Backward stimulated Raman scattering in gases provides a promising route to the compression and amplification of a Stokes seed pulse by counter-propagating against a pump pulse, as has been demonstrated already in various platforms, mainly in free space. However, the dynamics governing this process when seeded by noise has not yet been investigated in a fully controllable collinear environment. Here we report, to the best of our knowledge, the first unambiguous observation of efficient noise-seeded backward stimulated Raman scattering in a hydrogen-filled hollow-core photonic crystal fiber. At high gas pressures, when the backward Raman gain is comparable to, but lower than, the forward gain, we report quantum conversion efficiencies exceeding 40% to the backward Stokes at 683 nm from a narrowband 532 nm pump. Efficiency increases to 65% when the backward process is seeded by a small amount of back-reflected forward-generated Stokes light. At high pump powers, the backward Stokes signal, emitted in a clean fundamental mode and spectrally pure, is unexpectedly always stronger than its forward-propagating counterpart. We attribute this striking observation to the unique temporal dynamics of the interacting fields, which cause the Raman coherence (which takes the form of a moving fine-period Bragg grating) to grow in strength toward the input end of the fiber. A good understanding of this process, together with the rapid development of novel anti-resonant-guiding hollow-core fibers, may lead to improved designs of efficient gas-based Raman lasers and amplifiers operating at wavelengths from the ultraviolet to the mid-infrared.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Backward stimulated Raman scattering (BSRS) has been investigated as a route to generate short pulses that, through compression, reach peak powers exceeding those of the parent pump pulses [1–3]. Compared with solid materials, Raman-active gases are suitable for these studies, providing large Raman frequency shifts, narrowband emission lines, high stimulated Brillouin scattering thresholds, and high optical damage thresholds . Free-space BSRS experiments on pulse compression and amplification in gases typically employ a two-stage arrangement—a seed pulse first generated by forward stimulated Raman scattering (FSRS) and then launched into a second gas cell, counter-propagating against a pump pulse [1,2]. Although single-stage studies of BSRS have been reported, the results are difficult to interpret due to the complex interplay between FSRS and BSRS, and depend strongly on parameters such as pump-pulse duration, focusing conditions, interaction length, and gas pressure [4–7]. Moreover, the threshold for these processes is usually very high, typically requiring pulse energies in the multi-mJ range. Introduction of wide-bore capillaries reduced the required pump-pulse energies to some extent, although at the expense of high attenuation of the generated signals [8,9].
The advent of hollow-core photonic crystal fibers (HC-PCFs), which offer low confinement loss, broad transmission windows, tight confinement of light in cores few tens of micrometers in diameter, and pressure-tunable dispersion, has made it possible to reduce the FSRS threshold by orders of magnitude [10,11]. HC-PCFs have been used in, for example, efficient Stokes and anti-Stokes emission, generation of Raman frequency combs , and molecular modulation of arbitrary optical signals . Hydrogen-filled HC-PCFs have also been used to amplify ns laser pulses via rotational BSRS in two-stage experiments . Compression factors of , defined as the ratio of the initial to final Stokes pulse duration, were achieved. However, there are to date no published reports in which pure noise-seeded BSRS and its competition with FSRS are studied in a gas-filled HC-PCF.
In this paper, we report for the first time clear noise-seeded BSRS in a -filled kagomé-style HC-PCF, pumping at 532 nm. In our experiments, we used hydrogen, which has the highest material Raman gain and frequency shift of any gas, and is transparent down into the ultraviolet. Using narrowband pulses of 3.2 ns duration (physical length 96 cm) and a 114 cm length of fiber with a core diameter of 22 μm filled with 38 bar of hydrogen, the noise-seeded backward Stokes signal (at 683 nm) was always stronger than the forward, reaching efficiencies exceeding 40%. Even higher backward conversion efficiency (65%) was obtained when a 14 cm length of fiber was used—in this case, the pump pulse is substantially longer than the fiber, so that the backward Stokes process could be seeded by a small fraction of the forward Stokes signal, back-reflected at the window of the gas cell.
To understand the in-fiber temporal dynamics of backward Raman scattering, we recorded the temporal profiles of all interacting sidebands along with their energy and compare the results with numerical simulations based on a bi-directional set of Maxwell–Bloch equations [14,15,16]. This allowed us to relate the dynamics of the BSRS process to the evolution of forward and backward Raman coherence waves (i.e., synchronous molecular oscillations driven by the beat-note created by the pump and Stokes signals), which turns out unexpectedly to favor the onset and amplification of the backward signal, even though the actual gain coefficient for FSRS is higher than that for BSRS.
The paper is organized as follows: in Section 2 we will briefly revise general aspects of the Raman gain in hydrogen gas. In Section 3, we present the experimental setup employed to demonstrate self- and noise-seeded BSRS in a HC-PCF, followed by a discussion of the experimental and numerical results (Section 4). In Section 5, we discuss the key role of the interplay between forward and backward coherence waves in the dominance of BSRS over FSRS at high gas pressures. Finally, in Section 6 we summarize the conclusions of the present study and provide an outlook of potential implications of the results across different fields.
2. RAMAN GAIN IN MOLECULAR HYDROGEN
The steady-state material Raman gain for the fundamental vibrational frequency shift of is lower for BSRS than for FSRS. This asymmetry originates mainly from a difference in Raman linewidth . Moreover, it has also been predicted  and observed experimentally [6,17] that the efficiency of the BSRS process drops with increasing pump linewidth. In particular, when the Raman linewidth of the FSRS process exceeds the pump linewidth (a condition fulfilled in our experiments), the BSRS/FSRS gain ratio can be approximated as , where and are, respectively, the forward and backward Raman scattering linewidths . At room temperature, for pressures far below 1 bar, and are strongly influenced by Doppler broadening, which is more pronounced for BSRS, and . As the pressure increases, the Doppler-broadened Raman linewidths for both processes shrink under the influence of Dicke narrowing . With further increase in pressure, collisional broadening starts to influence both and , eventually dominating at high enough pressure. A simple formula, based on fits to experimental data at 298 K, captures the pressure dependence of the forward Raman linewidth :1) describes the contribution from Dicke narrowing and the second term describes the contribution from collisional broadening. While Eq. (1) is not directly applicable to the backward case, it has been experimentally observed that the backward Raman linewidth, , also follows a similar pressure dependence , although no fitting formula has been reported. Collisional broadening in starts to dominate over Dicke narrowing at pressures above 3 bar for and 31 bar for , the difference being attributed to the strong influence of Doppler broadening in BSRS. However, beyond 31 bar, increases linearly with pressure, whereas decreases and .
The steady-state FSRS gain [cm/W] of the fundamental vibrational transition of , (), is given by 20]. Equation (2) is valid over the range of 1–100 amagats, depending as it does on Eq. (1).
In the simulations, we used FSRS gain values from Eqs. (1) and (2). The BSRS gain was obtained using . At our working pressure (38 bar), we used based upon experimental measurements of the forward and backward Raman linewidths . This is justified since the 1064 nm parent laser emits pulses with FWHM duration of with a linewidth of —parameters similar to those used in . Moreover, at 38 bar, , which is an order of magnitude larger than the laser linewidth.
3. EXPERIMENTAL SETUP
The experimental setup is sketched in Fig. 1(a) and 1(b). A frequency-doubled Nd:YAG laser operating at a repetition rate of 3 kHz delivered linearly polarized 532 nm pump pulses with FWHM duration of (corresponding a pulse length of ). Two kagomé-style HC-PCFs with different core diameters and fiber lengths were employed [see Fig. 1(c) for scanning electron micrographs (SEMs) of the fiber structures]. In the first set of experiments, we used a 14-cm-long fiber with a core diameter of (Fiber 1). In the second set, we used a 114-cm-long fiber with a core diameter of (Fiber 2). The first fiber was placed inside a 16-cm-long monolithic gas cell, whereas the second fiber was placed in an arrangement of two 8-cm-long gas cells connected by a -m-long tube. Both fibers were filled with 38 bar of hydrogen—the highest pressure attainable with the gas system.
In all the experiments, the launch efficiency of the pump pulses was , limited by a mismatch between the spatial profiles of the focused pump light and the fundamental core mode. A dichroic mirror (DM1) transmitting the first vibrational Stokes line at 683 nm and fully reflecting the 532 nm pump line was placed in front of the in-coupling lens. Beams emerging at both ends of the fiber were collimated and diverted to different detectors. The energies of the pump and the generated forward and backward Raman pulses were measured with a calibrated power meter using customized band-pass filters. An optical spectrum analyzer was used to measure the spectral content of the output signals. The far-field profile of the backward Stokes signal was also recorded with a CCD camera.
Alongside the energy-spectral measurements, we performed thorough time-resolved analysis of the generated signals to understand the competing dynamics of FSRS and BSRS. The temporal profiles of the pump, and the forward and backward Stokes pulses were recorded with fast photodiodes triggered by the pump pulse. The position of these photodiodes was chosen carefully to ensure their synchronization [see Fig. 1(b) for schematics]—a basic requirement for subsequently comparing the temporal evolution of the signals in an unambiguous manner.
In order to check the effects of self-seeding, we specifically designed two different window holders for the gas cells [see schematics in Fig. 1(a)], mainly for the output end: a flat holder for normal incidence and an angled holder for 40° incidence. On these holders, 3-mm-thick windows were mounted in such a way that the distance between the fiber output end and the window was preserved.
4. EXPERIMENTAL RESULTS AND DISCUSSION
To demonstrate and unambiguously distinguish self- and noise-seeded generation of the backward Stokes signal, two main gas-cell configurations were employed for both fibers [see Fig. 1(a)]: (a) a flat input window and a flat output window (FIFO), and (b) a flat input window and an angled output window (FIAO). Furthermore, for the experiments with the short fiber, an additional configuration with an angled input window and a flat output window (AIFO) was employed.
When the uncoated flat output window is in place, a fraction of the noise-seeded forward Stokes pulse diverging from the output tip of the fiber undergoes Fresnel specular reflection and can be partially coupled back into the fiber (constituting a backward-propagating seed for BSRS, as we will see below). In contrast, in an angled output window configuration, most of the light reflected at the window is diverted away from the fiber axis, thereby strongly minimizing the coupling of the divergent Stokes signal back into the fiber and, hence, the potential seeding of BSRS. The experimental and simulation results for the two different HC-PCFs with the FIFO and FIAO configurations will be discussed separately below.
A. BSRS Seeded by Back-reflected FSRS
In these experiments, pulses of were launched into the 14-cm-long fiber with a core diameter of [Fiber 1 in Fig. 1(c)] and filled with 38 bar of . The measured temporal profiles of the pump, and forward and backward Stokes (averaged over 200 pulses) for the FIFO and FIAO configurations are shown in Fig. 2, along with numerical simulations obtained by solving a set of bi-directional Maxwell–Bloch equations (see Supplement 1 for details). Throughout this manuscript, time is defined such that when the peak of the pump pulse enters the fiber input. We define time of flight as the time taken for the peak of the initial pump pulse, in the absence of SRS, to reach the output face of the fiber, i.e., the fiber length divided by group velocity. For Fiber 1, , whereas for Fiber 2, it is 3.8 ns.
It is evident that the backward Stokes signal is strongly suppressed in the FIAO configuration due to the absence of self-seeding, whereas it becomes about 12 times stronger in the FIFO configuration. Moreover, in the FIFO configuration, the backward Stokes signal appears earlier in time [see Fig. 2(a) and 2(b)], strongly suggesting that the forward Stokes signal is reflected back into the fiber at the output window, acting as a seed for BSRS and triggering a quicker onset of backward amplification.
Although the differences between the two configurations are clear, these measurements alone cannot be used to discriminate whether the weak backward Stokes signal observed in the FIAO configuration is fully noise-seeded, because back-reflection of light at the slanted output window, although strongly suppressed, cannot be completely excluded. Note that the reflections at the output window are completely switched off in the simulations (FIAO configuration), so that no BSRS signal appears in Fig. 2(d).
Interestingly, in the FIFO configuration the backward Stokes signal emerges in time between the first peak of the forward Stokes signal and its revival toward the trailing edge of the pump pulse. This double-peak structure [Fig. 2(a)] is also reproduced accurately in the simulations [Fig. 2(c)]. Indeed, we have numerically corroborated that the threshold and revival of the FIFO forward Stokes signal (i.e., the second hump delayed by with respect to the peak of the initial pump) are influenced by the back-reflection of the backward Stokes signal at the input window of the gas cell (see Supplement 1). As a result, the backward Stokes signal is temporally gated and compressed to 540 ps duration, with evident practical applications. Based on this understanding, we increased the launched pump energy to 58 μJ in the same fiber but in an AIFO geometry so as to inhibit the growth of the forward Stokes signal, and observed quantum conversion efficiency for backward Stokes generation (see Fig. 3) in a pure fundamental fiber mode.
B. Noise-Seeded BSRS
To study the temporal dynamics of pure noise-seeded BSRS, we must first ensure that the pump pulse is significantly depleted before reaching the output end of the fiber. This will avoid any back-seeding, leaving the FSRS process unaffected. To implement this, we used a 114-cm-long fiber (longer than the FWHM length of the pump pulse) with a smaller core diameter of (Fiber 2), again filled with 38 bar of hydrogen gas. The increased pump intensity in the smaller core and the longer fiber length dramatically reduce the SRS threshold, with the result that the pump is strongly depleted before reaching the fiber end. Under these circumstances, the backward Stokes signal is most likely be generated solely from noise.
Using the FIAO configuration, we monitored the backward and forward Stokes signals, as well as the residual out-coupled pump light, while increasing the input pump energy [Fig. 4(a)]. The data points are the average over measurements from 10 separate runs. The backward Stokes appears at pump energy of , thereafter growing at an average slope efficiency of . At the maximum launched energy of , the backward Stokes energy was , corresponding to energy conversion and quantum efficiency.
Although the gain for BSRS is lower than that for FSRS (the threshold for FSRS is of pump energy), the backward Stokes signal clearly overtakes the forward Stokes signal at of pump energy, beyond which the backward Stokes signal keeps growing, whereas the first forward Stokes signal and the residual pump light remain saturated at and , respectively. Note that this saturation effect is also modified by conversion to higher-order Raman bands, both vibrational and rotational, and fiber losses. All these features are also confirmed by numerical simulations (see parameters in Supplement 1), which show excellent agreement with the experimental results [see Fig. 4(b)]. In our simulations, we employ a uniform low-amplitude field of 50 V/m as the noise floor for all the lines (Supplement 1) to achieve a close agreement with the experiments. This accounts for processes such as spontaneous Raman scattering, vacuum fluctuations, and initial thermal phonon population. Other effects such as Rayleigh scattering from the gas molecules and scattering from the inner surfaces of the fiber core wall may also add complexity to the determination of the noise floor when the BSRS and FSRS processes influence each other. However, simple theoretical considerations indicate that these effects are likely to become significant only at wavelengths much shorter than those used in the current experiments, and can be safely neglected.
The numerical results are identical in both FIFO and FIAO configurations, pointing to the noise-seeded nature of the BSRS in this case. To further verify this experimentally, we measured the signals at pulse energies of 0.8, 2.9, and 5.3 μJ in the FIFO configuration [marked as colored circles in Fig. 4(c)]; they almost perfectly agree with those obtained in the FIAO configuration. This is in sharp contrast to the previous results for self-seeded BSRS, where the FIFO configuration was found to greatly enhance the generation of the backward Stokes signal. This is further confirmed by time-resolved measurements, as shown in Fig. 4(d). The depletion of all the lines shown in Fig. 4(d) is due to the appearance of a second forward Stokes signal at 953.6 nm (not shown), where fiber loss is high (see Supplement 1 for a loss measurement). We believe the measurements represent the first unambiguous observation of efficient noise-seeded BSRS in a hydrogen-filled HC-PCF.
The spectra of the forward- and backward-propagating lines for of pump energy in Fiber 2 are shown in Fig. 5. The forward-propagating signal shows several Raman lines [see Fig. 5(a)], generated from both vibrational and rotational SRS. These may be explained by the long interaction length for co-propagating pump and Stokes/anti-Stokes lines, along with a shallow dispersion landscape that permits interactions with different forward coherence waves (which, among other effects, allows generation of up-shifted anti-Stokes signals via molecular modulation [21–24]). In contrast, the counter-propagating Stokes light is concentrated solely at 683 nm, corresponding to the first vibrational Stokes line [see Fig. 5(b)].
As already mentioned, this behavior may be understood by reference to the dispersion diagram in Fig. 6, which plots the frequency-dependent propagation constants, , of the forward- () and backward- () propagating fundamental modes of Fiber 2 for 38 bar of , based on the modified Marcatili–Schmelzer model (see Supplement 1). The solid arrows represent the four vectors of the coherence waves () generated by interference between the pump and both the forward and backward Stokes and anti-Stokes signals:
For efficient anti-Stokes generation, the momentum component of a coherence wave must be closely similar for Stokes and anti-Stokes processes. The dephasing rate can be written as , which works out at 3.1 rad/cm for FSRS and for BSRS, corresponding, respectively, to dephasing lengths of 1 cm and 65 nm. This strongly favors the generation of a forward frequency comb, while very strongly suppressing the generation of a backward comb. This explains the simplicity of the observed backward spectra and the strength of the backward Stokes signal.
Furthermore, the backward Stokes signal is always emitted in a clean fundamental core mode [see insets in Fig. 5(b) for a far-field profile]. Very strong dephasing also means that BSRS is not impaired by coherent Raman gain suppression  (see Supplement 1).
5. COMPETING FORWARD/BACKWARD GAIN
In Section 4.B, we saw that at high pressure and high pump power, the backward Stokes signal is always stronger than the forward signal, despite the higher forward Raman gain. This may be explained as follows: after the pump pulse enters the fiber, the forward Stokes signal emerges earlier in time and also with a lower threshold than the backward due to its higher Raman gain (see Fig. 4). Simultaneously, the pump also gives rise to a small backward Stokes signal from noise-driven spontaneous scattering. This weak backward signal gets amplified as the pump pulse travels through the fiber, leading to an enhancement of the backward coherence wave. Meanwhile, the FSRS process continues uninterrupted until the backward Stokes build-up is strong enough to cause pump depletion at the leading edge and central part of the pulse. Nevertheless, the backward coherence wave, left behind once the backward Stokes signal has left the fiber via the input end, keeps aiding the scattering of further Stokes photons from the trailing edge of the pump pulse. It is important to note that, irrespective of the nature of the BSRS seeding process, the backward Stokes signal and the backward coherence have access to an un-depleted counter-propagating pump, something not possible for the forward Stokes signal, which gets amplified as it co-propagates with the pump pulse. As a result, depletion of the pump by BSRS close to the fiber input reduces the pump power available for FSRS along the rest of the fiber. Finally, FSRS depletes the residual pump light, gradually weakening the BSRS gain along the fiber.
The remarkable agreement between the experimental measurements and numerical simulations makes it possible to obtain additional information about the system by examining the competing dynamics of the forward and backward coherences. Figure 7 shows the simulated spatio-temporal evolution of the pump, and forward and backward Stokes signals for the parameters used in the FIFO configuration in Fig. 2(c). The causal sequence of scattering events may be traced clearly. Conversion to the backward Stokes signal takes place within a very narrow space-time window, close to the entrance face of the fiber where the backward coherence wave is strongest (see Fig. 8). In contrast, the forward coherence (Fig. 8) peaks in the second half of the fiber, extending from to (the secondary forward coherence peak, centered at , is caused by reflection of the backward Stokes signal at the input of the fiber). The short backward interaction length means that the backward Stokes signal is unable to generate its own Stokes lines [see Fig. 5(b)], with the result that the Stokes energy is concentrated within a narrow spectral band, and also has the consequence that fiber losses play only a minor role, unlike for forward SRS.
In conclusion, backward Stokes light can be efficiently generated in a short length of gas-filled HC-PCF in a simple arrangement involving only a monolithic gas cell. The system allowed observing, for the first time, unambiguously noise-seeded BSRS in a hydrogen-filled HC-PCF, with quantum efficiency of 41%. When the BSRS is self-seeded by back-reflected forward Stokes light, the quantum efficiencies can be as high as 65%, even though the forward Raman gain of the gas is higher than the backward gain. The efficiency of the effect will be even higher for pumping in the ultraviolet, when the Raman gain is much stronger . The backward Stokes light is spectrally very narrow and has a high-quality -like mode profile, while the backward Raman coherence is concentrated close to the input face of the fiber, preventing the generation of higher-order Stokes sidebands. Together with recent developments in hollow-core fiber technology , the results pave the way to a new generation of fiber-based Raman lasers and amplifiers, ideal for operation in otherwise difficult-to-access spectral regions such as the ultraviolet [26,27] and the mid-infrared [28–30]. The HC-PCF system also provides a novel platform for ultrafast pulse compression and amplification in counter-propagating geometries .
See Supplement 1 for supporting content.
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