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Abstract
A new approach to sub-phonon lifetime pulse compression by stimulated Brillouin scattering (SBS) is presented. Triangular and step pulse pumps are both used as a pump source in a single-cell SBS compression setup. Compared with a Gaussian pump (shortest compressed pulse is the phonon lifetime with the highest energy conversion, approximately 60% under the same conditions), the compression ratio is significantly improved in the case of triangular and step pulse pumps, and there is some improvement in the energy conversion when a step pulse pump is used. A pulse as short as a quarter of a phonon lifetime is produced by a triangular pulse pump, with an energy conversion above 30%. The pump pulse shape is identified as the key parameter in achieving sub-phonon lifetime pulse compression. By using a step pulse shape, a 4.5 ns pump pulses with a 60mJ at 1064-nm are compressed down to 292 ps (below semi-phonon-lifetime) in 3M Fluorinert Electronic Liquid FC-770 with an energy conversion above 65%. This work presents a route to reliable generation of sub-semi-phonon-lifetime pulses by SBS compression.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The nonlinear process of stimulated Brillouin scattering in gases, liquids, and solids is currently widely used as a tool to improve the beam quality and compress nanosecond laser pulses down to the subnanosecond region with remarkable conversion efficiency [1–7]. High peak-power enhancements up to 65-fold can be achieved via this technique, as demonstrated in [8]. Meanwhile, phase conjugation of stimulated Brillouin scattering can remove the effect of optical distortion imposed by aberrations in optical components [9]. Lasers employing internal SBS pulse compression are valuable for both scientific and commercial applications [10].
For a given compression technique, it is interesting to investigate the achievable minimum pulse duration.The dependence of the compressed pulse duration on pump pulse duration has been investigated extensively both experimentally and theoretically. In the case that input pulses is much longer than the phonon lifetime, the limit to the pulse compression is set by the phonon lifetime [4]; However, for an input pulse duration that is close to the phonon lifetime, the compressed pulse is limited by half-cycle gain [11].
For optical configuration of SBS pulse compression, two-cell designs are easier to obtain high compression ratio. By using a double compression scheme, Velchev et al. [11] compressed 5-ns Gaussian pulses to an intermediate duration close to the phonon lifetime (τB = 295 ps) in first sindegle-pass compression, and further compressed the pre-compressed pulses to 160 ps (0.54τB) using a second single-pass compression with low energy (i.e., only a few mJ). For high-energy scalability, Dane et al. [4] designed an efficient amplifier–generator two-cell SBS structure in which the input pulse can be scaled to large laser-pulse energy with a 2.5-J pulse duration compressed from 15.8 to 1.7 ns (2.83τB) in carbon tetrachloride (CCl4) (τB = 600 ps) [4]. To further explore the potentials of this configuration, Xu et al. [12] demonstrated pulse compression (down to ~580 ps) (~τB) with a 1-J, 12-ns pulse using 73.5% FC-72 (τB = 590 ps), and Feng [13] achieved a 1.2-J, 300-ps (~τB) compressed duration from a 2.4-J, 12-ns pulse in water. For the amplifier–generator design, pump energy is split to generate and amplify a Stokes seed pulse. In a generator, high energy is required to generate short Stokes seed pulses. In a Brillouin cell, high energy is also needed for sufficient amplification. Moreover, large amounts of optical components increase the losses. Therefore, this design is appropriate only in the case of high pump energy, which limits its application in internal pulse compression of commercial lasers.
However, when possible, it is desirable to employ single-cell simple compressor geometry to achieve minimum compression pulse duration, highest energy-conversion efficiency, and simplest design [9]. A single-cell setup can reduce the losses caused by optical surfaces. Feng et al. [14] realized sub-phonon-lifetime compression in a single pass by the means of sufficient interaction length. Long focal length reduces the power density in the focal region and increases the absorption in a medium. To obtain a high compression ratio, high pump energy is also required.
For single-pass SBS compression, the Gaussian pulse pump and SBS threshold effect set two constraints for obtaining the minimum compressed pulse duration: low-power leading edge and unfixed interaction length [17]. To alleviate the constraints, it is necessary to explore an alternative waveform as a pump source.
In the process of SBS compression, the SBS threshold is reached by the leading edge of the pump pulse in the focal region. As the SBS pulse sweeps backward, it beats with the remainder of the incident wave to create a strong acoustic wave, which, in turn, acts as a bulk grating to reflect the incident wave further to strengthen the SBS wave coherently. The leading edge of the phonon envelope forms the mirror that reflects, and owing to its growing reflectivity, compresses the pulse [7]. In a Gaussian distribution pump pulse, due to the low-intensity leading edge, the generation position of the Stokes seed pulse moves from peak forward to leading edge as the energy increases [17–19]. Hence, this constraint could be eliminated by using a triangular or step pump pulse with a steep leading edge. The front part of the pump pulse generates the acoustic grating, and the spike delivering enough energy to the medium will play a crucial role in creating the acoustic grating [15]. The existence of a spike greatly reduces the acoustic field setup time of the SBS process, and the acoustics grating is sufficiently grown [20].
In this work, we focus on the single-pass compression of nanosecond pulses below the phonon lifetime in a single-cell setup using new pump shapes. First, by waveform shaping based on SBS, we achieve more ideal pump waveforms–triangular pulse and step pulse. Compared with a Gaussian pump at the same condition (minimum compression pulse duration is the phonon lifetime), the shortest compressed pulse can reach a quarter-phonon-lifetime via a triangular pump and a half-phonon-lifetime via a step pulse pump. Compared Gaussian pump with energy conversion 59% in the same condition, the energy conversion can reach 38.4% with a triangular pump and 67% with a step pulse pump.
2. SBS Pump Source
Owing to the threshold effect of SBS, the pump pulse with a high-power leading edge is better suited to pulse temporal compression [17]. Previous works show that a pump shape with a steep leading-edge contributes to a high pulse compression ratio [16]. For ideal pump waveforms, the leading edge, which can establish acoustic field in the fully transient regime, should have a rising time shorter than the phonon lifetime of medium and power strong enough to excite strong acoustic field; meanwhile, the falling time should be much longer than the phonon lifetime of medium to keep the SBS amplification under the steady-state condition. A triangular pulse and a step pulse are obviously ideal choices.
In the present investigation, the special waveform generator is based on SBS compression. The experimental setup is discussed further below. The primary pump for the special waveform generation is a custom-built Q-switched neodium:yttrium-aluminum-garnet (Nd:YAG) laser delivering single-longitudinal-mode laser pulses with a pulse duration of 8 ns and a wavelength of 1064 nm. The laser resonator is capable of supplying an output energy of approximately 7 mJ at a repetition rate of 1 Hz. The temporal SBS compressor employing a single cell is used as temporal waveform shaper to generate triangular pulses and step pulse pump pulses. An isolator comprised of a Faraday rotator (FR) and two polarizers (P1 and P2) is used to avoid backscattered light returning to the resonator. A combined half-wave plate and polarizer P3 are employed to provide incrementally controlled incident laser energy. The light beam is subsequently expanded to 5 mm in diameter using a beam expander comprising lenses L1 and L2. The expanded beam is introduced into SBS cell1 through P3 and a quarter-wave plate. The pump energy is amplified by a double-pass flash-lamp-pumped Nd:YAG amplifier to an energy greater than 60 mJ. The circularly polarized laser beam is focused into cell1 by a 30-cm-focal-length lens. After amplification, the special waveform pulses are output from P3. By varying the SBS medium and pump energy, we can obtain different waveforms. When necessary, reflecting mirror M4 can displace SBS cell1 to generate Gaussian pulses. Here, 3M Fluorinert Electronic Liquids FC-70 and FC-770 were used to obtain expected waveforms. The SBS-related parameters of FC-70 and FC-770 are listed in Table 1. As shown in Fig. 1, the triangular output pulse is obtained by using FC-770 and the step pulse by using FC-70. The rising time of triangular and step pulse are 270 ps and 285 ps, respectively. The interference between counter-propagate pump pulse and Stokes pulse creates a growing density grating that scatters the energy from the pump into the leading edge of Stokes, which lead to amplified Stokes with a sharp rising edge. With insufficient interaction length, the Stokes leading-edge left SBS medium before the pump enters the cell completely and the density grating scatters the energy from the pump into the tailing edge of Stokes in the decay time of the acoustic field before new acoustic field is established. For FC-770 with long phonon lifetime, triangular output pulse is obtained as shown in Fig. 1(b), while step pulse is generated for FC-70 with short phonon lifetime as shown in Fig. 1(c).
Table 1. Parameters of SBS medium used in experiments.
Fig. 1 Oscilloscope trace of (a) Gaussian pump (b) Output triangular pulse generated by the FC-770 (c) Output step pulse generated by FC-70
3. Experimental setup
The experimental setup shown in Fig. 2 includes the SBS generator described earlier, which is followed by an 80-cm-long quartz cell containing distilled FC-770. Lens L4, with a focal length of 60 cm, is employed to focus the special waveform output radiation beam into cell2. FC-770 liquid, which has a slow SBS relaxation time, is selected from many heavy fluorocarbons to promote measurement precision. The laser energy is recorded by a laser energy meter (PE50DIF-ER, Ophir Optronics, Israel), the pulse duration characteristics are recorded by a digital oscilloscope (DPO71254C, Tektronix Corp., USA; bandwidth, 12.5 GHz; sampling rate, 100 Gsamples/s) and a fast photo-detector (UPD-40-UVIR-D, ALPHALAS GmbH, Germany; rise time <40 ps).
Fig. 2 Schematic of experimental setup for (a) special waveform generator and (b) single-pass SBS compressor.
4. Experimental results
The measured SBS compressed pulse durations versus input energy in an input Gaussian pump pulse are presented in Fig. 3. The value of each point is the average value of 50 pulses, and the pulsed durations in Fig. 3(a) are the entire beam. It is clearly seen that, in the case of a Gaussian pump, the temporal compression of pulse duration is limited by the phonon lifetime τB with an increase of input energy. This result is in agreement with all available experimental results in single-cell setups on compression of long (τ>>τB) pulses [4, 22]. As the input energy increases, the measured energy conversion increases slowly and shows a saturation effect. A maximum energy conversion of approximately 59% is obtained at a 50-mJ input energy. Although it is not optimal, the results provide follow-up experiments under the same conditions with a beneficial reference.
Fig. 3 Gaussian pump in FC-770 using a single-cell setup. (a) Typical measured temporal waveforms of output pulse, and (b) SBS energy conversion.
As shown in Fig. 4, the pulse duration of output Stokes pulses are measured with the increase in pump energy. Previous work shows that the asymmetry of amplification at the front and tail parts of the Stokes pulse results in SBS compression. For a wave shape that power increases gradually, the leading edge of the pulse can acquire most of pump energy and be amplified sufficiently, and the remaining part of the Stokes pulse can only achieve a certain degree of amplification. The synchronous amplification is the main limiting factor of SBS compression in compression with an initial duration around or above the phonon lifetime. A pump shape with decreasing power benefits the restraint of the amplification of the tail edge of the Stokes pulse. A significant increasing leading edge with a hardly amplified trailing edge can be seen in the inset of Fig. 4(a). As the pump energy increases, the trailing edge of the Stokes pulse receives more energy and the pulse duration broadens, which eventually forms the typical waveform with a sharp leading edge and relatively slow trailing edge, as displayed in Fig. 4. The highest compression radio is obtained near the gain saturation region. When 12-mJ input energy is used, the compressed pulse with minimum duration of 215 ps (0.358τB) is obtained. The asymmetry amplification of leading and tailing edge is maximized. For a triangular pump, the part used to excite the acoustic field is its peak. Compared to a Gaussian pump, a triangular pump generates a stronger acoustic field which needs a shorter oscillation starting time [20].
Fig. 4 (a) Pulse duration evolution of compressed pulses across the entire beam with respect to input energy in the case of a triangular pump in FC-770 using single-cell setup. Solid circles denote measurements of output duration. Error bar shows the maximum deviation of pulse duration from the mean value. Three insets show typical compressed pulse shapes for corresponding input energy. (b) Shape of 165-ps output pulse sampled at the beam center with 12-mJ input energy.
In addition to temporal waveform, the transverse distribution of the pump pulse (Gaussian spatial mode) also has effect on the output pulse duration [8]. The temporal profiles shown in Fig. 4(a) were measured covering the entire beam diameter. Before deeply enter saturation region, a pump beam such as a Gaussian spatial mode was only highly compressed near the center of the beam for higher power while the compression effect was much less in the remaining part of beam. When the wings of the pump beam are strong enough to compress sufficiently, the center part begin to broaden. Thus, the pulse shape of the output beam was a mixed pulse that had a combination of fast rise time in the center and a slow falling time in the wings of the beam [8]. We can obtain the minimum value of compression duration in the center part when the SBS process has just entered gain saturation. In experimental results on a saturation condition of approximately 12 mJ, the central part of the inner 2-mm-diameter aperture (6-mm-diameter of beam waist) is compressed close to the minimum pulse width of 165 ps (~0.28 phonon lifetime), as shown in Fig. 4(b).
The energy performances are summarized in Fig. 5, with the energy efficiency saturating at approximately 38%. Compared with a Gaussian pump, there is a significant reduction in energy efficiency, mainly for the following reasons. First, in the SBS compression process, the front part of the pump pulse is mainly used for the generation of the acoustic grating. The energy of the front part makes up a small fraction of a Gaussian pulse, but it accounts for a large share of a triangular pulse. Second, the trailing amplification suppression of a Stokes pulse for a triangular pump leads to a reduction of energy efficiency.
Fig. 5 Experimentally measured dependence of system energy efficiency on pump energy of triangular pump.
In the case of a triangular pulse pump, most of the energy is used to drive the acoustic grating rather than to amplify the Stokes radiation. A significant increase in energy efficiency can be accomplished by a step laser pulse shape as shown in Fig. 1(c). It consists of a spike for exciting the acoustic grating and a following flat platform to amplify the Stokes pulse.
Figure 6 presents the energy characteristics of energy conversion and output energy as the pump energy increases. The energy conversion grows rapidly as the pump energy increases from 2.24 to 20.4 mJ. When the pump energy is higher than 20 mJ, the increase in efficiency slows in the gain saturation region; as the pump energy reaches 30 mJ, the Stokes extraction efficiency remains at approximately 65%. Since the laser intensity during the power spike is considerably higher than that during the flat-top pulse, a high acoustics wave field will be driven rapidly. Stronger acoustic field and shorter oscillation starting time contribute to the high energy efficiency. In spite of high peak power, only a small fraction of the pulse energy is used to excite the acoustics field. Crucially, a high-energy flat-top pulse is beneficial to further amplification.
Fig. 6 Experimentally measured dependence of system energy efficiency on pump energy of step pulse pump.
The variation of the output Stokes pulse duration is shown in Fig. 7. Before the SBS process reaches the gain saturation region, the output Stokes pulse duration narrows quickly as the pump energy increases. When the SBS process has just entered the gain saturation, the output pulse reached 292 ps (0.488τB). In the partially enlarged detail of the inset of Fig. 7, we observe the broadening phenomena as the pump intensity deeply enters the gain saturation region. The pulse broadening process is nicely captured by the measured waveforms. As a demonstration, pulse duration evolution with respect to input energies of 27, 43, and 62 mJ is shown in Figs. 7(b), 7(c), and 7(d), respectively. The duration evolution demonstrates the formation of the tailing edge of a typical SBS compression shape. When the pump energy is deep in the gain saturation region, the tailing edge undergoes an asymmetric amplification, and the mostly leading edge gains more energy. Therefore, the optimum pump energy is the value that just reaches the gain saturation region of highest energy efficiency and compression ratio.
Fig. 7 SBS pulse compression of nanosecond step pulses in FC-770 at 1064 nm. (a) Experimentally measured dependence of compressed pulse duration on the input pulse energy; the inset shows the detail view. Compressed pulse shape when the pump energy (b) just enters gain saturation region [27 mJ in (a)], (c) is fully into gain saturation region [43 mJ in (a)], and (d) is deep into gain saturation region [62 mJ in (a)].
The output pulse duration characteristics include two processes: compression phase and broadening phase. In the compression phase, the amplification of the Stokes pulse leading edge is far greater than the remaining part. In the broadening phase, the remaining part of the Stokes pulses is greatly enhancement compared with the compression phase. The compression contributes to the amplification of the leading edge and the inhibition of the remaining part in the compression phase. Crucially, a triangular pump and step pump are more efficient in leading-edge amplification. Compared with a conventional pump, in the initial phase of Stokes pulse generation, the spike at the front of a pump pulse can excite a stronger acoustic wave field for a shorter time, which is favorable for improving leading-edge amplification. For a triangular pump and step pump, stronger interaction between the leading edge of Stokes radiation effectively inhibits amplification of the remaining part of Stokes radiation. For a triangular pump, decreasing power goes against the energy transduction from the pump to the oppositely propagating Stokes radiation, but the effect is more severe for the tail edge of Stokes radiation. Therefore, a triangular pump can obtain the highest compression ratio with the lowest energy conversion. For a step pulse pump, the flat-top part benefits from further amplification of the leading edge. Therefore, a step pulse pump can achieve the highest energy conversion with a considerable compression ratio.
5. Conclusions
In this work, we demonstrated SBS pulse compression below half-phonon-lifetime by employing a single-cell setup. The pump pulse shape is identified as the key factor in achieving sub-phonon lifetime pulse compression. We showed that the single-pass compression of long triangular pulses to a quarter-phonon-lifetime with energy conversion above 30% can be realized. Energy-conversion improvement to approximately 70% with 0.488τB output pulse duration was achieved by using a step pulse pump. We expect that the single-pass compression of nanosecond pulses to less than 100 ps is possible, using triangular or step pump pulses, if we choose a SBS medium with shorter phonon lifetime [23] or compress input pulses at shorter wavelength since τB is proportional to λ2 [24]. Meanwhile the waveform generator can be further optimized. The waveform can be generated by a combination of fiber laser and fiber intensity modulator driven by arbitrary waveform generator [25]. This will lay a foundation for further SBS compressor application in the case of high pump using cascade two-cell configuration. We expect that, combined with controlled pulse shaping techniques, large aperture high energy pump laser and coated optics, this approach will be a highly effective way of obtaining high output power/energy ultrashort pulse laser.
Funding
National Science Foundation (NSF) (61378007, 61138005);; National Science Fund for Excellent Young Scholars (61622501).
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