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Abstract
A high temporal waveform fidelity stimulated Brillouin scattering phase conjugate mirror (SBS-PCM) with high energy efficiency, based on a novel medium, Novec-7500, is proposed and practically achieved in this study. A theoretical analysis reveals that the temporal-domain waveform distortion is caused by the inherent pulse duration compression effect of the SBS, and this undesirable phenomenon can be significantly suppressed by decreasing the compression coefficient (CC afterwards), which is defined as the gain coefficient divided by the phonon lifetime, which coefficient and is identified as the key parameter for high waveform-fidelity in SBS-PCM. The feasibility of this approach was demonstrated experimentally, in which a reflected pulse with waveform symmetry equals to the pump and an average pulse duration of 0.974 τp (τp is the duration of pump) with an energy efficiency of over 90% was achieved using Novec-7500.
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1. Introduction
A large-scale laser system with a high average-power shows promise for applications such as space debris detection [1], Thomson scattering diagnosis [2,3], and material laser processing [4]. Currently, these systems are moving toward high-pulse repetition rates, large single-pulse energies, and high beam quality to achieve better performance in specific applications. To increase the laser output intensity, multistage amplifiers and high-intensity pump sources have been widely used. However, the wavefront distortion caused by the thermal lens effect and thermally-induced birefringence effect, significantly affect the laser beam quality. Numerous studies have demonstrated that a stimulated Brillouin scattering phase-conjugate mirror (SBS-PCM) is an effective technique for compensating beam aberrations in master oscillator power amplifier (MOPA) laser systems, which exhibit characteristics of phase conjugation, high energy-conversion efficiency, and small frequency shift [5–7]. To enhance the PCM loading capacity, Wang et al. first verified that a purified liquid medium had a higher optical breakdown threshold [8]. Kang et al. [9] used an ultraclean closed-type SBS-PCM with controlled microparticles of medium FC-770 down to 40 nm. Operating at an output power of 550 W, ∼1.1 J pulse energy, and beam quality M2 of ∼2 was realized at a pulse repetition frequency (PRF) of 500 Hz with no optical failure or severe thermal effects. For an ideal high-power laser system, Kong et al. [10] proposed a promising beam combination laser system using self-phase-locked SBS-PCMs filled with liquid medium FC-75, whose output energy can be escalated by increasing the number of individual amplifiers. It was demonstrated that more than 96% of the laser pulses exhibited fluctuations in the relative phase difference of less than 1/4 at an operation frequency of 10 Hz. Using a self-locking SBS-PCM with rotating wedges to reduce thermal accumulation, Park et al. successfully demonstrated a four-beam combined laser that can handle high-average-power lasers over the kilowatt level, where the relative phase between the beams could be precisely controlled to below λ/24.7 within 10 min [11]. For a higher pulse repetition frequency, Wang et al. demonstrated that there is less coma-aberration using a rotating off-centered focusing lens than with a rotating wedge, achieving SBS-PCM with a kHz-level operation [12].
Although previous studies have made great progress in avoiding wavefront distortions caused by thermal effects, they still exist in the temporal domain; for example, steep leading-edge waveforms caused by the SBS pulse duration compression mechanism [13–16]. Irregular steep leading-edge pulses are not suitable for specific physical applications. Moreover, amplifiers and other optical components are easily damaged owing to the extremely high peak-power pulses during laser operation. Therefore, avoiding the temporal-domain waveform distortions of SBS-PCM remains a serious challenge. The parameters of the SBS medium are vital factors that affect the counter-propagating Stokes pulse waveform. Throughout the development of SBS-PCMs, heavy fluorocarbon liquids have been the most widely used medium because of their high optical breakdown threshold, low absorption coefficient, and high Brillouin gain, which can achieve high energy reflectivity [17–19]. However, the high SBS transient gain causes the leading edge of the backward Stokes pulse to be overamplified by extracting pump energy.
In this study, we focus on constructing an SBS-PCM with high temporal-domain waveform fidelity and achieving a reflection pulse whose duration and waveform symmetry are coincident with those of the pump. The temporal waveform distortion of the SBS-PCM was attributed to the intense compression effect of conventional SBS gain media. We demonstrated that the compression coefficient (CC afterwards) of the medium, which is defined as gB/τB, (where gB is the gain coefficient and τB is the phonon lifetime), is a key factor in suppressing the Stokes pulse waveform distortion. As the pump intensity increases, the Stokes pulse wavefront first encounters the pump and amplifies, resulting in a steep leading edge. By numerically comparing the Stokes temporal-domain characteristics generated by different media, we found that a low CC medium provided the weakest Stokes pulse wavefront amplification. To suppress the waveform distortion of the SBS-PCM reflected pulses, it is necessary to use a medium with a low CC. By choosing a low CC medium 3 M hydrofluoroether (HFE) liquid Novec-7500, in a classical SBS-PCM setup, accompanied by an energy conversion efficiency of over 90%, pulses with a waveform symmetry equal to that of the pump and a duration of 0.974 τp (τp is the duration of pump) were achieved.
2. Theoretical analysis
SBS is a typical third-order non-linear effect, in which the counter-propagating Stokes pulse interacts with the pump and is amplified through the excitation of the acoustic field. The waveforms of the SBS-PCM output pulses are generally narrowed as a result of asymmetric amplification of the Stokes signal [20,21]. Weakening the pulse compression effect of SBS-PCM is the most feasible approach for improving the waveform fidelity of the Stokes pulses. For structural optimization, the control of the effective interaction length and Stokes generation position cannot avoid pulse compression, and the complex optical system is difficult to regulate. By contrast, optimizing the parameters of the SBS medium and exploring a new type of medium is an effective way to suppress the waveform distortion of SBS-PCMs. According to previous studies, the SBS compression effect is jointly determined by two parameters of the SBS medium. The large SBS gain coefficient can effectively suppress the shift of the Stokes generation position towards the pump during high-intensity operation to increase the effective interaction length of the Stokes with the pump [22]. In addition, under the same conditions, shorter compression pulses can be generated if an SBS gain medium with a shorter phonon lifetime is chosen [15]. Therefore, a parameter CC (gB/τB) was introduced to measure the output waveform fidelity of SBS-PCMs. The fidelity of the PCM output pulse duration and waveform are negatively related to gB/τB. Currently, FC-770 is commonly used in SBS-PCMs for large laser installations, and its main parameters are listed in Table 1. Although these measures effectively compensated for the beam wavefront aberrations and improved the beam quality, severe temporal pulse shape aberrations still existed in the output pulses [23].
Table 1. Parameters of several kinds of PFC and HFE medium
An accurate calculation of the gain coefficient and phonon lifetime is necessary for the exploration of a low CC medium. Considering the effect of liquid viscosity on the damping coefficient and the inverse relationship between the phonon lifetime (τB) and Brillouin linewidth (ΓB), that is, τB = 1/(2πΓB), the phonon lifetime can be expressed as
A novel medium Novec-7500, whose CC is smaller than FC-770 was considered, and shares many of the inertness and dielectric properties of perfluorocarbons (PFCs) and perfluoropolyethers (PFPEs), and has low global warming potential [26]. For further research and applications, the SBS parameters of the novel medium Novec-7500 were calculated for the first time, as shown in Table 1. Meanwhile, to theoretically demonstrate that using a low CC medium can suppress the temporal domain distortion of the output waveform, the parameters of a practically applied medium FC-770 and a medium with large CC FC-43 are also given.
The effect of the CC on the output waveform at different focusing parameters was analyzed using numerical simulations. We focus on the SBS generator model with a focusing lens and the cell [27] to analyze the temporal-domain characteristics of the output pulses. The focal length of the lens and the cell length determine the focusing length and the media length, respectively. Figure 1 shows the simulation results of the Stokes radiation temporal waveforms reflected by SBS-PCMs filled with FC-43, FC-770, and Novec-7500 at the same pump intensity, where L is the lens focal length of the PCM system. Owing to the asymmetric amplification from the SBS, the Stokes waveform shows a steep leading edge with spiking. The pulse leading-edge amplification of Novec-7500 was much weaker than that of the other two media, particularly in the case of short focal length lenses. This indicates that a low CC of medium leads to weaker pulse-duration narrowing capability for maximum Stokes temporal-domain waveform fidelity.
Fig. 1. Theoretical simulation of Stokes temporal-domain waveform in FC-43, FC-770 and Novec-7500 for focusing parameters (a) L = 100 mm and (b) L = 150 mm.
The output characteristics of Novec-7500 were calculated numerically for a pump pulse duration of 8 ns. The evolution of the output pulse duration, conversion efficiency, and corresponding Stokes waveforms with pump intensity are shown in Fig. 2. The output pulse duration and the energy efficiency both increased rapidly as the pump intensity increased and then saturated at pump intensities above 12 MW/cm2. Notably, the pulse compression effect still exists when the SBS process does not enter the gain saturation region. As the pump intensity increased, the output Stokes pulse waveform tended to be Gaussian, accompanied by the SBS process reaching the gain saturation region. Therefore, SBS-PCMs operate in the deep-saturation region for practical applications. The theoretical energy efficiency was close to 100%.
Fig. 2. Evolution of pulse duration (black circle) and conversion efficiency (red square) with respect to input pump intensity in Novec-7500 PCM. The inset shows the typical shapes of the output Stokes pulse for specific injection intensities.
3. Experimental setup and results
A schematic diagram of the experimental setup for the classical SBS-PCM system is shown in Fig. 3. The pump source was a Q-switched Nd:YAG laser that delivered a single longitudinal mode (SLM) output with a wavelength of 1064 nm. Twisted-mode cavity and resonant-reflector-mediated operation were used to suppress the spatial hole burning and axial mode selection of the cavity [28]. A Gaussian laser pump with an energy of 200 mJ and an average pulse duration of 7.6 ns was obtained. A classical SBS-PCM system of a focused single cell, with a simple structure and low optical loss, was attached after the pump pulse. A spatial optical isolator was inserted to prevent powerful backward scattering pulses which could damage the laser oscillator. For sufficient acoustic-optical interaction, the SBS-PCM units were set to 80 cm, which covers the full adjustable operating range of the phase-conjugate mirror. The combination of the half-wave plate and polarizer was set as an adjustable energy attenuator to control the pump intensity of the injected PCM system experimentally. The polarization states of the pump were altered as they passed twice through a quarter-wave plate and the phase-conjugated pulse output was eventually reflected by the polarizer. Moreover, the laser energy was recorded using a laser energy meter (Vega Pyroelectric PE50BB-DIF-C (s/n:917609), Ophir Optronics, Israel), and the pulse duration characteristics were measured using a fast phototube (UPD-35-UVIR-P, Alphalas GmbH, Germany; rise time < 35 ps) combined with a digital oscilloscope (DPO71254C, Tektronix, USA; bandwidth: 12.5 GHz; sampling rate: 100 Gsamples/s).
Fig. 3. Schematic of the experimental setup. P: polarizer; QW: quarter-wave plate; HW: half-wave plate; L: lens; M: mirror; ISO, spatial optical isolator.
The waveform fidelity of the SBS-PCM mainly depends on the consistency of both the output pulse duration and temporal waveform with the pump. To further reveal the effect of the ratio gB/τB on the waveform fidelity, experiments were performed using Novec-7500 with a low CC. The Stokes duration was compressed when using longer focus lenses owing to the sufficient length of interaction provided for the SBS. Narrowed output Stokes pulse durations of a few hundred picoseconds were experimentally demonstrated at a high pump intensity when the lens focal length was chosen as 300 mm. Hence, the output pulse characteristics of the PCM were measured experimentally using lenses with focal lengths of 100, 150, and 200 mm.
The evolution of the measured pulse duration as a function of the input pump intensity for different focal lengths is shown in Fig. 4, where the value of each point is the average of 50 pulses. Over the pump intensity range, the duration of the Stokes pulse was short at a low pump, and as the injection intensity increased, the Stokes pulse first rapidly broadened, and then the evolution of the pulse duration stabilized, saturating at pump intensities above 100 MW/cm2. In the saturation region (gray region), the average output pulse of the SBS-PCM system was 7.41 ns (∼0.974 τp). The SBS process enters the gain saturation region when the pump intensity reaches the generation threshold and Stokes is compressed by the asymmetric amplification mechanism, which originates because the counter-propagating Stokes wavefront encounters and extracts the pump first. Subsequently, as the pump intensity was further increased, the SBS process was within the deep gain saturation region and leads to Stokes broadening resulting from the amplification of the trailing edge. Here, the broadening of the Stokes pulse is beneficial because of the requirement for consistency of the PCM backward pulse with the pump temporal-domain characteristics.
Fig. 4. Experimentally measured output pulse duration evolution with the pump intensity for different lenses with focal lengths of 100 mm (red), 150 mm (white), and 200 mm (green), respectively.
In addition, the effect of the focusing parameters on the duration of the output pulses were investigated. It can be observed that when using a shorter focal length lens in low-pump-intensity operation, the duration of the output pulse is closer to that of the pump and saturates more rapidly with increasing pump intensity, with a slope of 0.10657. This is attributed to the fact that when using short focal length lenses, the optical power density at the focal point in the cell rapidly exceeds the Brillouin threshold with the pump increasing, and the Stokes generation position rapidly shifts toward the input window of the pump [29], which sharply shortens the genuine interaction length and the compression effect is significantly suppressed. The rapid broadening of the output pulse duration leads to high slope values in the case of using short focal length lenses (red line), which facilitates the extension of the energy applicability of the SBS-PCM system on the basis of ensuring energy efficiency. Therefore, suppressing the compression effect at a particular pump intensity by choosing a short focal-length lens is one of the key ways for obtaining high waveform fidelity.
Another vital parameter, the consistency of the Stokes waveform with the pump, is shown in Fig. 5, where a lens with a short focal length of 100 mm is chosen. Waveform symmetry γ (defined by τrising/τfalling) was introduced to measure the waveform consistency of the Stokes and pump waveforms, where τrising and τfalling are the rising and falling times of the waveforms, respectively. As shown in Fig. 5(a), under the high pump intensity operation satisfying the SBS deep-saturation state, γ remained consistent at 0.34 with the pump, demonstrating excellent waveform fidelity. Figure 5(b) shows the temporal-domain waveforms of the Stokes pulses (red line) at different pump intensities compared to the pump waveforms (green line). As the pump intensity increased, the steepness of the pulse leading edge decreased, accompanied by an increase in the pulse duration, which was caused by the smaller Brillouin gain obtained from the Stokes signal. At low pump intensities, Stokes signals were generated close to the Rayleigh region, providing sufficient amplification of the wavefront. Subsequently, as the injected pump intensity further increased, the initial generation position of the Stokes signals moved closer to the pump, which significantly reduced the effective interaction length of the SBS and thus diminished the amplification of the Stokes leading edge. The high consistency of both the temporal-domain symmetry and the duration of the Stokes pulse with the pump indicated that a medium with low CC is an excellent medium for achieving high temporal-domain waveform fidelity of SBS-PCM.
Fig. 5. (a) Evolution of the temporal-domain waveform symmetry γ of output pulses with the pump intensity. (b) The shapes of the Stokes pulse at a specific pump with a lens of L = 100 mm.
The output efficiencies of the Novec-7500 based SBS-PCM with different focusing parameters were synchronously recorded, as shown in Fig. 6. As the pump intensity increased, the output energy steadily increased monotonically, the energy efficiency first rapidly increased, and the rising trend slowed down when the SBS process was within the gain saturation region. The energy efficiencies were over 90% at a particular pumping intensity, except for the 200 mm focal length, because of the smaller beam waist radius at the in-cell focal point after focusing by a shorter focal length lens, which means a higher input power density. The output and input energy stabilities with a focal length of 100 mm lens at a pump intensity of ∼150 MW/cm2 were shown in the inset. The results showed that the root mean square (RMS) of output energies was 1.8% for the pump and 2.7% for the Stokes pulses. Owing to the instability caused by thermal effect of the liquid medium in SBS process and the environmental vibration, the RMS of the output Stokes pulse was higher than that of the pump. By purifying the liquid SBS media and further improving the experimental conditions, higher energy stability of the SBS-PCM may be obtained [9,12].
Fig. 6. Output efficiency of Stokes pulses versus input pump intensity correspond to lens of 100 mm, 150 mm, and 200 mm, respectively. The inset shows the energy of the pulses of Stokes and pump in three minutes when using a 100 mm lens.
Based on the results of this study, a new parameter affecting the temporal-domain waveform fidelity of SBS-PCMs in terms of the CC (gB/τB) is introduced. The fidelity of the Stokes waveform could be improved by reducing the compression coefficient. It should be noted that the method is applicable to any other PCM structure, and several optical elements used were uncoated, which limits the energy conversion efficiency and loadable intensity of the pump. By improving the experimental conditions, higher energy-conversion efficiencies can be achieved.
4. Conclusion
In summary, high-waveform fidelity phase-conjugate output pulses were demonstrated in a classical SBS-PCM system by suppressing SBS compression. A new parameter affecting the pulse compression capability of SBS-PCM, the CC (gB/τB), was defined. By choosing a novel medium, Novec-7500, with a small CC, we achieved laser outputs with highly consistent temporal-domain waveform symmetry and pulse duration with the pump, accompanied by an average output duration of 0.974 τp and an efficiency of over 90%. In addition, controlled experiments were conducted on the effect of the focusing parameters on the SBS-PCM system, and the results showed that a smaller focal length lens resulted in a more stable pulse duration with higher efficiency. By further optimizing the structural parameters and improving the experimental conditions, the SBS-PCM with high waveform fidelity can be applied to the development of lasers with high pulse repetition rates, large single-pulse energy, and high beam quality.
Funding
National Natural Science Foundation of China (61905064, 61927815, 61975050); China Postdoctoral Science Foundation (2022M711960); Natural Science Foundation of Hebei Province (F2019202320); Research Projects of Higher Education Institutions of Hebei Province (QN2019201, JBKYXX2002); Postdoctoral Funding Project of Hebei Province (B2022005003); Key Laboratory Foundation of Shanxi Province (HI2224); Hebei Province Graduate Innovation Funding Project (CXZZBS2021030, CXZZSS2021040).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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