, in this work). All these effects can be kept under control by exciting a proportion of higher-order modes in the pump light and chirping the input pulses. We note that coherent gain suppression could potentially be fully eliminated by designing a single-ring HC-PCF so that the first anti-Stokes band lies exactly at an anti-crossing with resonances in the glass walls of the core, causing Eq. (1) to be violated regardless of gas pressure.
The system reported is simple yet robust, making it attractive for generation and spectro-temporal shaping of mid-IR pulses at high repetition rates. Using lasers oscillating at 1.55 µm or longer wavelengths (limited to 2.4 µm for vibrational transitions in hydrogen) it should be possible to generate ultrashort Stokes pulses deep into the mid-IR [30], where optimized HC-PCFs provide excellent performance [31,32].
Funding
Max-Planck-Gesellschaft.
Acknowledgment
We thank Francesco Tani and Daniel Schade for useful discussions and help with various aspects of the project.
Disclosures
The authors declare no conflicts of interest.
See Supplement 1 for supporting content.
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