1. Introduction

Stimulated Brillouin scattering (SBS) is a well-known nonlinear process that has broad range of applications [1]. Among others, SBS pulse compression has been widely employed to compress nanosecond laser pulses to as short as hundreds of picoseconds in different states of medium, such as gases [2, 3], liquids [4, 5] and solids [6, 7]. Due to its excellent energy conversion efficiency, SBS pulse compression represents one of the ideal techniques for laser peak power enhancement. To push further its performance, researches on SBS pulse compression have focused on either maximizing the energy load capacity or minimizing the compressed pulse duration. So far, several publications [3,5,8] have reported high-energy (Joule-level) SBS pulse compression. In those demonstrations, since high-energy pump pulses are directly dumped into the beam focus, further increase of the compressible energy is drastically limited by other nonlinear competing processes or even optical breakdown. A recent demonstration of high-energy SBS pulse compression with collimated beam [9] is free of the aforementioned issue. It however suffers from the relatively low energy efficiency, as well as the stringent requirement of super-Gaussian shaped pump pulses. Using a energy-controllable two-cell setup [4], Feng et al. have recently demonstrated the genuine energy-scalable SBS pulse compression [10, 11], where the compressible energy can be easily scaled up by increasing the beam cross section.

For the purpose of peak power enhancement, it is always desirable to obtain the shortest compressed pulses, which can be limited by the following factors. First, stimulated Raman scattering (SRS) has been mentioned quite often as a nonlinear competing process that is against SBS [8,12,13]. However, close examination on how SRS affects SBS, especially for the case of pulse compression, is still lacking. A recent study [14] has shown that SRS can even be driven by the SBS of high intensity during pulse compression process. Second, the phonon lifetime has been considered by some studies [4,12,15] as the lower limit for the compressed pulse duration. Such limitation has however been disproved by the experimental observations of sub-phonon lifetime pulse compression [2, 3, 8, 16, 17]. A third limitation has been attributed to the input pulse duration. The detailed study by Velchev et al. [13] has shown that, for input pulses much longer than the phonon lifetime, the compressed pulse duration is limited by the phonon lifetime; while for input pulse duration that is close to the phonon lifetime, pulse compression below the phonon lifetime can be realized by half-cycle gain. By using a double-pass compression scheme, Velchev et al. [13] have experimentally demonstrated that the 5 ns Gaussian pulses can be first compressed to an intermediate duration close to the phonon lifetime (τ_B=295 ps) via a single-pass compression, and the pre-compressed pulses can be compressed further to as short as 160 ps (0.54τ_B) via a second single-pass compression, but with fairly low energy (i.e., only a few mJ).

In this work, we focus on the single-pass compression of nanosecond Gaussian pulses below the phonon lifetime in a single-cell setup, with 100s mJ energy. We show that the key factor in achieving sub-phonon lifetime pulse compression is the effective interaction length between the Stokes and pump pulses. In a single-cell setup, the focusing length (f) inside the SBS medium is considered as the interaction length if it is equal to or less than the full length at half maximum (FLHM) of the input pulses (c/n) τ_p, where n is the refractive index of the SBS medium and τ_p is the full width at half maximum (FWHM) of the input pulses. For f larger than (c/n) τ_p, the effective interaction length is the FLHM of the input pulses. Conventionally, interaction length has often been chosen to match approximately (c/2n) τ_p (i.e., half of the FLHM). Such choice works well for the rectangular-shaped input pulses to achieve sub-phonon lifetime pulse compression, as theoretically demonstrated in [18, 19]. In the case of Gaussian input pulses, it however sets a constraint for obtaining the minimum compressed pulse duration, since the pump pulse is not completely involved in the compression process and the portion that contributes to pulse compression also varies with the pump pulse energy. To alleviate such constraint, it is necessary to increase the interaction length.

By choosing the interaction length to match approximately (c/n) τ_p of the input pulses, we experimentally demonstrate a single-pass compression of >20τ_B long Gaussian pulses to as short as 0.5τ_B in a single-cell setup, with ~100 mJ pulse energy. The experimental observations are well reproduced by the numerical simulations, confirming the importance of the interaction length in compressing nanosecond Gaussian pulses below the phonon lifetime. By employing a energy-scalable generator-amplifier setup, we demonstrate high-energy sub-phonon lifetime compression of 9 ns, 2 J pulses at 532 nm into 170 ps, 1.3 J per pulse in water, with pulse width and energy fluctuations to be as low as 5% and 1.5%, respectively. Those high-energy sub-nanosecond laser pulses find wide applications, including the study of nonlinear pulse propagation in air [20, 21], the investigation of efficient excitation of stimulated Raman scattering in liquids [14], the use as pump source in the optical parametric chirped-pulse amplifier system [22] among others.

2. Experimental setup

The energy-scalable generator-amplifier setup utilized for high-energy sub-phonon lifetime SBS pulse compression is sketched in Fig. 1. The SBS compressor is composed of SBS generator and SBS amplifier. The input of SBS compressor is derived from a home-designed Nd:YAG laser system [23, 24], capable of delivering single longitudinal mode and super-Gaussian transverse mode pulses with up to 5 J (3.5 J) per pulse at 1064 nm (532 nm). As discussed in [24], gain saturation effects inside the laser amplifiers lengthen the laser pulses. Therefore, shorter pulses with lower energy can be obtained from the laser system by having less amplification. By doing so, frequency-doubled pulses at 532 nm with pulse duration from 7 ns to 9 ns can be obtained from the laser system, with their corresponding energy varying from 120 mJ to 2 J per pulse, respectively. At the maximum output energy of 3.5 J, the green laser pulses are as long as 11 ns.

 

Fig. 1 Schematic of energy-scalable generator-amplifier setup for high-energy sub-phonon lifetime SBS pulse compression. Both SBS generator and amplifier cells are 2.5 m long. HW: Half Wave-plate; QW: Quarter Wave-plate; TP: Thin-film Polarizer; L: Plano-convex lens; TS: Translation Stage; PD: Photodetector.

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As a high-energy pulse enters the SBS compressor, a half wave-plate (HW1) and a thin-film polarizer (TP1) are used to tune the energy of the generator input pulse. The s polarized generator input pulse is then reflected by two polarizers TP1 and TP2, and focused by a plano-convex lens (L) into the SBS generator to create a pre-compressed Stokes seed pulse propagating in the backward direction. After passing through the quarter wave-plate (QW1) twice, the generated Stokes seed pulse becomes p polarized, therefore transmits through TP2 and reaches into the SBS amplifier. The main portion (i.e., about 90%) of the SBS compressor input, which passes through TP1 with p polarization, is sent into the SBS amplifier from the right hand side as the SBS pump. The linearly polarized Stokes seed and pump pulses are then modified to be circularly polarized once passing through QW2 and QW3, respectively. After the interaction inside the SBS amplifier, the polarization of the two counter-propagating pulses are changed by QW3 and QW2, respectively, to be s, which allows them to be reflected out by TP3 and TP2, respectively. The characterization of both Stokes seed and amplified Stokes pulses are performed with the pulse detection setup shown on top of Fig. 1. The pump beam is blocked before transmitting through TP3 while characterizing the Stokes seed. A translation stage and a 200 μm size pinhole are employed to scan through the beam profile and spatially resolve the compressed pulses.

3. Theoretical modeling

To confirm the experimental observations as well as to understand the mechanism of sub-phonon lifetime pulse compression in a single-cell setup, numerical simulations are carried out based on the model that has been detailed in [13, 25]. This model is 1-dimensional and simulates only the center of a beam. Gaussian beam propagation is used to calculate the beam size (hence the intensity) and phase at different positions z between the focusing lens and the beam focus. The SBS process involves two counter-propagating optical fields Ê₁(z,t) and Ê₂(z,t), and an acoustic field $\tilde{\rho }(z,t)$. These three fields are represented as follows

The SBS pulse compression process can be described by three coupled differential equations [13, 25]. By introducing a modified phonon field amplitude ρ′ (z, t) $[{\rho }^{\prime }(z,t)=-\rho (z,t){\mathrm{\Omega }}_B/({\mathit{ϵ}}_0{\gamma }_e{q}_B^2)]$ and a steady-state Brillouin gain factor g_B $[g_B={\gamma }_e^2{\omega }^2/(nv{c}^3{\rho }_0{\mathrm{\Gamma }}_B)]$ [26], the coupled differential equations can be rewritten as

To obtain the above equations, slowly varying envelope approximation (SVEA) has been applied to both pump and Stokes fields. It should be emphasized that the second order time derivative in the Navier-Stokes Eq. (2c) has been kept to account for the SBS pulse compression in the transient regime [13], where the spectral bandwidth of the phonon field approaches its center frequency. All the parameters associated with the SBS media (FC72 and Water), which will be used in solving Eqs. (2), are summarized in Table 1. γ_e is the electrostrictive constant of SBS medium [26], with its value included in the steady-state gain factor g_B. The input laser parameters, such as the pulse duration and beam size, are chosen to match the experimental values. A split-step method is employed to numerically solve the coupled differential equations.

Table 1. Parameters used in simulations

View Table

4. Results and discussion: sub-phonon lifetime pulse compression in single-cell setup

In this section, we demonstrate, both experimentally and numerically, the single-pass compression of nanosecond pulses below the phonon lifetime from the SBS generator only, shown in the bottom of Fig. 1. In this case, the laser beam from the pump arm is blocked before transmitting through TP3. SBS pulse compression in FC72 at 1064 nm and in water at 532 nm are both performed, demonstrating the universality of achieving sub-phonon lifetime pulse compression. It is known that the pulse compression ratio varies across the beam because of the spatial intensity distribution of the pump beam. The variation is small in this case because the pump beam has a super-Gaussian profile, and the detailed characterization of spatial variation has been discussed in [24]. The measurements presented here are performed at the beam center.

4.1. Sub-phonon lifetime pulse compression in FC72 at 1064 nm

To reveal the importance of interaction length, two lenses with effective focal length of 120 cm and 200 cm in FC72 are used in the SBS pulse compression of 9 ns (FWHM) Gaussian input pulses at 1064 nm. The two focusing/interaction lengths are chosen to match closely with (c/2n) τ_p and (c/n) τ_p, respectively. The input beam size is fixed at 20 mm diameter (full width at 1/e² maximum intensity). The compressed pulses sampled with the pinhole are characterized by a 25 GHz InGaAs biased photodetector (Newport model: 1417) combined with an Agilent DSO90254A digital oscilloscope (bandwidth: 2.5 GHz; sampling rate: 20 Gsa/s).

The experimentally measured and numerically simulated dependence of compressed pulse duration on pump pulse energy with two different interaction lengths are demonstrated in Figs. 2(a) and 2(b), respectively. The dashed line represents the phonon lifetime of FC72 at 1064 nm (i.e., τ_B=590 ps). It is worth noting that the phonon lifetime used here follows the definition of Boyd [26], which is half of the phonon decay or relaxation time defined somewhere else [18, 27]. The difference in pulse compression with two different interaction lengths is clearly shown. Experimentally, the compressed pulse duration is limited to the phonon lifetime, when the interaction length only matches closely with (c/2n) τ_p or half of the FLHM. This observation agrees with that reported in [13]. However, with twice the interaction length that matches approximately with (c/n) τ_p, sub-phonon lifetime pulse compression is achieved, with the pulse duration saturating around 0.67τ_B. It should be emphasized that the input pulse duration is about 15τ_B, much longer than the phonon lifetime, in which case it has been concluded in [13] that sub-phonon lifetime pulse compression can not be achieved with single-pass compression. As demonstrated here, the key parameter to achieve single-pass sub-phonon lifetime pulse compression is the interaction length, which has not been identified earlier [13]. Even though larger loss due to linear absorption is expected with longer interaction length, the measured energy efficiency is still as high as 79% at the highest input energy, thanks to the very low absorption coefficient (α < 10⁻⁵cm⁻¹) of FC72 at 1064 nm [11]. The numerical simulation shown in Fig. 2(b) matches qualitatively the experimental result, confirming the importance of interaction length in sub-phonon lifetime SBS pulse compression.

 

Fig. 2 SBS pulse compression of 9 ns (FWHM) Gaussian pulses in FC72 at 1064 nm; (a) Experimentally measured and (b) numerically simulated dependence of compressed pulse duration on the input pulse energy with two different focusing/interaction lengths, which are expressed in fraction of the pulse Full Length at Half Maximum [FWHM=(c/n) τ_p]; (c)-(e) Experimentally measured compressed pulses obtained with different initial conditions as marked out in (a);

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The compressed pulses obtained with different initial conditions are also shown in Figs. 2(c)–2(e). It can be seen that the compressed pulse [Fig. 2(d)] obtained with interaction length matching with (c/n) τ_p is free of pre/post-pulse modulations as observed in the other case [Fig. 2(c)], which stands for another advantage of choosing longer interaction length. One explanation on the observation of pre/post-pulse modulations is the following. In the case of short interaction length, a Stokes pulse is generated around the beam focus when the very beginning part of the pump pulse arrives. The Stokes pulse then counter-propagates with the pump and extracts the energy from the latter. Due to large beam divergence at short focusing length, the intensity of the Stokes pulse drops quickly, leading to very inefficient energy extraction. This Stokes pulse will leave the cell and form a pre-pulse. A second Stokes pulse created from the pump closer to its peak can have higher intensity therefore much better capability in energy extraction, which leads to the generation of the main Stokes pulse. However, as the main Stokes pulse leaves the cell, there is still undepleted pump from its tail because of not enough interaction length. The undepleted pump tail will then create another Stokes pulse as the post-pulse. Depending on the pump energy and the focusing condition, there could even be multiple post-pulses. In the case of long interaction length (c/n)τ_p, the beam divergence is reduced and the interaction length is increased by almost a factor of two. Contributions to the pre/post-pulse modulations are greatly minimized. As the pump energy increases, the compressed Stokes pulse [Fig. 2(e)] obtained with interaction length of (c/n) τ_p gets shorter, mainly featured by the sharpening of its trailing edge. The simulated pulse (not shown here) exhibits similar behavior, which will be analyzed in detail below.

4.2. Sub-phonon lifetime pulse compression in water at 532 nm

Knowing that the interaction length is crucial in achieving sub-phonon lifetime pulse compression, a plano-convex lens with effective focal length of 220 cm is used to compress nanosecond pulses in water at 532 nm. The 9 ns input pulses with corresponding FLHM of 203 cm in water are employed to investigate in detail the mechanism of sub-phonon lifetime pulse compression as well as the limitation of compressed pulse duration. Shorter input pulses of 7 ns with corresponding FLHM of 158 cm in water are also deployed to study the dependence of pulse compression on the input pulse duration, as reported in [13]. Since the focusing length is longer than the FLHM of both input pulses, the interaction lengths are limited to the FLHM of each pulse, respectively. In the experiment, the pump beam diameter is 30 mm (full width at 1/e² maximum intensity), mainly limited by the 2″ mirror working at 45°. Two benefits are gained from using large input beam size. On the one hand, the initiation of Stokes pulse can be more localized to the beam focus such that the interaction length is maintained to the designed value. On the other hand, the energy load capacity of the SBS compressor is higher with larger beam size, as discussed in [11]. The compressed pulses are characterized by a Hamamatsu R1328U-52 biplanar phototube (rise time: 60 ps; spectral response: 185–650 nm; detection area: 10 mm diameter) and a Tektronix DPO 70804 digital oscilloscope (Bandwidth: 8 GHz; Sampling rate: 25 Gsa/s).

The experimentally measured dependence of compressed pulse duration on input pulse energy with two different input pulse durations is presented in Fig. 3(a). The dashed line represents the phonon lifetime of 295 ps in water at 532 nm, which is much shorter than the input pulse duration. It can be seen that sub-phonon lifetime pulse compression is achieved with both input pulses of different duration. When 9 ns input pulses are used, the compressed pulses with minimum duration of 180 ps (0.6τ_B) and output energy of 240 mJ per pulse are obtained at the input pulse energy of 300 mJ. As the input energy further increases, the compressed pulses become longer and exhibit larger pulse width fluctuation, as indicated by the error bar. It will be explained in Section 4.4 that the pulse width fluctuation is closely related to the generation of backward stimulated Raman scattering (BSRS). The vibrational Raman shift in water is about 3400 cm⁻¹, leading to the Raman wavelength of 650 nm when pumped at 532 nm. The BSRS is observed as the input pulse energy approaches to 350 mJ, agreeing with the previous observation [14]. As discussed in [14], the strong SRS propagating in the backward direction (same direction as the SBS) is actually driven by the compressed SBS instead of the pump, therefore representing a forward SRS process. In the case of 7 ns input pulses, compressed pulses as short as 150 ps (0.5τ_B) are obtained at the maximum input energy of 120 mJ, the maximum energy available from the laser for 7ns pulses. The behavior of saturation in compressed pulse duration and its further increase is expected, if higher input energy would be available. As compared to 9 ns input pulses, shorter compressed pulses are obtained with shorter input pulses, which agrees with the simulation results reported in [13]. The energy performances are summarized in the inset of Fig. 3(a), with energy efficiency saturating around 76% for both cases.

 

Fig. 3 SBS pulse compression of nanosecond Gaussian pulses in water at 532 nm with a focusing length of 220 cm; (a) Experimentally measured dependence of compressed pulse duration on the input pulse energy with two different input pulse durations; The inset shows the corresponding energy efficiency. (b)-(e) Compressed pulse shapes with different initial conditions as labeled in (a). Compressed pulses presented in (e), which are both normalized to the same peak of the pulse with higher peak intensity, are obtained from two different laser shots at the input pump pulse energy of 400 mJ. Two pulses are temporally shifted for better visibility.

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The dependence of compressed pulse duration on the input pulse energy is also simulated, as demonstrated in Fig. 4(a). The numerical simulation reproduces several features observed from the experiment, such as the direct compression of nanosecond pulses below the phonon lifetime, the dependence of compressed pulse duration on the duration of input pulses, and the saturation and further increase of the compressed pulse duration with increased input energy. One distinct discrepancy between the experiment and simulation is that the compressed pulse duration saturates at quite different input pulse energy. As will be analyzed in Section 4.4, the discrepancy reveals two mechanisms that cause the saturation in compressed pulse duration and the temporal pulse spreading. The simulation only accounts for one of these mechanisms.

 

Fig. 4 SBS pulse compression of nanosecond Gaussian pulses in water at 532 nm, with focusing length of 220 cm being chosen to match with experimental condition. (a) Simulated dependence of compressed pulse duration on the input pulse energy with two different input pulse durations; (b)-(e) Compressed pulse shapes with different initial conditions as labeled in (a). Two pulses presented in (e), which are normalized to the same peak of the pulse (i.e., the peak of pulse 1) with higher peak intensity, are obtained with two different input pump pulse energies. Two pulses are temporally shifted for better visibility. The inset illustrates the energy exchange between pump and Stokes pulses inside the SBS cell, at the input energy of 550 mJ.

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4.3. Mechanism of sub-phonon lifetime pulse compression

The mechanism of sub-phonon lifetime pulse compression has not been fully explored so far. Velchev et al. have attributed it to the half-cycle gain [13] in compressing pulses with initial duration on the order of the phonon lifetime. While compressing pulses that are much longer than the phonon lifetime, a different mechanism can be understood by examining the evolution of compressed pulse shapes obtained from both experiment and simulation, as displayed in Figs. 2(d)–2(e), Figs. 3(b)–3(d) and Figs. 4(b)–4(e). As can be seen in Fig. 2(d), Fig. 3(b) and Fig. 4(b), the compressed pulses exhibit the typical feature of sharp leading edge and relatively slow trailing edge, when their durations are around or above the phonon lifetime. However, as the pulse compression enters into the sub-phonon lifetime regime, the compression of pulse trailing edge becomes much faster than that of the leading edge with increased input energy. Consequently, compressed pulses with symmetric shape [Fig. 2(e), Fig. 3(c) and Fig. 4(d)] or even sharper trailing edge [Fig. 4(e1)] are obtained. Similar pulse shapes have also been observed somewhere else [8,13] with the compressed pulse duration below the phonon lifetime. Therefore, the major contribution to sub-phonon lifetime pulse compression of nanosecond pulses is the steepening of the Stokes pulse trailing edge, which is realized by transferring its energy back to the pump pulse.

The energy exchange process is nicely captured by the simulation. As a demonstration, the intensity distribution of both pump and Stokes pulses, at the time when Stokes pulse arrives at the position near z=50cm, is shown in the inset of Fig. 4(e). Since the Stokes pulse leading edge is strong enough to deplete the pump before the back of the Stokes pulse, the tail of the Stokes pulse can then interact with the acoustic wave and return its energy back to the pump. As a result, the trailing edge of the Stokes pulse gets sharpened and a second pump pulse is regenerated to the right of the Stokes pulse. The further interaction between the newly generated pump and the undamped acoustic phonon can then foster a second Stokes pulse following the main one, as observed from the simulated pulses. It will be discussed in Section 4.4 that the energy exchange process can cause temporal pulse spreading as well, but accounting for a mechanism different from the SRS. The energy exchange process in SBS pulse compression has been theoretically investigated in detail with rectangular input pulses [19], mainly focusing on the study of pulse modulation. As demonstrated above, the energy transfer mechanism can be well employed in achieving sub-phonon lifetime compression of long Gaussian pulses, provided that the essential requirement of long enough interaction length is satisfied.

4.4. Limitation of minimum compressed pulse duration

By comparing Fig. 3 (experimental measurements) and Fig. 4 (theoretical simulations of SBS process only), two mechanisms leading to saturation and spreading of compressed pulse width can be identified. The first mechanism is the onset of competing nonlinear effect such as Stimulated Raman Scattering (SRS), which is driven by the peak of the SBS pulse [28]. This is evidenced by the observation of SRS line centered at 650 nm, as well as the cutoff of the SBS pulse peak [Fig. 3(e)] as the input pulse energy increases. The consequence is broadening of the pulse width. The second mechanism is the energy back conversion from the Stokes to the pump. This does not show in our experiments due to the lower threshold of SRS in water. However, the energy back conversion (with a higher threshold) is clearly shown in simulation, where only SBS process is included (Fig. 4). Similar to the process of energy back conversion from Stokes pulse tail to pump as described in Section 4.3, the pump depletion point moves forward towards the Stokes pulse leading edge at higher input energy. Then, the peak of the Stokes pulse can interact with the undamped acoustic phonon and return its energy back to pump, leading to temporal pulse spreading.

4.5. Optimum focusing condition

It has been demonstrated that the compressed pulse duration has strong dependence on the interaction length. It is therefore of great interest to explore the optimum focusing length for the best pulse compression. Figure 5 illustrates the simulation results of SBS pulse compression in water from the generator, with two different input pulse durations. Similar dependence of compressed pulse duration on the focusing length and input pulse energy is observed for both cases. The minimum compressed pulse duration obtained with shorter input pulse (i.e., 7 ns) is shorter than that achieved with 9 ns input pulse, as indicated by the positions of two gray planes shown in Figs. 5(a) and 5(b). The difference might be attributed to both effects of half-cycle gain and energy exchange, where the former acts on shortening the leading edge of the Stokes pulse and the latter applies to sharpen the pulse trailing edge. Both effects should be stronger when shorter input pulse is employed. A further study is needed to fully interpret the observation. It is important to note that the maximum intensity of the SBS compressed pulses is clamped by the nonlinear competing process. Therefore, the shorter compressed pulses obtained with shorter input pulses can only carry lower pulse energy.

 

Fig. 5 Simulation on SBS pulse compression in water from the generator, demonstrating the dependence of compressed pulse duration on both focusing length and input pulse energy with input pulse duration of (a) 9 ns and (b) 7 ns. The input beam diameter is chosen to be 30 mm for both cases. The gray planes in (a) and (b) indicate the minimum compressed pulse duration of 140 ps and 110 ps, respectively. The two white curves in (a) label the pulse duration of 160 ps, while the two white curves in (b) label the pulse duration of 125 ps. Therefore, the valley areas within the white curves in (a) and (b) contain the compressed pulse durations within the range of 140 ps-160 ps and 110 ps-125 ps, respectively. (c) A schematic comparing the beam cross section within the SBS interaction region for the same inputs focused by two lenses with different focusing length (≥FLHM). The beam cross section within the major SBS interaction region is smaller at longer focusing length.

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It can be seen that, if the focusing length only matches closely to 0.5FLHM or (c/2n) τ_p, pulse compression can not reach to the minimum duration even at very high input energy. At a fixed input energy of 800 mJ, the compressed pulse duration first gets shorter as the focusing length increases. The minimum compressed pulse duration (i.e., 140 ps for the case of 9 ns input pulse or 110 ps for the case of 7 ns input pulse) is obtained when the focusing length matches approximately with FLHM or (c/n) τ_p. As the focusing length exceeds FLHM and increases further, the compressed pulse becomes longer. The dependence of compressed pulse duration on the focusing length shown here is quite similar as the dependence of compressed pulse duration on the input pulse energy demonstrated in Fig. 4(a). The increase in compressed pulse duration can be attributed to the increase in pump intensity at longer focusing length. It should be noted that the major interaction between pump and Stokes pulses happens within the region that is away from the beam focus. As the focusing length increases, the interaction length stays almost unchanged as FLHM. But the beam cross section within the major interaction region becomes smaller, as illustrated in Fig. 5(c). Therefore, the equivalent effect of using focusing length longer than the FLHM is to increase the pump intensity, which would lead to pulse spreading if exceeding an optimum value as demonstrated in Fig. 4(a). In order to keep the compressed pulse duration at minimum, one can reduce the pump energy to compensate for the intensity increase. The arrows in Figs. 5(a) and 5(b) show the dependence of required pump energy on the focusing length to obtain minimum compressed pulse duration. It is interesting that there is no further shortening in the minimum compressed pulse duration, as indicated by the color code. This is further emphasized by marking out the valley areas (i.e., the area within two white curves) that contain the compressed pulse durations within the range of 140 ps-160 ps in Fig. 5(a) and 110 ps-125 ps in Fig. 5(b), respectively. Therefore, SBS sub-phonon lifetime pulse compression is not benefited from using focusing length much longer than the FLHM. Instead, the very long SBS cell even imposes severe constraints on the SBS compression, such as the higher optical loss, more difficulty in maintaining the uniformity of SBS gain medium and a larger footprint required. Overall, it is suggested to choose the optimum focusing length of (c/n) τ_p. It is worth mentioning that similar interaction length requirement should also apply to the cascaded two-cell setup for shortest pulse compression.

5. High-energy sub-phonon lifetime pulse compression in generator-amplifier setup

To push the energy of the pre-compressed pulses obtained from SBS generator to Joule level, a SBS amplifier is included to form the energy-scalable generator-amplifier setup as sketched in Fig. 1. Due to its much better thermal stability [11], water is employed as the SBS medium. The input laser parameters such as pulse width (9 ns) and beam diameter (30 mm 1/e²) are the same as those mentioned in Section 4.2. The total input pulse energy to the SBS compressor is 2 J, mainly limited by the generation of SBS feedback inside the amplifier from the pump itself. Lowering the pump intensity by increasing the beam cross section, which requires larger size optics, can easily scale up the compressible energy. The Stokes seed pulses obtained from SBS generator detailed in Section 4.2 are used to interact with the pump pulses inside the amplifier. The input to the generator cell is controlled to be less than 250 mJ, the threshold for the amplified Stokes pulse to generate forward SRS that would degrade the stability of the compressed pulses. It would also be beneficial to obtain amplified Stokes pulse free of the second Stokes pulse by using lower input energy to the generator, if SRS was not the primary limitation.

Figure 6 shows the energy performance of the SBS compressor. The output energies from the SBS generator (bottom axis) and SBS amplifier (left axis) as well as the corresponding overall efficiency (right axis) are assessed at three different generator input energies (top axis). The overall efficiency is defined as the ratio between the amplifier output energy and the total input energy of 2 J. It can be seen that the maximum output energy of 1.3 J is obtained, with the energy fluctuation of less than 1.5% (not shown here). The corresponding overall efficiency is up to 65%. Since the intensity of the Stokes seed pulse exceeds that of the pump pulse, saturation in energy efficiency is observed, which is in good agreement with previous conclusion [11].

 

Fig. 6 Experimentally measured amplified Stokes pulse energy (left) and the corresponding overall energy efficiency (right). The insets show typical pulse shape of the amplified Stokes pulses at corresponding generator input (amplifier pump) energy of 120 mJ (1.88 J), 180 mJ (1.82 J) and 240 mJ (1.76 J), respectively. The corresponding Stokes seed pulse durations are 380 ps, 260 ps and 200 ps, respectively

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The amplified Stokes pulses, corresponding to three different generator inputs, are characterized by the setup described in Section 4.2 and displayed as insets in Fig. 6. After the amplification process, further compression of the Stokes seed pulses is observed. For instance, the Stokes seed pulse of 200 ps is compressed to 170 ps at the generator input energy of 240 mJ. Simulation on the SBS amplification has confirmed the observation of further compression, as reported in a previous work [24]. It is worth emphasizing that the compressed pulses obtained here are free of clear amplitude modulation as observed in [8]. Therefore, the peak power enhancement has been truly achieved. The pulse width fluctuations are measured to be as low as 5% over 50 laser shots at the repetition rate of 1.25 Hz.

6. Conclusion

In this work, we have demonstrated SBS pulse compression in liquids with Joule-level energy and sub-200 ps duration, by employing a energy-scalable generator-amplifier setup. We show that the single-pass compression of long Gaussian pulses (> 20τ_B) below the phonon lifetime can be realized in SBS generator, provided that the interaction length is chosen to match closely with (c/n) τ_p of the input pulses. The shortest compressed pulses of 150 ps (only 0.5τ_B) with 90 mJ per pulse have been obtained in water at 532 nm. The mechanism of sub-phonon lifetime compression has been discussed, based on both experiment and simulation, as due to the steepening of the Stokes pulse trailing edge via energy exchange process. Utilizing the method described here, the single-pass compression of Q-switched nanosecond pulses to less than 100 ps can be expected, by either choosing a SBS medium with shorter phonon lifetime [29] or compressing input pulses at shorter wavelength since τ_B is proportional to λ² [26].

To boost the energy of compressed Stokes pulses, a energy-scalable generator-amplifier setup, which outperforms other configurations in energy scalability, has been employed to obtain compressed pulses of 170 ps, 1.3 J per pulse with very good stability in both pulse energy and duration. In the current setup, the maximum compressible energy is limited by the SBS generation from the pump inside the amplifier, the SRS generation, as well as the amplitude modulation to the Stokes pulses. By increasing the input beam size, the aforementioned limitations could all be alleviated. Therefore, sub-phonon lifetime pulse compression with very high compressible energy can be expected, and demonstrated by further experimental work.