We demonstrate long-term stable passive synchronization between two-color Ti:sapphire (master) and Yb-doped fiber (slave) mode-locked lasers in the master-slave configuration. Active temperature stabilization suppresses the repetition fluctuation of the slave laser, and with the aid of temperature stabilization in combination with simple repetition locking of the master laser, long-term stable synchronization as long as 6 h was realized. The repetition rates of both lasers are locked in submillihertz precision. A timing jitter of 0.75 fs was obtained at a detection bandwidth of 350 kHz.
© 2014 Optical Society of America
Synchronization between two-color ultrashort laser pulses has become crucial in ultrafast science for a variety of applications such as time-resolved pump-probe spectroscopy , nonlinear microscopy , optical parametric amplification [3–5], coherent pulse synthesis [6–9], and clock dissemination [10,11]. Among the various schemes, the passive synchronization utilizing nonlinear optical effect is capable of achieving low timing jitter with a simple experimental setup without any complicated electronics [12–20]. There have been many attempts to reduce jitter, and subfemtosecond synchronization has been reported with passive  and active-passive hybrid schemes [14,20]. In the master-slave configuration with fiber lasers, the master laser pulses are injected into the fiber of the slave laser cavity [13,16,20]. The cross-phase modulation between the copropagating two-color pulses induces a spectral shift in the slave pulses. The sign of the shift, which is dependent on the relative timing of two pulses, behaves in a negative feedback manner to enable self-synchronization in combination with the negative intracavity dispersion [21,22]. From a practical perspective, long-term stability of synchronization is obviously an important issue. However, the passive scheme has difficulties with long-term stable operation because of the small tolerance of the cavity length mismatch, which is typically ~10 μm corresponding to a difference of a few hundred hertz in a repetition rate of 100 MHz . Such cavity-length fluctuation is quite common because of temperature variation of the base plate and/or the fiber. It is possible to directly lock the repetition rate of the master laser by active control of the cavity length with a piezo-actuated mirror. However, it would be difficult to stabilize the cavity length of the slave laser in similar manner, because there is no way to detect the free-running repetition rate of the slave laser during synchronization. Therefore, temperature stabilization of the slave laser is one of the solutions to realize long-term stable operation.
Here, we actively stabilize the temperature of the base plate and the fiber of an Yb-doped fiber (YbF) mode-locked laser. With the aid of the temperature stabilization, we demonstrate long-term stable synchronization in the master-slave configuration between the fiber laser (slave) and a Ti:sapphire (TiS) mode-locked laser (master). Under the best environmental conditions, the repetition-rate fluctuation of the fiber laser was suppressed to 2.0 Hz in 4 h. Long-term stable synchronization was achieved for 6 h with the repetition frequencies of both lasers locked in submillihertz precision. In addition, the presented system shows a timing jitter of 0.75 fs over a short time scale at a detection bandwidth of 350 kHz.
2. Temperature stabilization of Yb-doped fiber laser
The layout of YbF mode-locked laser is shown in Fig. 1. The unidirectional ring cavity is designed in a manner similar to the system described previously . The fiber section includes 30 cm of single-mode Yb-doped gain fiber with a pump absorption of 1200 dB/m and approximately 1 m of single-mode silica fiber. The gain fiber is pumped by a single-mode fiber- coupled laser diode delivering an approximate power of 300 mW at a wavelength of 976 nm. The dispersion of the fiber is compensated for with a pair of gratings with a groove density of 600 lines/mm. Stable mode locking based on nonlinear polarization rotation occurs by fine adjustment of a half-wave plate and two quarter-wave plates. The output pulses are extracted from the rejection port of the polarizing beam splitter. The typical output power is 60 mW, and the repetition rate is 100 MHz. After the output pulse train is detected with a fast photodiode, the repetition rate is counted with a frequency counter (Agilent 53132A) with a gate time of 1 s.
To suppress the fluctuation of the repetition rate, the base plate temperature is actively stabilized with a heater and a temperature controller. We employed a simple scheme of one-way proportional-integral control without cooling equipment. We used five metal-clad resistors with a resistance of 2 Ω connected in series for heating. The current amplifier circuit provides a maximum current of 1.3 A and a maximum power of 17 W. Most of the fiber section is attached to the base plate to heat the fiber simultaneously. Two platinum temperature sensors (PT100) are used to monitor the temperature. One sensor is connected to the temperature controller, and the other is used for out-of-loop measurement. The aluminum base plate is placed on heat insulator for thermal decoupling. The entire system is placed inside an aluminum box covered with heat-insulating material for protection against air turbulence and acoustic noise.
Figure 2 shows the dependence of the repetition rate on the base plate temperature. The variation in temperature (blue) and repetition rate (red) are shown when the heater is switched on and off alternately. The slight delay seen in the two curves is due to heat flow by the nonnuniform temperature distribution. An increase of 1700 Hz in repetition rate was observed for a temperature decrease of 1 K. The corresponding thermal coefficient of the repetition-rate variation is estimated as (dfrep / dT) / frep ~−1.7 × 10−5 (K−1), where frep and T represent the repetition rate and the temperature, respectively. The thermal variation in optical path length is caused by thermal expansion of the fiber, and that of the base plate, and the variation in group index of refraction of the silica fiber. As frep is related to the optical path length L of the cavity by frep = c / L, where c is the speed of light in vacuum, the fractional change of repetition rate is related to that of optical path length as Δfrep / frep = −ΔL / L. As L = Lfiber + Lfree, when the optical path length L consists of those of the fiber Lfiber and the free space Lfree, the contribution of each part is proportional to the ratio of lengths, i.e.,24]. Given these values, we obtain a theoretical value of thermal coefficient (dfrep / dT) / frep ~−1.3 × 10−5 (K−1), which reveals reasonable agreement with the experimental result. The discrepancy would be attributed to nonuniform temperature distribution on the base plate and/or the fiber.
Figure 3(a) shows the best performance of long-term temperature stabilization. The temperature (blue) gradually increased and reached a fixed value in 8 h. In accordance with temperature stabilization, the repetition rate was also stabilized, although the oscillatory feature was observed in the first 3 h. As shown in the zoom (b) from 8 h to 12 h, the repetition rate fluctuation was suppressed to 2.0 Hz (rms) for 4 h as a result of the suppressed fluctuation of temperature of 2.4 mK (rms). The stabilization behavior depends to a certain extent on the environmental conditions such as ambient temperature variation. Figure 3 is the best result obtained under our conditions, although there are some results with longer duration (> 24 h) and relatively more fluctuation. In some cases, we observed repetition-rate fluctuation of several tens of hertz possibly due to air flow from the air conditioner, although the system was completely shielded in a metal box. Nevertheless, we concluded that the stabilization is effective for long-term synchronization because such fluctuation is within the tolerance of passive synchronization, which will be clarified in the next section.
3. Long-term passive synchronization between Ti:sapphire laser and Yb-doped fiber laser
We demonstrate long-term passive synchronization between a TiS mode-locked laser (master) and the temperature-stabilized YbF mode-locked laser (slave). The experimental setup is shown in Fig. 4. The temperature of the YbF laser is actively stabilized as described in the previous section. The repetition rate of the master laser should also be stabilized to achieve long-term synchronization. Although it could be attained by active temperature stabilization as well as the slave laser, the direct locking of the repetition rate is rather simple and straightforward, because coarse locking within the tolerance of the passive synchronization is sufficient for this purpose. In addition, the clock transfer of the master reference pulses with well-stabilized repetition rate into the slave laser is one of the important scopes of this work. Thus we actively lock the repetition rate of TiS laser to a 100-MHz reference signal from the RF synthesizer by use of the piezo-actuated mirror of the cavity. We used a simple technique of coarse RF phase locking at fundamental repetition frequencies with a slow feedback bandwidth (< 10 kHz), whereas fine locking would require gigahertz harmonic frequency comparison with rather complicated electronics and faster feedback bandwidth .
Figure 5(a) shows the variation of 1-s gated repetition rate of TiS laser for 6 h. The measured fluctuation of 0.76 mHz (rms) is limited to the resolution of the frequency counter.The output of the TiS laser is split into two branches with a broadband beam splitter after dispersion compensation with chirped mirrors. The beam in one branch is injected into the YbF cavity from the rear of the dielectric mirror after adjustment of polarization (shown in Fig. 1). The beam in the other branch is combined with the dispersion-compensated YbF laser output by use of the beam splitter for jitter measurement. Figure 6 shows the temporal profiles of dispersion-compensated pulses out of both lasers measured with two-dimensional spectral shearing interferometry (2DSI) . The pulse durations of TiS laser and YbF laser are 13 fs and 51 fs, respectively. The passive synchronization occurs by tuning of the repetition rate of TiS laser to be closer to the repetition rate of YbF laser. We observed long-term stable synchronization for 6 h. In this experiment, the repetition locking of TiS laser failed in 6 h because of limited range of the piezoelectric actuator. The use of an actuator with longer range would improve the duration of synchronization. Figure 5(b) shows the variation of the repetition rate of YbF laser. As a consequence of synchronization, the stability of the repetition of TiS was successfully transferred into that of YbF laser. The fluctuation of the repetition of YbF laser was suppressed to 0.72 mHz (rms), which is comparable to that of TiS laser [Fig. 5(a)]. The calculated difference of two repetition rates shown in Fig. 5(c) indicates that the repetition rates of the two lasers are locked with a precision of 0.93 mHz (rms), which is almost the resolution limit of the frequency counter.
To evaluate the short-term stability of passive synchronization, we measured the timing jitter between two-color pulses. As shown in Fig. 4, the collinearly combined two-color pulses are focused with an off-axis parabolic mirror into a Type-I β-barium borate crystal 0.4 mm thick for sum-frequency generation (SFG). The SFG output at a wavelength around 460 nm is passed through the spectral filter and detected with the photomultiplier tube. The relative delay is adjusted at half maximum of the cross-correlation. The coefficient of the SFG fluctuation to the timing jitter is calibrated by oscillating the piezo-actuated delay stage. Figure 7 shows the power spectral density and the rms integration of the jitter measured by the SFG fluctuation. An rms integration of 0.75 fs in a detection bandwidth of 350 kHz was obtained, which reveals low-jitter feature of the passive synchronization scheme. The long-term drift in the extracavity delay paths would possibly pose the problem in some applications, however, it could be resolved by employing the active-passive hybrid scheme to implement the slow feedback control of the extracavity delay line [14,20].
We have demonstrated long-term stable passive synchronization in the master-slave configuration between two-color mode-locked Ti:sapphire (master) and Yb-doped fiber (slave) lasers. The fluctuation of repetition rate of the slave laser was suppressed by simple active stabilization of temperature. In combination with the active repetition locking of the master laser, the long-term stable synchronization as long as 6 h was realized. In addition, the short-term jitter in the subfemtosecond regime was also achieved. The presented scheme will realize the long-term stable synchronization with relatively low timing jitter characteristics without necessity of complicated electronics, and would be helpful for applications requiring stable two-color synchronization.
This work was supported in part by JSPS KAKENHI Grant Numbers 22686010 and 25390105.
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