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Abstract
Thermal problems of high-repetition-rate stimulated Brillouin scattering (SBS) pulse compression in liquid media are theoretically and experimentally analyzed in detail. A wedge lens with less coma-aberration was designed using the ray tracing method and the thermally induced beam-pattern distortion was compensated by inhibiting thermal convection. The heat transfer form and fluid state were quantitatively analyzed for different SBS liquid media. For a 74-W pump power, 3-kHz pulse-compressed phase-conjugation mirror with an energy efficiency of 36.2% is achieved. A potential optimization method of continuously adjusting SBS output characteristics using a mixed medium is proposed and theoretically demonstrated, to improve energy efficiency.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
A high-repetition-rate single-longitudinal-mode laser with good beam quality and a sub-nanosecond pulse shows promise for applications in the fields of fast ignition lasing radiation [1,2], space debris detection [3–5], Doppler wind LIDAR [6], etc. Stimulated Brillouin scattering (SBS) based on a liquid medium, with the advantages of no high pressure, a small absorption coefficient, and a high laser damage threshold compared with gas and solid media [7–9], is widely used in high-energy laser systems, such as SBS phase conjugation mirrors (SBS-PCM) and pulse compressors for compressing long nanosecond pulses to sub-nanosecond pulses and improving the beam quality [10–13]. By combining SBS technology with a highly efficient compression and main oscillation power amplification technology with a high-energy advantage [14–17], a SBS phase-conjugation pulse compressor is a simple and reliable technique for obtaining a high-power hundred picosecond pulse laser with a kilohertz-level repetition rate.
Many research groups have contributed to higher repetition-rate SBS pulse compression with a liquid medium. For below 1-Hz operation, Zhu et al. [14] reported a 360-ps compressed pulse with a 3-J energy by SBS with a non-focusing scheme. For 1-Hz operation, Wang et al. [18] reported a 393 ps compressed pulse using an interferometric scheme. For 1.25-Hz operation, Xu et al. [13] obtained a high pulse width compression ratio of approximately 40 times using a combination of theoretical modeling and experiments to identify and optimize some key parameters. For 3-Hz operation, Dane et al. [7] obtained a 1.7 ns pulse with 80% energy efficiency using an efficient two-cell SBS pulse compressor. For 10-Hz operation, Tarasov et al. [19] obtained a 400-750 ps pulse duration laser with 1.1 J using a multi-pass SBS liquid cell with a small overall length of 15-20 cm. For 20-Hz operation, Andreev et al. [20] compressed a 30 ns laser pulse with 1 J energy into 1.7 ns, and the reflected energy efficiency is 75%. For 100-Hz operation, Shilov et al. [21] reported a 350-ps compressed pulse of 6.5 mJ, which is finally amplified to 36 mJ using a single-cell structure. For 200-Hz operation, Kang et al. [22] obtained a 376-ps pulse width using an amplifier-generator cascaded two-cell setup by employing a multi-layer membrane circulating ultrafiltration technology for controlling the impurity-particle size to below 0.1 µm, and there is no optical breakdown in the generator cell. Wang et al. [23] reported remarkable research results on high-repetition-rate SBS pulse compression and obtained a sub-nanosecond pulse output with a 1-kHz repetition rate.
Our team found that the laser-induced heat could enhance the output characteristics of high-power SBS pulse compression in some cases [24], and the negative impact of thermal effects became a main limiting factor when the laser repetition rate increased above 2-kHz. Most studies have demonstrated that thermal problem is one of the key issues limiting the applications of SBS pulse compression in high-repetition-rate laser systems. Andreev et al. pointed out that the thermal defocusing of the medium is a major factor affecting the performance of SBS [25] and believed that the optical breakdown is caused by microparticles in the liquid medium [20]. Shilov et al. [21] pointed out that the laser absorption of microparticles in a liquid medium limits the improvement possibilities in the operating repetition rate of SBS. Kmetik et al. [26] also believed that optical absorption is an important parameter affecting the output characteristics of SBS. Xu et al. [13] pointed out that the refractive index gradient of a liquid medium caused by thermal effects can lead to wave-front distortions in the reflected light. Kang et al. [22] pointed out that the thermal effects of the SBS medium limit the high-repetition-rate operation of SBS. Based on the above mentioned, there are two main factors affecting the characteristics of high-repetition-rate SBS pulse compression: thermal effects, such as thermal defocusing caused by laser absorption, and laser-induced optical breakdown. The existence of these problems can easily lead to degradation or even failure of the SBS compression characteristics.
Researchers have developed methods for alleviating thermal effects, which can be divided into two categories. The first is the liquid purification method [15,27] used to remove large impurity particles from the liquid medium. The second category involves a flowing liquid [28,29] or a wedge-based moving focal spot [28,30,31], which are used to alleviate the local focusing heat accumulation in the generator cell. Kang et al. [15] obtained a 500-Hz SBS-PCM with impurity particles in the liquid medium of below 40 nm using a 10-nm filter membrane multi-stage filtration, which greatly improves the heat load capacity of the closed SBS-PCM, and there are no optical breakdown phenomena or significant thermal effects. Yoshida et al. [28] proposed a laminar flow cell scheme for suppressing heat accumulation at the focal spot, and the SBS-PCM’s reflected energy is 90% for a 40-W pump power. Kiriyama et al. [31] used a rotating wedge to move the focus spot to alleviate focusing heat accumulation, and the SBS-PCM is operated at a repetition rate of 1,000 Hz. However, most of the work in this field has focused on the generator cell of the SBS pulse compression, and there have been few studies on SBS pulse compression that involved higher repetition rates (> 1 kHz) or a systematic thermal problem analysis based on a liquid medium. If we combine the above methods and clarify the key factors influencing the thermal problems of high-repetition-rate SBS pulse compression, a sub-nanosecond pulse laser above the kilohertz level based on liquid media can be obtained.
In this study, to analyze the compression characteristics at high repetition rates, a 3-kHz repetition-rate SBS pulse compression is experimentally demonstrated using the combination of a rotating wedge lens, medium purification, and suppression of thermal convection methods. The thermal problems limiting the increase in the repetition rate operation of SBS pulse compression are systematically investigated and analyzed. A potential optimization method for continuously adjusting the SBS output characteristics using the mixed medium is proposed and theoretically demonstrated. The experimental setup is described in Section 2. In Section 3, theoretical simulation of the beam profiles of the focal spot using the wedge lens is presented. In Section 4, an analysis of the thermal problem of high-repetition-rate SBS pulse compression is presented. In Section 5, the experimental results and discussions are presented, and Section 6 concludes the paper. This work has important reference value for applications of SBS technology in high-power laser systems.
2. Experimental setup
Commonly used SBS pulse compression structures include single-cell [32], amplifier-generator cascaded two-cell [33], and amplifier-generator parallel two-cell setups [10]. Among them, the amplifier-generator parallel two-cell setup is suitable for joule-level high-energy SBS pulse compression [13]. A long focal length lens is often employed in the single-cell setup for SBS pulse compression, and the thermal self-defocusing effect [25] emerges for the transmission of a high-repetition-rate laser in liquid media, which enlarges the focal spot size and reduces the SBS energy efficiency. Therefore, the single-cell setup and amplifier-generator parallel two-cell setup are not suitable for high-power SBS pulse compression. The amplifier-generator cascaded two-cell setup is the most suitable for high-repetition-rate SBS pulse compression owing to its long interaction distance and good focusing properties [11,29].
The experimental setup for SBS pulse compression employed in this study is shown in Fig. 1. The pump beam has a pulse width of 10 ns operating at a 3 kHz repetition rate and a fundamental wavelength of 1064 nm. The pump beam imaged the laser image plane at the position of lens L3 through a pair of imaging lenses, composed of lenses L1 and L2 with focal lengths of 20 and 40 cm, respectively. A half-wave plate (HWP1) and a polarization beam splitter (PBS1) were used to control the input beam energy. The pump light was introduced into an amplifier cell with a length of 80 cm through a quarter-wave plate (QWP). The beam was then focused into a 20-cm generator cell using a focusing lens (L4). The Stokes beam generated by the SBS is backscattered. The reflected beam was separated using a system consisting of a QWP and a PBS1. The reflected beam pattern was relayed using a relay-imaging system composed of L5 and L6. These lenses relayed the image from the object plane at the QWP to the image plane using a camera (WinCamD-LCM, DataRay Inc.). The sub-nanosecond pulse was detected by a Thorlabs DET02 photodetector (bandwidth: 1.2 GHz; rise time: 50 ps; fall time: 250 ps). The signal waveform was recorded using a digital oscilloscope with a bandwidth of 3 GHz.
Fig. 1. Schematic of the experimental setup for the cascaded two-cell setup for SBS pulse compression (HWP1–2, half-wave plates; QWP, quarter-wave plate; PBS, polarization beam splitter; L1–L6, lenses).
Galden HT PFPE fluid was used as the SBS medium in this study. The parameters of the SBS medium at room temperature used in these experiments are listed in Table 1 [34–36]. HT110 and HT270 were chosen because of their substantially different kinematic viscosity coefficients and boiling points. The absorption coefficients of the HT110 and HT270 liquid are 3 × 10−4 cm−1. The specific heats of the HT110 and HT270 medium are 0.23 cal/g·°C.
3. Theoretical simulation of focal spot profile using the wedge lens
With the increase of the laser repetition rate, the heat accumulation of the medium becomes more and more serious, resulting in serious thermal effect, which affects the SBS process. Heat is the main reason for the degeneration of SBS output characteristics with the increase of the repetition rate. Especially in the generator cell, the temperature even could reach the boiling point of the liquid medium at the focal spot, which can cause the jiggling effect of beam pattern, inhibiting the generation of SBS. Therefore, it is necessary to take some means to reduce the temperature of the focal spot in the generator cell.
Most research has so far been focused on the thermal effects in the generator cell. The effective thermal mitigation methods described in the literature can be divided into two categories. The first is the liquid purification method for removing large impurity particles from the liquid medium, which can appropriately reduce the total heat absorption generated by impurity particles within the medium and reduce the optical breakdown probability. The second category involves a flowing liquid or a wedge-based moving focal spot, which are used to alleviate the local focusing heat accumulation. The former method has a complex structure and easily leads to unstable output beams, whereas the latter method has obvious coma distortion of the focal spot and a large optical loss.
We fabricated a custom lens L4, referred to as a wedge lens, by cutting a plano-convex lens. The new center of the wedge lens is “a” distant from the center of the original lens, and the diameter of the wedge lens is one inch, as shown in Fig. 2. In this setup, a rotating wedge focusing lens was employed for reducing the heat accumulation at the focal spot for high-repetition-rate operation and improve the beam quality with lower coma aberration and optical loss.
Fig. 2. Structure of the wedge focusing lens, a is the displacement distance between the center of the wedge lens and the center of the original lens, b is the diameter of the wedge lens.
In SBS pulse compression, the intensity distribution of the beam focal spot can affect the generation of SBS, while the diameter of the pump beam, the focal length of the wedge lens and the displacement “a” apart from the original lens center can affect the intensity distribution of the focal spot. Therefore, it is necessary to theoretically simulate the focal spot intensity distribution using the parameters above. Figure 3 illustrates the intensity patterns of the beam focal spot for different parameters when using a wedge lens by employing Monte Carlo ray-tracing method. Our own program for focal spot beam pattern simulation was developed using Microsoft Visual C++. The pump light had a Gaussian intensity distribution pattern and was composed of 10,000 random rays. The graph of focal spot profile was generated by integrating the focal spot intensity pattern centered at these points. In the simulation, the pump light propagated along the optical axis and the wedge lens was fixed. The crosshairs and black circles in Fig. 3 indicate the position of the focal beam spot center and Gaussian beam size without coma aberration, respectively.
Fig. 3. Focal spot beam patterns for different parameters using the wedge lens. (a) Beam radius 3 mm, f4 = 15 cm, a = 6.4 mm, (b) Beam radius 5 mm, f4 = 15 cm, a = 6.4 mm, (c) Beam radius 5 mm, f4 = 15 cm, a = 15 mm, (d) Beam radius 5 mm, f4 = 10 cm, a = 15 mm.
Figures 3(a) and 3(b) illustrate the simulated focal spot beam patterns for a lens with the focal length of 15-cm, 6.4-cm off-center displacement, and beam radius of 3 and 5 mm, respectively. The beam pattern of the focal spot for the 5-cm pump beam radius is smaller than that for the 3-cm one, and the offset from the center of the crosshairs is also larger. Figures 3(c) and 3(d) illustrate the simulated focal spot beam patterns for a 15-cm off-center displacement, beam radius of 5 mm, and lenses with focal lengths of 15 cm and 10 cm, respectively. Comparing Figs. 3(a) and 3(c), it is obvious that the larger the pump beam radius, the more serious the coma aberration of the focal spot, and the larger the focal spot beam size. Comparing Figs. 3(c) and 3(d), it can be seen that the smaller the focal length of the wedge lens, the more serious is the aberration of the focal spot. According to the theoretical simulations, the focal spot beam pattern using a wedge focusing lens with a 6.4-mm off-center displacement and a 15-cm focal length had less coma aberration and a smaller focal spot size. In this study, a rotating wedge lens with a 6.4-mm off-center displacement and a 15-cm focal length was employed for reducing the heat accumulation at the focal spot for high-repetition rate operation and improving the beam quality in terms of less coma aberration and lower optical loss compared with the rotating wedge method.
4. Thermal problems analysis
To investigate the influence of heat on the SBS process for a high-repetition-rate operation in a two-cell setup, as shown in Fig. 1, the thermal effects in the generator and amplifier cells are analyzed experimentally and theoretically.
4.1 Experimental analysis of thermal effects
To avoid the influence of the SBS amplifier on the two-cell structure, a single-cell setup with only a generator cell was employed, as shown in Fig. 4. The quality of the SBS pulse compression is inextricably linked to the beam profiles. To explore the reasons for the quality deterioration in high-repetition-rate SBS pulse compression, it is necessary to measure and analyze SBS-reflected beam profiles. For a 50-W power laser, the SBS-reflected beam patterns were compared using a normal lens and a rotating wedge lens with an HT110 liquid medium, as shown in Fig. 4. Figures 4(a1) and 4(a2) show the reflected beam patterns for the single-cell setup with normal lenses with focal lengths of 10 and 15-cm, respectively. Figures 4(b1) and 4(b2) show the reflected beam patterns for the single-cell setup with rotating wedge lenses with focal lengths of 10 and 15-cm, respectively. For the single-cell setup with a normal lens, the reflected beam pattern in Fig. 4(a) was distorted, and the beam quality was degraded. Beam pattern distortion and the hot-spot effect can severely inhibit the SBS process. Comparing Figs. 4(a1)-4(b1) and 4(a2)-4(b2), it can be seen that the reflected beam patterns had obvious distortion with normal lenses in the single-cell setup, while the SBS reflected beam patterns using the rotating wedge lens had no distortion. The results showed that the rotating wedge lens method could compensate for the beam profile distortion resulting from the focusing thermal effects in the SBS generator cell.
Fig. 4. Beam profiles for single-cell setup using (a) normal lens and (b) rotating wedge lens with the focal length of 10 cm and 15 cm.
The dependence of the SBS-reflected power on the rotating speed of the wedge lens is shown in Fig. 5. With an increase in the rotating speed, the reflected powers rapidly reached their maximum values of 3, 17, and 30 W for input powers of 10, 30, and 47 W, respectively, and remained stable. In Fig. 5(b), the dashed lines indicate the critical rotating speeds at which the reflected power reaches its maximum value. The critical rotating speeds for input powers of 10, 30, and 47 W were 5, 10, and 16 r/min, respectively. It is evident that with an increase in input power, the critical rotating speed increases. This indicates that the heat at the focal spot accumulated with an increase in the input power.
It is generally believed that the focusing thermal effect was the main factors limiting the improvement of the laser repetition rate of the SBS pulse compression without considering the thermal problems in the amplifier cell. Figure 6(a) illustrates the beam profile of the SBS-reflected beam for a two-cell setup with a rotating wedge lens at 50-W pump power, which had obvious beam pattern distortion and a hot spot effect. Comparing the beam patterns between Figs. 4(b) and 6(a), with the rotating wedge lens, the beam pattern of the single-cell setup in Fig. 4(b) has no pattern distortion, whereas it shows obvious pattern distortion for the two-cell setup in Fig. 6(a). The experimental results showed that there are thermal problems in the amplifier cell that affects the SBS process. Therefore, to clarify the phenomenon appeared in the amplifier cell, the beam pattern transmitting the amplifier cell was measured under an input power of 25 W, as shown in Fig. 6(b), which showed a V-shaped beam pattern with an obvious distortion. The beam spot size increased owing to the defocusing effect. In Fig. 6(c), Mach–Zehnder interference was employed to understand what happened in the amplifier cell by measuring the interference beam spot patterns. The interference fringes in the lower half-beam pattern were evenly distributed, whereas the upper part became sparse and chaotic. This is because natural convection originates from heat accumulation and thermal conduction, resulting in sparse and irregular isotherms.
Fig. 6. Beam profiles of (a) SBS reflected beam for two-cell setup using rotating wedge lens at 50 W, (b) transmitting beam pattern of amplifier cell at 25 W, and (c) Mach–Zehnder interference at 50 W.
To clarify the main factors of the pattern distortion of the SBS-reflected beam, the process in a generator cell and an amplifier cell was analyzed separately. The reflected beam pattern of the two-cell setup SBS pulse compression based on the rotating wedge lens shows an obvious beam pattern distortion, as shown in Fig. 6(a). As shown in Fig. 6(b), the laser beam transmitting the long amplifier cell exhibited beam profile distortion resulting from thermal problems, which is also a key issue affecting the application of SBS pulse compression in high-power laser systems.
4.2 Theoretical analysis of thermal problems
We analyzed the thermal problems of the SBS pulse compression for the two-cell setup shown in Fig. 1. In high-power lasers, the absorbed laser is converted into heat, causing serious heat production within the medium. Especially at the focal spot, the maximum temperature within the generator cell is much higher than the room temperature for a high-repetition rate laser [23]. With an increase in thermal absorption, the temperature at the focal spot is prone to increase the probability of optical breakdown and cause beam pattern jiggling in the SBS generator cell. When SBS pulse compression operates with a high-repetition-rate laser, it is necessary to reduce the heat accumulation at the focal spot due to laser energy absorption.
A high pulse-width compression ratio requires a long interaction length; therefore, the transmission characteristics of high-power lasers in a long liquid medium cell are also one of the key issues affecting high-repetition-rate SBS pulse compression. Laser heating of the liquid medium causes heat accumulation in the medium and changes the spatial temperature distribution along the radial direction owing to the continuous heat diffusion from the beam area into the liquid medium, which then affects the density gradient of the SBS liquid medium. The uneven density gradient results a spatial change in the liquid buoyancy and flow of the liquid layer. This convective motion leads to an upper and lower asymmetric distribution of the temperature and density of the liquid medium. The intensity of thermal convection in a liquid is affected by its viscosity and the buoyancy force generated by laser heating. For an amplifier cell, high-power absorption laser heats the liquid medium and causes thermal conduction, an uneven spatial distribution of the medium temperature around the optical axis causes significant thermal convection, an uneven distribution of medium-density gradient, laser beam deflection, and other phenomena, as shown in Fig. 7. With an increase in the laser repetition rate, these phenomena interact with each other and exhibit strong coupling characteristics, which cause more serious beam distortion and affect the quality of the compressed beam.
Fig. 7. Thermal problem analysis of high-repetition rate SBS pulse compression for the two-cell setup in liquid medium.
For the two-cell setup of SBS pulse compression, the absorption heat increased with an increase in the laser repetition rate. The influence of serious heat production within the liquid medium on SBS pulse compression has two aspects. First, the high power density at the focal spot can easily cause optical distortion, thermal defocusing and optical breakdown, which reduce the fidelity of the SBS phase conjugation and negatively affect the energy reflectivity and output stability of the SBS. The second is the appearance of hot-spots and natural convection during the transmission of a high-power laser in a liquid medium cell with a long physical length. Beam distortion affects the generation of the SBS phase conjugate wave at the focal spot, deteriorates the quality of the reflected beam patterns, and even inhibits the generation of SBS.
For quantitative analysis, two dimensionless parameters, Grashof number (Gr) and Rayleigh number (Ra), were used to describe the heat transfer form and fluid state of a liquid medium. Gr is a dimensionless number in fluid dynamics and heat transfer, which approximately represents the ratio of buoyancy to viscous force acting on the fluid. The governing equation of natural convection heat transfer is described by the momentum equation of boundary layer, gravity, natural convection momentum equation and momentum equation outside boundary layer. To simplify the analysis, the heat conduction and convection in the axial direction of the liquid medium cell were ignored, and only the fluid and heat transfer properties of a section of the HT110 and HT270 liquid medium cell were concerned. The Grashof number [37] can be expressed as:
where g is the acceleration of gravity with 9.8 m/s2, β is the coefficient of thermal expansion, T is the temperature of the liquid inside the laser beam, and T∞ is the temperature of the environment. η is the kinematic viscosity. L is the characteristic length.The kinematic viscosity coefficient of HT110 and HT270 varies with the temperature of the medium, as shown in Fig. 8(a). When the medium temperature is increased from 0°C to 70°C, the kinematic viscosity of HT110 decreases from 1.1 cSt to 0.4 cSt, and the kinematic viscosity of HT270 decreases from 36.4 cSt to 2.8 cSt. The change of kinematic viscosity of the HT270 medium with temperature is much larger than that of HT110 medium.
For a vertical interlayer, the expression of flow state is defined as follows [37]:
The Gr number with respect to the medium temperature is shown in Fig. 8(b). For HT270 medium, when the temperature of the liquid medium increases to 42°C, the heat exchange changes from heat conduction to convective heat transfer, and the convective heat transfer begins to play a leading role gradually. However, for HT110 medium, the heat exchange of thermal convection begins when the medium temperature increases to 25.2°C. For the generator cell, it cannot occur thermal convection at the focal point according to the Gr calculation.
Ra is also a dimensionless number related to buoyancy driven convection (also known as free convection or natural convection). When Ra is lower than the critical value, the main form of heat transfer is heat conduction. Conversely, the main form of heat transfer is convection. Rayleigh number is the product of Gr and Prandtl number (Pr). Therefore, Ra is regarded as the product of the ratio of buoyancy to viscous force and the ratio of momentum to thermal diffusion coefficient:
where c is the specific heat with 0.23 cal/g·°C, $\lambda$ is the thermal conductivity with 0.065 W/m·K. In ANSYS-FLUENT software, the critical value of Rayleigh number with 108 is recommended. The calculated Ra is below 106 over the temperature range shown in Fig. 8. Obviously, Ra is less than the critical value of flow turbulence in this study. Therefore, the flow state is laminar flow.According to the above-mentioned analyses, in this study, three methods of improving the average injection power of the SBS pulse compression were adopted. The first is liquid ultrafiltration to remove large impurity particles from the liquid medium that absorb radiation light for removing optical breakdown. The second method is the rotating wedge focusing lens method. To alleviate heat accumulation near the focal spot in the generator cell, the effective operating repetition rate of the SBS pulse compression can be reduced by employing a wedge lens. The third method is to use a liquid medium with a large kinematic viscosity coefficient and a high boiling point, which can improve the non-uniformity of the beam profiles caused by thermal convection in the experiment and eliminate the jiggling of the beam pattern owing to the high local temperature at the focal spot, which exceeds the boiling point.
5. Experimental results and discussion
The thermal effects mainly arise from the heat converted by the absorption of laser energy in the medium, especially the energy absorbed by the impurity particles in the liquid. When the impurity particles absorb sufficient laser energy, causing avalanche ionization, laser-induced optical breakdown will appear owing to laser focusing in the generator cell. The competition between optical breakdown and the SBS process reduces the SBS energy efficiency, phase conjugation fidelity, and output stability. To reduce the probability of heat absorption and optical breakdown of the medium, the liquid medium was purified using a vacuum ultrafiltration system [24]. The liquid was passed through organic filter membranes with pore sizes of 250 and 25 nm made of cellulose and nitrocellulose, respectively. A membrane with a 250-nm pore size was used to filter large impurity particles in the ultrafiltration system, and a 25-nm membrane was used to filter small impurity particles in the SBS liquid medium. Each filtration process lasted for 2 h. The impure particles were nearly eliminated from the liquid medium after seven filtration processes, and we considered the purification process to be complete at that point. Finally, the purified liquid SBS medium was pressed into a glass cell. A medium with a larger impurity particle size and higher concentration corresponded with a higher optical-breakdown probability. The ultrafiltration system can effectively remove impurity particles in the SBS liquid medium and reduce the occurrence probability of optical breakdown in the generator cell by 14 times compared with the case without medium purification. The medium purification is an effective means of reducing the optical breakdown probability of high-repetition-rate SBS pulse compression.
5.1 SBS pulse compression with different setups
Experimental research on the output characteristics of the three SBS compression setups was conducted, as shown in Fig. 9. The dependences of the output energy, energy efficiency and compressed pulse width on the injection energy under the SBS setups of “X-20 cm”, “X-15 cm” and “1.5 m-15 cm” are compared in Fig. 9. As shown in Fig. 1, L3 represents the lens located in front of the amplifier cell, and L4 represents the lens located in front of the generator cell. The focal length of L3 is 1.5 m. X represents the working condition in which the lens L3 is removed. The focal length of the L4 lens is 15 cm or 20 cm. The “X-20 cm” structure was the experimental setup with a L4 lens with a 20-cm focal length and without an L3 lens in Fig. 1; the “X-15 cm” structure was the setup with a L4 lens with a 15-cm focal length and without L3 lens in Fig. 1; the “1.5 m-15 cm” structure was the setup with the L3 and L4 lenses with focal lengths of 1.5 m and 15 cm, respectively, as shown in Fig. 1. To exclude the influence of thermal effects, a 10 Hz repetition rate laser was used as the pump beam in this section. Figure 9(a) illustrates the reflected energy and energy efficiency with respect to the input energy using HT270. The output energy increased linearly with an increase in the injected energy. The reflected energies were 38.35 ± 1.51 mJ, 39.76 ± 1.46 mJ, and 41.49 ± 0.73 mJ for the structures “X-20 cm,” “X-15 cm” and “1.5 m-15 cm”, respectively, at a 70-mJ pump energy, and the corresponding energy efficiencies were 54.68%, 56.52%, and 58.91%, respectively.
Fig. 9. Measured (a) reflected energy and energy efficiency, (b) pulse width of HT270 for different SBS setups at 10 Hz.
Figure 9(b) illustrates the compressed pulse width with respect to the input energy, and the pulse width gradually decreased with an increase in the input energy. The compressed pulse widths were 0.86 ± 0.04 ns, 1.28 ± 0.28 ns and 0.66 ± 0.01 ns for “X-20 cm,” “X-15 cm” and “1.5 m-15 cm,” respectively, at a 70-mJ pump energy. The pulse width RSDs of “1.5 m-15 cm” are smaller than the other two cases probably due to the higher power density. By comparing the output energy and the compressed pulse width of these three compression structures, the “1.5 m-15 cm” setup had the highest energy efficiency and the narrowest compressed pulse width. Therefore, the “1.5 m-15 cm” structure was chosen for subsequent experiments.
5.2 SBS pulse compression in different media
To avoid the influence of thermal effects, a 10-Hz low repetition rate laser was used to compare the output characteristics of the SBS pulse compression using different media. Figure 10 illustrates the output parameters of the reflected energy, energy efficiency, and compressed pulse width with respect to an input energy of 10 Hz for the HT110 and HT270 media. The output energy increased linearly with an increase in the input energy. The reflected energies were 41.49 ± 0.73 mJ and 47.53 ± 0.52 mJ using the HT270 and HT110 media, respectively, at a 70-mJ pump energy, and the corresponding energy efficiencies were 58.91% and 67.34%, respectively. Figure 10(b) illustrates the compressed pulse width with respect to the input energy, and the pulse width gradually decreased with an increase in the input energy. The compressed pulse widths were 0.66 ± 0.01 ns and 0.69 ± 0.01 ns for the media HT270 and HT110, respectively, at a 70-mJ pump energy. The results showed that the energy efficiency of HT110 was 14% higher than that of HT270 at the low repetition rate of 10 Hz and 70-mJ pump energy, whereas the compressed pulse width of HT110 was 4.5% wider than that of HT270.
Fig. 10. Output parameters of (a) reflected energy and energy efficiency, and (b) compressed pulse width with respect to input energy at 10 Hz for different media.
Experiments on the SBS pulse compression output characteristics with respect to the pump power, comparing the use of HT110 and HT270, were carried out using the setup shown in Fig. 1, and the results are presented in Fig. 11. Figures 11(a), 11(b) and 11(c) show the output energy, energy efficiency, and compressed pulse width with respect to the pump power at a 40-mJ pump energy, respectively. Figure 11(a) illustrates the variations in the SBS-reflected power with the pump power using HT110 and HT270 media. When the laser repetition rate was lower than 400 Hz, the reflected power for the HT110 medium was higher than that for HT270. When the laser repetition rate was higher than 400 Hz, the reflected power for the HT110 medium no longer increased, and the reflected power for HT270 kept increasing. The maximum output powers of SBS pulse compression were 7.10 ± 0.52 W at a 600-Hz repetition rate and 25.20 ± 0.49 W at 1,500 Hz using the media of HT110 and HT270, respectively. When the repetition rate increased to above 600 Hz, the reflected beam pattern for HT110 and the transmitted beam pattern of the generator cell were severely distorted, as shown in Fig. 6(a). Most of the laser beam was not reflected by the SBS but passed through the rear window mirror of the generator cell, and the very high power density spot on the transmitted beam profile caused irreversible optical damage to the rear mirror window. When the laser repetition rate exceeded 600 Hz at 40 mJ, the rear-window mirror of the generator cell exhibited optical damage. For HT270, the output power gradually increased with an increasing repetition rate and pump power.
Fig. 11. Output parameters of (a) reflected energy, (b) energy efficiency, and (c) pulse width with respect to pump power at a pump energy of 40 mJ, and (d) pulse waveforms with different media.
Figure 11(b) illustrates the dependence of the SBS energy efficiency on the pump power using the HT110 and HT270 media. As the pump power increased, the energy efficiency of HT110 decreased from 71.2% at 100 Hz to 33.9% at 600 Hz, whereas the output energy of HT270 did not change substantially with the repetition rate from 100 Hz to 1,500 Hz. It was shown that the reflected energy of the SBS pulse compression using HT270 is insensitive to changes in the laser repetition rate. The gain coefficient is the main factor affecting the energy efficiency of the SBS pulse compression operation. The energy efficiency of HT270 decreased by 70% compared with HT110 because of the smaller gain coefficient at 100 Hz, whereas an energy efficiency of 41.4% was obtained at a 1,500-Hz repetition rate and 40-mJ pump energy for HT270 owing to its large kinematic viscosity. The results show that the HT110 medium is suitable for SBS pulse compression with a repetition rate below 400 Hz, while the HT270 medium is suitable for SBS pulse compression at the kilohertz level of operation.
Figure 11(c) shows the compressed pulse widths using HT110 and HT270 with respect to the pump power. The average pulse widths using HT110 increased from 0.84 ± 0.03 ns at 100 Hz to 2.37 ± 0.32 ns at 600 Hz with a 40-mJ pump energy, and the average pulse widths using HT270 changed from 0.76 ± 0.03 ns at 100 Hz to 0.89 ± 0.08 ns at 1,500 Hz with a 60-W pump power. The pulse widths using HT110 and HT270 gradually broadened with an increase in the repetition rate, and the difference in the pulse width between the two media increased with an increase in the repetition rate at a pump energy of 40 mJ. For the same input parameters, the compressed pulse width using HT270 was always narrower than that using HT110. Figure 11(d) illustrates the compressed pulse waveforms of the SBS pulse compression for the two media. The average pulse widths at the energy of 40 mJ at 600 Hz were 2.43 ns and 1.07 ns for the media of HT110 and HT270, respectively, and the compressed pulse width for HT110 was 2.7 times larger than that for HT270. The average pulse width is 0.87 ns at 60-W pump power at 1.5 kHz using HT270.
The experimental results showed that under the same input conditions, the thermal effects within the amplifier cell with HT110 were more serious than those with HT270, as shown in Fig. 6. The reflected energy efficiency and compressed pulse width of the SBS pulse compression using HT270 were less affected by the repetition rate than those using HT110. The experimental results are consistent with the theoretical calculations in Section 4.2 of theoretical analysis of thermal problems. The SBS-reflected beam profiles using the HT110 medium appeared pattern distortions at 600 Hz due to thermal convection over a small range of medium temperature, as shown in Fig. 6(b), whereas the SBS-reflected beam profiles for HT270 had no pattern distortions from 100 Hz to 1,500 Hz over a wide range of medium temperature. By comparing the output characteristics for the HT110 and HT270 media at 10 Hz and kilohertz-level repetition rate, respectively. For high repetition rate lasers, the SBS pulse compression output is more sensitive to the kinematic viscosity parameter of liquid medium than its gain coefficient and phonon lifetime. The HT270 medium with a large kinematic viscosity and high boiling point is found to be more suitable for high-repetition-rate SBS pulse compression than HT110.
5.3 SBS pulse compression for 3,000 Hz operation
According to the analysis of the thermal problems in section 4, to alleviate the thermal effects in high-repetition-rate SBS pulse compression for a two-cell setup, this study adopted a combination of medium purification, rotating wedge lens, and the high-viscosity coefficient medium of HT270. The kinematic viscosity coefficient and boiling point of the HT110 medium are 0.77 cSt and 110°C, respectively. The viscosity coefficient and boiling point of the HT270 liquid medium are 11.7 cSt and 270°C, respectively. The experimental setup used in this study is illustrated in Fig. 1. Both the generator and amplifier cells were filled with the HT270 medium. The focusing lens in the two-cell setup was a wedge lens with a 15-cm focal length. The output parameters of the SBS pulse compression with respect to the input energy are shown in Fig. 12 for different repetition rates.
Fig. 12. Measured dependence of the SBS (a) reflected power and (b) energy efficiency on pump power at a repetition rate of 2,500 Hz and 3,000 Hz.
Figures 12(a) and 12(b) illustrate the SBS-reflected power and energy efficiency with respect to the input power at a repetition rate of 2,500 Hz and 3,000 Hz, respectively. As the input power increased, the reflected power increased linearly with the input power, and the energy efficiency also increased gradually. The SBS energy efficiencies were 42.8% at a pump power of 72 W at 2,500 Hz, and 36.2% at a pump power of 74 W at 3,000 Hz, respectively. Under this pump condition, the reflected power does not reach the saturation region. If the input power is increased further, the SBS reflected power and energy efficiency is expected to increase beyond this value.
Figure 13 shows the compressed pulse width and the pulse waveforms at a repetition rate of 2,500 Hz and 3,000 Hz. The compressed pulse width became gradually narrowed with an increase in the input power, and the average pulse widths were compressed from about 10 ns to 1.63 ns under the pump power of 72 W at 2,500 Hz, and compressed to 2.09 ns under the pump power of 74 W at 3,000 Hz, respectively. When the pump power was increased further, the compressed pulse width narrowed and their RSDs become larger. If the input power is increased further, the SBS pulse compression is expected to decrease beyond this value. The increasing of the compressed pulse width RSD at 70 W was due to thermal effects; with an increase in the injected power, the liquid medium absorbed the laser energy and caused a thermal defocusing effect in the medium cell, which increased the size of the beam spot and reduced the power density of the pump beam, easily affecting the intensity of thermal noise. Figure 13(b) shows the pulse waveforms of the compressed beams with repetition rates of 2,500 Hz and 3,000 Hz, respectively. A 10-ns pulse was compressed to 1.51 ns at 72 W for 2,500 Hz, and 2.04 ns at 74 W for 3,000 Hz, respectively. By using a rotating wedge lens and the HT270 medium with a high viscosity coefficient and boiling point, a 3000-Hz repetition rate pulse compression without beam pattern distortion is obtained in this study using a liquid medium.
Fig. 13. (a) Measured dependence of the compressed pulse width on input energy, and (b) Waveforms of the reflected beams at a repetition rates of 2,500 Hz and 3,000 Hz.
The results have been demonstrated that one of the key parameters limiting the improvement of the laser repetition rate of SBS pulse compression is the thermally induced beam-pattern distortion owing to the transmission of the high-power laser in the liquid medium. This beam pattern distortion affects the beam quality and the process of SBS generation. However, SBS medium with a large kinematic viscosity coefficient is easy to obtain reflected laser light with good beam pattern, but its energy efficiency is also low. Therefore, it is necessary to improve the SBS output parameter characteristics by optimizing the medium parameters.
5.4 Potential optimization method with continuous adjustment
The viscosity coefficient of medium has an important influence on the uniformity and stability of SBS reflected beam pattern. SBS liquid medium with large kinematic viscosity coefficient is beneficial to obtain stable beam pattern output, but it will reduce the energy efficiency of SBS. Therefore, the best compromise between viscosity coefficient and gain coefficient may be a way to improve the output characteristics of SBS. At present, the common optimization method to improve the output characteristics of SBS is to test and select excellent SBS media [35,36]. In fact, this method is often limited by the type of laboratory media, and it is difficult to obtain SBS media with good performance. Based on the physical characteristics of commonly used liquid media, this paper proposes a potential optimization method based on the mixing of two SBS liquid media [39] to realize the continuous adjustment of media parameters. The realization of this method needs to meet the following conditions: (1) the two media have good mutual solubility; (2) The mixture between the media will not cause intermolecular interaction; (3) The parameters of the mixed medium change regularly with the mixing ratio.
In this article, HT270 and HT110, having large differences in kinematic viscosity coefficient, are chosen for theoretical calculation. The reduced kinematic viscosity [40] of the non-associative mixed liquid medium is given as
The relationship between the frequency of the Stokes component and the acoustic vector can be deduced from the energy conservation and momentum conservation relationship in Brillouin scattering [41]. The gain coefficient [35] of the medium is expressed as
where $Y$ is the electrostriction coefficient of the medium, $n$ is refractive index of medium, the relationship between $Y$ and $n$ is $Y = ({n^2} - 1)({n^2} + 2)/3$, $c$ is speed of light in vacuum, $v$ is the acoustic velocity of medium, $\eta$ is the kinematic viscosity of medium, $\rho$ is the density of medium.The relationship between the refractive index of the mixed medium and the mixing ratio is given by $n = \sqrt {[1/(\frac{{{\varphi _1}}}{{n_1^2 + 2}} + \frac{{{\varphi _2}}}{{n_2^2 + 2}})] - 2}$[42], where ${n_1}$ and ${n_2}$ are the refractive index of the two media, ${\varphi _1}$ and ${\varphi _2}$ are the volume fractions of the two media. The expression for the acoustic velocity of the weakly interacting binary mixed medium is expressed by $v = \frac{{{M_1}{x_1}/{\rho _1} + {M_2}{x_2}/{\rho _2}}}{{\sqrt {({M_1}{x_1} + {M_2}{x_2})({M_1}{x_1}/\rho _1^2v_1^2 + {M_2}{x_2}/\rho _2^2v_2^2)} }}$[43], where $M$ is the molecular weight, $v$ is the acoustic velocity. According to the Eqs. (4) and (5), the relationships among the kinematic viscosity coefficient, gain coefficient and energy efficiency of the HT110/HT270 mixed liquid medium and the volume fraction of HT270 can be obtained, as shown in Fig. 14. The calculations of SBS energy efficiency didn’t consider the effect of the laser repetition rate.
Fig. 14. Calculated kinematic viscosity, gain coefficient, and energy efficiency of HT110/HT270 mixed medium with respect to the volume fraction of HT270, the shaded circles represent the critical kinematic viscosity coefficient of the mixed medium without thermal convection phenomenon for different laser repetition rates.
The prerequisites of the medium selection for high-repetition rate and high power SBS pulse compression are: (1) SBS medium with a viscosity coefficient greater than the critical viscosity coefficient to avoid thermal convection, and (2) SBS medium with large gain coefficient to obtain high energy efficiency. It can be seen from Fig. 14 that the continuous adjustment of the viscosity coefficient and gain coefficient of the liquid medium can be achieved by controlling the volume fraction of HT270. As the increase of the volume fraction of HT270, the kinematic viscosity coefficient increases monotonically from 0.77 cSt to 11.7 cSt and the gain coefficient decreases monotonically from 5.6 cm/GW to 0.27 cm/GW.
The relationship between the viscosity coefficient and the repetition rate is characterized with the parameter of temperature. The repetition rate parameter is included in the formula of the laser heat source. The heat source of the heat conduction equation [44] can be written by
Theoretically, the mixed medium method can realize the continuous control and adjustment of kinematic viscosity coefficient and Brillouin gain coefficient, which can be used for the optimization of SBS pulse-compressed phase-conjugation mirror and improvement of the energy efficiency. By choosing the mixed medium with the optimal viscosity coefficient and gain coefficient, the output characteristics of SBS can be optimized to meet the requirements of different SBS systems for medium parameters.
6. Conclusions
In this study, a pulse-compressed phase-conjugation mirror with a 3-kHz repetition rate was reported using a combination of medium purification, rotating wedge lens, and the suppression of thermal convection methods. The thermal problem limiting the increase in the laser repetition rate of SBS pulse compression were theoretically and experimentally analyzed in detail, and the heat transfer form and fluid state were quantitatively analyzed for different SBS liquid media. The influences of the pump spot size, off-center displacement, and focal length of the wedge lens on the focal spot pattern were studied theoretically, and a wedge lens with less coma-aberration was designed and analyzed by Monte Carlo ray-tracing method. The rotating wedge lens method alleviated the focusing thermal effects and improved the output energy efficiency of SBS pulse compression. At a pump energy of 40 mJ, the energy efficiency of SBS pulse compression is 41.4% at a repetition rate of 1,500 Hz, and the pulse width is compressed from 10 ns to 0.87 ns. The SBS energy efficiency is 36.2% at a pump power of 74 W at 3,000 Hz. Knowledge of the influence of the viscosity coefficient, gain coefficient, and phonon lifetime on high-power SBS pulse compression is important for improving its output characteristics. To improve the energy efficiency, a potential optimization method of continuously adjusting SBS output characteristics is presented and theoretically demonstrated by employing a mixed medium. These experimental results can provide output optimization guidance for high-power SBS technology. The laser repetition rate and medium thermal characteristics need be taken into account in a detailed calculation model of SBS pulse compression in the follow-up research.
Funding
National Natural Science Foundation of China (62105303); Fundamental Research program of Shanxi Province (20210302124026); Shanxi Scholarship Council of China (2020-102); Scientific and Technological Innovation Programs in Shanxi (2020L0265); 2021 China-Korea Young Scientist Exchange Program.
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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