We demonstrate ∼ 40X pulse compression (down to ∼ 300 ps) with ∼ 1 joule, nanosecond pulses for high energy applications requiring ≥ 1 gigawatt of peak power. Our method is based on the established principle of stimulated Brillouin scattering (SBS). To push the SBS technique to its highest peak-power limit, a combination of theoretical modeling and experiments is used to identify and optimize all critical parameters, including optical configuration, interaction length, intensity matching, choice of gain medium and thermal stability. Pulse compression results are presented both at 1064 nm and 532 nm, with performances close to the theoretical limit and excellent shot-to-shot reproducibility.
© 2014 Optical Society of America
The efficiency of many nonlinear light-matter interaction processes depends critically on the peak power of the laser pulse. This is particularly true in the cases of higher-order processes such as four-photon ionization of gaseous nitrogen and filamentation in air, where the required peak power exceeds gigawatt. There is a family of techniques commonly used to increase the peak power of laser pulses by pulse compression. In the ultra-short (<ps) regime, methods such as chirp compensation are used to compress an optical pulse to its Fourier-transform-limited duration. However, these methods are generally not applicable to nanoseconds pulses.
Pulse compression from nanoseconds to sub-nanoseconds is commonly achieved by utilizing nonlinear light-matter interactions. Stimulated Brillouin scattering (SBS) is a classic example of this type of technique. In its simplest realization, a high-energy laser pulse is focused into a SBS active medium. At the focus the field is strong enough to initiate a backward scattered “Stokes” field which interferes with the remaining of the incoming field, producing a wave that moves at the velocity of sound. Due to electrostriction, through which the material tends to concentrate where the light field is stronger, this interference wave generates a density grating (i.e. phonon field). The expanding phonon field, acting like a “moving” mirror, backscatters more energy from the incident field into the Stokes field, leading to depletion of the incident pulse and a compressed Stokes pulse with a sharp rising edge. The result is an optical pulse with most of the initial energy but much reduced temporal width.
Compressed pulses by SBS were first reported by Maier et al  and later observed in fibers . Hon  demonstrated controlled SBS for pulse compression applications. Kmetik  showed stable SBS compression in liquid fluorocarbon FC-75 at 1064 nm. The liquid fluorocarbon family has remained the medium of choice in subsequent studies [5–9] for its short phonon lifetime, high SBS gain and low absorption in a broad spectral range from the visible to the near infrared. Schiemann et al [10–13] showed that water can also be used as a SBS medium at 532 nm. However, their study was limited to low energy and therefore low peak power amplification. Dane  upgraded a parallel two-cell configuration  which increased the energy capacity of SBS compression in liquid to beyond 1 J.
The goal of this paper is to explore the limits of SBS pulse compression in liquids for high energy applications. To this end, we use a combination of theoretical modeling, computer simulation and experiments to elucidate the critical parameters in the SBS generation process and show how optimizing these parameters leads to highly reproducible (< 5 % shot-to-shot variation in pulse energy and width) pulses at both 532 nm and 1064 nm with < 600 ps temporal duration (compressed from 12 ns pulses) and more than 1 GW peak power. To our knowledge, these results represent the best combination of peak power and stability using the SBS technique.
2. Energy-scalable two cell setup for high energy SBS pulse compression
Since its first demonstration, SBS pulse compression has evolved from the tapered waveguide geometry [3,16,17], the single long focusing setup  to the cascaded-two-cell arrangement  and eventually the parallel-two-cell configuration . The principle of SBS pulse compression is based on the strong interaction between pump and Stokes. The Stokes pulse is either generated from the leading edge of the pump pulse via SBS (i.e. the tapered wave-guide, single focusing and cascaded-two-cell setup), or pre-generated using a separated pump pulse (i.e. the parallel-two-cell setup). As illustrated in Fig. 1(a), the pump pulse (blue, from left to right) and the Stokes pulse (red, from right to left) counter-propagate inside the SBS medium (shaded area). The interference between them creates a growing density grating that scatters the energy from the pump into the leading edge of the Stokes, which, with sufficient interaction length, leads to a compressed, amplified Stokes pulse with a sharp rising edge.
Although simple in its implementation, the SBS pulse compression by a single-cell, or a cascaded two-cell setup, is strongly limited for stable high energy application by its low energy capacity and instability due to thermal disturbance . Of all the SBS compression geometries, the polarization controlled parallel two-cell setup  has demonstrated the largest energy capacity. The idea of this setup is to first generate a Stokes seed pulse with low energy in a single long focusing generator cell, then amplify the Stokes seed pulse in an amplifier cell where the beams are collimated. The energy in the focusing generator cell can be controlled to the minimum value needed for efficient energy extraction from the pump, without exceeding the energy limit and with no further attenuation. The energy in the amplifier cell can be scaled up by simply increasing the beam size while keeping the intensity under the SBS threshold (i.e., a single-pass gain factor of G = 20 to 25 ). In this way, the energy capacity can be greatly increased, limited only by the size of the optics and the homogeneity of the SBS medium. Moreover, the energy density can be even higher by choosing a SBS medium with a smaller gain parameter.
The experimental arrangement used in this work is sketched in Fig. 1(b). The input is from a custom-built single-mode Q-switched Nd:YAG oscillator and a 6-stage single-pass amplifier system operating at 1.25 Hz. A novel real-time resonance tracking method  is implemented to ensure that every single shot from the injection seeded Q-switched oscillator is single mode with a smooth temporal profile. The system outputs pulses of 12 ns at FWHM, 5 J at 1064 nm and 3.5 J at 532 nm (doubling with a LBO SHG crystal). A small portion of the laser is extracted by the combination of a half-wave plate and a thin film plate polarizing beam splitter (TFP #1). The split output is directed into a generator cell by a polarizer (TFP #2) and two directing mirrors. The largest fraction of the source is sent into the Brillouin amplifier cell from the left side in Fig. 1(b) and interacts with the Stokes seed pulse entering from the opposite side. A quarter-wave plate (Q-W #1) is used to ensure that the Stokes seed pulse is reflected from the generator with its polarization angle rotated by 90° and transmitted through the TFP #2 into the amplifier. Two quarter-wave plates Q-W #2 and Q-W #3 are oriented with their fast axis aligned such that the depleted pump can be reflected by the TFP #2 without entering the generator and the amplified Stokes can be extracted by a polarizer (TFP #3). The energy scaling is realized by a beam-size expanding telescope before the half-wave plate (H-W). As will be detailed in Section 4, the meeting point of the pump and Stokes seed pulse (solid blue and red arrows in Fig. 1(b)), the intensity of pump and seed pulse, the interaction length inside the amplifier and finally the thermal stability can be optimized to achieve efficient and stable pulse compression.
3. Theoretical modeling
In modeling the SBS process in the energy-scalable generator-amplifier setup, we consider the interaction of the counter-propagating pump pulse Ẽ1(z,t) and Stokes pulse Ẽ2(z,t) and an acoustic phonon pulse ρ̃(z,t):21] without the SVEA since the bandwidth of the phonon field is close to its frequency. Therefore, the second order term in the phonon wave equation (∂2/∂t2) cannot be neglected . In other words, the phonon field is an ultra-short pulse, especially for the material with very short phonon lifetime. The wave equations can then be described as: Eqs. (2), gB is the steady-state Brillouin gain parameter, ΓB/2π is the full width half maximum of the SBS gain spectrum, τB = 1/ΓB is the phonon lifetime, and ΩB is the Brillouin shift. ρ′ is defined as . t is the time axis and z is the spatial axis along the propagation direction of the pump. The SBS process in both the generator where a Stokes seed is generated from the spontaneous noise, and in the amplifier where the pump and Stokes seed interact and the Stokes gets amplified, are described by the set of Eqs. (2). We use the split-step method to numerically solve Eqs. (2).
The input is assumed to have a Gaussian shape in time and a flat top intensity distribution across the beam in space. A Stokes seed is first numerically generated from a focusing geometry. Its leading edge is assigned to be at the right side of the SBS medium. The peak of the pump pulse is adjusted at different z locations for various relative delays of the pump and the Stokes seed. Both heavy fluorocarbon (FC-72) and water with their parameters summarized in Table 1 are used as the SBS medium in the simulation to optimize the experimental parameters. In turn, the experimental results validate the simulation.
4. Experimental parameters optimization
In this section we discuss experimental parameters that we found critical to achieve SBS compression at high power. We also show how to optimize these parameters.
4.1. Optimizing the relative delay between the pump and the Stokes seed pulse
Since the pump and Stokes seed pulse counter-propagate, their temporal overlap is critical for efficient energy exchange. The amplifier cell needs to be positioned correctly with respect to the crossing point between pump and seed. Figure 2(a) illustrates three simulated situations in which the leading edge of the pump and Stokes seed meet at different locations relative to the SBS cell. In all three panels, the vertical axis on the right (blue) represents the pump intensity, the vertical axis on the left (red) represents the Stokes intensity, both in arbitrary unit. The horizontal axis represents the spatial dimension. The SBS medium is 2.5 m long and is located in space from 0 to 2.5 m. The solid red, dotted blue and solid blue pulses with shaded areas illustrate the amplified Stokes, input pump and the depleted pump, respectively. The arrows point to the propagation directions. The rectangle with a blue and red arrow pointing at opposite directions in the inset indicates the SBS medium relative to the meeting point of the pump and the Stokes seed. When the two pulses meet outside the right entrance of the SBS amplifier cell, as shown in the left panel of Fig. 2(a), the Stokes pulse interacts with only a portion of the pump pulse, leaving a large amount of un-depleted energy (shaded area). The overall result is a low pump energy extraction efficiency and therefore a small peak power amplification. As shown in Fig. 2(a) middle panel, meeting at the right entrance of the cell ensures persistent interaction with the SBS medium throughout the spatial-temporal overlap of the pump and Stokes pulses, leading to efficient energy exchange and high peak power amplification. The Stokes still extracts most of the energy from the pump when the pump and Stokes meet inside the cell (right panel). However, the energy is transferred to the stokes trailing edge, rather than the leading edge, after the leading edge exits the cell. This leads to a low peak power amplification and compression ratio due to the short interaction length. In conclusion, there is an optimal delay Δt between the pump and the Stokes seed pulse for best compression performance.
How to experimentally guarantee optimal overlap? We find that in addition to the optical path length difference (Δt1 in Fig. 1(b)), the extra delay during the Stokes seed generation process (Δt2) should also be taken into account, i.e.Figure 2(b) is a direct experimental measurement of Δt2 (with 1064 nm pulses in FC-72). The black dashed line is the input pulse shape and the colored solid lines are reflected Stokes pulses with different input energies. The energy dependence of the time of arrival Δt2 of the Stokes pulse is plotted in the inset of Fig. 2(b). The variation of Δt2 can be as large as the FWHM of the input pulse, which is several nanoseconds. To visualize the correlation between Δt2 and the seed energy, we use an input pulse of 16 ns and an amplifier cell of 150 cm long. The peak power of the amplified Stokes as well as the energy in its “tail” as function of the Stokes seed energy are plotted in Fig. 2(c). The mapping of seed energy to Δt2 is plotted in the inset. As the seed energy increases, the peak power of the amplified Stokes increases and then decreases with more energy distributed in the “tail” of the Stokes pulse. This counter-intuitive result was also shown in the result of  but with no explicit explanation.
With both Δt1 and Δt2 taken into account, an optimal delay can be found by using a fixed Stokes seed energy and adjusting Δt1 to make sure the pump and Stokes seed meet at the right side of the cell’s entrance for maximum power amplification.
4.2. Optimizing the pump and the seed pulse intensities for best energy extraction
Being a third order [χ(3)] nonlinear process, the higher the intensity, the more efficient the SBS interaction is inside the amplifier. However, the intensity of the pump should not be too high to initiate a SBS back reflection by the pump itself. In our experiment, we adjust the beam size until the pump beam alone reaches the SBS threshold.
In order to search for an optimum Stokes seed intensity to achieve efficient energy extraction from the pump, we carried out both simulation and experiment in water at 532 nm. In both cases, the pump intensity is kept at threshold intensity of SBS in the amplifier cell. In the experiment, to avoid time-energy coupling as discussed in section 4.1, we send a fixed input energy of 120 mJ into the SBS generator (220 cm focusing distance), create a compressed Stokes seed of 87 mJ and 325 ± 7 ps (mean ± s.d.) at its FWHM. The actual Stokes seed energy that enters the amplifier cell is adjusted by an extra half-wave plate and a thin film polarizing beam splitter between Q-W #3 and TFP #2. Figure 3 shows the energy extraction efficiency as a function of the Stokes seed energy. In the simulation (magenta dashed line), the extraction efficiency increases quickly as the seed intensity increases and saturates to a maximum value when the seed intensity is comparable to the pump. Our measurements show a similar trend (full triangle in Fig. 3). The observed SBS extraction efficiencies are smaller than those given by the simulation. This difference can be attributed to the “square” beam profile used in the simulation, while the real laser beam has a 4th order super-Gaussian profile.
In summary, a Stokes seed with the same peak power as the pump is desired to effectively extract energy from the pump. Because the Stokes seed is pre-compressed in our setup, the energy needed from the seed is relatively small. In our experiment in water with 532 nm pulses, the seed pulse is compressed down to 1/37 of the input pulse width and therefore a seed energy of less than 3% of the pump energy is sufficient for optimum energy extraction.
4.3. Optimizing the interaction length
The interaction length is the length of the amplifier cell, provided the delay between the pump and Stokes has been optimized. As shown in Fig. 2(a), a short interaction length gives rise to incomplete compression with a long tail in the Stokes pulse. However, long interaction length brings in loss due to absorption and makes the system inefficient as well as bulky. Our goal is to find an amplifier cell length that is at the saturation point for the power amplification, which represents the optimum combination of compression ratio and efficiency.
In Fig. 4, the simulated power amplification is plotted as a function of the relative delay, Δt, between the pump and the Stokes seed at different amplifier lengths. The colored curves are a quantitative representation of the effect of delay on power amplification, which are shown in Fig. 2(a). The black dashed line tracks the peaks of the power amplification curves. As the amplifier length increases, the output peak power becomes less sensitive to the delay and saturates. It can be argued that, for an infinitely long cell, the pump and Stokes can always overlap in the medium and the effect of delay is negligible. The peak power amplification reaches a saturation point when the amplifier length exceeds 250 cm (≈ FWHM of the spatial pulse length). This is the length used in our experiments.
4.4. SBS medium: absorption and thermal disturbance
It is critical to select the right SBS medium for high power applications. The major factors to consider are intrinsic optical absorption and thermal stability. Here we restrict our discussion to FC-72 and water, two of the most popular SBS mediums.
Due to the relative long (∼m) interaction length required for efficient compression, material absorption can be a severe limiting factor for power throughput. For example, water is most transparent (α < 0.001 cm−1) in the visible range (300–600 nm) and absorbs strongly in the near IR (α ≈ 0.5 cm−1 at 1064 nm)  due to vibronic overtones. On the other hand, FC-72 has small absorption (α < 10−5) throughout the visible and near IR . As a result, water can be used as the SBS gain medium in the visible (e.g. 532 nm) in which the absorption is relatively small. FC-72 is preferred outside the transparent window of water (e.g. 1064 nm), especially when low loss and high reflectivity are critical.
Thermally induced motion in the SBS medium strongly limits the stability of the compressed Stokes seed pulse generation. The same limitation applies for the long focusing single cell setup and the cascade two cell setup [4, 8]. As for the amplifier cell in the parallel two-cell setup, thermal fluctuation induces inhomogeneity of the medium due to thermal-optical effect, which introduces aberrations to the Stokes wavefront. This effect is extremely significant in the FC-72 liquid, the temperature dependent refractive index of which is six times higher than that of water (−4.7×10−4/K compared to −0.8×10−4/K). After propagating through the 2.5 m long liquid cell with no thermal control, a round beam becomes elliptical with its major axis parallel to the optical table and also deflects downwards in the vertical direction. The thermal effect can be modeled by the ABCD propagation of a Gaussian beam in a lens-like medium . As the temperature of the environment around the cylindrical cell increases, a positive index gradient from the center to the side of the cylinder develops because of the negative dn/dt, making the liquid cell act like a positive lens. In presence of gravity, the warmer medium rises to the top while the cooler medium stays at the bottom, leading to a vertical index gradient. The overall effect of temperature variation and gravity gives rise to a cylindrical lens with stronger focusing power in the vertical direction, which makes a round beam elliptical and bend downward.
To quantify the thermal effect and evaluate the thermal isolation performance, the deflection angle of a 2.5 mm in diameter beam sent through the 2.5 m long liquid cell is measured. The results for a cell filled with liquid FC-72 are compared with the results for a water filled cell, using different thermal isolation methods, in a laboratory where the temperature is actively controlled to within 2°C.
In a liquid FC-72 (filtered with 25 nm membrane filter) cell with no thermal control, the beam deflects quickly by 2 mrad within half an hour, and the SBS compression is very unstable even at low input energy of several tens of mJ. With a thermal insulation housing, the SBS compression becomes stable. The thermal insulation housing is made of 1” thick styrofoam with windows at its entrance and exit. A 1” air gap in between the styrofoam and the glass cell is designed to have air as an extra layer of thermal insulation without air convection. The probe beam deflects by 2 mrad after three hours (solid triangle in Fig. 5), corresponding to an index difference of 5.3×10−4 between the center of the 48 mm diameter cell to the side of it. An extra layer of styrofoam housing further slows down the thermal effect, shown in blue cross in Fig. 5. The enclosed thermal housing ensures stable pulse compression. However, some wave front distortion on the Stokes beam caused by index gradient in the liquid is still noticeable.
A significant improvement is achieved when water is contained in a specially designed double-walled glass cell, shown in empty circles in Fig. 5. The inner tube of the double-walled glass cell is filled with highly distilled and purified water (OmniSolv brand from EMD Milipore and filtered with 25 nm membrane filter) as the SBS medium. The space between two walls is filled with circulating water allowing active temperature stabilization. The combination of the double-walled cell and the thermal isolation housing successfully controls the beam deflection angle to be below 30 μrad for hours. This is almost two orders of magnitude smaller than the result in a FC-72 cell. We also expand the beam to 32 mm and monitor the far field pattern of it after propagation through the water cell. No significant aberration is observed on the beam wave front.
In summary, water is particularly well suited for applications in the visible (e.g. 532 nm) that require minimum wave front distortion, while FC-72, thanks to its low absorption over a broad spectral range, is ideal when high reflectivity is desired. In either case, careful thermal isolation is critical to ensure stable compression.
5. Pulse compression results and discussions
As we optimize the energy scalable two-cell setup discussed in section 4, stable, efficient high energy SBS compression is achieved. Here we show the result of compressing 1064 nm pulses in FC-72 and 532 nm pulses in water (see Fig. 6). We measure the 1064 nm pulse with a 25 GHz InGaAs biased photodetector (model: 1417) from Newport and the 532 nm pulse with a biplanar phototube (model: R1328U-52, rise time: 60 ps) from Hamamatsu combined with an Agilent digital oscilloscope (bandwidth: 2.5 GHz; Sampling rate: 20 Gsa/s).
At 1064 nm with FC-72 as the SBS medium (panel (a)), the final output is compressed down from a 1 J, ∼12 ns pump pulse (inset, blue dotted line) to a FWHM width of ∼580 ps. Note that this value is below the phonon lifetime of FC-72 (∼ 1 ns ). The overall energy reflectivity in this case is 73.5%. We thus achieve an output peak power of ∼1 GW which represents a factor of 11 enhancement compared to the input pulse. To quantify the stability of our setup, we measure the shot-to-shot fluctuation in pulse width to be ∼ 2 % and shot-to-shot fluctuation in energy to be below 1.3 %. Part of the fluctuation might come from the randomness in the SBS initiation process .
In the case of 532 nm and with water as the SBS medium (panel (b)), we achieve an output pulse with energy of 1.2 J and pulse width of 330 ps ± 17 ps (mean ± s.d.) at its FWHM (pulse width histogram is shown in the inset). This corresponds to a peak power of over 3 GW, the largest ever achieved at this wavelength using the SBS compression technique. The ringing on the pulse leading edge is due to the limited bandwidth (2.5 GHz) of the measurement oscilloscope.
Also clearly visible in the measured pulse shapes shown in Figs. 6(a) is a signal resurgence at ∼ 2 ns. This secondary pulse is more pronounced in the case of FC-72 (phonon life time: ∼1 ns at 1064nm) compared to water (phonon life time: 295 ps at 532 nm ). We attribute this interesting phenomenon to the energy exchange between pump and Stokes under the condition of transient SBS compression . As the leading edge of the Stokes pulse gets amplified, it depletes the pump pulse quickly (panel (a) inset, depleted pump trace between −5 to 3 ns). The tail of the Stokes pulse continues to interact with the phonon field and transfer its energy back into a “regenerated” pump, as indicated by the peak near 5 ns in the depleted pump trace (panel (a) inset). This Stokes-to-pump back transfer sharpens the falling edge of the Stokes pulse, resulting in a highly compressed pulse shape. As the Stokes is compressed down to below the phonon lifetime of the SBS medium and its tail gets depleted, the pump-to-Stokes transfer resumes domination, giving rise to a weak secondary pulse in the amplified Stokes after its main peak. This process continues as they propagate across each other, thus creating a Stokes pulse with a modulated tail. In panels (c)–(d) of Fig. 6, we show the calculated pulse shapes of the amplified Stokes. Our theoretical modeling successfully reproduced the relative pulse width in the two cases as well as the and relative amplitude of the secondary pulse when compressing in the FC-72. The second pulse contains ∼ 25% of the pulse energy and presents a limit to the peak power enhancement. It can be avoided by choosing a medium with short phonon lifetime (wavelength dependent) or compressing the Stokes to be above the phonon lifetime.
In summary, we demonstrate how to produce sub-nanosecond pulses with GW of peak power via the SBS process at both 1064 nm and 532 nm. This is achieved by systematically optimizing the generator-amplifier configuration in terms of energy-dependent optical delay, seed/pump intensity ratio, interaction length, and thermal isolation. To our knowledge, this is the first comprehensive effort to optimize SBS compression in the GW power regime and the resulting design principle directly lead to the generation of the highest peak power at 532 nm. Our setup also shows the highest shot-to-shot stability compared to present literature, which is critical to the integration of this setup to downstream optical components.
We believe that this work not only provides scientists with a step-by-step manual to produce high energy pulses using SBS technology, it also clarifies a number of previously obscure aspects of the SBS process, such as energy-delay coupling, thermal effects and secondary pulse formation. The generated GW, sub-nanosecond optical pulses will have many applications. For example, when frequency converted to UV (266 nm), this setup will open new possibilities in high energy light-matter interactions such as creation of ionized plasma channels in air and time-resolved laser-induced breakdown spectroscopy (LIBS) for analysis of organic samples.
This work was supported by DTRA grant HDTRA-11-1-0043 and the ARO MURI grant W911NF1110297.
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