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Actively mode locked Raman lasing in a ring PM-fiber cavity pumped by a linearly polarized Yb-doped fiber laser is studied. At co-propagating pumping, a stochastic pulse with duration defined by the AOM switching time (~15 ns) is generated with the round-trip period. At counter-propagating pumping, one or several sub-ns pulses (within the AOM switching envelope) are formed. It has been found that the formation of such stable multi-pulse structure is defined by the single-pulse energy limit (~20 nJ) set by the second-order Raman generation. Adding a NPE-based saturable absorber in the actively mode locked cavity, results in sufficient shortening of the generated pulses both in single- and multi-pulse regimes (down to 50 ps). A model is developed adequately describing the regimes.
© 2016 Optical Society of America
1. Introduction
Raman gain in passive fibers offers laser generation beyond the spectrum of active rare-earth (RE) doped fibers thus extending the spectral band of fiber lasers to almost full near-IR range (1-2 μm) [1]. Raman fiber lasers (RFLs) are also featured by a broad-range wavelength tuning and/or multi-wavelength operation, high conversion efficiency of the pump radiation into the first or higher Stokes orders, an all-fiber design with high stability and reliability, which are important for applications such as telecommunications, sensing and medicine [2–4].
The most efficient pumping of RFLs is provided by Yb-doped fiber lasers (YDFLs) with high-power output at ~1.06 μm in single transverse mode. As an example, 150 W at 1120 nm has been obtained for the YDFL-pumped Raman fiber laser with 85% efficiency [5]. Even higher optical efficiency is possible in the RFL schemes utilizing random distributed feedback via Rayleigh backscattering in single-mode fibers [6,7]. As shown recently, direct pumping of a gradient-index fiber by high-power laser diodes offers high-power RFL operation at short wavelengths (980 nm [8], 954 nm [9] and 835 nm [10]) that may be treated as an alternative to RE-doped fiber lasers being free of their drawbacks, such as photodarkening.
RFLs usually operate in continuous-wave (CW) mode, but pulsed operation is also possible being achieved by pulsed pumping [4,10,11], passive [12] or active [13] Q-switching, and various mode locking (ML) schemes [14–23]. The ML regime of RFLs is produced either with synchronous pumping by a mode-locked laser (see e. g [14]. and citation therein) or with a CW pump and passive mode-locking by a saturable absorber [15–17]. Both these schemes require using of specialty highly nonlinear fibers. In addition, the second one has very low conversion efficiency, but it enables generation of coherent picosecond parabolic pulses of 22 nJ energy [15]. Later on, high-efficiency generation of Raman dissipative solitons with comparable energy and ultrashort dechirped duration (~200 fs) has been demonstrated at synchronous pumping by a ML YDFL in a common [18,19] or external [20] polarization-maintaining (PM) fiber cavity. The parameters of femtosecond Raman fiber lasers are close to the best ultrashort pulses obtained in RE-doped fiber lasers operating in dissipative soliton regime [21, 22]. Recently, the first attempt on active mode locking of RFLs has been reported [23], but the obtained pulses are rather long (2 ns) as compared to other variants of ML RFLs.
Here we report on the next step in the study of RFLs with active mode locking. We add a saturable absorber and obtained sufficiently shorter pulses (of ~50 ps duration) in single- and multi-pulse regimes. We have found that the single-pulse energy limit is defined by the conversion of the generated pulses to the next Stokes orders, similar to chirped dissipative solitons and Raman dissipative solitons [18–22], though the ML RFL pulses are measured to be not chirped. Necessary steps to reach the result are described below.
2. Experiment
The studied ML Raman fiber laser is made by a transformation of linear scheme of actively Q-switched RFL [13] into a ring one and switching of the acousto-optic modulator (AOM) synchronously with the pulse roundtrip thus providing mode locked operation, similar to [23]. The laser scheme is presented in Fig. 1. A linearly-polarized CW YDFL with output power up to 12 W at the wavelength of 1064 nm is used as a pump source. The pump radiation is coupled through coupler WDM1 (1064/1120 nm) into PM fiber (Fujikura SM98-PS-U25D-H) with length up to 500 m, at the opposite end of which another coupler WDM2 exempts unabsorbed pump radiation from the resonator. Unidirectional laser propagation is ensured by an optical isolator. The laser schemes with co- and counter-propagation of signal and pump waves are examined. Laser emission is extracted from the cavity by a 50/50 PM fiber coupler. The fiber cavity is all-PM and hence it is highly stable against environmental disturbances.
Repetition rate of the AOM was set close to the round trip frequency (f = c/nL) in the ring cavity. The AOM was driven by rectangular electrical pulses and its opening time was varied from 30 to 100 ns at rise/fall time ~15 ns. Output signal is analyzed by an ultrafast photodiode and an oscilloscope with bandwidth of 3 GHz. Besides, optical and radio-frequency (RF) spectra were recorded by optical and RF spectrum analyzers, accordingly. Duration and compressibility of the pulses were studied with a FROG analyzer and a diffraction grating compressor, described in [19]. In addition to active mode-locking, a saturable absorber based on nonlinear polarization evolution (NPE) was inserted into the laser cavity at the final stage. In this case, the output coupler is replaced by a polarization controller (PC) spliced to a 1.5-m SMF and polarization beam splitter (PBS) (see cloud inset in Fig. 1).
2. Results
First experiments were performed with the cavity length of 500 m. When counter-propagating pump power reaches ~1.2 W and repetition rate of AOM is set nearly equal to the signal round trip frequency, a pulse forming begins. At ~1.5 W pumping, the output pulse becomes stable. Varying power and repetition rate, different generation modes are observed: either single or multi-pulse. In Fig. 2 output pulses with their optical spectra, FROG traces and corresponding auto-correlation functions (ACF) are shown for different repetition rates at the pump power of 3 W. At 395.58 kHz rate a nearly single pulse is formed with the duration of ~1 ns that is close to the results of [23]. This regime is near threshold, so ACFs show some instability with narrow spikes at long wavelengths. With increasing AOM repetition rate (or increasing pump power) pulses become shorter (down to 300 ps), the time interval between them also shortens and the number of pulses increases until they fill the window. At the same time, spectral broadening of the Raman peak at 1110 nm to shorter wavelengths is observed. The second Stokes order (1160 nm) is also present being ~10 dB lower. At 395.667 kHz rate the average output power reaches 70 mW. The measured ACF contains narrow stochastic peak and the pulses aren’t compressed by the diffraction grating compressor. Herewith, the RF spectrum near the roundtrip frequency (see inset of Fig. 2(a)) is stable and the peak width and contrast vary by <5% at the variation of parameters within the stability range.
Fig. 2 Pulse profiles, optical and RF (inset) spectra and FROG traces with ACFs at (a) 395.586 kHz, (b) 395.634 kHz and (c) 395.667 kHz AOM repetition rates at 3 W backward pumping.
When the scheme was modified to co-propagating one, the average output power became significantly lower (15.8 mW), since the signal interacts only with a small part of co-propagating pump wave. The pulses are born from a background noise and have random phases at the cavity roundtrips. As a result, averaging in the time domain gives a bunch with ~15 ns envelope corresponding to the AOM opening time.
To analyze temporal dynamics of the second-order Stokes wave, a PM-fiber based Lyot filter was inserted. It suppresses the signal at ~1110 nm by ~20 dB (Fig. 3(a)). After the filter, the signal became 10-15 dB weaker than the second Stokes wave at 1160 nm (Fig. 3(b)). Nevertheless, the multi-pulse structure is preserved (Fig. 3(c)) that indicates its synchronous transfer from primary pulse when the second threshold is reached. The energies of each pulse in the multi-pulse output signal are measured to be nearly equal (~12 nJ). As far as the output coupler has coupling ratio of 50/50, the intracavity energy of single pulse is 24 nJ that corresponds to the threshold for energy transfer to the next Stokes order [18–22].
Fig. 3 (a) Lyot filter transmission spectrum, (b) filtered signal spectrum and (c) 2nd order Raman pulse profile.
As mode locking is highly dependent on such parameters as pump stability, AOM jitter, refractive index fluctuations etc., it was decided to add to the laser scheme a NPE-based saturable absorber (inset in Fig. 1). This modification has led to the threshold reduction and output pulse narrowing down to 50 ps. Figure 4 shows output pulse profile, its spectrum and ACF at repetition rate of 394.216 kHz, AOM opening time of 40 ns and pump power of 2.6 W. As far as short resonators are more preferable for mode locked laser with coherent (chirped) pulses [18, 19], experiments with cavity lengths of 160 (80) m were performed. At that, the threshold for stable pulses raised to 3 (6) W, the pulse duration did not shorten, and multi-pulse mode is also observed with increasing AOM repetition frequency. The NPE piece insertion led to a shortening of the output pulses and decreasing pumping threshold, similar to the 500-m cavity. However, a typical stochastic peak was still observed, and the pulses could not be compressed with diffraction gratings.
Fig. 4 (а) Output pulse profile, (b) optical spectrum of signal and (c) FROG trace and ACF of signal before and after (inset) compressor at the AOM repetition rate of 394.216 kHz.
3. Model and its comparison with the experiment
Denote the frequency of AOM opening as ν, and the roundtrip time of Raman scattered light as τrt, δt = (ν−1–τrt) is the delay of light relative to the AOM opening. Then the pulse shape Pn(t) at n-th roundtrip is modified to the next (n + 1)-th roundtrip as
where G is the gain, R is the loss per roundtrip, (1–t2/T2) is the АОМ temporal shape. In the steady state Pn + 1(t) = Pn(t). Assuming small δt and low excess gain δg = ln(GR)<<1 when lasing occurs near the threshold, we come to the continuous time and get the pulse shape P(t) fromwhere τ2 = δgT2. When t>τ, the loss exceeds the gain and the boundary condition is P(τ) = Psp, where Psp is the power of spontaneous emission. When t<τ, the solution is transformed toTo determine roundtrip time τrt, the unsaturated pump power (at WDM2 output) versus the AOM repetition rate was measured (Fig. 5(a)). Since the model does not account for the influence of the second-order SRS, the input pump power was set as low as possible. The maximum pump absorption (and hence the maximum power of output signal) occurs at AOM frequency equal to the cavity roundtrip frequency, that amounts to 395.770 kHz. In 395.706 – 395.716 kHz range the laser generates single pulses with duration about 5 ns.
Fig. 5 Average output power and transmitted pump power (a); calculated pulse shape (dashed line) compared to the experimental one (solid line) and AOM opening (dotted line) at frequency (b) 395.716 kHz and (c) 395.737 kHz.
Figure 5(b) shows a comparison of the calculations with the experiment for the 500-m cavity at the AOM repetition rate of 395.716 kHz (pump power is 1.6 W, AOM time is 40 ns). Because it is not possible to accurately measure excess gain δg and any slight deviation of this parameter gives an exponential contribution, it was found from the best fit of experimental data, δg = 0.38. At a positive δt offset, every roundtrip shifts the pulse to the front edge of the AOM opening profile, until its maximum reaches a point of equilibrium (−10 ns). At the same time, the output pulses are shorter than the AOM profile, just like in experiments.
With increasing repetition rate and reduction of δt the pulse energy becomes so large that 2nd order Stokes P2 (t) appears and begins to play a decisive role in pulse shortening at the front edge. However, the trailing edge is still described by the model (3). Figure 5(c) shows the output pulse at repetition rate of 395.737 kHz and the theoretical profile. A more accurate calculation of the pulse shape requires a consideration of the 2nd order Stokes wave in (1).
Let us use the conservation of the number of photons in the Raman conversion: the second Stokes power P2(t) is nearly equal to the loss of power P(t). In this approximation, from the right side of the expression (1) we should subtract P2(t), then instead of (3) we obtain
Power P2(t) could be estimated from the equation where ∆β is group velocity difference of the 1st and 2nd order Stokes waves. At condition of small δt, the generated 2nd Stokes wave depletes the leading edge of the pulse due to the difference in the group velocities, thus effectively reducing the pulse duration. When the duration becomes smaller than group delay time ΔβL, the pulse energy is limited by a threshold level of ~20 nJ. Figure 6 shows the calculated profile of multi-pulse mode arising from the energy conversion to the 2nd Stokes order. Obviously, the theory is in qualitative agreement with the experiment, i.e. the model explains the nature of the multi-pulse mode.4. Conclusion
Thus, the shortest pulses (300 ps) in actively mode locked Raman fiber laser with backward pumping have been obtained. A hybrid active-passive mode locking with NPE-based saturable absorber has been proposed and realized demonstrating pulse shortening to 50 ps. It has been shown that the pulse energy has a limit (~20 nJ) in both cases, which is defined by the next-order Stokes generation threshold. Its excess results in multi-pulse regime with number of pulses and distance between them depending on the AOM repetition rate and pump power. In both the schemes (active and hybrid), the output pulses could not be compressed by the grating compressor since they have a noisy component. The developed model explains the transition to multi-pulse regime at the offset of AOM from the round trip frequency with involvement into consideration of the second Stokes wave. The developed laser can be used in applications requiring synchronization, e.g. nuclear physics, time-resolved spectroscopy etc.
Acknowledgments
The authors acknowledge financial support of the Russian Science Foundation (project 14-22-00118) and technical assistance of E. A. Zlobina.
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