Open Access
Add to BibSonomy
Abstract
We demonstrated sub-10 fs pulse generation by the post-compression of a 100 TW Ti:Sapphire laser to enhance the peak-power. In the post-compression, the laser spectrum was widely broadened by self-phase modulation in thin fused silica plate(s), and the induced spectral phase was compensated with a set of chirped mirrors. A spatial filter stage, consisting of two cylindrical lenses and a spherical lens, was employed to reduce the intensity modulation existing in the laser beam, which effectively suppressed intensity spikes induced by self-focusing. The laser beam was post-compressed from 23 fs to 9.7 fs after propagating through a 1.5 mm fused silica plate, resulting in the peak-power enhancement by a factor of 2.1.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Since the chirped pulse amplification technique(CPA) [1] has been adopted for ultrashort high power lasers, the peak-power of lasers has rapidly increased. Ti:Sapphire has been widely adopted for ultrahigh power femtosecond lasers due to its excellent optical properties and broadband gain spectrum. Petawatt (PW) lasers have been constructed in several institutes [2], and the laser intensity recently reached 1023 W/cm2 [3]. Such lasers can provide an excellent tool to investigate particle acceleration and strong field quantum electrodynamics [4–6]. To further enhance the peak-power of CPA lasers, the pulse shortening by post-compression has been investigated. This method can effectively increase the peak-power without adding a stage of costly amplifiers.
The post-compression of high power CPA lasers has been actively investigated to generate few cycle laser pulses while enhancing the laser power. The post-compression process consists of the spectral broadening stage via self-phase modulation (SPM) and the compression stage to compensate for the induced dispersion with dispersive optics [7,8]. The spectral broadening has been widely investigated in various nonlinear media such as fiber [9–11], hollow-core fiber (HCF) [12–14], and bulk material [15–17]. The hollow-core-fiber-based post-compression technique has been developed and widely applied for the generation of mJ-level few-cycle laser pulse [18–20]. Though the HCF method is effective for milijoule femtosecond laser pulses, it cannot be applied to Joule-level laser pulses. On the other hand, the solid plate-based post-compression has been experimentally demonstrated at the Joule level [21], but the configuration including free propagation requires techniques to suppress self-focusing, such as self-filtering [21] and wavefront correction [22]. The detailed comparison of post-compression experiments in the TW regime can be found from Ref. [20,21]. For the post-compression of multi-TW laser pulses, the spectral broadening using thin solid plates can provide a proper way to shorten a joule-level laser pulse because of the applicability to lasers with large beam size. Mourou et al. proposed a highly efficient post-compression of a quasi-uniform beam with an intensity of ∼TW/cm2 using solid plates [23]. Ginzburg et al. presented the pulse compression of an 18-J laser pulse from 64 fs to 11 fs [22], and Shaykin et al. showed the high-energy pulse compression to 10 fs through the post-compression using a 4-mm-thick KDP crystal [24]. In addition, the post-compression of a laser pulse with 3-J energy from 24 fs to 13 fs was reported [25].
In this paper, we demonstrated the generation of sub-10 fs pulses through the post-compression process for the peak-power enhancement of a 100-TW Ti:sapphire laser [26]. In order for smoothing the beam profile, a vacuum spatial filter system was employed before the post-compression, since strong intensity spikes induced during spectral broadening can seriously damage subsequent optical components. The laser beam was post-compressed by propagating through a 1.5-mm fused silica plate and compensating for the induced chirp with a set of chirped mirrors.
2. Experiment
The post-compression for generating sub-10 fs pulses was carried out with a 100-TW Ti: sapphire laser with an energy of about 2.5 J and a pulse duration of 23 fs [26]. The schematic setup for post-compression of high energy ultrashort pulses and the characterization of post-compressed pulses is shown in Fig. 1. In the vacuum spatial filter of Fig. 1, deployed between the final amplifier and the compressor, the laser beam with energy of 3.9 J with a beam diameter of 40 mm was filtered in the vertical and the horizontal directions through two cylindrical lenses and a spherical lens [27], all of which had focal lengths of 2.4 m. After the filter, the expander, and the grating compressor, the laser pulse passed through a set of thin fused silica plates and the laser spectrum was widely broadened due to SPM. The spectrally broadened laser pulse was, then, recompressed with chirped mirrors (CMs) after the beam was attenuated because of the dispersion added due to SPM and material dispersion. A set of chirped mirrors (UltraFast Innovations) with reflectivity over 99% in the spectral range from 600 to 950 nm and the group delay dispersion (GDD) of -100 fs2 was used to compensate for the GDD induced by SPM and material dispersion.
Fig. 1. Schematics of the experimental setup for post-pulse compression and characterization. M1: dielectric mirror, FS: fused silica plates for spectral broadening, A1 and A2: uncoated glass for attenuation of pulse’s energy, M2, M3 and mirrors at diagnostics: silver-coated mirror, CM: Chirped mirror, CC and CX: silver-coated concave and convex mirror, W: chamber window, L: AR-coated achromatic lens, ND: a neutral density filter, CP: compensator for residual dispersion and E: energy meter.
The post-compressed laser pulses were characterized in the diagnostic table installed outside the vacuum chamber. The post-compressed pulse was attenuated with four uncoated glasses by a factor of 4×10−5 to prevent any nonlinear process in the window. The large aperture beam was demagnified by a factor of 6 with two silver-coated concave mirrors in the vacuum chamber. The B-integral of the laser pulse going through the window was ensured to be much smaller than 1. The laser beam size was additionally reduced by 2 times with silver-coated concave mirrors before measuring the pulse duration. The pulse duration was measured with a spectral phase interferometry for direct electrics-field reconstruction (SPIDER) device. The central 50% of the laser beam radius was sent to the SPIDER to select a quasi-flat area of the beam. The additional dispersion induced by the vacuum window and the air in the optical path to the SPIDER, corresponding to GDD of 104 fs2, was taken into account when compensating for the chirp with four CMs installed inside the vacuum chamber. For characterizing the spatial quality of post-compressed laser pulses, the beam profile was measured by using an image relay system. The spatial evolution of post-compressed laser pulses along the propagation direction was measured also. In addition, the spatial distribution of Fourier-transform-limited (FTL) pulse duration was measured by spectrally resolving the post-compressed pulse with a set of bandpass filters with 10 nm full width at half maximum (FWHM) bandwidth.
3. Results and discussion
3.1. Spectral broadening with solid plates
For enhancing the peak-power of a 100-TW laser by post-compression, the spectral broadening after passing through 0.5-mm-thick fused silica plates was examined. The measured spectra with respect to the number of plates are shown in Figs. 2(a)-(c), in which the solid red line and the dotted black line represent the experimental result and the simulated result, respectively, and the gray-filled area is the input laser spectrum. The intensity of the laser pulse at the fused silica plates was 2.8 TW/cm2. The output spectrum was broadened as the number of plates increased, and the spectral width was most broadened when 3 fused silica plates were used. The spatial profile of the laser pulse was degraded when adding more plates. The FTL pulse duration (FWHM) of the broadened pulses for the cases of 1 plate and 2 plates were 12.7 fs and 9.6 fs, respectively. With 3 plates, the FTL pulse duration reached the pulse duration of 8.6 fs.
Fig. 2. Spectral broadening after propagating through 0.5-mm fused silica plates: 1 plate (a), 2 plates (b), and 3 plates (c). Measured spectra are shown in solid red lines and simulation results in dashed black lines. The gray area is the input laser spectrum.
The spectral broadening was simulated using the Python nonlinear optics package (PyNLO) [28]. In the simulation, GDD, third order dispersion (TOD), self-phase modulation, self-steepening, and delayed Raman response were taken into account, along with the transmittance of uncoated fused silica plates. The values of GDD, TOD, and the nonlinear refractive index n2 used in the calculation were 35.8 fs2/mm, 27.6 fs3/mm, and 2.4×10−7 cm2/GW [29,30], respectively. The values for the Raman response were taken from Ref. [31]. The simulated spectra showed good agreement with the measured results, as shown in Fig. 2. The spectral broadening was mainly caused by the SPM that broadens the spectrum symmetrically in the frequency domain. Since self-steepening and delayed Raman responses cause asymmetric broadening, the simulation results matched the experimental results when all three nonlinear effects were included.
In order to reduce the reflection loss, the spectral broadening through a single fused silica plate with 1.5 mm thickness, instead of 3 fused silica plates, was examined. Since the energy loss by the surface reflection of the three uncoated plates reduced the transmission efficiency, a single plate with the same total thickness may improve the spectral broadening. The output spectrum of the pulse with the 1.5 mm fused silica plate is presented in Fig. 3(a). The B-integral induced in the plate was 8.0. The spectrum increased in the long wavelength region over 900 nm, leading to the reduction of FTL duration from 8.6 fs to 8.3 fs. With the measured spectral phase for the pulse, the pulse duration is 8.5 fs (FWHM), as shown in Fig. 3(b). This laser pulse was compressed with four chirped mirrors. And the residual GDD of the laser pulse was removed by inserting two thin fused silica plates with 360-um thickness before the SPIDER. For the estimation of peak-power enhancement, the post-compression process should be carefully analyzed for the full beam, as the compressed pulse duration varies spatially depending on local laser intensity.
Fig. 3. (a) Broadened laser spectrum obtained from the experiment (solid line) and the simulation (dashed line) after propagating through a 1.5 mm fused silica plate. The gray area shows the input laser spectrum. (b) Temporal profiles of a post-compressed pulse (solid line) and input pulse (dashed line) measured by the SPIDER.
3.2. Spatial characteristics of a spectrally broadened pulse
The spatial beam quality is a critical factor in performing post-compression of an ultrahigh power laser. As spatial nonuniformity is enhanced while going through a nonlinear process, the use of a smooth flat-top beam profile is necessary for the spectral broadening process. In order to improve the spatial beam uniformity, the input beam was smoothened by installing a set of vacuum spatial filters before the compressor. The input laser beam profiles, measured through an imaging system without the fused silica plate, are shown in Figs. 4(a) and (b) taken with and without the spatial filter, respectively. The white circles in Figs. 4(a) and 4(b) show the high intensity regions. After the spatial filtering, the highest intensity peak in the central circle was removed, as shown in Fig. 4(b). The beam profiles with and without the spatial filtering, measured after the fused silica plate, are shown in Figs. 4(c) and (d), respectively. The output beam profile shows the improved spatial uniformity after the spatial filtering.
Fig. 4. Spatial characteristics of post-compressed laser pulses measured after going through a 1.5-mm fused silica plate. The beam profiles with and without (w/o) the spatial filtering are compared: input beam profiles (a) without and (b) with the spatial filtering, and output beam profiles (c) without and (d) with the spatial filtering. The dotted lines in (c) and (d) connect the fluence peaks inside the two circles containing the highest fluence areas. Evolution of the output beam profile along the dashed line in (c) and (d) with respect to the laser propagation (e) without and (f) with the spatial filtering, respectively. The peak fluence of the output beam with spatial filtering is set to unity at the fused silica plate. All beam profiles were measured through an imaging system. (g): Evolution of standard deviation of the lineout intensity with propagation for those shown in (e) and (f). The standard deviation was calculated for the central 80% of the lineout profile.
The effect of the spatial filtering was further examined for the laser beam profile with respect to the propagation after the post-compression. The evolution of the beam profile with the laser propagation was measured, as shown in Figs. 4(e) and (f) for the output beam without and with the spatial filtering, respectively. Here the lineout profiles of the fluence were taken along the dotted lines in Figs. 4(c) and (d). Figure 4(e) shows that the fluence spikes existing in the unfiltered case grow about two times after the propagation of about 10 m. On the other hand, in the case of the spatial filtering, the fluence in the beam center increases by 15% and the modulation is significantly reduced, as shown in Fig. 4(f). For the comparison of the beam profile modulation during propagation for the two cases, the standard deviations were calculated, as shown in Fig. 4(g), in which the blue dashed line and the red dashed line represent the output beam without (Fig. 4(e)) and with (Fig. 4(f)) the spatial filtering, respectively. After the propagation of about 10 m, the standard deviation for the case with the spatial filtering was two times lower than that of the unfiltered case. Consequently, this spatial filtering could effectively mitigate the damage issue of subsequent optical components by improving the spatial uniformity of the input laser beam.
3.3. Peak-power enhancement after post-compression
The peak-power enhancement by the post-compression can be estimated by measuring space-resolved spectral broadening. As the spectral broadening depends on local laser intensity, the duration of a post-compressed pulse was not uniform. The spectrally resolved beam profile was obtained using a set of 10 nm (FWHM) bandpass filters covering from 650 to 910 nm with 27 filters. The pulse duration map for the FTL case was, then, reconstructed from the spectrally resolved beam profile, as shown in Fig. 5(a). As expected from intensity-dependent spectral broadening, the pulse duration map in Fig. 5(a) resembles the input beam profile in Fig. 4(b). The lineout profile (red line) of the FTL duration in Fig. 5(b), drawn along the dashed line in Fig. 5(a), shows that the profile has a complementary shape to the output beam profile (black line). In Sec.3.1, the FTL pulse duration estimated from the spectrum obtained with the spectrometer of the SPIDER was 8.3 fs. This duration was quite comparable to the FTL duration, 8.4 fs, in Fig. 5(a) averaged over the central half of the beam - the measurement beam area of the SPIDER, which justifies the measurement of the space-resolved spectral broadening using the bandpass filters.
Fig. 5. Spatial characteristics of the spectral broadening after propagating through a 1.5-mm fused silica. (a) Pulse duration map of the FTL pulse reconstructed from the spectrally resolved beam profile. (b) Variation of the FTL pulse duration (red line) and the calculated GDD (blue dotted line) along the dashed line in (a), and the fluence (black line) along the dashed line in Fig. 4(d).
In order to obtain space-resolved pulse duration with a spectral phase, the spectral phase information from the SPIDER measurement was adopted. The pulse duration, 8.5 fs, of post-compressed pulses measured with the SPIDER was very close to the FTL duration, 8.3 fs, indicating the generation of near FTL post-compressed pulses. The theoretical calculation of the spectral broadening in the fused silica plate showed that a small amount of GDD was the major factor contributing to the small deviation from the FTL duration of the post-compressed pulses, as shown with the blue line in Fig. 5(b). The intensity-dependent GDD for 1.5 mm fused silica was computed, using the simulation explained in Sec.3.1, from which the GDD of the central half of the output beam was found to be 69 fs2, close to the GDD of 74 fs2 retrieved from the SPIDER measurement. From the measured spectral broadening with the bandpass filters, the calculated GDD, and measured dispersion by the SPIDER, the pulse duration in the central area was estimated to be 8.6 fs, very close to the SPIDER measurement of 8.5 fs, which validates the GDD calculation. The pulse duration of the full beam was, then, estimated to be 9.7 fs (FWHM). Consequently, considering the beam transmittance, 93%, of the fused silica plate, the peak-power was enhanced by 2.1 times by the post-compression.
4. Conclusion
The pulse shortening by the post-compression using a thin glass plate has been investigated to enhance the peak-power of the 100-TW Ti:Sapphire laser. Through the spectral broadening in a 1.5-mm fused silica plate and the GDD compensation using a set of chirped mirror, the pulse duration of the input beam was shortened from 23 fs to 8.6 fs in the central flat-top area and to 9.7 fs for the whole beam, the shortest pulse duration among 100-TW class lasers. To suppress the self-focusing in a nonlinear medium, a vacuum spatial filter stage with two line focusing optics was installed before the compressor, which effectively prevented hot spot generation. Through the post-compression, the peak-power of the 100 TW Ti:Sapphire laser could be enhanced two times. With another stage of post-compression, the pulse duration would be further shortened to below 5 fs. Such a two-cycle several hundred TW laser would prompt the investigations of carrier-envelope-phase-sensitive strong field physics, especially laser-driven charged particle acceleration. Furthermore, this post-compression method will be an effective tool in enhancing the power of PW lasers now available in a number of laser institutes around the world.
Funding
Institute for Basic Science (IBS-R012-D1); Gwangju Institute of Science and Technology(Ultrashort Quantum Beam Facility (UQBF) operation program (140011) through Advanced Photonics Research Institute).
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. D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56(3), 219–221 (1985). [CrossRef]
2. C. N. Danson, C. Haefner, J. Bromage, T. Butcher, J.-C. F. Chanteloup, E. A. Chowdhury, A. Galvanauskas, L. A. Gizzi, J. Hein, D. I. Hillier, N. W. Hopps, Y. Kato, E. A. Khazanov, R. Kodama, G. Korn, R. Li, Y. Li, J. Limpert, J. Ma, C. H. Nam, D. Neely, D. Papadopoulos, R. R. Penman, L. Qian, J. J. Rocca, A. A. Shaykin, C. W. Siders, C. Spindloe, S. Szatmári, R. M. G. M. Trines, J. Zhu, P. Zhu, and J. D. Zuegel, “Petawatt and exawatt class lasers worldwide,” High Power Laser Sci. Eng. 7, e54 (2019). [CrossRef]
3. J. W. Yoon, Y. G. Kim, I. W. Choi, J. H. Sung, H. W. Lee, S. K. Lee, and C. H. Nam, “Realization of laser intensity over 1023 W/cm2,” Optica 8(5), 630–635 (2021). [CrossRef]
4. I. J. Kim, K. H. Pae, C. M. Kim, H. T. Kim, J. H. Sung, S. K. Lee, T. J. Yu, I. W. Choi, C.-L. Lee, K. H. Nam, P. V. Nickles, T. M. Jeong, and J. Lee, “Transition of Proton Energy Scaling Using an Ultrathin Target Irradiated by Linearly Polarized Femtosecond Laser Pulses,” Phys. Rev. Lett. 111(16), 165003 (2013). [CrossRef]
5. H. T. Kim, K. H. Pae, H. J. Cha, I. J. Kim, T. J. Yu, J. H. Sung, S. K. Lee, T. M. Jeong, and J. Lee, “Enhancement of Electron Energy to the Multi-GeV Regime by a Dual-Stage Laser-Wakefield Accelerator Pumped by Petawatt Laser Pulses,” Phys. Rev. Lett. 111(16), 165002 (2013). [CrossRef]
6. A. Di Piazza, C. Müller, K. Z. Hatsagortsyan, and C. H. Keitel, “Extremely high-intensity laser interactions with fundamental quantum systems,” Rev. of Mod. Phys. 84(3), 1177–1228 (2012). [CrossRef]
7. A. Fisher, P. L. Kelley, T. K. Gustafson, and T. K. Gustajson, “Subpicosecond Pulse Generation Using The Optical Kerr Effect,” Appl. Phys. Lett. 14(4), 140–143 (1969). [CrossRef]
8. A. Laubereau, “External Frequency Modulation and Compression of Picosecond Pulses,” Phys. Lett. 29(9), 539–540 (1969). [CrossRef]
9. H. Nakatsuka, D. Grischkowsky, and A. C. Balant, “Nonlinear Picosecond-Pulse Propagation Through Optical Fibers with Positive Group Velocity Dispersion,” Phys. Rev. Lett. 47(13), 910–913 (1981). [CrossRef]
10. C. V. Shank, R. L. Fork, R. Yen, and H. Stolen, “Compression of femtosecond optical pulses,” Appl. Phys. Lett. 40(9), 761–763 (1982). [CrossRef]
11. W. H. Knox, R. L. Fork, M. C. Downer, R. H. Stolen, C. V. Shank, and J. A. Valdmanis, “Optical pulse compression to 8 fs at a 5kHz repetition rate,” Appl. Phys. Lett. 46(12), 1120–1121 (1985). [CrossRef]
12. M. Nisoli, S. De Silvestri, and O. Svelto, “Generation of high energy 10 fs pulses by a new pulse compression technique,” Appl. Phys. Lett. 68(20), 2793–2795 (1996). [CrossRef]
13. B. Schenkel, J. Biegert, and U. Keller, “Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum,” Opt. Lett. 28(20), 1987–1989 (2003). [CrossRef]
14. O. Hort, A. Dubrouil, C. Amelie, S. Petit, E. Mevel, D. Descamps, and E. Constant, “Postcompression of high-energy terawatt-level femtosecond pulses and application to high-order harmonic generation,” J. Opt. Soc. Am. B 32(6), 1055–1062 (2015). [CrossRef]
15. C. Rolland and P. B. Corkum, “Compression of high-power optical pulses,” J. Opt. Soc. Am. B 5(3), 641 (1988). [CrossRef]
16. C.-H. Lu, Y.-J. Tsou, H.-Y. Chen, B.-H. Chen, Y.-C. Cheng, S.-D. Yang, M.-C. Chen, C.-C. Hsu, and A. H. Kung, “Generation of intense supercontinuum in condensed media,” Optica 1(6), 400–406 (2014). [CrossRef]
17. J. Schulte, T. Sartorius, J. Weitenberg, A. Vernaleken, and P. Russbueldt, “Nonlinear pulse compression in a multi-pass cell,” Opt. Lett. 41(19), 4511–4514 (2016). [CrossRef]
18. T. Nagy, M. Kretschmar, M. J. J. Vrakking, and A. Rouzée, “Generation of above-terawatt 1.5-cycle visible pulses at 1 kHz by post-compression in a hollow fiber,” Opt. Lett. 45(12), 3313–3316 (2020). [CrossRef]
19. M. Ouillé, A. Vernier, F. Böhle, M. Bocoum, A. Jullien, M. Lozano, J.-P. Rousseau, Z. Cheng, D. Gustas, A. Blumenstein, P. Simon, S. Haessler, J. Faure, T. Nagy, and R. Lopez-Martens, “Relativistic-intensity near-single-cycle light waveforms at kHz repetition rate,” Light Sci. Appl. 9(1), 47 (2020). [CrossRef]
20. T. Nagy, P. Simon, and L. Veisz, “High-energy few-cycle pulses: post-compression techniques,” Adv. Phys. X 6, 1845795 (2021). [CrossRef]
21. 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]
22. V. Ginzburg, I. Yakovlev, A. Kochetkov, A. Kuzmin, S. Mironov, I. Shaikin, A. Shaykin, and E. Khazanov, “11 fs, 1.5 PW laser with nonlinear pulse compression,” Opt. Express 29(18), 28297–28306 (2021). [CrossRef]
23. G. Mourou, S. Mironov, E. Khazanov, and A. Sergeev, “Single cycle thin film compressor opening the door to Zeptosecond-Exawatt physics,” Eur. Phys. J. Spec. Top. 223(6), 1181–1188 (2014). [CrossRef]
24. A. Shaykin, V. Ginzburg, I. Yakovlev, A. Kochetkov, A. Kuzmin, S. Mironov, I. Shaikin, S. Stukachev, V. Lozhkarev, A. Prokhorov, and E. Khazanov, “Use of KDP crystal as a Kerr nonlinear medium for compressing PW laser pulses down to 10 fs,” High Power Laser Sci. Eng. 9, e54 (2021). [CrossRef]
25. S. Y. Mironov, S. Fourmaux, P. Lassonde, V. N. Ginzburg, S. Payeur, J.-C. Kieffer, E. A. Khazanov, and G. Mourou, “Thin plate compression of a sub-petawatt Ti:Sa laser pulses,” Appl. Phys. Lett. 116(24), 241101 (2020). [CrossRef]
26. J. H. Sung, J. W. Yoon, I. W. Choi, S. K. Lee, H. W. Lee, J. M. Yang, Y. G. Kim, and C. H. Nam, “5-Hz, 150-TW Ti:sapphire Laser with High Spatiotemporal Quality,” J. Korean Phys. Soc. 77(3), 223–228 (2020). [CrossRef]
27. H. Xiong, T. Yu, F. Gao, X. Zhang, and X. Yuan, “Filtering characteristics of a three-lens slit spatial filter for high-power lasers,” Opt. Lett. 42(22), 4593–4595 (2017). [CrossRef]
28. G. Ycas, D. Maser, and D. Hickstein, “Pynlo: Nonlinear optics modelling for python,” (2015), https://pynlo.readthedocs.io/en/latest/.
29. I. H. Malitson, “Interspecimen Comparison of the Refractive Index of Fused Silica,” J. Opt. Soc. Am. 55(10), 1205–1209 (1965). [CrossRef]
30. D. Milam, “Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica,” Appl. Opt. 37(3), 546–550 (1998). [CrossRef]
31. Q. Lin and G. P. Agrawal, “Raman response function for silica fibers,” Opt. Lett. 31(21), 3086–3088 (2006). [CrossRef]
