Open Access
Add to BibSonomy
Abstract
A pulse compressing technology of single-frequency Q-switched laser based on the cascaded four-wave mixing (CFWM) effect is demonstrated theoretically and experimentally, for the first time to the best of our knowledge. A theoretical model of the pulse compression is established through deconstructing the pulse duration evolution in the high-order Stokes and anti-Stokes lights of CFWM. A pulse compression ratio of (2|m|+1)1/2 is quantificationally obtained with m corresponding to the order number of the CFWM light. Utilizing dual-wavelength (DW) single-frequency Q-switched laser injected into a highly nonlinear fiber (HNLF), the pulse compression and the spectral broadening phenomenon are observed simultaneously. As the order number of the CFWM light increases from 0-order to 3-order, the pulse duration has reduced from 115 ns to 47 ns with a compression ratio of 2.45, which is essentially consistent with the theoretical analysis. The pulse compressing technique by CFWM is conducive to promoting the performance development of the single-frequency Q-switched laser, which can improve the system precision in the Lidar, trace gas detection, and high-precision ranging. Furthermore, this technology based on time-frequency transformation dynamics may be generally applicable to other single-frequency pulsed fiber lasers.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Single-frequency Q-switched fiber lasers have attracted great interest in various applications including the Lidar system [1], trace gas detection [2], and high-precision ranging [3]. In particular, the pulsed laser with a narrow pulse duration contributes to the improvement of the ranging accuracy and precision for the applications above, such as the heterodyne laser radar [4]. Besides, the pulsed laser with tens of nanoseconds duration is a promising light source in the interaction with plasmonic nanostructures, which can be further used for cell nanosurgery, such as the destruction of molecular and cellular structures [5]. However, in most cases, the pulse duration of a single frequency Q-switched fiber laser is µs-scale or a hundred ns-scale limited by its narrow spectral linewidth and the pulse transform limit [6–8]. By use of Bi2Se3 working as a saturable absorber, Chen has achieved the dual-wavelength (DW) operation of the passive Q-switched fiber laser in a ring cavity with a minimum pulse duration of 13.4 µs [9]. Besides, a high-energy and ultra-broadband tunable passively Q-switched erbium-doped fiber laser is demonstrated later by the use of TI: Bi2Te3. With single pulse energy up to 1.525 µJ, a wide wavelength tuning range from 1510.9 to 1589.1 nm is obtained [10]. In 2015, Liu has obtained stable noise-like square-wave mode-locked pulses with a fundamental repetition frequency of 195 kHz, pulse packet duration tunable from 15 ns to 306 ns, and per-pulse energy up to 200 nJ [11]. However, in these cases, the discussion about the monochromaticity of the Q-switched laser is not adequate and the single-longitudinal-mode operation is not confirmed experimentally, which limits its application in high-precision fields, such as sensing and ranging. Thus, it is of vital importance to develop an efficient pulse compression technology for single-frequency Q-switched fiber lasers.
In recent years, different schemes have been proposed to realize the compression of pulsed lasers, including dispersion management [12], stimulated Brillouin scattering (SBS) [13,14], and stimulated Raman Scattering (SRS) [15–17]. Dispersion management, as a valid approach to utilizing grating or prism pairs, has been proved to generate ultrashort pulsed lasers with a high compression ratio by inducing the positive and negative chirp. However, dispersion management is not suitable for compressing pulsed lasers with good monochromaticity such as single-frequency Q-switched lasers without any chirp. The SBS effect is an efficient method in the compression of Stokes light, while it causes the distortion of the pulse shape with a steep leading edge and an elongated falling edge. This deficiency results from a strong saturation of the pump light by the leading edge of the counterpropagating Stokes light [18,19]. Besides, the SRS effect is also widely used in pulse compression with a fixed frequency shift depending on the type of medium. Since the frequency shift of SRS is irrelevant to the wavelength of the pump lights, it is relatively difficult to generate a Stokes light with a specific wavelength. The deformation and lengthening of the falling edge of Stokes pulses are also observed in SRS process [20]. In addition, the threshold condition of SRS, in this case, is usually up to mJ-scale pulse energy, which puts forward more stringent requirements for the amplification system.
Apart from that, utilizing an ultrafast laser as the pump source and bulk solid as the nonlinear medium, cascaded four-wave mixing (CFWM) has demonstrated the compression potential of ultrashort pulses in third-order nonlinear media, such as bulk media [21–24]. However, the ultrafast CFWM process requires not only phase matching but also group velocity matching, which combined with the complex spatial structure has increased the operational complexity and working uncertainty of this pulse compression system. Furthermore, to date, the theoretical analysis and experimental demonstration of the pulse compression based on CFWM in single-frequency pulse lasers is surprisingly lacking, especially in optical fiber nonlinear medium systems.
In this article, the pulse compression of a single-frequency Q-switched laser is presented based on fiber-based CFWM. Considering the propagation of two monochromatic pump lights, a theoretical model and simulation of the pulse duration evolution in high-order light generated in CFWM are demonstrated. In the theoretical analysis, a pulse compression ratio of (2|m|+1)1/2 is obtained with m corresponding to the order number. In the propagation process of dual-wavelength (DW) Q-switched laser in highly nonlinear fiber (HNLF), the pulse compression and spectral broadening of the high-order channel lights are observed experimentally. As the order number grew from 0-order to 3-order, the pulse duration reduced from 115 ns to 47 ns with a compression ratio of 2.45, which is consistent with the theoretical results. It is worth mentioning that this pulse compression technology by CFWM is also applicable to single-frequency pulsed fiber lasers.
2. Theory analysis
Figure 1 illustrates the schematic description of CFWM. The summed amplitudes of the pump lights corresponding to the -0 and +0 order channels are as followed,
In order to investigate the pulse evolution in the Stokes and anti-Stokes lights, the solution to the optical power for the m-order channel light and the pump lights firstly should be given. The solution for a single-channel light in CFWM can be solved by substituting Eq. (1) into the nonlinear Schrödinger equation as displayed below,
The solution to the power of the m-order channel light in CFWM is given [25,26]:
Since the intensity of the m-order channel light is proportional to the power, it can be expressed as
In the case of ϕNL<<1 and I+0≈I-0, J|m|(ϕNL)>>J|m|+1(ϕNL), Eq. (4) can be simplified as
In regard to Eq. (5), the intensity of the m-order channel light is modulated by the intensity of the pumps in CFWM. For a DW Q-switched laser, the power of the pumps satisfies the relationship of I-0≈I+0. Meanwhile, in a single cycle, the power of a Gaussian-shape DW Q-switched pulse conforms to the following the Gaussian distribution with
Thus, the power of the m-order channel light in CFWM can be solved by substituting Eq. (6) to Eq. (5), following the Gaussian distribution:
The pulse duration of the m-order channel light can be expressed as
According to Eq. (9), the pulse duration of the m-order channel light is compressed significantly compared to the pump lights. With a pulse compression ratio of (2|m|+1)1/2, this phenomenon can be explained as the temporal convolution of two synchronized Gaussian pulses. The nonlinear gain in the CFWM process leads to higher gain at the center of the Stokes and anti-Stokes pulses than at the edge. Thus, the Stokes and anti-Stokes pulses exhibit a steeper gaussian pulse shape and smoother pulse edges.
The simulated single pulse shapes from +0 order to +3 order are normalized as shown in Fig. 2(a). With the increase of the order number of the Stokes light, the pulse shapes present gradually inward compressing characteristics, and always maintain a good Gaussian shape. Assumed the pulse duration of pump light as 100 ns, a more detailed evolution of the pulse duration of the Stokes lights is displayed in Fig. 2(b). The results indicate that the pulse duration experiences a rapid decrease to be less than 60 ns at the 1st order, and then the decline rate gradually slows down with the boost of the order number of the Stokes light. For the 10th order Stokes light, the pulse duration has approached 20 ns level. The simulation results indicate that CFWM can provide superior compression ability of pulse duration, which can improve the performance development of the single-frequency pulse laser.
Fig. 2. (a) Theory analysis of the simulated normalized single pulse shape in the Stokes lights from +0 order to +3 order. (b) Simulated pulse duration versus the order number of the Stokes light (assumed the pulse duration of pump light as 100 ns).
3. Experimental setup
The experimental setup of pulse compression of single-frequency Q-switched fiber laser based on CFWM is shown in Fig. 3. The pump of the CFWM is provided by a DW single-frequency Q-switched fiber laser. The resonant cavity of the DW laser is composed of a semiconductor saturable absorber mirror (SESAM), a 20-mm-long homemade highly Er3+/Yb3+ co-doped phosphate fiber (EYDF), and a polarization-maintaining narrow-band partial-reflected fiber Bragg grating (PM-FBG). The absorbance of the SESAM is 10% at 1560 nm with a modulation depth of 4%. The PM-FBG has two reflection peaks which correspond to the slow and fast axes of the PM fiber due to the stress birefringence. The spacing between the two reflection peaks is 0.4 nm, which are located at 1559.9 nm and 1560.3 nm with the same 3-dB bandwidth < 0.08 nm and the common reflectivity >60%. Placed in the glass capillary, the resonant cavity is laid on a U-shaped groove which is fixed on a thermoelectric cooler (TEC) with a resolution of 0.01 °C. The temperature of the resonator cavity is controlled by the TEC at 25 °C to ensure a robust dual-wavelength operation of the resonant cavity. Following a backward pump scheme, the resonant cavity is pumped by a single-mode 976 nm laser diode (LD) with a maximum power of 250 mW. Propagating through a 980/1550 nm wavelength division multiplexer (WDM), an isolator (ISO) is used to prevent the reflected light from damaging the resonant cavity.
Fig. 3. Experiment setup of pulse compression of single-frequency Q-switched fiber laser based on CFWM. (SESAM: semiconductor saturable absorber mirror; EYDF: Er3+/Yb3+ co-doped phosphate fiber; PM-NB-FBG: polarization-maintaining narrow-band partial-reflected fiber Bragg grating; WDM: wavelength division multiplexer; ISO: isolator; LD: laser diode; TEC: thermoelectric cooler; MOPA: master oscillator power amplifier; HNLF: highly nonlinear fiber; NB-FBG: narrow-band high-reflected fiber Bragg grating.)
The DW laser is amplified by a homemade master oscillator power amplifier (MOPA) before passing through a 250 m highly-nonlinear fiber (NL1550-Zero, YOFC inc.) where the CFWM happens. The parameters of the HNLF are as follows: the nonlinear coefficient is 10 W−1·km−1, the dispersion slope is 0.03 ps/nm2/km at 1550 nm, the attenuation coefficient is 1.5 dB/km, and the zero-dispersion wavelength is ∼1560 nm. A 1 × 3 circulator and a narrow-band high-reflected fiber Bragg grating (NB-FBG) are utilized to separate a single channel light generated by the CFWM processes. In order to effectively filter out the light of different channels in CFWM optical spectra, several NB-FBGs with different central wavelengths and a 3-dB bandwidth of 0.2 nm are used. A coupler is used to split the filtered light into two parts, where the test port is connected to the measurement equipment and the other port is laser output. The optical signal-to-noise ratio (OSNR) is monitored by an optical spectrum analyzer with a span resolution of 0.02 nm and the pulse parameters are measured by a high-speed photodetector with a 3 dB bandwidth of 1 GHz and an oscilloscope with a working bandwidth of 2 GHz. A scanning Fabry-Perot interferometer (FPI) with a resolution of 7.5 MHz and a free spectral range of 1.5 GHz is used to identify the single-longitudinal mode (SLM) operation of the single-channel laser and measure the spectral linewidth.
4. Results and discussion
Under a pump power of 102 mW and a temperature of 25 °C, the DW single-frequency Q-switched operation of the laser cavity reaches a stable state with an average power of 10.5 mW and a repetition rate of 405 kHz. At this time, Fig. 4(a) presents the spectrum of the DW Q-switched laser, indicating that the difference in the intensity between the two signal peaks is less than 1 dB. The central wavelengths of the two peaks are 1559.904 nm and 1560.304 nm with an OSNR of 65 dB and 64 dB, respectively. Worked as the pump of CFWM, the DW laser corresponds to the -0 and +0 order channels of the CFWM. Via a polarization beam splitter (PBS), DW single-frequency Q-switched lasers are separated into two orthogonal components. The SLM operations of the two laser beams are confirmed utilizing the scanning FPI, as exhibited in the insert of Fig. 4 (a), without mode-hop and mode competition phenomena. The single pulse shape of the +0 order light (1560.304 nm) is shown in Fig. 4(b), which has a near-Gauss feature with a pulse duration of 115 ns. The spectral linewidth of the Q-switched laser can be estimated from the envelope of the pulse train in the scanning FPI signal yields. As demonstrated in Fig. 4(c), the spectral linewidth of the +0 order light (1560.304 nm) is measured as 10.2 MHz. Besides, by similar methods, the optical characteristics of the -0 order light (1559.904 nm) are also investigated, with a pulse duration of 108 ns and a linewidth of 9.5 MHz. The slight differences in the optical parameters are mainly attributed to the discrepancies in the refractive index and gain dynamics of the two orthogonal polarization directions in the laser resonant cavity.
Fig. 4. DW Q-switched laser at a pump power of 102 mW. (a) The optical spectrum of DW laser. Insert: the scanning result of SLM characteristic of the DW laser. (b) The normalized single pulse shape of the +0-order light. (c) The measured linewidth result of the +0 order light.
The long-term spectrum characters of this DW single-frequency Q-switched fiber laser are demonstrated in Fig. 5(a), which are measured every 10 minutes for 40 minutes. Thanks to the polarization hole burning effect of PM-FBG, the Q-switched laser has maintained a steady DW operating condition with a spectral intensity difference of less than 1.2 dB, which exhibits admirable spectrum stability in 40 mins. Meanwhile, under precise control of the pump power and the cavity temperature, the stable pulse trains in the time domain are shown in Fig. 5(b).
Fig. 5. The long-term stability of DW single-frequency Q-switched fiber laser. (a) spectrum characters. (b) pulse trains.
Before entering into the HNLF, the DW Q-switched laser is boosted to an average power of 120 mW by the MOPA, while it is difficult to further improve due to the limitation of the SBS effect. Meanwhile, the CFWM phenomenon emerged simultaneously as the power of the DW laser increased. The spectrum of the CFWM in Fig. 6(a) exhibits 20-tone signals spanning from 1556.39 nm to 1564.03 nm with a wavelength spacing of 0.4 nm. The intensity of the single-channel light gradually decreases from the low order to the high order. The initial 8-channel combs corresponding to -3 to +3 order have a signal intensity of -15.8, -13.3, -12, -8.7, -8.1, -11.4, -13.6, -17 dBm, respectively. Under the action of the circulator and NB-FBG, the +1 order single-channel light is effectively filtered to be investigated. As shown in the insert of Fig. 6(b), the SLM operation of this channel light is strictly confirmed without mode-hop and mode competition phenomena. Interestingly, the pulse duration of the +1 order signal is compressed to be 79 ns compared with that of 115 ns in the +0 order pump light, as illustrated in Fig. 6(b). A pulse compression ratio of 1.46 is acquired, and the single-pulse shape remains in a good Gaussian linear shape. At the same time, the spectral broadening phenomenon is also observed. As shown in Fig. 6(c), the linewidth of the +1 order channel light has increased to 15 MHz, which means that a linewidth broadening factor is 1.47. The pulse width compression ratio and the linewidth broadening factor are almost consistent, which results from the time-frequency transformation dynamics of the pulsed laser in the CFWM.
Fig. 6. (a) The optical spectrum of CFWM. (b) The normalized single pulse shape of the +1 order light. Insert: the scanning result of SLM characteristic of the +1 order light. (c) The linewidth of the +1 order light.
In order to further investigate the compressing characteristics of the CFWM process, these pulse durations of high-order signals are measured for comparison. Figure 7(a) and (b) show the single-pulse shapes from -0 order to -3 order and +0 order to +3 order respectively. Limited by the operating bandwidth of the filter device, the higher-order laser signal is difficult to measure further. It is obvious that the pulse shape has been compressed dramatically at the -1 and +1 order signal and tends to be steady with almost no distortion compared to the initial pump pulses. Thanks to the extremely short cavity length, the DW Q-switched pulses with a Gaussian shape from the resonator cavity are synchronous in the time domain. As a result, the propagation of fast and slow axis light in HNLF has induced the temporal overlap of the pulses with different central wavelengths. This basic has introduced the nonlinear gain of the CFWM process, which is the temporal convolution of the two Gaussian pulses essentially. As a consequence of nonlinear gain, the high-order Stokes and anti-Stokes light of CFWM exhibit a steeper Gaussian shape with a compressed pulse duration. Besides, the spectral intensity of high-order channel light is the integral of the spectral intensity of the DW laser, which contributes to the broadening effect of the spectral linewidth in the high-order channel lights.
Fig. 7. The normalized single-pulse shape from (a) -0 order to -3 order light. (b) +0 order to +3 order light.
According to Eq. (3) and (4), the nonlinear gain is mainly related to the pump power and the order number of the laser signals. For a DW Q-switched laser, the pump power of P-0, +0 can be expressed as Gaussian functions. Following the relationship between the pump, Stokes, and anti-Stokes lights in Eq. (9), the simulated pulse duration of high-order channel lights is exhibited in Fig. 8. As the order number grows, the progress of pulse compression slows down. The evolution of the pulse duration in the experiment is consistent with the theoretical results, which indicates the applicability of the theoretical model mentioned above. With the pulse duration compressed from 115 ns to 47 ns, a maximum compression ratio of 2.45 is obtained.
An important factor limiting the advance of the compression ratio is the product numbers and operation bandwidth of CFWM. Thereinto, the operation bandwidth of the CFWM effect mainly depends on the optical properties of the nonlinear medium including nonlinear coefficient, zero-dispersion wavelength, and dispersion slope. By the use of high nonlinear coefficient, steady zero-dispersion wavelength, and dispersion flat fibers, the bandwidth of CFWM may expand several hundreds of nanometers [27]. Besides, the product numbers and spectral bandwidth of CFWM are related to the optical parameters of the pump lasers including the peak power and the wavelength spacing [28–30]. Thus, the operation bandwidth of the four-wave mixing effect is affected by various factors as mentioned above. By advancing the CFWM operation bandwidth to further generate higher-order Stokes light, it is expected to achieve higher pulse compression ratios.
With the development of SBS suppression and fiber preparation technology, an elevated compression ratio may be obtained in the high-order channel lights produced by CFWM in the future. Different from other pulse compression technology, CFWM may produce virtually distortion-free compressed pulses with a wide range of application scenarios including Q-switched and mode-locked lasers. In particular, for single-frequency fiber lasers, this technology is conducive to the improvement of ranging accuracy and precision in Lidar system, trace gas detection and high-precision ranging. Thereinto, the heterodyne detection applied in Lidar system is an efficient detection technique to scale the velocity and distance of the target by measuring the round-trip time of the emitted pulsed laser. The pulsed compression laser with a narrower pulse duration has more concentrated pulse energy and will produce a higher target detection probability which brings higher range accuracy [4]. This pulse compression strategy combined with existing photonics technology can significantly promote the development of autonomous driving [31], space debris detection [32], satellite orbit determination [33], and other fields.
5. Conclusion
Based on the nonlinear gain of CFWM, we report the pulse compression phenomena of single-frequency Q-switched pulses in HNLF. The pulse duration evolution in high-order channel lights generated in CFWM is demonstrated based on the theoretical model and simulations. With m corresponding to the order number of the channels, a pulse compression factor of (2|m|+1)1/2 is obtained by theoretical analysis. As the DW Q-switched laser propagates through HNLF, the production of 20-channel Stokes and anti-Stokes lights by CFWM in the experiment is observed. Accompanied by spectral broadening and pulse compression, the pulse duration has reduced from 115 ns to 47 ns with a compression ratio of 2.45 as the order number grows from 0-order to 3-order. The pulse compressing technique is conducive to promoting the performance development of single-frequency pulsed laser, which can improve the ranging accuracy and precision in Lidar system, trace gas detection and high-precision ranging.
Funding
Key-Area Research and Development Program of Guangdong Province (2018B090904001, 2018B090904003, 2020B090922006); Major Program of the National Natural Science Foundation of China (61790582), (62035015); Fundamental Research Funds for the Central Universities (2020CG03, 2020ZYGXZR073, D6223090); Leading talents of science and technology innovation of Guangdong Special Support Plan (2019TX05Z344); China Postdoctoral Science Foundation (2021M701256); Basic and Applied Basic Research Foundation of Guangdong Province (2022A1515012594); Local Innovative and Research Teams Project of Guangdong Pearl River Talents Program (2017BT01X137); Guangzhou Basic and Applied Basic Research Foundation (202201010003); Independent Research Project of State Key Lab of Luminescent Materials and Devices, South China University of Technology (Skllmd-2022-13).
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.
References
1. U. Sharma, C. S. Kim, and J. U. Kang, “Highly stable tunable dual-wavelength Q-switched fiber laser for DIAL applications,” IEEE Photonics Technol. Lett. 16(5), 1277–1279 (2004). [CrossRef]
2. L. Goldberg, J. Koplow, D. Lancaster, R. Curl, and F. Tittel, “Mid-infrared difference-frequency generation source pumped by a 1.1–1.5-µm dual-wavelength fiber amplifier for trace-gas detection,” Opt. Lett. 23(19), 1517–1519 (1998). [CrossRef]
3. C. S. Gardner, “Effects of random path fluctuations on the accuracy of laser ranging systems,” Appl. Opt. 15(10), 2539–2545 (1976). [CrossRef]
4. H. Luo, X. Yuan, and Y. Zeng, “Range accuracy of photon heterodyne detection with laser pulse based on Geiger-mode APD,” Opt. Express 21(16), 18983–18993 (2013). [CrossRef]
5. E. Boulais, R. Lachaine, A. Hatef, and M. Meunier, “Plasmonics for pulsed-laser cell nanosurgery: Fundamentals and applications,” J. Photochem. Photobiol., C 17, 26–49 (2013). [CrossRef]
6. W. Li, J. Zou, Y. Huang, K. Wang, T. Du, S. Jiang, and Z. Luo, “212-kHz-linewidth, transform-limited pulses from a single-frequency Q-switched fiber laser based on a few-layer Bi2Se3saturable absorber,” Photonics Res. 6(10), C29–C35 (2018). [CrossRef]
7. K. Li, S. Xu, H. Deng, C. Yang, W. Lin, X. Guan, Q. Zhao, Y. Zhou, W. Wang, and Z. Yang, “Multi-Wavelength, Passively Q-Switched, Single-Frequency Fiber Laser,” IEEE Photonics Technol. Lett. 31(18), 1479–1482 (2019). [CrossRef]
8. Y. Zhang, C. Yang, Z. Feng, H. Deng, M. Peng, Z. Yang, and S. Xu, “Dual-wavelength passively q-switched single-frequency fiber laser,” Opt. Express 24(14), 16149–16155 (2016). [CrossRef]
9. Y. Chen, C. Zhao, H. Huang, S. Chen, P. Tang, Z. Wang, S. Lu, H. Zhang, S. Wen, and D. Tang, “Self-Assembled Topological Insulator: Bi2Se3 Membrane as a Passive Q-Switcher in an Erbium-Doped Fiber Laser,” J. Lightwave Technol. 31(17), 2857–2863 (2013). [CrossRef]
10. Y. Chen, C. Zhao, S. Chen, J. Du, P. Tang, G. Jiang, H. Zhang, S. Wen, and D. Tang, “Large Energy, Wavelength Widely Tunable, Topological Insulator Q-Switched Erbium-Doped Fiber Laser,” IEEE J. Sel. Top. Quantum Electron. 20(5), 315–322 (2014). [CrossRef]
11. J. Liu, Y. Chen, P. Tang, C. Xu, C. Zhao, H. Zhang, and S. Wen, “Generation and evolution of mode-locked noise-like square-wave pulses in a large-anomalous-dispersion Er-doped ring fiber laser,” Opt. Express 23(5), 6418–6427 (2015). [CrossRef]
12. E. A. Khazanov, S. Y. Mironov, and G. Mourou, “Nonlinear compression of high-power laser pulses: compression after compressor approach,” Phys.-Usp. 62(11), 1096–1124 (2019). [CrossRef]
13. Z. Liu, Y. Wang, Y. Wang, S. Li, Z. Bai, D. Lin, W. He, and Z. Lu, “Pulse-shape dependence of stimulated Brillouin scattering pulse compression to sub-phonon lifetime,” Opt. Express 26(5), 5701–5710 (2018). [CrossRef]
14. A. A. Kuz’min, O. V. Kulagin, and V. I. Rodchenkov, “Formation of nanosecond SBS-compressed pulses for pumping an ultra-high power parametric amplifier,” Quantum Electron. 48(4), 344–350 (2018). [CrossRef]
15. M. K. Mridha, D. Novoa, and P. S. J. Russell, “Dominance of backward stimulated Raman scattering in gas-filled hollow-core photonic crystal fibers,” Optica 5(5), 570–576 (2018). [CrossRef]
16. E. Migal, A. Pushkin, N. Minaev, B. Bravy, and F. Potemkin, “Control of spectral shift, broadening, and pulse compression during mid-IR self-guiding in high-pressure gases and their mixtures,” Opt. Lett. 47(4), 985–988 (2022). [CrossRef]
17. P. Carpeggiani, G. Coccia, G. Fan, E. Kaksis, A. Pugžlys, A. Baltuška, R. Piccoli, Y.-G. Jeong, A. Rovere, and R. Morandotti, “Extreme Raman red shift: ultrafast multimode nonlinear space-time dynamics, pulse compression, and broadly tunable frequency conversion,” Optica 7(10), 1349–1354 (2020). [CrossRef]
18. D. T. Hon, “Pulse compression by stimulated Brillouin scattering,” Opt. Lett. 5(12), 516–518 (1980). [CrossRef]
19. C. B. Dane, W. A. Neuman, and L. A. Hackel, “High-energy SBS pulse compression,” IEEE J. Quantum Electron. 30(8), 1907–1915 (1994). [CrossRef]
20. S. Akhmanov, A. Chirkin, K. Drabovich, A. Kovrigin, R. Khokhlov, and A. Sukhorukov, “Nonstationary nonlinear optical effects and ultrashort light pulse formation,” IEEE J. Quantum Electron. 4(10), 598–605 (1968). [CrossRef]
21. J. L. Silva, R. Weigand, and H. M. Crespo, “Octave-spanning spectra and pulse synthesis by nondegenerate cascaded four-wave mixing,” Opt. Lett. 34(16), 2489–2491 (2009). [CrossRef]
22. T. Kobayashi, J. Liu, and Y. Kida, “Generation and optimization of femtosecond pulses by four-wave mixing process,” IEEE J. Sel. Top. Quantum Electron. 18(1), 54–65 (2012). [CrossRef]
23. J. L. Silva, H. M. Crespo, and R. Weigand, “Generation of high-energy vacuum UV femtosecond pulses by multiple-beam cascaded four-wave mixing in a transparent solid,” Appl. Opt. 50(14), 1968–1973 (2011). [CrossRef]
24. W. Liu, L. Zhu, and C. Fang, “Observation of sum-frequency-generation-induced cascaded four-wave mixing using two crossing femtosecond laser pulses in a 0.1 mm beta-barium-borate crystal,” Opt. Lett. 37(18), 3783–3785 (2012). [CrossRef]
25. E. Lichtman, A. A. Friesem, R. G. Waarts, and H. H. Yaffe, “Exact solution of four-wave mixing of copropagating light beams in a Kerr medium,” J. Opt. Soc. Am. B 4(11), 1801–1805 (1987). [CrossRef]
26. S. Gao and X. Xiao, “All-optical wavelength multicasting based on cascaded four-wave mixing with a single pump in highly nonlinear fibers,” Opt. Commun. 285(5), 784–789 (2012). [CrossRef]
27. A. Cerqueira S Jr, J. M. C. Boggio, A. A. Rieznik, H. E. Hernandez-Figueroa, H. L. Fragnito, and J. C. Knight, “Highly efficient generation of broadband cascaded four-wave mixing products,” Opt. Express 16(4), 2816–2828 (2008). [CrossRef]
28. Y. Li, J. Hou, Z. Jiang, L. Huang, and J. Leng, “Cascaded four-wave mixing seeded by two continuous wave signals,” Appl. Opt. 53(8), 1583–1590 (2014). [CrossRef]
29. Y. Li, J. Hou, Z. Jiang, J. Leng, and L. Huang, “Generation of broadband cascaded four-wave mixing products pumped in the anomalous dispersion regimes,” J. Opt. 16(2), 025202 (2014). [CrossRef]
30. Z. Luo, M. Zhong, Q. Ruan, Y. Huang, C. Guo, H. Xu, K. Che, B. Xu, and Z. Cai, “0.1–1-THz High-Repetition-Rate Femtosecond Pulse Generation From Quasi-CW Dual-Pumped All-Fiber Phase-Locked Kerr Combs,” IEEE Photonics J. 8(2), 1–7 (2016). [CrossRef]
31. F. Roos, J. Bechter, C. Knill, B. Schweizer, and C. Waldschmidt, “Radar Sensors for Autonomous Driving: Modulation Schemes and Interference Mitigation,” IEEE Microwave 20(9), 58–72 (2019). [CrossRef]
32. T. Pisanu, L. Schirru, E. Urru, F. Gaudiomonte, P. Ortu, G. Bianchi, C. Bortolotti, M. Roma, G. Muntoni, G. Montisci, F. Protopapa, A. Podda, A. Sulis, and G. Valente, “Upgrading the Italian BIRALES system to a pulse compression radar for space debris range measurements,” in 2018 22nd International Microwave and Radar Conference (IEEE, 2018), pp. 317–320.
33. A. Morselli, P. D. Lizia, G. Bianchi, C. Bortolotti, S. Montebugnoli, G. Naldi, F. Perini, G. Pupillo, M. Roma, M. Schiaffino, A. Mattana, E. Salerno, A. Magro, K. Z. Adami, R. Armellin, A. L. Sergiusti, W. Villadei, F. Dolce, M. Reali, and J. Paoli, “A new high sensitivity radar sensor for space debris detection and accurate orbit determination,” in 2015 IEEE Metrology for Aerospace (IEEE, 2015), pp. 562–567.
