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Abstract
Nonlinear optical gain modulation (NOGM) in a Raman fiber amplifier is numerically simulated with the generalized nonlinear Schrödinger equation. In the NOGM setup, a single frequency continuous wave seed laser is gain modulated into femtosecond pulses by an ultrafast pump, which can induce strong stimulated Raman scattering in a piece of single mode optical fiber. Different parameters regarding seed, pump and nonlinear gain medium (Raman fiber) are investigated in detail to find the best condition for higher Raman conversion efficiency. Simulated results reveal that the walk-off between pump and Raman pulses due to dispersion is one of the most important factors affecting the NOGM pulse’s performance. Only when the speed of walk-off matches with the one of Raman conversion process can the conversion efficiency be optimized. This work offers a guild-line for the design of a fiber-based NOGM laser, which is able to produce wavelength-agile, femtosecond laser pulses with µJ-level pulse energy under more than 85% efficiency.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In the past two decades, ultrafast lasers have been widely explored for their numerous applications in fundamental research, biomedicine and industrial processing [1–3]. Many approaches have been developed to generate ultrafast pulses including mode-locking [4–6], Kerr-microresonators [7,8] and external modulation of continuous wave (CW) laser. In terms of the external modulation technique, it can be divided into electrical gain modulation [9,10], electro-optic (EO) modulation [11,12] and nonlinear optical gain modulation (NOGM) [13–16]. NOGM is a method to transform CW laser into femtosecond-scale pulses by nonlinear optical effect. Compared with other external modulation techniques, NOGM can generate highly coherent, wavelength-agile femtosecond pulses with high pulse energy and optical conversion efficiency.
The principle of NOGM is to utilize optical pulses as the pump to amplify and reshape a single frequency CW seed laser through a nonlinear optical gain medium (e.g., a piece of optical fiber [13,14] or a nonlinear crystal [15,16]). The pump pulses which have high peak power can offer strong nonlinear gain (either χ(2) or χ(3), e.g., optical parameter amplifier (OPA) or stimulated Raman scattering (SRS)) so that the CW laser can be modulated into pulses inside the nonlinear optical gain medium. In previous works [13], we experimentally verified the feasibility of a fiber-based NOGM by utilizing SRS to offer nonlinear optical gain through a piece of optical fiber. In the demonstration, 26 nJ Raman pulses at 1120 nm were generated under 37 nJ pump pulses with an optical conversion efficiency of 70% through a piece of 5-meter-long conventional passive fiber. Some preliminary simulations were performed under µJ-level pump pulse energy, which gave 0.7 µJ and 188 fs Raman pulses, showing better characteristics with higher pump pulse energy. In another demonstration [16], researchers generated mid-infrared ultrafast pulses by using OPA to offer nonlinear optical gain. Pulses with above 200 mW average power and 84 fs duration centered at 3.45 µm were obtained with a conversion efficiency of 27% through a MgO-doped periodically poled lithium niobate (PPLN) crystal. Comparing the two structures, the OPA-modulation setup can directly generate mid-infrared few-cycle pulses, which has critical applications in dual-comb spectroscopy. While the SRS-modulation one is able to generate pulses with more than 80% conversion efficiency in an all-fiber configuration, which has been proved to be a simple, compact, reliable and efficient solution to generate femtosecond pulses with flexible wavelength.
As there exist dispersion and varieties of nonlinear effect in conventional single-mode fiber, complex dynamics processes exist in the fiber-based NOGM. The different group velocities between pump and Raman pulses due to dispersion would result in walk-off. The walk-off effect can have detrimental influences on the generated Raman pulses, such as asymmetrical spectrum, irregular pulse shape and nonlinear chirp accumulation. On the other hand, a proper walk-off effect is helpful to optimize conversion efficiency of Raman pulses by making full use of the pulsed pump on its tails. Therefore, in order to obtain NOGM pulses with higher conversion efficiency, it is necessary to balance various factors by adopting appropriate parameters in the NOGM setup. However, no systematic simulations on fiber-based NOGM have been reported to provide guidance for optimizing experimental results.
In this work, we numerically simulated NOGM in a Raman fiber amplifier under different parameters. Systematical analyses on seed, pump and optical fiber medium are performed to investigate their influences on the NOGM process. The simulations give several insights into the design of a fiber-based NOGM laser. Detailed studies on the pump and Raman pulses evolutions in the NOGM Raman fiber amplifier are useful to optimize the conversion efficiency, which can offer instructions for designing wavelength-agile femtosecond laser sources with high pulse energy and optical conversion efficiency.
2. Numerical model
A numerical model based on the generalized nonlinear Schrödinger equation (GNLSE) is used to simulate the pump and Raman pulse evolutions along the optical fiber through the NOGM process:
The left side of the Eq. (1) builds a model of linear propagation effects, where A is the slowly varying pulse envelope, α is the linear power attenuation, β2 accounts for the group velocity dispersion, z denotes the propagation distance, and T is the pulse local time [17]. While the right side of the Eq. (1) describes nonlinear optical effects including self-phase modulation (SPM), cross-phase modulation (XPM), and SRS. Here γ is the nonlinear coefficient, and R(T) represents the nonlinear response function, which is modeled as
where fR = 0.18 is the fractional contribution of delayed Raman response [18–20] and δ(t) is the Dirac delta function. hR(t) is the oscillator impulse response function, which is given by D. Hollenbeck and C. Cantrell [20]:The NOGM process is simulated by solving the GNLSE with the fourth-order Runge-Kutta method, which has been used to simulate supercontinuum generation and synchronously pumped Raman fiber laser successfully [17,21,22]. The schematic of a NOGM Raman amplifier is shown in Fig. 1(a). A delta function is added in the frequency domain to simulate the single frequency CW seed laser. A white Gaussian noise is added in the temporal domain to simulate the influence of noise, which would contribute to the spontaneous Raman scattering. The average power of the noise is set as 10−9 W, which has been proved to be feasible in previous simulations of the Raman amplified spontaneous emission [23–25]. To accurately estimate the influence of fiber length, the pump pulses are coupled with the seed laser by a wavelength division multiplexer (WDM) at the input of the Raman fiber (z = 0). The pump pulses are gradually converted into Raman pulses through the optical fiber. The fiber with a length of L is equally divided into 200 units and sampled at each unit to observe the temporal and spectral evolution of the pump and Raman pulses along the fiber. The Raman pulses are finally output at the end of the fiber (z = L) accompanied with the residual pump pulses and high-order Raman pulses.
Fig. 1. (a) Schematic of the simulated NOGM configuration. WDM: wavelength division multiplexer; a typical example of (b) pump and (c) Raman pulses evolutions through the optical fiber
A typical numerical simulation result on evolutions of pump and Raman pulses through a piece of 5-meter-long fiber under 100 nJ pump pulse energy, 15 ps pulse duration and 10 mW seed laser power are shown in Fig. 1(b) and (c), to illustrate the pulses’ dynamic during the NOGM process. As the pump pulse propagates through the fiber, the middle part of pump pulse with higher peak power is firstly converted into the Raman pulse, which leaves a M-shaped pulse envelope (at 1.2 m). Afterwards, due to the normal dispersion of silica fiber around 1 µm, the group velocity of the generated Raman pulse is faster than that of the pump pulse, which causes temporal walk-off between them. Under this condition, only the leading part of pump pulse, which has not been separated from Raman pulse, kept the conversion process (from 1.2 to 3.7 m). Too strong walk-off effect would make pulse separated from each other before the pump pulse was completely converted into the Raman one, which would suppress the conversion efficiency. On the other hand, if the walk-off effect was too weak, the leading part of the pump pulse could not be fully used to further transfer the energy to the Raman pulse, since the 1st-order Raman pulse would start to convert into the 2nd-order one with longer fiber (after 3.7 m). This would also limit the scale-up of the conversion efficiency. Therefore, there exist a maximum of the conversion efficiency of the generated Raman pulse, and matching the speed of conversion process and the walk-off effect is important to optimize the maximum of the conversion efficiency.
In the following sections, some parameters which would influence the speed of the conversion process or the walk-off effect, including Raman fiber length, seed laser power, pump pulse energy, pump pulse duration and GVD, were investigated to optimize the conversion efficiency. In order to better compare with the experimental results from previous reported NOGM works [13,14], the simulation parameters used in the following sections are selected as shown in Table 1.
Table 1. Parameters used in the simulations
3. Numerical simulations and optimizations
3.1 Raman fiber length
First, the influences of the Raman fiber length are investigated. In this section, we employ chirp-free Gaussian pulses with 100 nJ pump pulse energy and 15 ps pulse duration as the pump pulses, and a 10-mW single frequency CW laser as the seed laser.
The evolutions of the conversion efficiency of 1st-order and 2nd-order Raman pulses along the Raman fiber is shown in Fig. 2. At the first 1 m, the conversion process was not obvious because the nonlinear gain accumulated from the fiber is not strong enough. Afterwards, the conversion process started and kept a high conversion speed. During the subsequent 1st-order conversion process, the conversion speed was gradually slowed down due to a drop in peak power of the pump pulse. Later, the conversion speed reduced to zero and the conversion efficiency of 1st-order Raman pulses reached a maximum of 82.3% at the length of 3.5 m. After that, the 2nd-order Raman conversion process played a dominant role, when the generated 1st-order Raman pulses were converted to high-order Stokes pulses and thus made the 1st-order Raman conversion efficiency decrease.
Fig. 2. The simulated evolutions of conversion efficiency of 1st-order (blue curve) and 2nd-order (orange curve) Raman pulses along the Raman fiber.
We define the maximum of the optical conversion efficiency as:
where Ep is the energy of input pump pulse and ERmax is the maximum output 1st-order Raman pulse energy achievable at certain fiber length. A higher ηmax represents a better utilization of the pump within NOGM process under the specific condition. For the convenience of understanding, we employ Lc to denote the fiber length required for the Raman pulses to achieve the ηmax, and Lw to express the fiber length at which the Raman pulses are separated from the pump pulses, so that the residual part of the pump pulse is difficult to be converted into the Raman pulse, which has little effect on the conversion efficiency.The temporal pulse shape and chirp of the Raman pulses at the ηmax before compression is shown in Fig. 3(a). The pulse duration is 16.38 ps, which is a little longer than that of the pump pulse. The walk-off effect results in an asymmetrical Raman pulse shape, which is accompanied with nonlinear chirp on both wings of the pulses. Yet, the chirp of the Raman pulse is mainly linear in the middle, indicating that the pulse is compressible to a shorter pulse duration. The pulse envelope and chirp of Raman pulses after compensating for the 2nd-order dispersion are plotted in Fig. 3(b), showing a pulse duration of 240 fs. When pulses propagated through the fiber, the nonlinear chirp accumulated in Raman pulses led to a pedestal on the trailing edge of pulse. After compression, such pedestal will become a temporal modulation on the pulse’s tail, which was also observed in the previous demonstration [18]. A dechirped pulse envelope and chirp of Raman pulses at 3 m and 4 m are plotted in Fig. 3(c) and (d) to make a comparison. As the fiber length increased, the modulation intensity at the trailing edge of the dechirped pulses was stronger, which was caused by a more serious walk-off effect. The spectra of Raman pulses at a fiber length of 3.0 m and 4.0 m are shown in Fig. 3(e) and (f). The spectra were broadened by stronger SPM after propagating through a longer fiber, which allowed the pulses to be compressed to a narrower pulse duration. Therefore, the dechirped pulse duration was shorter with a longer Raman fiber as shown in Fig. 3(b)-(d).
Fig. 3. The pulse envelope and chirp of Raman pulses at 3.5 m with the maximum of the conversion efficiency (a) before and (b) after compression; the pulse envelope and chirp of Raman pulses at (c) 3.0 m and (d) 4.0 m; the spectrum of Raman pulses at (e) 3.0 m and (f) 4.0 m.
The results of this section show that only by selecting proper Raman fiber length can the NOGM laser reach the maximum of the conversion efficiency, and a longer Raman fiber will result in a more serious walk-off, producing a pedestal with stronger modulation in compressed Raman pulses.
3.2 Seed laser power
The results of the Section A show that a longer Lc will lead to serious walk-off effect, which was detrimental to the generated Raman pulses. To weaken the walk-off effect, increasing the seed laser power is a method to accelerate the conversion process. In this section, chirp-free Gaussian pulses with 100 nJ pump pulse energy and 15 ps pulse duration are employed under varieties of seed laser power from 1 µW to 100 mW to study its influence on the NOGM process.
The evolutions of the conversion efficiency along the Raman fiber under different seed laser power are shown in Fig. 4. The conversion process started earlier as the seed laser power increased. Therefore, shorter fiber was required to reach the ηmax, which lightened the walk-off effect. In addition, the 2nd-order Raman conversion process was stronger under a longer Lc, which decreased the value of ηmax of the 1st-order one. The simulations explain that increasing seed laser power can shorten the Lc, which is an effective way to obtain Raman pulses with higher ηmax.
Fig. 4. The evolution of conversion efficiency along the Raman fiber under varieties of the seed laser power from 1 µW to 100 mW.
3.3 Pump pulse energy
Since the gain of SRS in a piece of optical fiber is determined by the intensity of pump light [26], increasing the pump peak power, or the pump pulse energy when the pulse duration is fixed, is another way to accelerate the NOGM process. Therefore, in this section, chirp-free Gaussian pulses with a same pulse duration of 15 ps under varieties of pump pulse energy from 100 to 1000 nJ are employed to develop the evolutions of the ηmax. The seed laser power is set as 10 mW.
The Lc and ηmax with respect to different pump pulse energy are shown in Fig. 5. As pump pulse energy increases, a higher Raman conversion efficiency accelerates the NOGM process, hence shortening the Lc. A highest ηmax of 86.8% could be achieved under 400 nJ pump pulse energy. For the pump pulse energy lower than this, the Lc is longer than the Lw. Therefore, the pulses are separated before the conversion process is completed, which leads to the decrease of ηmax. However, further increase in pump pulse energy leads to a shorter Lc than the Lw. While the leading part of pump pulses would not be properly converted into Raman pulses under this condition, which makes the ηmax decreases. Therefore, Raman pulses with the highest ηmax can be obtained by selecting a proper pump pulse energy to make the Lc matches with the Lw.
Fig. 5. The maximum of the conversion efficiency and the fiber length to reach the maximum of the conversion efficiency with respect to varieties of pump pulse energy from 100 to 1000 nJ.
3.4 Group velocity dispersion
As summarized in the above discussion, matching the Lc with Lw is an important approach to optimize the ηmax. Apart from changing the Lc, one can also adjust Lw by manipulating the pulses’ group velocity. Reducing GVD of the fiber will decrease the velocity difference between pump and Raman pulses, hence directly weaken the walk-off effect and make the Lw longer. In this section, chirp-free Gaussian pulses with 15 ps pump pulse duration under three different pump pulse energy are developed with varieties of GVD from 0.001 to 0.05 ps2·m-1. The seed laser power is set as 10 mW.
The ηmax with respect to GVD is shown in Fig. 6 under three different pump pulse energy. In 100 nJ pump pulse energy case, NOGM process reach a highest ηmax of 86.6% when GVD is set as 0.01 ps2·m-1. For GVD higher than this, the Lw is shorter, so the pulses are separated before conversion process is completed, which leads to the decrease of the ηmax. For GVD lower than this, the walk-off effect has less impact on the conversion process. The two sides of pump pulses with a relatively low peak power are hard to be converted into Raman pulses, which leads to a significant decrease of the ηmax. A detailed analysis on the pulses’ dynamic is discussed in the following paragraph. In 400 nJ case, the ηmax shows a same trend with the 100 nJ case. The highest ηmax of 86.7% is obtained at a GVD of 0.03 ps2·m-1. Higher pump pulse energy results in a shorter Lc. Therefore, a shorter Lw, which can be obtained with larger GVD, is required to match the Lc. In the 1000 nJ case, the ηmax continuously increases as the GVD becomes larger. The highest ηmax will appear at higher GVD with a value over 0.05 ps2·m-1 because a shorter Lc caused by the higher peak power demands a corresponding shorter Lw.
Fig. 6. The maximum of the conversion efficiency with respect to the GVD from 0.001 to 0.05 ps2·m-1 under three kinds of pump pulse energy.
To better understand the significant decrease of ηmax under small GVD, the temporal evolutions of the pump and Raman pulses at 100 nJ pump pulse energy with GVD of 0.001 ps2·m-1 along 10-meter-long Raman fiber are performed, as shown in Fig. 7(a) and (b). The pulse shape and the chirp of the pulse under three typical Raman fiber length (4.0 m, 5.7 m, 7.5 m) are plotted in Fig. 7(c)-(e). At first, the middle part of the pump pulses with the highest peak power is transformed into Raman pulses (Fig. 7(c)). However, under the case of small GVD, the pump and Raman pulses propagate with a nearly identical velocity. Therefore, the leading and lagging parts of the pulse envelope, which have a relatively low peak power, are difficult to be converted into the Raman pulses (Fig. 7(d)). After 7.5 m, as the pulse energy of Raman pulses are getting higher, high-order Raman conversion process appears, showing a similar evolution with the 1st-order conversion process (Fig. 7(e)). The middle part of the 1st-order Raman pulses starts to transform to the 2nd-order one, which limits the increase of the conversion efficiency. The results of the simulation show that the impact of walk-off effect on the NOGM laser could cut both ways. Too long walk-off distance may produce considerable nonlinear chirp and lead to irregular pulse shape and long pulse tailing after compression. However, when there is little walk-off between pump and Raman pulses, the leading part of pump pulses is hard to be transferred into Raman pulses, which eventually results in the decrease of the ηmax.
Fig. 7. The simulated evolutions of (a) pump pulse and (b) Raman pulse; the pulse envelope and chip of pump and Raman pulse at (c) 4.0 m, (d) 5.7 m and (e) 7.5 m under the pulse energy of 100 nJ and the GVD of 0.001 ps2·m-1.
The temporal evolutions of the pump and Raman pulses at 100 nJ pump pulse energy with GVD of 0.01 ps2·m-1 along 5-meter-long Raman fiber are shown in Fig. 8 (a) and (b), to illustrate the situations with the highest ηmax clearly. Compare with the case of 0.001 ps2·m-1 GVD, a larger GVD accelerates the walk-off effect between pump and Raman pulses, which makes more leading part of pump pulses overlap with the Raman pulses. As the growth of Raman pulses is proportional to the product of instantaneous powers of both pump and Stokes pulses [26], the leading part of pump pulses with relatively low peak power start its transformation when it overlaps with the high intensity Raman pulses. The pulse envelope and chirp of pump and Raman pulses at 4.2 m with the highest ηmax of 86.6% are plotted in Fig. 8 (c) and (d). When the leading part of pump pulses completes most of the energy conversion (Fig. 8(c)), the Raman pulses have not begun to transform to a high-order ones (Fig. 8(d)). Therefore, highest ηmax can be obtained at an appropriate GVD.
Fig. 8. The simulated evolutions of (a) pump pulse and (b) Raman pulse; the pulse envelope and chirp of (c) pump and (d) Raman pulses at 4.2 m under the pulse energy of 100 nJ and the GVD of 0.01 ps2·m-1.
The full-width-half-maximum (FWHM) of spectrum and dechirped pulse duration of Raman pulses with respect to GVD under 100 nJ pump pulse energy is plotted in Fig. 9. When the GVD is smaller, the pulse duration of the generated Raman pulses will be shorter, corresponding to a wider spectrum. The wide spectrum is resulted from other nonlinear effect like four-wave-mixing when the GVD is small. Therefore, the dechirped pulse duration can be narrower when GVD reduces.
Fig. 9. The full-width-half-maximum Raman spectrum and the dechirped pulse duration at the maximum of the conversion efficiency with respect to GVD from 0.001 to 0.05 ps2·m-1.
The results of this section illustrate how to adjust the GVD to make Lw match with the Lc in detail, in order to optimize the ηmax. In addition, utilizing the fiber with smaller group velocity difference between pump and Raman pulses is useful to obtain Raman pulses with shorter pulse duration after compression in the sacrifice of some conversion efficiency.
3.5 Pump pulse duration
Apart from the GVD, changing the pump pulse duration is another method to adjust the Lw. In experiments, the pump pulse duration is usually stretched or compressed by manipulating dispersion. The pump pulse energy is fixed in such conditions, which means the peak power changes correspondingly with the pulse duration. Therefore, changing the pump pulse duration would have a comprehensive impact on both Lw and Lc at the same time. In this section, pump pulses with pulse energy of 100 nJ and 1000 nJ under varieties of pulse durations from 5 ps to 50 ps are simulated to develop their influences on ηmax. The seed laser power is set as 10 mW.
Figure 10 shows simulation results of the ηmax with respect to the pump pulse durations from 5 to 50 ps. The ηmax realizes a fast growth with the increasing of the pump pulse duration in the relatively small duration regime. Such positive growth of ηmax is slowed down or even reversed when the pump pulse duration exceeds a certain value. In our understanding, when the pump pulse duration is small, the peak power of pump pulse is strong enough so that the Lc is much shorter than Lw, which leads to an incomplete conversion of the pump pulse like the case shown in the simulations with a small fiber GVD. Increasing the pump pulse duration would result in a lower peak power, and thus makes both Lc and Lw longer at the same time. Yet, the drop of the peak power is significant, which has a strong impact on the Raman process. Therefore, the growth rate of Lc is faster than the one of Lw, which eventually leads to a match between Lc and Lw and thus obtains a highest ηmax. Such fast growth of ηmax in small pump pulse duration regime is more significant in the case of 1000 nJ pump pulse energy than the one of 100 nJ, since the drop of the peak power is more significant in the case of higher pulse energy with a little increase of the pump pulse duration. According to the simulations shown in Fig. 9, it is recommended to apply a pump pulse with a duration of 15 ps in the case of 100 nJ pump pulse energy. While a duration over 40 ps is favored when the energy is increased to µJ level, so that a conversion efficiency over 85% could be guaranteed.
Fig. 10. The maximum of the conversion efficiency with respect to pump pulse duration from 5 to 50 ps under pump pulse energies of 100 and 1000 nJ.
The pump pulse duration also has an impact on the dechirped pulse duration of Raman pulses. The spectrum FWHM and dechirped duration of Raman pulses with respect to the pump pulse duration under 1000 nJ pump pulse energy is shown in Fig. 11. Since the pump pulses with a shorter pulse duration have a wider spectrum, the generated Raman pulses would be modulated into ones with a broader spectrum as well, whose transform-limited pulse duration could be narrower. As shown in Fig. 10, Raman pulse duration less than 100 fs should be obtained when the pump pulse duration is set as 5 ps.
Fig. 11. The full-width-half-maximum of Raman spectrum and the dechirped pulse duration at the maximum of the conversion efficiency with respect to pump pulse duration from 5 to 50 ps under 1000 nJ pump pulse energy.
The results show that selecting a proper pump pulse duration according to certain pump pulse energy is essential to make Lw match with Lc, so as to achieve a high conversion efficiency over 85%. In addition, a longer pump pulse duration will lead to a longer Raman pulse duration. Therefore, in order to obtain Raman pulses with a duration less than 200 fs, some sacrifice on the conversion efficiency may be necessary.
3.6 Discussions
The simulations presented above illustrate that the walk-off effect between pump and Raman pulses plays a critical role in a fiber-based NOGM laser. Controlling the walk-off effect properly can help us to obtain the NOGM pulses with higher conversion efficiency.
The results in Section A show that Raman conversion efficiency in a fiber-based NOGM laser could be optimized to achieve a value of ηmax by selecting suitable length of Raman fiber. The key guide-line to optimize ηmax is by matching the Lw with Lc, so that the pump pulses could be transformed more thoroughly through the nonlinear process. Changing the seed laser power and pump pulse energy are two effective ways to control the speed of Raman conversion process, and thus to adjust the Lc. While manipulating the GVD of the Raman fiber is a direct way to control the speed of walk-off, and thus to adjust Lw. Changing the pump pulse duration with fixed pulse energy could affect both Lc and Lw, since the peak power of the pump pulse would be changed correspondingly. It is worth noticing that all these parameters mentioned above should be designed comprehensively with overall planning in order to eventually match the Lw with Lc. With proper arrangement of the seed, pump and Raman fiber, it is expected to obtain NOGM laser pulses with high pulse energy and conversion efficiency at any wavelength as long as within the transparent window of conventional optical fibers.
Comparing the different parameters between pump and Raman pulses in the simulations, it is also interesting to notice that a fiber-based NOGM laser is not only a nonlinear wavelength converter, but also a spectrum stretcher and a pulse duration reducer. The results shown in Section E give us an example regarding to such conversion of pulse parameters, that the 40 ps (chirp-free), 1064 nm pump could be transformed into 350 fs, 1120 nm Raman pulse with µJ-level pulse energy under more than 85% efficiency. However, if Raman pulse duration less than 100 fs is required for specific applications, one may need to reduce the pump pulse duration or apply fiber with a small GVD in the target pump and Raman wavelength. Such attempts could reduce the compressed Raman pulse duration effectively, yet with some sacrifice on the conversion efficiency.
In addition, there are some other parameters such as the seed linewidth and the initial chirp of pump pulse that may have influences on not only the maximum conversion efficiency, but also other output characteristic in the NOGM process. Detailed simulations regarding to seed linewidth and pump pulse chirp will be developed in our follow-up works.
4. Conclusion
To conclude, we simulated different parameters including Raman fiber length, seed laser power, pump pulse energy, GVD and pump pulse duration, to investigate how the walk-off effect influences the conversion efficiency in a NOGM Raman fiber amplifier. The results of the simulations reveal the importance of balancing the speed of walk-off with the one of Raman conversion, which offer instructions on optimizing the Raman conversion efficiency. Through the simulations, it is shown that the conversion efficiency could be optimized by selecting suitable length of Raman fiber. Changing the seed laser power and pump pulse energy are two effective ways to control the speed of Raman conversion process. Manipulating the GVD of the Raman fiber is a direct way to control the speed of walk-off. While changing the pump pulse duration with fixed pulse energy could affect the speed of Raman conversion and walk-off at the same time. All these simulation results clearly show that only when the speed of walk-off matches with the one of Raman conversion process can the conversion efficiency be optimized. In the near future, the experimental performances of fiber-based NOGM lasers are expected to be improved compared with previous reported works [13,14], which have the ability to generate wavelength-agile, femtosecond laser pulses with µJ-level pulse energy under more than 85% efficiency.
Funding
Youth Innovation Promotion Association of the Chinese Academy of Sciences (2022247); National Natural Science Foundation of China (62075226, 62175244); Natural Science Foundation of Shanghai (21ZR1472200).
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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