Synchronized time-lens source is suitable for various applications in coherent Raman scattering (CRS) imaging up to video-rate. Timing jitter between the time-lens source and the mode-locked laser is a crucial parameter for estimating the synchronization performance. Although it has been measured experimentally, there is a lack of theoretical investigation of this parameter. Here we demonstrate numerical simulation results of timing jitter in a synchronized time-lens system, with parameters similar to those in real experiments. Our results show that due to the optical delay between the time-lens source and the mode-locked laser, the timing jitter is close to the intrinsic timing jitter of the mode-locked laser. Further reduction in timing jitter can be achieved by matching the optical delays between the time-lens source and the mode-locked laser.
© 2015 Optical Society of America
CorrectionsPing Qiu and Ke Wang, "Timing jitter in synchronized time-lens source for coherent Raman scattering imaging: publisher’s note," Opt. Express 24, 1045-1045 (2016)
7 January 2016: A correction was made to the acknowledgments.
Time-lens compression is an alternative technique to generate ultrashort pulses to conventional mode-locking. A time-lens imposes a temporal quadratic phase modulation onto the light, analogous to a spatial lens imposing a spatial quadratic phase onto a wave front [1,2 ]. In practice, the quadratic phase modulation can be achieved approximately by applying a sinusoidal drive signal to electro-optic phase modulators. With proper dispersion compensation, ultrashort pulse trains typically as short as picoseconds (ps) can be obtained from a continuous-wave (CW) laser [2–5 ]. Using special techniques such as time-lens loop  or soliton self-frequency shift , even femtosecond (fs) pulses can be generated from a time-lens source.
While the repetition rate of a conventional mode-locked laser is determined and constrained by the cavity length, the repetition rate of a time-lens source is entirely determined by the electrical drive signal. Thus, a time-lens source has the remarkable capability of synchronizing to any mode-locked laser, on condition that the electrical drive signal is derived from the mode-locked laser. Recently, it has been experimentally demonstrated that the time-lens source can be synchronized to both fiber-based and solid-state femtosecond or picosecond mode-locked lasers [7,8 ]. Furthermore, picosecond synchronized-time lens source has become an ideal choice for coherent Raman scattering (CRS) imaging, which typically needs two-color picosecond synchronized laser source to probe the vibrational transition in biological or chemical samples [9,10 ]. Experimentally, synchronized time-lens source has found various applications in CRS imaging, such as single-frequency coherent anti-Stokes Raman scattering (CARS) and stimulated Raman scattering (SRS) imaging [7,8 ], and spectroscopic SRS imaging [11,12 ] with imaging speed even up to video-rate .
Timing jitter is the key parameter in evaluating the synchronization performance between synchronized sources. In terms of CRS imaging, a large timing jitter introduces dramatic signal fluctuation, which is devastating for descent image acquisition, not to mention quantitative analysis of the image . Experimentally, it can be measured by sum-frequency generation in a nonlinear crystal, and the measured value varies depending on the specific mode-locked laser used for synchronization [7,8,11 ]. However, so far there has been no theoretical prediction of timing jitter in a synchronized time-lens source. As a result, there is a lack of means to further reduce timing jitter for better image acquisition. In this paper, we address this issue by numerical simulation. Our results show that, due to the optical delay between the time-lens source and the mode-locked laser, the timing jitter is similar to the intrinsic timing jitter of the mode-locked laser quantitatively. Furthermore, an effective means of reducing the timing jitter is to match the optical delay between the time-lens source and the mode-locked laser.
2. Time-lens setup and simulation details
The simplified block diagram of a typical synchronized time-lens source [7,11 ] is shown in Fig. 1 . A fast photodetector converts the mode-locked laser output (e.g., 80 MHz) into an RF pulse train of the same repetition rate, which is then divided into two branches. One branch is filtered by a narrowband RF filter to get a 10-GHz sine wave to drive the phase modulator, while the other branch (80 MHz) drives the Mach-Zehnder intensity modulator (MZ) to carve a synchronized 80-MHz optical pulse train from the CW laser. After dispersion compensation with a dispersion compensator (DC) such as a chirped fiber Bragg grating or a free-space grating pair, chirping due to phase modulation can be largely compensated for and the pulse width can be compressed down to picosecond, suitable for CRS imaging. Since all the radio-frequency (RF) driving signals are derived from the mode-locked laser, synchronization can be achieved.
Similar to the real experimental setup, in our simulation, we assume the repetition rate of the mode-locked laser is 80 MHz. The 125th harmonic signal of this 80 MHz repetition rate (10 GHz) is filtered by a 50-MHz bandpass filter to drive the phase modulator for spectral broadening. Phase modulation is performed in the time domain, and the modulated electric field of the light is given byFig. 2(a) ] matches that in experiment for a 10-GHz RF drive. After pulse carving due to the MZ, the optical output is an 80-MHz, 70-ps pulse train with Gaussian pulse shape. A DC with quadratic phase compensation compresses the pulse width to 1.7 ps [Fig. 2(b)], analogous to that in experiment. The sidelobes are due to the nonlinear chirp introduced by sine wave modulation .
In our simulation, we use a Gaussian white noise generator to introduce intrinsic timing jitter (σML) of different root-mean-square (RMS) values to the optical pulse train from the mode-locked laser. To calculate the timing jitter between the time-lens source and the mode-locked laser (σsyn), we first find the peaks and the corresponding temporal positions of the two pulse trains, then do subtraction to get relative jitter, and finally calculate the RMS timing jitter between the two pulse trains. We want to emphasize that there is optical delay between the time-lens source and the mode-locked laser, due to the various RF components including RF cables and optical components including optical fibers. In experiment, the time-lens output pulse is delayed by ~112.5 ns, in other words, the time-lens output pulse is delayed by ~9 optical pulses compared with the mode-locked laser output. As has been demonstrated experimentally, temporal overlapping can be easily achieved through RF tuning . In simulation, we consider situations with and without optical delays between the two synchronized sources.
3. Simulated timing jitter in a synchronized time-lens source
3.1. With optical delay between the two pulse train
First we consider the situation with optical delays. Figure 3 shows simulation results from three typical runs, assuming σML = 200 fs and the time-lens output is delayed by 9 pulses. The black squares and the red circles in the figure mark the deviation of the peak positions of the optical pulses from their nominal positions without timing jitter. In other words, they are a measure of the timing jitter. Consequently, we can calculate σsyn between the two optical pulse trains. Figure 4 shows σsyn as a function of σML. Each data point (black square) is the average of ten successive runs for the same σML, and the error bars indicate the standard deviation. It can be clearly seen that σsyn follows σML, and on average, σsyn is 20~25% larger than σML. This extra timing jitter is due to the timing jitter of the time lens source.
Depending on the exact experimental setup of the time-lens source, such as whether the DC is all-fiber or free space based and the length of the optical fibers used, the time-lens output may not be delayed by nine pulses. So we calculated σsyn for various optical delays between the two pulse trains and σML, shown in Fig. 5 . Each data point is still statistics of ten successive runs. For various σML, if the time-lens output is delayed by two optical pulses or more, then the timing jitter σsyn doesn’t change much and is almost independent of the delay. However, when the time-lens output is only delayed by one optical pulse, σsyn is reduced by ~10% compared with those at larger delays (≥2 optical pulses).
3.2. Without optical delay between the two pulse trains
Next we consider the situation without optical delay between the two pulse trains, i.e., the first pulse from the time-lens source overlaps the first pulse from the mode-locked laser. In experiment, this can be achieved by introducing extra delay to the mode-locked laser output and shrinking the path length in the time-lens setup (e.g., using shorter RF cables and optical fibers). Figure 6(a) shows σsyn as a function of σML. When there is no optical delay between the two pulse trains, σsyn is only ~1/3 of those at larger delays (Figs. 4 and 5 ), and ~40% of the intrinsic timing jitter σML. This can be easily understood if we compare the peak positions of the two synchronized pulse trains [Figs. 6(b) and 6(c)]. Since the driving signals of the time-lens source are derived from the mode-locked laser, the fluctuation of the time-lens output follows that of the mode-locked laser almost instantaneously [Fig. 6(b)]. As a result, the relative timing jitter σsyn is small. If there is large optical delay between the two pulse trains, since the intrinsic timing jitter of the mode-locked laser is an independent event, there is no correlation between the time-lens output and the mode-locked laser anymore [Fig. 6(c)]. As a result, σsyn has contributions from both the timing jitter of the mode-locked laser and the time-lens source, so the resultant σsyn is much larger than that without optical delay. These results suggest that an efficient means in reducing the timing jitter in a synchronized time-lens source is to match the optical delays of the two pulse trains.
3.3. 10-GHz RF filtering with narrower pass band
Although in simulation and experiment a 50-MHz bandpass filter was used to filter the 10-GHz RF drive only, it is tempting to think that a filter with a narrower pass band will yield a cleaner 10-GHz sinusoidal drive for the phase modulators. As a result, the timing jitter σsyn might be smaller. We also tested this hypothesis in simulation, shown in Fig. 7 . Admittedly, a narrower pass band filter reduces the intrinsic timing jitter of the time lens-source (blue triangles), due to a cleaner sinusoidal drive. However, it is the relative timing jitter between the mode-locked laser and the time-lens source (σsyn) that we care most, especially for experiments involving synchronization such as CRS imaging. A RF filter with a broader pass band allows the time-lens source to better follow the fluctuation of the mode-locked laser, which leads to a smaller σsyn when there is no optical delay between the two pulse trains. Quantitatively, in the example given in Fig. 7, the RMS timing jitter σsyn with a 50-MHz filter (σsyn = 157 fs) is only 42% of that with a 10-MHz filter (σsyn = 373 fs). Admittedly, if there is optical delay the two pulse trains, there will be less timing jitter (σsyn) due to the less intrinsic timing jitter of the time-lens source. However, in this case, the lower limit will be the intrinsic timing jitter of the mode-locked laser, which is still more than twice larger than that with a 50-MHz filter and without optical delay between the two pulse trains.
In this paper we performed numerical simulation of timing jitter in a synchronized time-lens source, to better understand the origin of this fundamental parameter and provide general guidelines for further reducing timing jitter in experiments. Based on the simulation results, we propose an efficient means of reducing timing jitter is to match the optical delays of the time-lens source and the mode-locked laser, which yields timing jitter only ~1/3 of those at larger delays, and ~40% of the intrinsic timing jitter of the mode-locked laser. Reduction of timing jitter will offer great benefit for image acquisition and analysis in applications not only limited to CRS imaging, but also other imaging modalities involving two synchronized laser sources such as stimulated emission , two-photon absorption  and excited state absorption .
The authors are much obliged to Prof. Chris Xu from Cornell University for the inspiring discussion of this work. This work was supported by the National Natural Science Foundation of China (Grants No. 11404218 and No. 61475103); the Natural Science Foundation of SZU (Grant No. 00002701); and the Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry. This work was supported by the Project of Department of Education of Guangdong Province (No. 2014KTSCX114).
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