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Abstract
High-frequency, high-power picosecond lasers have important and wide-ranging applications in laser ranging, optoelectronic countermeasures, and ultrafine industrial processing. Pulse compression based on stimulated Brillouin scattering (SBS) can achieve a highly efficient picosecond laser output, while improving the peak power and beam quality of the laser. In this paper, a generator-amplifier two-cell structure with frequency-detuning was proposed to achieve a pulse output that combines high compression ratio and high energy reflectivity. The experiment proved that under a pump pulse width of 15 ns and repetition frequency of 10 Hz, when the generator cell and amplifier cell media were selected as HT-230, the highest energy reflectivity of 46% and narrowest compression pulse width of 1.1 ns were achieved, and the pulse compression ratio was 13.6. When the amplifier cell was selected as FC-770 and the generator cell was selected as HT-230, an energy reflectivity of 52% and a compression pulse width of 840 ps could be achieved simultaneously, and the pulse compression ratio was 18.
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1. Introduction
High-frequency, high-power picosecond lasers have important and wide-ranging applications in areas such as LIDAR [1–3], optoelectronic countermeasures [4–6], and laser cleaning [7–9]. For example, in the field of LiDAR, the geosynchronous orbit satellite Bei Dou carries LiDAR with a high frequency of approximately 10 kHz and pulse width of 18.6 ps, with a maximum measurement range of 36,000 km and minimum range accuracy of 3.2 mm [10]. Onboard radar ICESat-2, with a high frequency of up to 10 kHz, allows real-time monitoring of the global atmospheric system and precise measurements of mountain heights [11]. In the field of laser cleaning, high beam quality laser light sources with a high frequency of ∼100 kHz and pulse width of ∼10 ps are usually required to achieve the complete removal of oxide films from the surface of hot-rolled steel [12] or aluminum alloys [13]. Pulse compression based on stimulated Brillouin scattering (SBS) is an effective method for generating high-peak-power picosecond lasers with significant unique advantages such as a simple and compact structure, high compression ratio, and high beam quality [14–21]. For example, Wang et al. [22] obtained an output pulse with a pulse width of 820 ps and an energy reflectivity of 52.2% under a pump pulse of 50 mJ and heavy frequency of 1 KHz. Liu et al. [23] used a two-stage SBS compression structure to achieve transient SBS one-quarter acoustic cycle pulse compression with an energy reflectivity of more than 30%. Kang et al. [24] achieved an output pulse energy of 50 mJ without an optical breakdown at a pump frequency of 200 Hz.
In the above conventional compression structure, the Stokes pulse is generated and amplified in the same medium cell, and both theoretical studies and experiments have shown that the output energy reflectivity is paradoxical to the compression ratio, because the gain coefficient and phonon lifetime of the Brillouin medium [25] are both inversely proportional to its kinematic viscosity. A paradoxical relationship exists between the total number of photons scattered during the scattering process and the rate and duration of scattering. Therefore, if the phonon lifetime of the Brillouin medium varies linearly in the same direction as the effective gain coefficient, the energy reflectivity and compression ratio cannot be simultaneously optimized. Based on the above conclusions, we propose a generator-amplifier two-cell structure with frequency-detuning characteristics, and the novel structure is designed to achieve excellent output results considering both the energy reflectivity and compression ratio.
This study is devoted to investigating the effect of Brillouin frequency shift differences between different media on the SBS compression ratio and energy reflectivity in a generator-amplifier two-cell structure with frequency-detuning characteristics. We selected HT-230, FC-40, FC-770, and FC-72 as the Brillouin media with a pump pulse width of 15 ns and repetition frequency of 10 Hz. The experiment proved that when the generator cell and amplifier cell media were selected as HT-230, the highest energy reflectivity of 46% and the narrowest compression pulse width of 1.1 ns were achieved, and the pulse compression ratio was 13.6. When the amplifier cell was selected as FC-770 and the generator cell was selected as HT-230, an energy reflectivity of 52% and a compression pulse width of 840 ps could be achieved simultaneously, and the pulse compression ratio was 18. To the best of our knowledge, this is the first study to exploit the SBS frequency-detuning characteristics to optimize the output parameters.
2. Theoretical analyses
The SBS phenomenon arises from the interaction between the incident optical pump field and elastic acoustic wave field induced by electrostriction in the medium. The interaction between the frequency of the pump pulse, frequency of the Stokes pulse, and frequency of the phonon field [26] in the medium is given by
where ${v_a}$ is the frequency of the dielectric acoustic subfield, ${v_{in}}$ is the frequency of the pump pulse, and ${v_s}$ is the frequency of the Stokes pulse.The Brillouin shift ($\Delta v$) is the difference between the frequency of the pump pulse and that of the Stokes pulse, and is expressed as
According to Eq. (2), the Brillouin frequency shift is equal to the dielectric acoustic subfield frequency. The Brillouin shift ($\Delta v$) is expressed as
where n is the refractive index of the medium, v is the speed of sound in the medium, and $\lambda $ is the pump pulse wavelength.The Brillouin linewidth, which is numerically equivalent to the inverse of the phonon lifetime in the medium [27], is expressed as
where $\mathrm{\Gamma }$ is the Brillouin linewidth of the medium, n is the refractive index of the medium, $\eta $ is the kinematic viscosity of the medium, and $\lambda $ is the wavelength of the pump pulse.The Brillouin gain coefficient [28] can be expressed as
where $\mathrm{\gamma } = \frac{1}{3}({{\textrm{n}^2} - 1} )({{n^2} + 2} )$ is the coefficient of electrostriction, ${\omega _p} = \frac{{2\pi c}}{\lambda }$ is the pump pulse frequency, $\rho $ is the density of the medium, and $\mathrm{\Gamma }$ is the Brillouin linewidth of the medium. Substituting into Eq. (5) givesAs shown in Fig. 1(a), in the single-cell Brillouin structure, the Brillouin generation and amplification processes occur in the same media cell, which is prone to optical breakdown under short focus and high energy, affecting the stability of the Stokes pulse. As shown in Fig. 1(b), in the two-cell Brillouin structure, the Brillouin generation and amplification processes were performed separately, the generator cell was used to generate the backward Stokes pulse, and the amplifier cell was used for the energy transfer and amplification of the Stokes pulse. The conventional two-cell structure, in which both the generator and amplifier cells use the same medium, fails to achieve both a significant compression ratio and high energy reflectivity. In particular, the phonon lifetime and the gain coefficient are inversely related to the kinematic viscosity of the medium. The achievement of significant compression amplification depends on the short phonon lifetime and the high gain coefficient. Consequently, the traditional focusing two-cell structure inadequately meets the requirements of both narrow pulse width and high energy reflectivity.
In summary, in the focused two-cell structure, different combinations of media are selected to achieve a more optimal parameter output. Considering the different Brillouin media used in the generator and amplifier cells, different frequency shift differences were observed. Therefore, when energy is pumped into the amplifier cell, the actual gain effect of the Brillouin medium itself is affected by frequency-detuning. The gain coefficient of the Brillouin medium is jointly determined by the electrostriction effect of the phonon field and thermal absorption of the medium [29]
As shown in Fig. 2, when $\Delta \vartheta = 0$, the effective gain coefficient ($\textrm{g}$) is equal to the intrinsic gain coefficient (${\textrm{g}^e}$). The frequency shift of the Brillouin generator cell matches that of the amplifier cell. Consequently, the oscillation of the phonon field provides a significant gain, resulting in an increased energy extraction efficiency. Conversely, for $\Delta \vartheta {\; } \ne 0$, the effective gain coefficient ($\textrm{g}$) is less than the intrinsic gain coefficient (${\textrm{g}^e}$). If the difference between the Brillouin frequency shifts of the two media is not excessively large and a Brillouin linewidth intersection exists, the amplification effect on the Stokes pulse within the amplifier cell remains significant. As illustrated in Fig. 3, under the compact two-cell structure, with the amplifier cell selecting FC-770 as an example, if the generator cell selects other media, owing to the effect of frequency-detuning, the actual gain intensity varies with the difference in the Brillouin frequency shift; as the difference in the Brillouin frequency shift increases, the actual gain intensity gradually decreases. Therefore, when selecting different media, the effect of the Brillouin frequency shift difference on the actual gain should be emphasized.
Fig. 2. Schematic diagram of Brillouin frequency shift for different media, (a) same frequency shift and (b) different frequency shift.
Fig. 3. Variation curve of gain intensity with Brillouin frequency shift difference when the gain cell is FC-770.
3. Experimental setup and results
Experimental setup selection of Nd: YAG laser based on passive Q-switching. The laser output pulse had a width of 15 ns and was operated at a wavelength of 1064 nm with a repetition frequency of 10 Hz. The laser worked in single mode operation with a linewidth of 0.39 GHz. The pulse waveform is shown in Fig. 4. The experimental optical path is shown in Fig. 5. The energy modulation system consists of the half-wave plate (HWP) and the polarizing beam splitter (PBS), while the optical isolation system consists of the PBS, the HWP, and the Faraday rotor. This system prevents backward Stokes from the SBS from entering the laser resonant cavity, reducing the potential for oscillation-induced damage to the laser components. The pump pulse was linearly polarized. This pulse passed through the energy conditioning system consisting of the HWP and PBS, followed by an optical isolation system. Subsequently, the pulse passed through a quarter-wave plate (QWP) to convert it into a circularly polarized pulse. The circularly polarized pulse was focused through the lens into the SBS amplifier-generator system, producing a backward Stokes pulse. Finally, the Stokes pulse was reflected and output through the PBS.
The SBS amplifier-generator system consists of a long focus lens denoted as L1 (with a focal length denoted as ${f_1}$), a short focus lens designated as L2 (with the focal length denoted as ${f_2}$), the amplifier cell, and the generator cell. The pump pulse was pre-focused using a long focus lens L1. The purpose of this pre-focusing is to increase the power density of the pump pulse, thereby facilitating amplification of the Stokes pulse. The pulse was then focused on the generator cell using a short focus lens L2. When the SBS threshold was reached, the focal position excited the phonon field and generated a Stokes pulse. The interaction between the Stokes pulse, pump pulse, and acoustic field occurred within the Brillouin generator cell. The resulting Stokes pulse was again converted into an S-polarized pulse by the QWP, which was finally reflected and outputted from the PBS. This pulse exhibits the characteristics of narrow pulse width and high peak power. The pulse features were quantified using a rapid photodetector (UPD-35-UVIR-D) in conjunction with a digital oscilloscope (DPO71254C). The energy of the laser pulse was quantitatively assessed by using an energy meter (PE50DIF-ER).
The experimental setup involved four different media types: HT-230, FC-40, FC-770, and FC-72. The specific parameters associated with this medium are listed in Table 1. Under the compact two-cell structure, the significant difference in the frequency shift between different media can adversely affect the actual Brillouin amplification effect, resulting in reduced amplification efficiency. Further impact on system energy reflectivity. Therefore, selecting a medium characterized by a small Brillouin frequency shift difference can mitigate the effect of frequency-detuning between different media on the SBS system. Combined with Table 1 and Fig. 6, it can be seen that the Stokes linewidths of the media are all inversely proportional to the phonon lifetime. The shorter the phonon lifetime of the medium, the widener the Brillouin linewidth and the slower the change in actual gain intensity with Brillouin frequency shift. Therefore, the actual gain of the system is reduced by the effect of frequency-detuning. The energy reflectivity and narrowest output pulse width of the four media within the context of the SBS single-cell structure using a single-stage compression system and an optically selected lens focal length of 100 mm (owing to the inherent instability of the focused single-cell structure at a longer focal length) are shown in Fig. 7. After the SBS pulse compression of the four media, FC-72 had the highest energy reflectivity and widest pulse width, whereas HT-230 had the lowest energy reflectivity and narrowest pulse width. As shown in Fig. 7(b), the analysis of the narrowest pulse width law for different media took into account the unstable output pulse width under long focus conditions for the selected single-cell structure. The selected lenses were all short focus lenses whose distance was much shorter than the optimal interaction length, resulting in a short distance between the pump pulse and the Stokes pulse action and a limited compression capability of the Stokes pulse front. As a result, the narrowest pulse width occurred near the SBS threshold, and as the pump energy was increased, the remaining pump energy worked on the trailing edge of the Stokes pulse, finally leading to the phenomenon of pulse widening. The narrowest pulse width change rule was consistent for the different media outputs. The correspondence between the narrowest compressed pulse width and energy reflectivity is consistent with the inherent phonon lifetime of the medium itself, as well as the magnitude of the gain coefficient. This correspondence provides a robust foundation for subsequent experimental comparisons.
Fig. 6. (a) Variation of Brillouin linewidth with phonon lifetime, medium frequency shift (b) HT-230, (c) FC-40, (d) FC-770, and (e) FC-72.
Fig. 7. (a) Comparison of media energy reflectivity and (b) Comparison of the narrowest output pulse width of the media.
Table 1. Parameters of the media used in the experiment
The initial objective was to investigate the effect of frequency-detuning on the SBS pulse amplification process. Within the SBS system, uniformity was maintained by selecting the same medium for the amplifier cell and different media for the generator cell. This structure ensured that the compression effect on the generated Stokes pulse remained constant. This result was owing to the use of the same media for the amplifier cell, which guarantees equivalence in the total number of photons reflected from the pump pulse as it passes through the amplifier cell. Moreover, this choice resulted in an identical number of photons proceeding into the generator cell. Considering both the magnitude of the Brillouin frequency shift of the medium and the gain coefficient, FC-770 was selected as the medium for the amplifier cell in the experimental setup. HT-230, FC-40, FC-770, and FC-72 were selected as the generator cells. To optimize the system, we selected a combination of focal lengths as ${f_1}$=1500 mm+${f_2}$=50 mm. This choice is consistent with the optimal interaction length equation [30], $L = \frac{{{\tau _p}c}}{{2n}}$, where ${\tau _p}$ represents the pump pulse width, c is the speed of light, and n is the refractive index of the medium. The calculations indicate that the optimal interaction length for this experiment is approximately 1700 mm. Hence, a long-focus lens with a focal length of ${f_1}$=1500 mm was selected. Considering that the Brillouin generator cell produces only the Stokes pulse, a short focus lens was used to reduce the effect of the Stokes pulse energy amplification in the generator cell. Accordingly, a short-focus lens with focal length of ${f_2}$=50 mm was selected.
From Eq. (8), it can be seen that the actual gain is negatively correlated with the Brillouin frequency shift difference, so the larger the Brillouin frequency shift difference, the faster the gain decays. Table 2 shows the generator of cell selection for different media, subject to the influence of frequency-detuning between different media, calculated by the equivalent gain size of Eq. (8).
Table 2. Generator cell for different media, the actual gain strength under the influence of frequency-detuning
In terms of energy reflectivity, the experiment compared the trend of the highest energy reflectivity change for two focal lengths (${f_1}$=1000 mm+${f_2}$=50 mm and ${f_1}$=1500 mm+${f_2}$=50 mm). As shown in Fig. 8(a), at a focal length of ${f_1}$=1000 mm+${f_2}$=50 mm, the magnitude of the SBS energy reflectivity of the four media were as follows: FC-72 > FC-770 > FC-40 > HT-230. The highest energy reflectivity of the SBS occurred in the generator cell of FC-72 when the input energy was 30 mJ, and the highest energy reflectivity reached 65.5%. When the generator cell was FC-770, the highest energy reflectivity was 63.5%. Under different combinations of media, FC-72 was the most affected by frequency-detuning and had the largest attenuation of the actual gain effect, resulting in an energy reflectivity only slightly higher than that of FC-770. As shown in Fig. 8(b), at a focal length of ${f_1}$=1500 mm+${f_2}$=50 mm, the magnitudes of the SBS energy reflectivity of the four media were as follows: FC-770 > FC-72 > FC-40 > HT-230. The highest SBS energy reflectivity occurred in the generator cell of FC-770 when the input energy was 30 mJ, and the highest energy reflectivity reached 60%. When the generator cell was FC-72, the highest energy reflectivity was 55.4%. It was found that the change in energy reflectivity does not simply follow the high energy reflectivity characteristics of the large gain coefficient of the generator cell medium. However, the energy reflectivity of FC-770 was larger than that of FC-72. Under the compact two-cell structure, the amplifier cell was FC-770 and the generator cell was FC-72, and the actual gain intensity was shown in Table 2. Due to the large Brillouin frequency shift difference between FC-72 and FC-770, the actual gain intensity of the system was most reduced, which was only 0.54 times the gain intensity of FC-72. Therefore, under the influence of frequency-detuning, it was no longer simply the case that the medium of the generator cell had a high gain and its energy reflectivity was high.
Fig. 8. SBS energy reflectivity at (a) focal length of 1000 mm + 50 mm and (b) focal length of 1500 mm + 50 mm.
As an additional point of consideration, the energy reflectivity was further investigated using a focal length combination of ${f_1}$=1500 mm+${f_2}$=200 mm. When the generator cell was FC-770, the highest energy reflectivity was 56.7%; when the generator cell was FC-72, the highest energy reflectivity was 50.2%, and the relationship between the magnitude of the energy reflectivity was consistent with the focal length of ${f_1}$=1500 mm+${f_2}$=50 mm. This phenomenon occurred because the continuous increase of the interaction length before entering the gain saturation region reduces the pump power density at the focal point of the Stokes pulse generation efficiency. The actual gain of the system exhibited attenuation due to the effect of frequency-detuning, resulting in a decrease in the efficiency of the Stokes pulse during the energy transport phase of the amplifier cell. Finally, the energy reflectivity of the system decreased further compared to the case where only the interaction length was increased. Thus, for combinations of media with large differences in Brillouin frequency shifts, increasing the interaction length results in a more significant decrease in energy reflectivity. Therefore, when selecting different combinations of media for SBS pulse compression experiments at long interaction lengths, it is imperative to consider whether the effect of frequency-detuning on energy reflectivity is greater than that of the gain coefficient on energy reflectivity.
In terms of the output pulse width, as shown in Fig. 9(a) and 9(b), the Stokes output pulse widths for two different focal length combinations (${f_1}$=1000 mm+${f_2}$=50 mm and ${f_1}$=1500 mm+${f_2}$=50 mm) were consistent with the pulse compression characteristics of the focused single-cell structure. Thus, the Stokes pulse width at the output of the medium with a short phonon lifetime was narrower. The narrowest output pulse width was 1.4 ns and the pulse compression ratio was approximately 11 for the ${f_1}$=1000 mm+${f_2}$=50 mm focusing lens combination. The narrowest output pulse width was 840 ps, and the pulse compression ratio was approximately 18 for the ${f_1}$=1500 mm+${f_2}$=50 mm focusing lens combination. The narrowest output pulse widths occurred when the generator cell was selected as HT-230, which confirms that under the compact two-cell structure, when the frequency shifts between different media are close to each other and the amplifier cell medium is certain, the generator cell is selected as the medium with a short phonon lifetime, which can realize a narrower pulse width output.
Fig. 9. Minimum output pulse widths for (a) focal length of 1000 mm + 50 mm and (b) 1500 mm + 50 mm.
It should be noted that the high gain coefficient medium as the amplifier cell has a significant effect on the amplification of the Stokes pulse. However, if the difference in the gain coefficient between different media is large (high gain for amplifier cell media, low gain for generator cell media), it causes a decrease in the contrast between the main and secondary peaks, and the competition between the different peaks is obvious. As shown in Fig. 10, the output pulse waveform exhibited a multi-peak waveform from the normal waveform. The reason for the appearance of multi-peak pulses is that the phonon lifetime selected for the generator cell medium is short, the gain coefficient is low, and the gain saturation area of the Stokes pulse is narrow, making it easy to reach gain saturation. The Stokes pulse is amplified efficiently by the high-gain medium as it passes through the amplifier cell, and the residual energy after sufficient amplification of the Stokes pulse still meets the SBS threshold, resulting in the generation of a second Stokes pulse. As the pump energy continues to increase, multiple Stokes pulses are generated, resulting in a multi-pulse situation. The multi-peak pulse phenomenon occurred when the amplifier cell was FC-72 and the generator cell was HT-230. The medium gain difference was about 5.4 cm/GW, and the focal length was ${f_1}$=1500 mm+${f_2}$=50 mm. When the pump energy reached 8 mJ (at this time, the pump energy was close to the SBS threshold), the multi-peak phenomenon began to appear, and the multi-peak phenomenon appeared stably by further increasing the energy. Therefore, in the compact two-cell structure, if the medium of the generator cell is the same, the larger the gain coefficient of the medium of the amplifier cell within a certain range, the more favorable the pulse compression.
Fig. 10. (a) Normal waveforms and (b) multi-peak waveforms with different gain differences between media
According to the above experimental law, considering the realization of a narrower pulse width output while considering the high energy reflectivity, the short phonon lifetime medium HT-230 was selected for the generator cell, and the high gain coefficient medium FC-770 was selected for the amplifier cell. Their gain coefficient difference was approximately 3 cm/GW, so multi-peak competition did not occur. As a control, the HT-230 medium was selected for both conventional focusing two-cell, and under the same structural parameters, the highest energy reflectivity was 46%, the narrowest compression pulse width was 1.1 ns, and the pulse compression ratio was only 13.6. In the conventional focusing single-cell structure, the HT-230 medium was selected, the highest energy reflectivity was 43%, the narrowest compression pulse width was 1.2 ns, and the pulse compression ratio was only 12.5.
4. Conclusion
In summary, this study investigated the effect of the Brillouin frequency shift difference between different media on the output characteristics of SBS pulse compression in a novel generator-amplifier two-cell structure with frequency-detuning characteristics. The experimental evidence shows that the output results can be significantly improved by exploiting the frequency-detuning characteristics of the SBS. When the amplifier cell was selected as FC-770 and the generator cell was selected as HT-230, an energy reflectivity of 52% and a compression pulse width of 840 ps could be achieved simultaneously, and the pulse compression ratio was 18. When the generator cell and amplifier cell media were selected as HT-230, the highest energy reflectivity of 46% and narrowest compression pulse width of 1.1 ns were achieved, and the pulse compression ratio was only 13.6. In particular, the gain coefficient of the amplifier cell medium must not be too high, as this will cause multiple peaks in the Stokes pulse due to oversaturation of the amplification, which affects the purity of the final output waveform.
Funding
Natural Science Foundation of Hebei Province (F2022202035); National Natural Science Foundation of China (62075056).
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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