Amplification of Supercontinuum Seed Pulses at ~1078–1355 nm by Cascade Rotational SRS in Compressed Hydrogen

Abstract

Multiple higher-order Stokes of rotational stimulated Raman scattering (SRS) in compressed hydrogen covered the wavelength range from ~1.1 µm to ~1.4 µm using ~1.2 ps pump pulses from a Yb:YAG laser. In this study, the influence of polarization, energy, and the focusing conditions of the pump pulse, as well as gas pressure, on the conversion efficiency and modification of the spectral envelope of rotational and vibrational SRS was investigated. The use of a supercontinuum seed, as well as circular polarization of pump pulses at high hydrogen pressure, made it possible to significantly reduce the threshold for rotational SRS and suppress vibrational Stokes modes. The cascade excitation of rotational SRS, corresponding to a shift of 587 cm⁻¹, ensured a spectrum spanning four Stokes orders withs a conversion efficiency of 52% and an output energy exceeding 3 mJ. The synthesized spectrum corresponded to ~14 fs transform-limited pulses.

1. Introduction

Multiwavelength ultrafast radiation sources in the ~1–1.3 µm wavelength range are of great importance for the two-photon imaging of living tissues [1]. It has recently been shown that a ~50–100% greater imaging depth can be obtained using excitation at wavelengths of ~1050–1700 nm compared to 800 nm [2,3]. Increasing the wavelength of driving femtosecond laser pulses by nonlinear conversion makes it possible to generate attosecond X-ray pulses with higher photon energy [4] and improve the efficiency of THz generation [5]. In particular, the technology of intense THz radiation sources (with peak fields > 1 GV/cm²) is based on the optical rectification of femtosecond pulses in highly nonlinear organic crystals. The main challenge for such applications is the need for high-energy pump lasers at relatively difficult-to-reach wavelengths of ~1.1–1.5 µm. In this spectral range, the optical rectification provides the best phase-matching conditions, ideal for studying ultrafast processes in atoms and molecules [6]. The dominant laser source technologies here remain optical parametric amplification (OPA) [7] and optical parametric chirped-pulse amplification (OPCPA) [8]. However, the OPCPA conversion efficiency barely reaches ~15%, and the spectral bandwidth is limited by phase matching [9]. An alternative method for frequency conversion may be stimulated Raman scattering (SRS). The particularly wide spectral bandwidth inherent in cascade SRS opens up a promising path for the synthesis of sub-cycle coherent light pulses covering the range from UV to near-IR [10,11].

The phenomena of stimulated electronic Raman scattering (SERS), stimulated vibrational Raman scattering (SVRS, most often referred to SRS), and stimulated rotational Raman scattering (SRRS) allow for the expansion of the laser spectral range. In this two-photon inelastic scattering process, the energy difference between the incident and scattered photons is attributed to a molecular transition. Cascade SRS leads to the generation of a broadband comb of frequencies separated by the molecular transition energy [12]. Gas SRS converters, compared to solid-state ones, cover a wider range of wavelengths and have a higher damage threshold as well as operating at a repetition rate of 20 kHz [13]. Raman-active gases such as hydrogen, deuterium, and nitrogen recover even after ionization by high-intensity laser pulses. Moreover, the transmission of Raman-active gases spans from vacuum ultraviolet (VUV) to far infrared (FIR) radiation.

Hydrogen has gained popularity due to its largest vibrational shift of 4155 cm⁻¹ and high Raman gain. However, the rotational shifts of 587 cm⁻¹ and 342 cm⁻¹ [14,15,16] for ortho- and para-hydrogen are more attractive for generating optical frequency combs and ultrashort pulses [17]. Nevertheless, the vast majority of studies have focused on the excitation of steady-state SVRS, with conversion efficiencies reaching 68% [18] for nanosecond pump pulses. Meanwhile, for picosecond and femtosecond pulses, the efficiency drops significantly [19], since the stimulated Raman gain in the transient regime depends on the integrated energy of the pump pulses and not on the peak power. Moreover, an increase in the instantaneous field intensity leads to unfavorable nonlinear effects such as self-phase modulation (SPM), multiphoton ionization, and harmonic generation, which disrupt SRS [20]. On the other hand, despite the observation of SRRS with nanosecond pump pulses back in 1966 [21], methods for achieving its maximum energy and efficiency in the transient regime have not yet been exhaustively studied. A discrete SRRS spectrum at hydrogen pressures up to 120 atm was observed using 30 ps pump pulses at 1064 nm [22]. Meanwhile, more than 40 mainly anti-Stokes SRRS lines ranging from 239 to 993 nm were obtained [23] at 10 atm using a high-energy 800 fs Ti:sapphire laser. However, most studies lack information on the efficiency and energy of transient SRRS.

Thus, SRRS, together with nonlinear phase modulation, allows for the generation of broadband Stokes pulses with further compression to a pulse width significantly shorter than that of pump pulses. However, currently, the predominant technology for generating ultrabroadband Stokes pulses is based on the use of hollow fibers (HCFs) filled with gases. When pumped by femtosecond Yb laser pulses, this provides a spectrum broadening to 1.3 µm in N₂ [24] and up to 2 µm in N₂O [25]. Nevertheless, this expensive and bulky technique is inferior to more traditional and convenient high-pressure gas cells.

In this paper, for the first time to our knowledge, we report a highly efficient transient cascade SRRS in a hydrogen cell with high-energy output pulses ranging from ~1.1 to ~1.4 μm, which was obtained using ~1.2 ps pump pulses from a Yb:YAG laser at 1030 nm. The spectral synthesis of multiple higher-order Stokes of cascade SRRS is demonstrated. Particular attention was paid to lowering the SRRS threshold, as well as expanding the spectral bandwidth of the rotational mode comb. The influence of polarization, energy, and the focusing conditions of the pump pulse, as well as the H₂ pressure, on the conversion efficiency and the evolution in the spectral envelope of SRRS and SVRS was studied. The circular polarization of pump pulses and seeding with a white-light supercontinuum (WLC) made it possible to suppress SVRS. High H₂ pressure ensured the generation of multiple higher-order Stokes of cascade SRRS corresponding to a shift of 587 cm⁻¹. As a result, a SRRS conversion efficiency of 52% was achieved and a Stokes comb energy exceeding 3 mJ. The possibility of compressing Stokes pulses with a synthesized SRRS spectrum up to ~14 fs at a central wavelength of 1.2 μm is also discussed.

2. Experiment

The experimental setup for the investigation of cascade SRRS is shown in Figure 1. The laser source for both WLC seed excitation and SRRS pumping was a self-made two-stage, double-pass Yb:YAG chirped-pulse amplifier, providing transform-limited ~1.2 ps output pulses with an energy of up to 20 mJ at a repetition rate of 100 Hz after the grating compressor [26].

A small portion (~100 μJ) of the laser energy was used to generate WLC in the undoped YAG rod. The first thin-film polarizer (TFP 1), together with a half-wave retardation plate (λ/2), formed an attenuator of the incident pulse energy, and the iris aperture selected the central beam part with an initial diameter of 6.4 mm. The crystal length and a focusing lens (F1) with a focal length of 100 mm were chosen to obtain stable WLC spanning to ~1.4 μm. The WLC radiation spectrum was selected with a long-pass filter (F) FELH1050 (Thorlabs Inc., Newton, NJ, USA) and collimated using a lens (F2) with a focal length of 400 mm. The collinear propagation of the WLC seed and pump beams was provided using a custom-made dichroic mirror (DM) transmitting at 1030 nm and reflecting in a wavelength range of 1100–1400 nm, while precise temporal overlap was ensured by two plane silver mirrors (M2 and M3) in the delay line. A second attenuator formed by a thin-film polarizer (TFP 2), together with a half-wave retardation plate (λ/2), was used to vary the pump energy supplied to the Raman cell. A quarter-wave retardation plate (λ/4) provided the circular polarization of the pump to suppress SVRS. The WLC seed and pump beams were focused using a lens (F3) with a focal length of 750 mm to the center of the Raman cell. Both SVRS and SRRS occurred in a high-pressure gas cell that was 1 m long with MgF₂ windows 5 mm thick and filled with compressed hydrogen at a variable pressure from 1 MPa to 5 MPa.

Spectral measurements were carried out using a NIRQuest512-2.5 spectrometer (Ocean Optics, Orlando, FL, USA) with an integration time of 100 ms corresponding to 10 pulses. To do this, a small portion of the Stokes beam was split off by a fused silica wedge, and a diffuser was placed in front of the multimode fiber at the spectrometer input to ensure uniform spatial distribution. Beam intensity profiles were measured using a WinCamDLCM-C CMOS profiler (DataRay Inc., Redding, CA, USA). Pulse energy was measured using a LabMax-TOP console with J-10MB-HE energy sensors (Coherent Corp., Saxonburg, PA, USA). The combined energy of SRRS and SVRS was separated from the pump radiation using a FELH1050 long-pass filter, while the SRRS was rejected using a FELH1350 long-pass filter (Thorlabs Inc., Newton, NJ, USA). The compression of the Stokes pulses was verified using SF11 prisms with an apex angle of 59° spaced 80 cm apart. A Glan–Taylor prism sampled p-polarized Stokes radiation for characterization using homemade second harmonic generation frequency-resolved optical gating (SHG-FROG).

3. Results and Discussion

3.1. Stimulated Rotational Raman Scattering in Compressed H₂

In the steady-state SRS regime, the conversion efficiency to high-order Stokes increases with the elongated focusing of the pump beam [27]. In the transient SRS regime, when the pump pulse width is comparable to the molecular dephasing time (T₂), which, for SRRS in hydrogen, is ~1 ps [28], the threshold intensity increases drastically compared to the steady-state case [29], and the effects of SPM, self-focusing, and supercontinuum generation become predominant. Therefore, a loose focus with a long interaction length is most suitable for exciting cascade SRRS by picosecond or femtosecond laser pulses. On the other hand, loose beam focusing entails low peak power density. It is expected that the pump intensity should exceed the SRS threshold but remain below the self-focusing and self-phase modulation thresholds. The insufficient pump intensity caused by loose beam focusing is compensated by a longer interaction length. Thus, the focusing conditions and pump energy need to be optimized to excite more Stokes orders in SRRS and suppress parasitic nonlinear effects.

At the beginning of the studies, the WLC seed was not used for SRS generation, as described later in this section. Since a loose focus with a long interaction length is preferred for generating high-order rotational Stokes with picosecond pump pulses, the focal length of the F3 lens was varied from 500 to 1500 mm at a constant pump energy of 2 mJ and an H₂ pressure of 3 MPa. Indeed, the SRRS threshold was passed, but unwanted supercontinuum was not observed under these conditions. Since there were no significant differences in the conversion efficiency or SRS spectrum envelope with different lenses, the optimal lens with a 750 mm focal length was selected. Although the most studied vibrational shift of 4155 cm⁻¹ in hydrogen shows the best steady-state gain, a rotational shift of 587 cm⁻¹ was also expected. Moreover, the SRRS can dominate in the highly transient regime as pump pulses approach ~1 ps. However, with the linear polarization of the pump pulses, SVRS cannot be sufficiently suppressed (Figure 2). Regarding SRRS, although it is generally accepted that rotational SRS cannot be excited by a linearly polarized pump beam due to the parametric Stokes–anti-Stokes coupling [30], we confidently observed rotational Stokes components. Moreover, SRRS was reliably generated when the dichroic mirror (DM) and quarter-wave retardation plate (λ/4) were removed and when an additional thin-film polarizer was placed in the path of the pump beam to increase the polarization contrast. The windows in the cell were meticulously inspected not only for the absence of conventional depolarization but also for any manifestation of the nonlinear phenomenon of cross-polarized wave (XPW) generation. Finally, when a Glan prism was placed upon exit from the cell, the opposite polarization appeared strictly after the SRS excitation threshold was exceeded. The accompanying WLC generated by SPM is known to act as a seed beam for the generation of high-order rotational lines through four-wave Raman mixing. However, at the very threshold of SRS generation, one could expect only the first vibrational Stokes. With the circular polarization of the driving pulses, two units of angular momentum are transferred to hydrogen, which makes it possible to significantly increase the SRRS gain [23]. The dependence of the SRRS conversion efficiency on the pump energy for different polarizations of laser pulses at a hydrogen pressure of 3 MPa is shown in Figure 2a. Thus, the stably observed SRRS when using linear pump polarization was not associated with the inaccurate conduction of the experiment but has not yet found an exhaustive explanation.

The axis of the quarter-wave retardation plate (λ/4 in Figure 1) was initially set at an angle of 0° to ensure the linear polarization of the laser beam. The pump energy was limited to 7 mJ to avoid damaging the MgF₂ windows of the Raman cell. Under the linear polarization of the pump beam, the SRRS threshold (determined at an SRRS efficiency of 1%) was reached at an energy of 2.5 mJ (Figure 2a, black dashed line). With increasing pump energy, the efficiency of SRRS conversion rose sharply to 16%. However, due to the occurrence of anti-Stokes components, upon reaching a pump energy of 4.5 mJ, the SRRS conversion efficiency gradually saturated to a maximum value of 23%. The observed spectrum was formed by several peaks at ~1094 nm, ~1166 nm, and ~1251 nm (Figure 2b, black dashed line) with gradually decreasing intensity, within the measurement error corresponding to the first, second, and third Stokes orders of the cascade SRRS in hydrogen (spaced apart by a rotational Raman shift of 587 cm⁻¹). The first of the peaks in Figure 2b is at the 1030 nm pump wavelength of the Yb:YAG laser. In addition, two more lines were observed, associated with the measurement error with SVRS at ~1790 nm (based on the vibrational Raman shift of 4155 cm⁻¹) and roughly corresponding to the rotational Stokes from this radiation at ~1993 nm. Once the polarization of the pump beam was changed from linear to circular, a clear maximum in SRRS conversion efficiency of 33% was observed, along with a reduction in the threshold to 1.5 mJ (Figure 2a, red solid line). This was accompanied by a suppression of vibrational Stokes (Figure 2b, red solid line). Thus, it was confirmed that the circular polarization of the pump beam enhances the generation of SRRS, and this was adopted in further experiments.

The dependence of the SRRS spectra on the pump pulse energy at a hydrogen pressure of 3 MPa is shown in Figure 3a. Here, the first peak corresponded to the Yb:YAG laser pump wavelength at 1030 nm. In the spectrum near the threshold at ~3 mJ, only the first rotational Stokes line was observed. As the pump energy increased to ~5 mJ, the saturated first Stokes, in turn, served as a pump for second-order rotational Stokes excitation. Finally, at a maximum pump energy of 7 mJ, a third-order Stokes line was also observed. Thus, when choosing optimal excitation conditions in compressed hydrogen, the efficient cascade generation of a large number of equidistant rotational Stokes lines becomes possible.

Since the Raman gain is proportional to the density of the medium [23], the conversion efficiency of transient SRS strongly depends on the hydrogen pressure. Thus, the hydrogen pressure has also been optimized to ensure the most efficient generation of higher-order rotational Stokes components. Although the SRS linewidth broadens with increasing gas pressure [29], in our experiments, this effect was negligible since the pump laser linewidth exceeded the SRS linewidth [31]. The dependence of the SRS spectra on the hydrogen pressure at a pump pulse energy of 7 mJ is shown in Figure 3b. Here, as before, the first peak corresponded to the Yb:YAG laser pump wavelength at 1030 nm. Due to the low Raman gain, at a hydrogen pressure of 1 MPa, only the first rotational Stokes line was observed, while the number and intensity of higher-order Stokes components increased at higher pressures. It is noteworthy that even when the circular polarization of the pump beam made it possible to completely suppress the direct generation of vibrational SRS (Figure 2b, red solid line), at pressures above 3 MPa, the first rotational Stokes pulse in turn became a pump source for SVRS at ~2012 nm (Figure 3b, blue line). When the hydrogen pressure reached 4 MPa, the cascade generation of SVRS from second-order rotational Stokes was also observed at ~2074 nm (Figure 3b, green line). Thus, at increased hydrogen pressure, two vibrational Stokes components were generated at once (Figure 3b, green and violet line), corresponding to a Raman shift of 4155 cm⁻¹ from the first- and second-order rotational Stokes. It is also important to note that the nonlinear refractive index n₂ of the medium increases with increasing hydrogen pressure [32]. As a result, a spectral pedestal (background) was formed between the rotational Stokes lines in the ~1–1.4 μm wavelength range, where additional spectral components appeared due to the self-phase modulation.

The high pump pulse energy and hydrogen pressure not only contributed to the cascade generation of higher-order rotational Stokes comb but also significantly improved the overall SRRS conversion efficiency and lowered its threshold (Figure 4). The SRRS threshold decreased from 5 mJ to 0.95 mJ as the hydrogen pressure increased from 1 MPa to 5 MPa (Figure 4a,c). This dependence corresponded to the reciprocal function 4.9/p, where p is the H₂ pressure (Figure 4c, red dashed line).

It is well known that the conversion efficiency of transient SRS strongly depends on the density of the Raman medium. Therefore, the best SRRS conversion efficiency achieved at saturation also increased rapidly from 1.5% to 42% (Figure 4c, black solid line). However, a further increase in gas pressure and pump pulse energy will lead to an increase in n₂ and the instantaneous field intensity of the pump beam, respectively. This will cause stronger nonlinear effects such as SPM, multiphoton ionization, harmonic generation, etc., which will eventually suppress SRS. A similar behavior of SVRS was also observed (Figure 4b). However, the intensity of vibrational Stokes modes became noticeable only starting from a hydrogen pressure of 3 MPa with a cascade energy transfer from rotational Stokes. This was also evident from the change in the slope of the SRRS efficiency curve (Figure 4c, black solid line). The best conversion efficiency of the pump pulse energy into vibrational Stokes modes was 3.2%. It is noteworthy that even with a maximum pump energy of 7 mJ and a maximum hydrogen pressure of 5 MPa, the beam still remained smooth after the spatial filter (Figure 4d,e).

3.2. Stimulated Rotational Raman Amplification of Supercontinuum Seed in Compressed H₂

Since the SRS process usually occurs from a very low level of spontaneous Raman scattering, the use of coherent seed radiation with higher intensity corresponding to the wavelengths of the excited Stokes modes would significantly enhance it. Therefore, in this work, we also investigated stimulated rotational Raman amplification (SRRA) seeded with WLC, which was generated in a YAG crystal using the same pump laser. We expected that by covering the wavelength range of high-order Stokes modes with a WLC seed pulse, we would be able to further increase the conversion efficiency, lower the SRRS threshold, and significantly expand its spectrum [33]. The dependance of the spectral envelope of the stimulated Raman amplification (SRA) on the hydrogen pressure at a pump pulse energy of 7 mJ is shown in Figure 5a.

In contrast to SRS without a WLC seed (Figure 3b), the generation of rotational Stokes modes up to the third-order and even the fourth-order (corresponding to ~1351 nm) was observed at hydrogen pressures of 2 MPa and 5 MPa, respectively. A vibrational Stokes line at a wavelength of ~1795 nm and a first rotational Stokes line from it at a wavelength of ~2007 nm were also observed in the SRA output spectra. Thus, despite the WLC radiation being of low intensity, it is still sufficient for seeding the SVRS from the pump pulse. WLC seeding also drastically reduced the SRRS threshold to 1.15 mJ at 1 MPa and 0.25 mJ at 5 MPa (Figure 5c, red solid line), which is ~4 times lower compared to the case without seeding (Figure 4c, red solid line). This dependence corresponded to the reciprocal function 1.15/p (Figure 5c, red dashed line). The use of a WLC seed resulted in a significant enhancement of SRRS at all tested hydrogen pressures. As the pump energy increased, the SRRA conversion efficiency increased sharply (Figure 5b). However, due to the generation of anti-Stokes and vibrational Stokes components occurring at pump pulse energies exceeding 0.5 mJ and 1 mJ (Figure 5d), respectively, the SRRA conversion efficiency began to saturate. Accordingly, at a pump pulse energy of 7 mJ and a hydrogen pressure of 5 MPa, the conversion efficiency into anti-Stokes and vibrational Stokes components reached 10.4% and 5.8%, respectively. The best SRRA conversion efficiencies of ~28% to 52% were achieved at pressures ranging from 1 MPa to 5 MPa, with the maximum output Stokes pulse energies exceeding 3 mJ.

The widest spectrum of the SRRA comb was obtained at a hydrogen pressure of 5 MPa and a pump energy of 7 mJ (Figure 6a), and the positions of the observed peaks are given in

Table 1. SRRA output spectrum peak positions and corresponding wavelength shifts.

Peak Position, nm	Raman Shift, cm−1	Mode Assignment	Designation
1096	587	Rotational first-order Stokes	RS1
1166	1174	Rotational second-order Stokes	RS2
1252	1761	Rotational third-order Stokes	RS3
1351	2348	Rotational fourth-order Stokes	RS4
1795	4155	Vibrational Stokes from a pump pulse	VS
1997	4742	Vibrational Stokes from rotational first-order Stokes	RS1-VS

. Accordingly, the spectral peaks detected at wavelengths of 1096 nm, 1164 nm, 1252 nm, and 1351 nm (designated as “RS1–4”) were assigned, respectively, to the first, second, third, and fourth rotational Stokes modes, corresponding to a Raman shift of 587 cm⁻¹ in hydrogen pumped at 1030 nm. The spectrum also contained two long wavelength peaks centered at 1795 nm and 1997 nm. The first was assigned to the vibrational Stokes mode excited from the pump radiation and designated as “VS”, and the second was assigned to the vibrational Stokes mode excited from the first rotational Stokes component (“RS1”) and designated as “RS1-VS”.

According to the pump radiation, the SRRA output pulses were circularly polarized. The synthesized SRRA spectrum corresponded to ~14 fs transform-limited pulses at a central wavelength of 1.2 μm (Figure 6b). Thus, the cascade SRRA showed great potential for generating high-energy femtosecond pulses in the relatively difficult-to-reach spectral range of 1.1–1.4 µm.

3.3. Compression of Output Pulses after Stimulated Rotational Raman Amplification

Further experiments were conducted with the aim of exploring the compression capabilities of WLC pulses amplified in the stimulated rotational Raman amplifier. By adjusting the distance between two SF11 glass prisms, the pulses of the first-order rotational Stokes component were compressed to 152 fs, which was approximately eight times shorter than the pump pulse (Figure 7).

However, in the case of multiple higher-order rotational Stokes combs at the output of the SRRA, the linear compression methods turned out to be insufficient. Here, the proper control of the phases of several molecular modulation sidebands was required. One way to achieve this is to use transparent plates between prisms specific to each rotational Stokes component, with an adjustable thickness and position, thereby providing spectral control over the sideband generation process [34]. Also, the relative phases can be controlled using a spatial light modulator [17] or a spatial phase controller [35]. One example of such a modulator is a programmable liquid crystal spatial light modulator, which has tens of pixels. The refractive index of each pixel can be controlled electronically by applying a specified voltage from a computer [17]. Thus, when using appropriate compression methods, such a multiwavelength SRRS radiation source can potentially be used not only for broadband sensing but also for generating few-cycle optical pulses.

4. Conclusions

The generation of multiple high-order Stokes of cascade stimulated rotational Raman scattering in compressed hydrogen pumped by ~1.2 ps pulses at a wavelength of 1030 nm has been investigated. Pump polarization, energy, and the focusing conditions, as well as hydrogen pressure, were optimized to achieve the efficient generation of broadband cascade rotational Stokes radiation. When using the circular polarization of the pump beam, a twofold decrease in the stimulated rotational Raman scattering threshold was observed with the suppression of vibrational Stokes modes, which led to the conversion efficiency being increased to 42% at a hydrogen pressure of 5 MPa. Furthermore, the use of a white light supercontinuum seed made it possible to generate rotational Stokes combs up to the fourth order in a wide wavelength range of ~1.1–1.4 μm and reduce the threshold by another four times with an increase in conversion efficiency to 52%. Under optimal conditions, the maximum output pulse energy contained in the combs of the rotational Stokes components exceeded 3 mJ, with a spectral bandwidth sufficient for the generation of compressed to ~14 fs transform-limited pulses at a central wavelength of 1.2 μm. Although such extreme compression would require more complex techniques, using a pair of SF11 prisms, the first-order rotational Stokes pulses were compressed to 152 fs, which was approximately eight times shorter than the pump pulses.