Open Access
Add to BibSonomy
Abstract
Raman dissipative solitons (RDS) have been investigated numerically. It was found that the area of stable generation is bounded in terms of pump spectral bandwidth and pulse energy. Existing optimum is strongly affected by the net cavity dispersion. The spectral bandwidth of the generated RDS linearly depends on its energy and reaches more than 50 nm in the 5-meters long cavity. Developed numerical model reproduces all the effects observed experimentally. It predicts ability to generate high-quality pulses with energy up to 6 nJ compressible down to ∼100 fs duration. The work shows that RDS generation technique can produce high-energy ultrashort pulses at wavelengths not covered by typical active mediums.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Nowadays laser sources generating ultrashort pulses with central wavelength outside the gain bandwidths of the commercially available active mediums are highly demanded. Such devices are important for range of applications including multiphoton microscopy and bio-imaging techniques inasmuch as depth of penetration into living tissues is strongly depended on the wavelength. One of the most interesting spectral region is located near 1.3 µm, so-called water transparency window, where the effective attenuation coefficient has a local minimum.
Direct generation in bismuth-doped phosphosilicate fiber becomes possible just recently together with nonlinear conversion techniques. All-fiber femtosecond laser mode-locked by nonlinear loop mirror and operated at 1.3 µm was demonstrated in [1], showing 1.65 nJ pulse energy and 530 fs duration after compression. A bismuth-doped fibre amplifier allowed energy increase up to 8.3 nJ in the same work. Next, the same authors reported about stable self-starting generation of dissipative solitons in the laser cavity with single-walled carbon nanotubes as a saturable absorber [2]. However in this case only 117 pJ per pulse was obtained. The use of bismuth-doped fibers is surely one of the most perspective methods of generating ultrashort pulses at non-standard wavelengths, but despite the fact that they begun to be developed more than ten years ago [3], they still remain the subject of active research by itself [4]. Therefore, up to date researching efforts in any direction are important for facilitating multiphoton deep-tissue imaging or other related applications.
Significant progress in case of nonlinear frequency conversion techniques is connected with using almost unlimited pumps and variety of optical to achieve record pulse energies [5]. One of the most exciting results were obtained using a novel phenomenon of soliton self-mode conversion (SSMC) [6]. In fact, the authors discovered the new manifestation of Raman scattering of ultrashort pulses that is power scalable while yielding pure spatially coherent beams. The phenomenon is wavelength independent and limited only by available pump power. Thus, 74-fs long pulses with energy of 80 nJ were obtained at 1317 nm. Slightly less but still outstanding results were presented in [7]. The authors utilize self-phase modulation (SPM) effect to broaden initial spectrum centered at 1550 nm so that it reaches 1.3 µm. Next, an optical bandpass filter was used to select a narrowband part of the spectrum supporting 300-fs pulses. Such technique allows to obtain 16-nJ pulse energy experimentally and promises more than 100 nJ energy in the case of 1-µJ pumping.
Considerable efforts are also focused on building relatively low-cost and stable laser sources. Such sources are important for practical applications as could be used outside the optical labs. A progress here is also significant and employs diversity of approaches. One of them consists of generation of ultrashort pulses, called Raman dissipative solitons (RDS), at new wavelengths via stimulated Raman scattering (SRS) in the standard germanium-doped fibers [8,9], in the diamond crystal [10] and in the phosphosilicate ($\textrm {P}_{2}\textrm {O}_{5}$) fiber with the 39 THz Stokes shift [11,12]. In the case of external Raman cavity only exact matching between RDS and pump repetition rates is necessary. Consequently, net cavity dispersion together with the pump pulse energy, duration and spectral width could be adjusted independently, moreover different cavity designs are possible. For example, the last pump amplification stage can be placed inside the cavity [13]. As a result up to 10 nJ has been obtained for the pulses with 317-fs duration. Another approach is an optical parametric chirped-pulse amplification of pulses obtained by SPM broadening [14]. This case gives about 20 nJ per pulse at 1308 nm in all-fiber scheme with the duration after external compression of 306 fs.
In this work we study an external-cavity generation of compressible highly-chirped pulses near 1.3 µm in all-fiber scheme using a new type of $\textrm {P}_{2}\textrm {O}_{5}$ polarization maintaining (PM) fiber (FORC, Moscow). Existing freedom in the input parameters gives rise to the problem of their complex optimization and discovers another point of view on dissipative soliton generation. To solve it, we built a numerical model based on our previous work [15], which involves Raman response function of phosphosilicate fiber [16]. The considered spectral window is extremely large: from 700 nm to 2000 nm, so the influence of high-order Stokes has been taken into account. The corresponding dispersion curve has been obtained by fitting experimentally measured points near 1, 1.3 and 1.55 µm. All this allowed us not only to achieve agreement between the existing experimental data and simulation results, but also to make predictions about attainable absolute maximum ratings of the generated pulses. To the best of our knowledge such a detailed investigation was performed for the first time.
2. Basic relations for numerical simulation
Numerical simulation is based on the experimental results obtained in our previous work [12]. The laser cavity consists of 10 meters long PM $\textrm {P}_{2}\textrm {O}_{5}$ fiber, filtered wavelength division multiplexer (WDM, 1064/1120 nm) with a broad transmission spectrum, fiber coupler with 20% out at 1300 nm and an additional section of dispersion shifted (DSF) fiber to adjust the length. Here we start from the case of 30-meters long cavity as it offers relatively high energy level (up to 2 nJ) and large bandwidth (up to 25 nm) of the generated pulses. To achieve RDS generation in simulation we found round-trip delay first, propagating two coinciding in time pulses at pump and signal wavelengths through the cavity. Next we varied the obtained delay with 100 fs step and checked whether the selected value leads to the maximal RDS energy. The main characteristics of the pump pulses — temporal duration, spectral bandwidth and energy, are considered as optimization parameters. In the experiment we use an all-fiber highly-chirped dissipative soliton (DS) oscillator with the fiber stretcher and pre-amplifier to pump the external cavity. This laser system produces pulses with duration of ${\sim }$50 ps and energy level of ${\sim }$15 nJ. In simulation highly-chirped pump pulses with characteristic rectangular spectra were modelled as chirped super-gaussian pulses with the degree of edge sharpness $m = 4$. To model pulse propagation in $\textrm {P}_{2}\textrm {O}_{5}$ fiber we used generalized Nonlinear Schr$\ddot {o}$dinger equation, where the Raman response function was derived from the Raman gain spectrum according to relation from [17]:
where $s=t-t^{'}$ - time delay, $\Omega$ - frequency, $N_2^{''}(\Omega )$ - imaginary part of third-order susceptibility, which is proportional to the Raman gain. The approximate numerical Raman gain spectrum, shown in Fig. 1(a) (blue line), agrees well with the typical experimentally measured gain spectrum of the $\textrm {P}_{2}\textrm {O}_{5}$ fiber [18]. Black line in the same figure shows the Raman gain spectrum of standard fiber. At pump input all the spectral components at the wavelength above 1180 nm were shifted by 50-90 ps in time domain (depending on the cavity length) in order to compensate the delay of the pump pulse relative to the RDS. Special attention was paid to measuring and approximation of dispersion curve of $\textrm {P}_{2}\textrm {O}_{5}$ fiber. Group velocity dispersion (GVD) was measured at 1050 nm and 1550 nm by white light interferometry technique [19] ($\beta _2 = 25~\textrm {ps}^2/\textrm {km}$ and $-4~\textrm {ps}^2/\textrm {km}$ correspondingly). The GVD value at 1275 nm equaled to $12~\textrm {ps}^2/\textrm {km}$ was derived from direct measurement of time delay between pump pulse and RDS in the piece of fiber ($dt = 4.6 \pm 0.5~\textrm {ps}/\textrm {m}$) and corresponds to our previous estimation [11]. The dispersion curve in the whole spectral range, shown in Fig. 1(b), was obtained from second-order polynomial interpolation based on the three measured points. The dispersion coefficients calculated at 1090 nm are $\beta _2 = 22.56~\textrm {ps}^2/\textrm {km}$, $\beta _3 = 2.56\cdot 10^{-2}\textrm {ps}^3/\textrm {km}$ , $\beta _4 = -1.28\cdot 10^{-4}~\textrm {ps}^4/\textrm {km}$. For the sake of further simplicity we use this dispersion curve for both $\textrm {P}_{2}\textrm {O}_{5}$ and DSF fiber types. The spectral window considered in the model was extremely large: from 680 nm to 2700 nm. The temporal window was equal to 800 ps.
Fig. 1. Calculated Raman gain spectrum (a) and dispersion curve (b) of $\textrm {P}_{2}\textrm {O}_{5}$ fiber.
3. Results and discussion
At the first stage we performed numerical simulations of signal propagation inside the 30-meters long fiber cavity, supposing unlimited pump energy and 13-nm pump bandwidth. Calculated optical spectra of the output signal together with the experimental ones [12] are presented in Fig. 2. The spectral position of the generated RDSs and their energies are very close in the experiment and simulation. Here we also reproduced the SRS-induced upper limit for the RDS energy, which is about 2 nJ and corresponds to 7-10 nJ intracavity energy. This value is lower than what we observed earlier for highly-chirped DS generation at 1030 nm [20], which could be explained by two times lower GVD at 1275 nm. A tilt in the top of the RDS spectra is also well reproduced and could be explained by the influence of third-order dispersion. The intensity of the residual pump pulse in the simulation is greater than in the experiment due to the losses on the coupler, which were not optimized for 1093 nm. Such losses are not taken into account in the simulation as they do not affect RDS formation.
Fig. 2. Optical spectrum evolution of the generated RDS’s with increasing energy in experiment (a) and simulation (b).
One more practically important question, besides the SRS threshold, is the length of interaction between the pump pulse and RDS. This interaction length is clearly seen in Fig. 3(a), depicting intracavity dynamics in time domain. In our case it does not exceed 15 meters. So, a 10-meters length of $\textrm {P}_{2}\textrm {O}_{5}$ fiber used in the experiment is close to the optimal one. It is worth noting, however, that the $\textrm {P}_{2}\textrm {O}_{5}$ fiber length as short as 40 cm is suitable in the case of 5-ps pump pulse duration [13]. Evolution of the spectral profile (Fig. 3(b)) shows a low amplitude of second-order phosphorous related peak (in 1.5 µm region) and anti-Stokes pulses at 950 nm that are clearly seen in time domain. The last one is also observed in [13]. Pump bandwidth increase leads to growing of additional anti-Stokes peak at 1240 nm, generating from RDS at 1275 nm. However, we do not observe any peaks in the experiment. We can explain this by losses in WDM and coupler, which are not designed to work at 1550 nm. For this reason, additional short-pass filter was used in simulation to block wavelengths above 1450 nm and avoid influence of second-order Raman scattering.
Fig. 3. Calculated intracavity dynamics of the temporal pulse shape (left) and optical spectrum (right), corresponding to 7.7 nJ pump energy and 13-nm bandwidth. The cavity consists of 10 m $\textrm {P}_{2}\textrm {O}_{5}$ and 20 m standard fiber with the same dispersion curve.
The main goal of simulation is finding the way to achieve absolute maximum of RDS energy and its spectral bandwidth. We can not increase the pump energy unlimitedly because it leads to noise-like pulse generation. However a pump spectral width could be another degree of freedom affecting RDS generation. As a result, we built the areas of stable RDS generation in the plane of pump parameters for different lengths of external cavity (see Fig. 4). The color represents the energy of the generated pulse. Note, that the length of $\textrm {P}_{2}\textrm {O}_{5}$ fiber was equal to 10 meters according to the experiment (with the exclusion of the shortest 5-meters long cavity). First of all, simulations shows quite limited area of stable regime existence. The energy grows with the pump power increase but is limited by SRS threshold, which is lower in the long cavity (Fig. 4(a)). The 15-meters long cavity emits RDS with the maximum energy among all the cavities comprised of 10-meters $\textrm {P}_{2}\textrm {O}_{5}$. The fact is that noisy Raman pulse acts not only as an additional channel of the energy dissipation destroying DS, but on the contrary can support it resulting in formation of a complex of the bound DS and Raman pulse of comparable energy and duration [15]. Raman pulse stabilizes the DS via temporal-spectral filtering. In the 30-meters cavity decrease of the Raman threshold results in energy dissipation and corresponding decrease of the RDS energy. At the same time, the area of stable RDS generation is the largest among the cavities with 10 m $\textrm {P}_{2}\textrm {O}_{5}$ fiber. This is a result of spectral filtration induced by the noisy Raman pulse. In the 15-meters cavity Raman pulse still acts as a filter, while the Raman threshold increases, leading to energy increase. In the 10-meters cavity the amplitude of the Raman pulse is lower and it does not act as a filter, stabilizing the RDS. Another characteristic is the presence of some trends — the RDS energy is almost constant in the direction from the left bottom to the right upper corners of the figures. If the pump pulse has a fixed duration of 30 ps, growing of its spectral bandwidth (Y-axis) corresponds to increase of a chirp parameter. If the chirp increases at a fixed energy (vertical lines) the spectral power density decreases. So, to keep it constant we have to increase the energy as well. More interesting is the position of the energy maximum. It is located in the confined area of the pump parameters and further pump bandwidth increase does not help to extend this area (Fig. 4(b)).
Fig. 4. Calculated areas of stable RDS generation in the 30-m (a), 15-m (b), 10-m (c) long cavities comprised of 10-m $\textrm {P}_{2}\textrm {O}_{5}$ fiber and standard fiber with the same dispersion curve. Case (d) corresponds to 5-m long $\textrm {P}_{2}\textrm {O}_{5}$ cavity. Color shows the RDS energy.
To analyze the maximum attainable energy and optical spectrum width of the RDS, which directly determines the minimum duration of the compressed pulse, we depict these key parameters in Fig. 5(a) for all cavity lengths. Different lengths, depicted by points with different colors and shapes, form well separated clouds. Really unexpected is that they have clear linear trend despite the additional degree of freedom. Therefore, the spectral bandwidth of the RDS is strongly determined by its energy and we can not obtain solitons with a high bandwidth and small energy or vice versa. Such behavior also corresponds to the experimental one observed previously [12].
Fig. 5. Optical spectrum width (at the level of ${-}10$ dB) of the generated pulse vs. pulse energy for the all cavity lengths (a) and for the 15-m long with different dispersion curves (b).
Another observation contradicts to the experiment — behavior of the maximum energy and spectral bandwidth when the cavity is shortened. In simulation we could see that the RDS energy level obtained in the 15-meters long cavity is two times higher than the energy obtained in the 30-meter cavity. Further cavity shortening allows to reach more than 6 nJ pulses despite the fact that the length of $\textrm {P}_{2}\textrm {O}_{5}$ fiber was halved. Moreover, the bandwidth is not limited by 25 nm as in the experiment. For the 5-meters long cavity the spectrum reaches 50 nm wide that corresponds to ${\sim }$100 fs duration of the compressed pulse (Fig. 5(a)). Such duration is comparable to the best one obtained to date [6].
To explain this mismatch with the experiment we performed additional calculations for 15-m long cavity. We shifted the dispersion curve of the 5-m long standard fiber in upward and downward direction with a $4~\textrm {ps}^2/\textrm {km}$ step (Fig. 1(b)). Correspondingly, the net cavity dispersion was changed in the range from $-11$ and $+33$%. The results are presented in Fig. 5(b). The case with smaller GVD is more consistent with the experiment. The experimental setup, besides $\textrm {P}_{2}\textrm {O}_{5}$ fiber, includes standard fibers with zero dispersion wavelength around 1310 nm. Additionally, pump spectral bandwidth in the experiment was equal to 13 nm. We marked points corresponding to 13 nm pump bandwidth by crosses in Fig. 5(b). It was found out, that for a fixed bandwidth even 20% difference of the net dispersion results in one and half times drop of the RDS energy (the distance between the dashed vertical lines in the same figure). This is exactly what we observe in the experiment when shortening of the cavity results in dramatic decrease of RDS energy. In the same time, GVD increase leads to growing of the maximum energy due to increase of SRS threshold [20]. However, further energy growth should be limited even in the simulation. The germanium related scattering occurs in the $\textrm {P}_{2}\textrm {O}_{5}$ fiber as well as in the standard fiber (see Fig. 1(a)) and the dispersion of $\textrm {P}_{2}\textrm {O}_{5}$ fiber can not be also increased as it leads to smaller pulse interaction length and decrease of the amplification efficiency. Nevertheless, in terms of achievement high-energy ultrashort pulses at 1.3 µm the potential of dispersion managing is much higher than the potential of the cavity lengthening limited by SRS effect.
4. Conclusion
We have investigated RDS generation via stimulated Raman scattering in the $\textrm {P}_{2}\textrm {O}_{5}$ external fiber cavity numerically and perform a detailed comparison with the experimental data. Developed numerical model reproduces all the observed effects and demonstrates good quantity agreement. Assuming "unlimited" pump parameters when its spectral bandwidth and pulse energy are independent, the maximal RDS energy grows up to 6 nJ. The spectral bandwidth of the generated RDS is linearly dependent on its energy and reaches more than 50 nm that corresponds to $\sim$100 fs duration of the compressed pulse. It has been shown that deviations of the net dispersion affect achievable RDS energy dramatically — GVD decrease in the 15-m cavity leads to drop in the maximal energy. It is important to note that the area of stable RDS generation is bounded, so the found parameters are the absolute maximum ratings for RDS generation in such scheme with investigated type of fiber. Nevertheless, the demonstrated ratio of energy and pulse duration should already be enough for series of biological experiments, while further investigation and amplification can expand the scope of applications significantly.
Funding
Russian Science Foundation (17-71-20082); Russian Foundation for Basic Research (18-32-00409); State budget of the Russian Federation (AAAAA17-117062110026-3).
Acknowledgment
The authors contribute to this work as follows: A.E.B. - numerical modelling (RSF); D.S.Kh. and I.Zh. - experiment (RFBR); E.V.P. and S.A.B. - discussions and writing the article (IAE project)
Disclosures
The authors declare no conflicts of interest.
References
1. A. M. Khegai, F. V. Afanas’ev, K. E. Riumkin, S. V. Firstov, V. F. Khopin, D. V. Myasnikov, M. A. Mel’kumov, and E. M. Dianov, “Picosecond 1.3-µm bismuth fibre laser mode-locked by a nonlinear loop mirror,” Quantum Electron. 46(12), 1077–1081 (2016). [CrossRef]
2. A. Khegai, M. Melkumov, S. Firstov, K. Riumkin, Y. Gladush, S. Alyshev, A. Lobanov, V. Khopin, F. Afanasiev, A. G. Nasibulin, and E. Dianov, “Bismuth-doped fiber laser at 1.32 µm mode-locked by single-walled carbon nanotubes,” Opt. Express 26(18), 23911 (2018). [CrossRef]
3. E. M. Dianov, S. V. Firstov, V. F. Khopin, A. N. Gur’yanov, and I. A. Bufetov, “Bi-doped fibre lasers and amplifiers emitting in a spectral region of 1.3 µm,” Quantum Electron. 38(7), 615–617 (2008). [CrossRef]
4. S. V. Firstov, S. V. Alyshev, K. E. Riumkin, A. M. Khegai, A. V. Kharakhordin, M. A. Melkumov, and E. M. Dianov, “Laser-Active Fibers Doped with Bismuth for a Wavelength Region of 1.6-1.8 µm,” IEEE J. Sel. Top. Quantum Electron. 24(5), 1–15 (2018). [CrossRef]
5. L. Rishøj, G. Prabhakar, J. Demas, and S. Ramachandran, “30 nJ, ˜50 fs All-Fiber Source at 1300 nm using Soliton Shifting in LMA HOM Fiber,” in Conf. Lasers Electro-Optics, (OSA, Washington, D.C., 2016), p. STh3O.3.
6. L. Rishøj, B. Tai, P. Kristensen, and S. Ramachandran, “Soliton self-mode conversion: revisiting Raman scattering of ultrashort pulses,” Optica 6(3), 304 (2019). [CrossRef]
7. H.-Y. Chung, W. Liu, Q. Cao, L. Song, F. X. Kärtner, and G. Chang, “Megawatt peak power tunable femtosecond source based on self-phase modulation enabled spectral selection,” Opt. Express 26(3), 3684 (2018). [CrossRef]
8. S. A. Babin, E. V. Podivilov, D. S. Kharenko, A. E. Bednyakova, M. P. Fedoruk, V. L. Kalashnikov, and A. A. Apolonski, “Multicolour nonlinearly bound chirped dissipative solitons,” Nat. Commun. 5(1), 4653 (2014). [CrossRef]
9. D. Churin, J. Olson, R. A. Norwood, N. Peyghambarian, and K. Kieu, “High-power synchronously pumped femtosecond Raman fiber laser,” Opt. Lett. 40(11), 2529 (2015). [CrossRef]
10. J. Lin and D. J. Spence, “25.5 fs dissipative soliton diamond Raman laser,” Opt. Lett. 41(8), 1861 (2016). [CrossRef]
11. D. S. Kharenko, V. D. Efremov, E. A. Evmenova, and S. A. Babin, “Generation of Raman dissipative solitons near 1.3 microns in a phosphosilicate-fiber cavity,” Opt. Express 26(12), 15084 (2018). [CrossRef]
12. D. S. Kharenko, V. D. Efremov, and S. A. Babin, “Study on harmonic generation regimes of Raman dissipative solitons in an external fibre cavity in a spectral region of 1.3 µm,” Quantum Electron. 49(7), 657–660 (2019). [CrossRef]
13. O. Batjargal, Y.-H. Ou, K. Keikens, J. K. Barton, and K. Kieu, “All-Fiber Dissipative Soliton Raman Laser Based on Phosphosilicate Fiber,” IEEE Photonics Technol. Lett. 30(21), 1846–1849 (2018). [CrossRef]
14. Y. Qin, Y.-H. Ou, B. Cromey, O. Batjargal, J. K. Barton, and K. Kieu, “Watt-level all-fiber optical parametric chirped-pulse amplifier working at 1300 nm,” Opt. Lett. 44(14), 3422 (2019). [CrossRef]
15. A. E. Bednyakova, S. A. Babin, D. S. Kharenko, E. V. Podivilov, M. P. Fedoruk, V. L. Kalashnikov, and A. Apolonski, “Evolution of dissipative solitons in a fiber laser oscillator in the presence of strong Raman scattering,” Opt. Express 21(18), 20556–20564 (2013). [CrossRef]
16. G. Salceda-Delgado, A. Martinez-Rios, B. Ilan, and D. Monzon-Hernandez, “Raman response function and Raman fraction of phosphosilicate fibers,” Opt. Quantum Electron. 44(14), 657–671 (2012). [CrossRef]
17. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, “Raman response function of silica-core fibers,” J. Opt. Soc. Am. B 6(6), 1159–1166 (1989). [CrossRef]
18. FORC-Photonics, “Phosphorus doped fiber PDF-5/125,”.
19. J. Y. Lee and D. Y. Kim, “Versatile chromatic dispersion measurement of a single mode fiber using spectral white light interferometry,” Opt. Express 14(24), 11608–11615 (2006). [CrossRef]
20. D. S. Kharenko, E. V. Podivilov, A. A. Apolonski, and S. A. Babin, “20 nJ 200 fs all-fiber highly-chirped dissipative soliton oscillator,” Opt. Lett. 37(19), 4104–4106 (2012). [CrossRef]
