A mode-locked Er-doped fiber laser was triggered to synchronize with a separate ultrashort picosecond Yb-doped fiber laser by cross phase modulation. Square nanosecond pulses were generated in the long-cavity Er-fiber laser by the peak intensity clamp effect while the synchronization maintained. At the maximum pump power of 450 mW, a synchronous laser pulse duration of 5.5 ns has been achieved. This synchronous nanosecond and picosecond system has shown a large length mismatch tolerance of 2.6 mm and can work stably for days.
©2009 Optical Society of America
Stimulated by many promising applications in ultrafast laser spectroscopy , coherent anti-Stokes Raman scattering microscopy, difference frequency mixing for mid-infrared generation and so forth, much progress has been made in robust and accurate synchronization of different multi-colored ultrashort lasers. Most of these synchronization systems relay on actively or passively matching the cavity lengths and offset frequency drifts of different lasers by virtue of modulating the intracavity dispersion and nonlinearity [4, 5, 6]. Nevertheless, all of them are applicable to ultrashort mode-locked lasers but inapplicable to nanosecond-duration lasers, which are in most cases attained by Q-switching techniques. Nanosecond (ns) Q-switched laser pulse trains are conventionally synchronized by sharing the same electronic triggers, but such a temporal control offers quite large timing jitter as limited by the electronic circuits. Ultrashort pulses with ultrabroad spectra may be possibly stretched to ns region, but this requires very special and quite difficult optical designs, let alone the spectral chirps in the stretched pulses seriously limit their applications. It still lacks in efficient techniques to precisely synchronize ns laser pulse trains with an ultra-low timing jitter by an all-optical way.
On the other hand, synchronization of ns pulse trains and even precisely phase-locked ns laser arrays are required in many high-energy physics experiments, such as in the development of high-energy laser pulses for particle acceleration, and laser synchronization with x-rays or electron beams from synchrotrons [10, 11]. High-energy ns lasers synchronous with separate ps or fs lasers are desired in optical parametric chirped pulse amplification of ultrashort pulses [12, 13, 14], and particularly in fast ignition of laser fusion, where lasers of different pulse durations, such as a fs laser together with a high-intensity ns laser, should be controlled to interact with the target in sequence with an ultra-high precise temporal control . Moreover, coherent pulse synthesis even requires sub-cycle control (optical phase coherence) with the timing jitter much less than the duration of an optical cycle. Precise synchronization of ns laser pulses can be in principle achieved by synchronizing individual ns lasers to the same ultrafast laser trigger.
In this paper, we demonstrate a technique to synchronize a mode-locked Er-doped fiber laser of ns-duration to a ps-duration master laser, by means of nonlinear polarization rotation (NPR) induced by cross-phase modulation (XPM) between the master and the slave laser pulses. A long-cavity Er-doped fiber laser operated in the square ns mode-locking mode  was synchronized to an externally injected master pulse train from a ps Yb-doped fiber laser. The measurements on the timing jitter of the master and slave laser intensity envelopes showed that synchronization at several picoseconds of residual timing jitter was obtained. Interestingly, the slave laser generated square ns pulse train of stable flat tops, which were especially desirable for various applications. In addition, as a result of the peak-power clamping above a certain threshold power, the square pulses were stretched in duration, linearly dependent on the slave laser power but independent from the power of the external triggering pulse train. When both lasers were operated without synchronization, the repetition rate of the Yb-laser was twice that of the Er-laser. Upon the master injection, the square ns slave laser jumped from the fundamental to the 2nd-harmonic mode-locking and the pulse duration was narrowed to half, indicating that the XPM-induced NPR is indeed the mechanism responsible for the synchronization.
2. Experiment and results
A hybrid master-slave configuration was employed in the experiment, as shown in Fig. 1, to demonstrate the synchronous mode-locking in the long-cavity slave fiber laser with the master laser pulse injection. The master was a passively mode-locked Yb-fiber laser by the NPR effect, working at a repetition rate of 1.91 MHz. One of the fiber collimators was mounted on a moving stage so that the cavity length could be slightly changed. Without any dispersion-compensation components, the pulse duration of the master laser was 47 ps with the output spectrum centered at 1053 nm. The master laser was further amplified by an Yb-doped fiber amplifier to reach the average power of 150 mW. The amplified laser pulses were injected to the slave laser through a WDM of 1064/1550 nm. In order to optimize XPM-induced NPR in the slave laser pulses, the polarization of the master pulses was carefully adjusted by a fiber polarization-controller before injection.
The slave was a ring-cavity fiber laser with 2 m single-mode Er-doped fiber pumped by a 450 mW fiber-pigtailed diode laser at 980 nm. Two fiber polarization-controllers were installed in the slave cavity for precisely tuning the intra-cavity polarization. The polarization-dependent isolator allowed unidirectional lasing. Since a longer fiber cavity makes the nonlinear polarization switching more evident for peak power clamping, a 200-meter-long single-mode fiber was installed in the slave cavity to get the square ns pulses. Without the master injection, the slave fiber laser operated at its fundamental repetition rate of 956 kHz, which was half of the master laser’s repetition rate.
In general, solitary pulses were typically generated in the mode-locked Er-doped fiber lasers. However, with a long cavity, ns square mode-locking pulses can be generated due to the peak-power clamping effect. The round-trip transmission of the mode-locked slave laser pulse through the polarization dependent isolator (ISO2) was 
where L is the length of the birefringent fiber, θ the azimuth angle of the polarization-dependent isolator with respect to the fast axis and Ω the rotation angle induced by polarization controllers and fiber intrinsic linear birefringence. Assuming that the pulse is linearly polarized at θ = 45°, the beat length Lb is power-dependent as
where L b0 is the linear beat length of the birefringent element (in this case, the total power-independent birefringence of the cavity) and P is the normalized power defined as P = 2n 2 I/3Δn, where n 2 is the nonlinear refractive index, I is the light intensity and Δn is the refractive difference between the two birefringent axes. According to Eq. (2), the requirement for the lowest normalized power that maximizes the round-trip transmission in Eq. (1) is
The switching power decreases with the fiber length according to Eq. (3). Once the pulse power is sufficient to meet the maximum round-trip transmission, the peak power will be clamped to maintain the condition. In this situation, without the injection of the master laser, the slave laser could be operated in the square ns mode-locking mode by adjusting the polarization. The pump power threshold for the free running square mode-locking was 200 mW. And the slave exhibited tunable pulse duration linearly dependent on the intracavity power as shown in Fig. 2(a). With the pump power of 450 mW, the output pulse duration was 11 ns, as detected by a fast InGaAs photodiode (bandwidth of 2.57 GHz) and recorded by a digital oscilloscope with a time resolution of 500 ps.
As the master pulse was injected into the slave laser, the injected pulse induced a nonlinear phase shift of the slave laser between two orthogonal polarization modes as 
where Leff is the effective interaction length of XPM coupling between the master and slave lasers, Ep the electric field of the master laser injected in the slave laser cavity, and λ the central wavelength of the slave laser. As the XPM-induced nonlinear phase shift is only related to the power of the master pulse, it just functioned as an equivalent linear polarization rotating element Ω in Eq. (1). As a consequence, the master laser injection acted as a trigger to synchronize the mode-locking, while the power for the slave laser to reach its first maximum round-trip transmission was still maintained. Upon the master injection, the Er-laser was synchronized to run at its second harmonic repetition rate due to the XPM-induced NPR, and the threshold for the mode-locking was decreased to 50 mW. The pulse waveforms of the synchronous mode-locked Er-laser was recorded as a function of the pump power shown in Fig. 3(a). When the pump power was below 200 mW, the pulse trace was not square because the energy stored in the pulse was not sufficient to sustain the square wave. In this mode, the peak power increased with the pump power. When the pump power reached 200 mW, the tail part of the slave laser pulse arose obviously, and square mode-locking pulses were generated. As the pump power increased further, the pulse was stretched linearly with the pulse energy due to the peak-power clamping effect. At the maximum pump power of 450 mW, the synchronous square ns pulses exhibited a duration of 5.5 ns, exactly half that of the free-running pulses as an indicative of peak-power clamping at the same level due to the induced switch from the fundamental to the second harmonic mode-locking. The peak power was maintained around 3.3 W at different pump powers in the square mode-locking state as shown in Fig. 3(b). On the other hand, the pulse duration of the synchronous slave laser did not change when we changed the injection master laser power. It confirmed that the peak-power clamping effect was the main reason for square-shaped pulse and the injected master pulse just acted as a trigger to synchronize the square ns mode-locking. As a direct consequence of the peak-power clamping effect, much longer pulse duration was achieved with higher pump powers. Since the energy stored in the laser cavity was kept the same at the same pump power but the synchronized pulse repetition rate was doubled, the pulse energy in the free-running state was halved in synchronized mode-locking state and the peak power of each pulse was clamped at the same value. As a result, the pulse duration of synchronous Er-laser was half of that in the free-running state as shown in Fig. 2(a, c). The corresponding spectra of the two states exhibited little difference in Fig. 2(b, d), with a 3-dB bandwidth of 11.5 nm.
Note that passive synchronization of different mode-locked lasers has been achieved in coupled-cavity lasers sharing the same Kerr-type nonlinear medium [18, 19], or independently mode-locked lasers in the master-slave configuration with master pulse injection into the slave laser . Both schemes work efficiently for ps or fs mode-locked lasers even with some amount of cavity mismatch tolerance, which could guarantee a robust pulse synchronization against cavity length drifts. In the coupled-cavity configuration, laser modes of length-mismatched cavities could be sensitively pulled together by XPM effects in the shared nonlinear medium. Nevertheless, synchronous mode-lockings could only be operated with a limited cavity length detuning in the standard master-slave laser configuration. In our synchronization experiments, the master pulses were injected in slave laser at relatively high powers, and the induced XPM effects were further enhanced in intensity in the long slave cavity. On the other hand, ΔL/L (fractional length mismatch) is proportional to Δν (optical frequency mismatch), which relaxes the requirement of cavity length mismatch. As a consequence, XPM induced NPR in the long slave cavity could modulate the power-dependent beat length efficiently to balance the corresponding intracavity group delay, leading to robust ns-ps synchronization at relatively large cavity mismatch tolerance.
Part of the output pulses from the master and the slave were detected independently in order to monitor the synchronization of the two lasers. The oscilloscope was triggered by the signal from the master pulse trains, and the signal from the slave pulse trains could be clearly displayed on the oscilloscope, indicating the slave Er-doped fiber laser was stably synchronized. The repetition rate of the slave Er-fiber lase was monitored by a spectrum analyzer with a resolution of 1 Hz as we changed the master cavity length. As shown in Fig. 4(a), the fundamental repetition rate of the slave laser was fully restrained (at least 50 dB) when synchronized. The peak position of the RF spectrum of the slave laser was recorded while changing the cavity length of the master laser. As shown in Fig. 4(b), RF spectrum of the square ns pulse train from the slave changed linearly with the master cavity length mismatch from the -1.3 to 1.3 mm. While in this region, the repetition rate discrepancy of the master and slave was recorded with a digital counter in Fig. 4(c). The sub 0.1 Hz deviation indicated the two lasers were fully synchronized. Beyond the ±1.3 mm range, the Er-fiber laser jumped back to its fundamental repetition rate of 956 kHz. This maximum mismatch range of 2.6 mm made it possible to construct a robust ns-ps synchronization system against environmental vibrations. And the synchronization of both lasers could be maintained stably for days. The timing jitter of the synchronous lasers was achieved by measuring the intensity fluctuation of the cross correlation signal with a low pass filter of 100 Hz bandwidth. The signal was recorded at the rising edge of the cross correlation where the signal changed linearly with time delay as shown in the inset of Fig. 4(d), resulting a timing jitter of 4.3 ps. This ultra-low timing jitter indicates the square ns mode-locked Er-laser and the ps mode-locked Yb-laser were precisely synchronized.
In conclusion, with a master-slave configuration, a square ns Er-fiber laser was synchronized to a ps Yb-fiber laser by XPM-induced NPR. Unlike the solitary mode-locking, the square pulses of the slave were clamped in peak power and the pulse duration was dependent linearly on the pump power. The largest square pulse duration of 5.5 ns has been achieved at the maximum pump power of 450 mW in our experiment. It can be inferred that the pulse duration of the slave laser could be further stretched if a higher power pump was used. In this way, the pulse duration can be programmed by controlling the pump power while keeping synchronized to the ultrashort laser. Moreover, the cavity mismatch between the two lasers reached ±1.3 mm, ensuring the synchronous system robust to external environment vibrations. Since accurately synchronized ns lasers could be separately amplified to very high energies in array and if synchronization is achieved at sub-cycle timing jitter, the amplified square pulses could be stacked for coherent accumulation of pulse energy, this technique is anticipated to stimulate technology innovation in high-energy high-density physics . Note that coherent pulse synthesis requires sub-cycle timing jitter of the synchronization, while the timing jitter measured here was still at least 2 orders of magnitude more than the duration of an optical cycle. As the XPM sidebands are generated in a phase-coherent way through intracavity nonlinear frequency mixing, the longitudinal modes of the master and slave lasers should be in principle phase-locked. The corresponding degree of phase (in-)coherence deserves further experimental exploration and dramatic improvement on jitter of the synchronization may be achieved for phase-locking the underlying optical carrier at sub-cycle levels of jitter. We emphasize that such an all-optical synchronization is realized without any feedback control, providing a robust but simple technique to control the synchronization between square nanosecond laser pulses and ultrashort pulse triggers.
This work was funded in part by National Natural Science Fund (Grant No. 10374028, 60478011, 10774045 and 10525416), National Key Project for Basic Research (Grant No. 2006CB806000 and 2006CB921105 ), Projects from Shanghai Science and Technology Commission (Grant No. 06JC14025 and 06SR07102), Program for Changjiang Scholars and Innovative Research Team, and ECNU PhD Research Fund.
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