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Abstract
Nonlinear optical gain modulation (NOGM) is a method to generate high performance ultrafast pulses with wavelength versatility. Here we demonstrate coherent femtosecond Raman pulse generation through cascaded NOGM process experimentally. Two single-frequency seed lasers (1121 and 1178 nm) are gain-modulated by 117 nJ 1064 nm picosecond pulses in a Raman fiber amplifier. Second-order (1178 nm) Stokes pulses are generated, which have a pulse energy of 76 nJ (corresponding to an optical conversion efficiency of 65%) with a pulse duration of 621 fs (after compression). Dynamic evolution of both pump and cascaded Stokes pulses within the Raman amplifier are investigated by numerical simulations. The influences of pump pulse duration and energy are studied in detail numerically. Moreover, the simulations reveal that NOGM pulses with higher energy and shorter pulse duration could be obtained by limiting the impact of walk-off effect between pump and Raman pulses. This approach can offer a high energy and wavelength-agile ultrafast source for various applications such as optical metrology and biomedical imagining.
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1. Introduction
Ultrafast fiber lasers are necessary tools for various of applications including fundamental research, biomedicine and industrial processing [1–5]. Limited by the emission band of rare earth doped fibers, conventional fiber lasers can only emit in specific spectral ranges. Thus, Raman fiber lasers, which can produce wavelength-agile light, have been widely researched in the past decade [6–9].
Mode-locking has been proved to be an effective way to generate ultrafast Raman pulses [10–14]. However, due to the relatively low Raman gain efficiency of optical fiber, tens of, or even hundreds of meters of fibers are required in the condition of continuous wave (CW) pump. This results in large dispersion and nonlinear phase accumulation in the mode-locked oscillator, which would bring challenges for achieving balance between dispersion and nonlinearity. Owing to that, mode-locked Raman fiber lasers usually have narrow working regime for single pulse operation, resulting in low pulse energy. Compared to passive mode-locking, synchronously pulse pumping has an advantage of high Raman gain at unit length [15–19]. However, a basic technical complexity of this method is the synchronization between pump pulse period and cavity round-trip time. Additional techniques such as free-space delay line [20] or repetition rate adjustable pump laser [21] have to be applied. Another possible way to overcome the difficulty of synchronization is by distributed feedback. A pulse pumped Raman fiber laser with random distributed feedback is reported to emit Raman pulses, utilizing Rayleigh feedback to adjust the cavity length adaptively with the pulse repetition rate to achieve self-synchronizing [22]. Nevertheless, the output pulse is noise-like with poor pulse coherence.
Recently, we proposed a new method, namely nonlinear optical gain modulation (NOGM), to obtain highly-coherent Raman pulses without the demand on the synchronization [23]. In our previous demonstration, a single frequency CW seed is modulated by a picosecond pump laser and transformed into highly coherent Raman pulses after propagating in a piece of short Raman gain fiber. Modulated by 14 ps 1064 nm pump pulses, the reported setup can generate stable and highly-coherent laser at 1121 nm with a pulse energy of 25.7 nJ, a pulse width of 436 fs, and an optical efficiency of 69.4%. However, in order to fill up all the spectrum gap left by the emission bands of rare earth doped fibers, cascaded Raman progress is necessary. The potential for NOGM to generate cascaded Raman pulses has not been demonstrated yet.
In this contribution, we report second-order-cascaded Raman pulse generation by NOGM. In the demonstration, both 1121 nm and 1178 nm single frequency laser are injected into a Raman fiber amplifier, which is pumped by a 1064 nm picosecond pulse laser. The two-stage NOGM setup generates 1178 nm pulses with a pulse energy of 76 nJ and a pulse duration of 621 fs (after compression) under an optical conversion efficiency of 65%. Numerical simulation is performed to understand dynamic evolution of both pump and Raman pulses. Besides, our simulations reveal that NOGM pulses with higher energy and shorter pulse duration can be obtained by limiting the impact of walk-off effect between pump and Raman pulses. Moreover, it can be expected that, by changing the wavelength of pump and seed lasers, sources at different wavelength can be generated by the NOGM amplifier.
2. Experimental setup
The experimental setup is shown in Fig. 1. Two seed sources were applied. One is a 10 mW 1121 nm single frequency CW laser (LD-PD Inc.); the other is a 10 mW 1178 nm single frequency laser (QD-Laser). The linewidth of the 1121 nm and 1178 nm seed lasers are 400 kHz and 1 MHz, respectively. They were coupled together by a 1120/1178 polarization-maintaining (PM) wavelength division multiplexer (WDM). The seed sources were coupled with the pump laser by a 50:50 1064 nm PM coupler. The pump laser is a home-made Yb-doped fiber laser, which can produce 1064 nm ultrafast pulses with a pulse duration of 14 ps and a repetition rate of 26.5 MHz [24]. A power amplifier was applied to scale up the pump pulse energy to 117 nJ. A piece of 3.7-metre-long PM single mode fiber (Nufern, PM980-XP), which serves as the nonlinear optical gain medium in the setup, is connected with the amplifier. The NOGM process, which transfers energy from 1064 nm to 1121 nm, and then to 1178 nm, is accomplished in this Raman gain fiber. The whole laser setup is in all-PM fiber configuration. The 2nd-order Raman pulses were separated from the residual pump pulses and 1st-order ones by a pair of 1200 lines/mm free-space gratings, which were also acted as a pulse compressor.
Fig. 1. The configuration of the cascaded NOGM setup. Amp: amplifier, WDM: wavelength division multiplexer; CPS: cladding power stripper.
3. Experimental results
Spectra at different pump power of the cascaded Raman amplifier are shown in Fig. 2(a), which were measured by an optical spectrum analyzer (OSA) Yokogawa AQ6370D with 0.02 nm resolution. At low pump power, a spectral pedestal appeared around the 1121 nm spectral peak of the single frequency seed. The pedestal rose and broadened when the pump power was increased. As the pump power became higher, similar process occurred when the power of the 1st-order Stokes light was converted to the 2nd-order Stokes one. The spectrum of 1178 nm with a 10 dB bandwidth of 10.6 nm is generated at 3.11 W pump power. Meanwhile the 3rd-order Stokes amplified spontaneous emission could also be observed in the spectrum, which indicates a possibility of higher-order cascaded Raman pulse generation with an additional 1240 nm single frequency seed injection.
Fig. 2. (a) Spectral evolution with respect to pump power of 0.02, 0.70, 1.67, 2.05, 3.11 W; (b) 1st-order and 2nd-order output power and conversion efficiency as a function of the pump power.
The 1121 nm and 1178 nm output power as a function of the pump power are shown in Fig. 2(b). The total output power was measured by a power meter (Thorlabs Inc., S415C), and the powers of each Stokes order were then calculated according to their spectrum proportion. The 1121 nm laser power begins to increase at an average pump power of about 0.29 W, and reaches 1.09 W at an average pump power of 1.51 W with a highest optical conversion efficiency of 72.8%. The 1121 nm laser power continues increasing, but the conversion efficiency decreases as a result of the appearance of the 2nd-order Stokes light. The 1178 nm laser continuously increases to 2.01 W (corresponding to 76 nJ pulse energy) with an optical conversion efficiency of 65% when pump power reaches maximum 3.11 W. Limited by the maximum available pump power, higher power and conversion efficiency of 2nd-order Stokes light cannot be obtained in this experiment.
The temporal characteristic of the 2nd-order Stokes pulse is measured with a 25 GHz InGaAs-based photodetector (New Focus, 1414-50), as shown in Fig. 3(a). The pulse train shows a uniform intensity with a temporal spacing of 37.8 ns, which matches well with the 26.5 MHz repetition rate of the pump pulse. The RF spectrum of the 2nd-order Raman pulse is measured at a resolution of 10 Hz, which is shown in Fig. 3(b). The fundamental frequency spectrum indicates a peak at 26.5 MHz with a signal-to-noise ratio (SNR) of 75 dB. These characteristics show the good temporal stability of the 2nd-order Raman pulse. The autocorrelation traces of the 2nd-order Stokes pulse at 76 nJ pulse energy before and after compression are shown in Fig. 3(c)&(d) respectively, which is measured by an autocorrelator (APE pulsecheck, SM1200). The 1178 nm output pulse has a pulse duration of 9.2 ps, which can be compressed to 621 fs with a pair of free-space gratings. The compressed pulse has an obvious pedestal, which is also seen at 1st-order Stokes pulse dechirped autocorrelation trace in our past work [23]. This incompressible pedestal is due to the group velocity mismatching between the pulses of each order. Detailed explanation of this issue will be discussed in the following numerical simulation section.
Fig. 3. Characteristics of the 1178 nm Raman pulse. (a) pulse train; (b) radio frequency (RF) spectrum; (c) autocorrelation trace before and (d) after compression.
4. Numerical simulations and discussions
In order to better understand the pulse dynamics of the cascaded NOGM, we simulated a numerical model based on generalized nonlinear Schrödinger equation (GNLSE), covering dispersion and multiple nonlinear effects such as self-phase modulation (SPM), cross-phase modulation (XPM), and stimulated Raman scattering (SRS). A Raman response function with the K. J. Blow and D. Wood model is applied [25]. A white Gaussian noise is added to simulate the spontaneous Raman emission. The simulations were performed under varieties of pump pulse energy, duration and Raman gain fiber length to systematically discuss their influences on the cascaded NOGM.
The dynamic evolution of the pump and two Stokes pulses along the fiber are simulated and plotted in Fig. 4. The pump pulse duration and pulse energy are set as 13 ps and 117 nJ, respectively, which follows the experimental setup mentioned above. The Raman fiber was equally divided into 200 units and sampled at each unit to study the evolution of optical conversion efficiency along the fiber. At about 0.8 m, the middle of the pump pulse, which has the highest power, is firstly converted to the 1st-order Stokes pulse. Afterwards, the pump pulse evolves into an M-shaped structure with further Raman conversion, as shown in Fig. 4(a). When the pump and Raman pulses propagate together in the Raman gain fiber, the group velocity dispersion (GVD) mismatching leads to a walk-off effect between them. The walk-off effect causes the seperation of the pump and Raman pulses, hence the lagging part of the pump pulse cannot be transformed into the Stokes pulse effectively [Fig. 4(a)]. This leads to an asymmetrical shape of the 1st-order Stokes pulse [Fig. 4(b)]. The conversion efficiency of the 1st-order Stokes pulse saturates at 1.5 m, and the 1st-order Stokes pulse starts to be converted into the 2nd-order one. As the walk-off effect continuously influenced the cascaded NOGM process, the impact accumulated from the whole process makes the shape of the pulse envelope more asymmetrical, as shown in Fig. 4(c). The simulation shows that the walk-off effect will influence the high-order NOGM process more seriously, which results in a lower conversion efficiency of high-order Stokes pulses.
Fig. 4. The simulated temporal evolution of the (a) pump pulse, (b) 1st-order Stokes pulse and (c) 2nd-order Stokes pulse.
Apart from the pulse dynamic evolution, a temporal result of the simulated 2nd-order Stokes pulse before compression are shown in Fig. 5(a). Due to the walk-off effect, the pulse has an asymmetric shape, which results in a triangle-like autocorrelation trace as shown in Fig. 5(b). It can be noticed that a strong temporal modulation exits on the right side of the pulse, which should be resulted from SPM. The nonlinear chirp accumulated from the walk-off effect cannot be dechirped by the gratings, which leaves a tailing in the compressed pulse, as shown in Fig. 5(c). The tailing appears as a pedestal in the autocorrelation trace of the dechirped pulse [Fig. 5(d)], which is the same as the one in Fig. 3(d). The dechirped pulse has a pulse duration of 374 fs. The longer dechirped pulse duration in the experiment may be caused by higher-order dispersion or larger nonlinear chirp accumulated from the optical fiber in the pump amplifier, which was not taken into account in our present simulations.
Fig. 5. The simulated temporal characteristics of the 2nd-order Stokes light (a) before and (c) after compression; the autocorrelation trace of the 2nd-order Stokes light (b) before and (d) after compression
Different pump pulse parameters are simulated to optimize the NOGM system. Firstly, the influence of pump pulse energy is simulated. Three different pump pulse energies of 80 nJ, 117 nJ and 154 nJ are employed. The pump pulse duration is set as 14 ps. The results are shown in Fig. 6. For 80 nJ pump pulse energy, the energy of the 1st-order Stokes pulse starts to increase at about 0.7 m and saturates with an optical conversion efficiency of 64% at 2.5 m. After that, the pulse energy of the 1st-order Stokes pulse decreases and starts to transform into the 2nd-order Stokes pulse. The 2nd-order Stokes pulse appears at 2.1 m and continuously increases to a conversion efficiency of 60%. As for 117 nJ and 154 nJ pump pulse energy, higher pump pulse energy leads to stronger SRS. The energy of the 1st-order Stokes pulses of both cases saturates at a conversion efficiency of 67% and 69% at shorter Raman fiber. The conversion efficiency is clamped by the generation of 2nd-order Stokes light. In the case of 117 nJ, the energy of the 2nd-order Stokes pulse saturates at 4.5 m and shows a decreasing trend. This decrease of efficiency appears earlier at 2.9 m in the 154 nJ case and decreases obviously due to the generation of the 3rd-oder Stokes light. The simulation shows that with enough nonlinear effect by improving pump power, the Raman amplifier can obtain high-order cascaded coherent Raman pulse with high pulse energy. The results of the 117 nJ case are similar to the experimental ones. Yet, the simulated conversion efficiency of the 1st-order Stokes pulse is a little smaller than the experimental one. We think this is mainly due to the fact that Raman conversion has already occurred in the gain fiber of the Yb-doped amplifier, which was not taken into account in our present simulations.
Fig. 6. The simulated conversion efficiency of 1st-order and 2nd-order Stokes pulse with respect to the fiber length under three different cases of pump pulse energy of 80 nJ, 117 nJ and 154 nJ.
The influence of pulse width is simulated as well. The conversion efficiency with respect to the gain fiber length under three different cases of pump pulse duration (5 ps, 10 ps and 30 ps) are shown in Fig. 7. In this part of simulation, the pump pulse energies are set as 200 nJ. With the same pulse energy, a longer pulse duration represents a lower peak power, which means a relatively weaker nonlinear optical gain to drive the gain modulation process. For 30 ps case, the 1st-order Stokes appears at 0.9 m. The pulse energy continuously increases to 129 nJ at 2 m. The 2nd-order conversion process is accomplished at 4.6 m with a conversion efficiency of 67%. In contrast with that, the energy of the 2nd-order Stokes pulse of both 10 ps and 5 ps cases saturate in a shorter optical fiber with a conversion efficiency of 72% and 57%. Noting that the conversion efficiency of the case of 10 ps is higher than the other two cases in both 1st-order and 2nd-order Raman conversion process. When pulse duration is too short, the same walk-off effect has a more serious influence on the pulse envelope of pump and Raman pulses, therefore more lagging parts of the pump pulse cannot be transformed into the high-order Stokes light effectively. However, when the pulse duration is too long, a long Raman fiber is needed to accomplish the Raman conversion process, which leads to more severe walk-off effect. Results of the simulation show that highest conversion efficiency can be obtained by optimizing the pump pulse duration.
Fig. 7. The simulated conversion efficiency of 1st-order and 2nd-order Stokes pulse with respect to the fiber length under three different cases of pump pulse duration of 5 ps, 10 ps and 30 ps.
From the simulations, it is clearly shown that the walk-off between pump and Raman pulses has a huge impact on the cascaded-NOGM process, which leads to an irregular shape of high-order Raman pulses, a reduction of the optical conversion efficiency and a longer dechirped pulse duration. One approach to reduce the impact of the walk-off effect is by increasing the pump pulse energy. When pumped with higher pulse energy, shorter Raman fiber is required to offer adequate nonlinear optical gain, which will reduce the walk-off and increase the conversion efficiency. A simulated compressed pulse under 154 nJ pump pulse energy at highest conversion efficiency is shown in Fig. 8(a). Compared to Fig. 5(c), the 2nd-order Stokes pulse of 154 nJ case can be compressed to 333 fs because of a shorter Raman gain fiber. Besides, the walk-off effect can be suppressed when the pump and Stokes pulses have similar group velocities. A simulated conversion efficiency of 2nd-order Stokes pulse with respect to the fiber length at 117 nJ pump pulse energy under different GVD is shown in Fig. 8(b). When reducing the GVD from 24 to 10 ps/(nm×km), the highest conversion efficiency can be scaled up from 67% to 73%. Therefore, it is predictable that Raman pulses with higher quality can be obtained when the wavelength of pulse is near the zero-dispersion regime of the Raman gain fiber.
Fig. 8. (a) The simulated temporal characteristics of the 2nd-order Stokes light after compression at 154 nJ; (b) The simulated conversion efficiency of 2nd-order Stokes pulse with respect to the fiber length at 117 nJ pump pulse energy under different GVD of 10 and 24 ps/(nm×km).
5. Conclusion
In summary, we experimentally demonstrated a cascaded femtosecond Raman pulse generation by NOGM. Compared with other methods of generating ultrafast Raman pulses, the cascade NOGM process can obtain highly coherent and stable Raman pulses with high pulse energy and optical conversion efficiency in a simple and compact all-fiber configuration. Pumped by a mode-locked laser with 117 nJ pulse energy and 14 ps pulse duration, 1064-1121-1178 nm cascaded coherent Raman pulse is obtained with a pulse energy of 76 nJ, an optical conversion efficiency as high as 65%, and a pulse duration of 621 fs (after compression). Numerical simulation indicates that by designing the NOGM amplifier with proper Raman fiber length, pump pulse energy and pump pulse duration to reduce the walk-off effect, high pulse energy and wavelength-agile femtosecond pulses can be obtained with higher conversion efficiency and shorter pulse duration. Systematic simulation will be researched to better optimize the parameter of the amplifier in our follow-up work. We believe that the proposed cascaded-NOGM amplifier offers a simple approach to generate high energy, wavelength-agile ultrafast pulses, which has a bright application prospect in the future.
There are also other approaches to generate high-order cascaded Stokes pulses such as cascaded FWM of two solitons [26,27]. In the approach, high-order Stokes pulses are generated from two mutual coherent frequency-shifted dissipative solitons. However, the NOGM pulses are generated in a single pass fiber amplifier with two independent seed lasers, so there is no mutual coherence of them. Nevertheless, mutual coherent cascaded Raman pulses are important, which may allow the generation of ultrashort few-cycle pulses. The mutual coherence can be achieved with two phase locked seed lasers for the cascaded NOGM process, which is one of the research focuses to further develop the technology.
Funding
National Key Research and Development Program of China (2020YFB0408300, 2020YFB1805900); 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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