Quantum-limited timing jitter characterization of ... - OSA Publishing

Vol. 25, No. 1 | 9 Jan 2017 | OPTICS EXPRESS 10

Quantum-limited timing jitter characterization of mode-locked lasers by asynchronous optical sampling HAOSEN SHI, YOUJIAN SONG,* JIAHE YU, RUNMIN LI, MINGLIE HU, AND CHINGYUE WANG Ultrafast Laser Laboratory, Key Laboratory of Opto-electronic Information Technical Science of Ministry of Education, School of Precision Instrument and Opto-electronics Engineering, Tianjin University, Tianjin 300072, China * [email protected]

Abstract: We demonstrate a novel time domain timing jitter characterization method for ultra-low noise mode-locked lasers. An asynchronous optical sampling (ASOPS) technique is employed, allowing timing jitter statistics on a magnified timescale. As a result, sub femtosecond period jitter of an optical pulse train can be readily accessible to slow detectors and electronics (~100 MHz). The concept is applied to determine the quantum-limited timing jitter for a passively mode-locked Er-fiber laser. Period jitter histogram is acquired following an eye diagram analysis routinely used in electronics. The identified diffusion constant for pulse timing agrees well with analytical solution of perturbed master equation. © 2017 Optical Society of America OCIS codes: (320.7100) Ultrafast measurements; (270.2500) Fluctuations, relaxations, and noise; (140.4050) Modelocked lasers; (120.0120) Instrumentation, measurement, and metrology.

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#277832 Journal © 2017

http://dx.doi.org/10.1364/OE.25.000010 Received 29 Sep 2016; revised 8 Dec 2016; accepted 13 Dec 2016; published 3 Jan 2017


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intracavity pulse energy w is 600 pJ, the saturable absorption coefficient α is 0.2, the net cavity dispersion coefficient D is + 5500 fs2, and the excess spontaneous emission factor Θ is supposed to be between 2 and 10. The notations are from Ref [7]. The experiment matches well with analytical model, confirming the validity of this timing jitter measurement method.

Fig. 4. Experimental results at a fixed offset repetition rate of 2 kHz. (a). The obtained STDEV of visual timing jitter versus tp. The inset shows typical jitter histogram of the measured Tp . (b). The retrieved period jitter STDEV of LUT versus tp. The inset shows the estimated jitter PSD and the comparison with analytical model.

The same experiment is conducted by changing the offset repetition rate to 1.5 kHz. The measurement results are compared with that conducted under 2 kHz offset repetition rate, as shown in Fig. 5(a). When t p is fixed, the obtained visual timing jitter STDEV at 1.5 kHz offset repetition rate is apparently larger than that at 2 kHz offset repetition rate, in accordance with Eq. (1). This means that, lower offset repetition rate is also favorable for enhanced jitter measurement sensitivity. The retrieved optical period jitter is identical at different offset repetition rates. This is easy to understand because slight repetition rate change will not affect the laser noise character. Taking into account the impact of both t p and ∆f r , the ultimate resolvable optical period jitter STDEV in the presence of electronic limited measurement sensitivity ( σ e ) can be expressed as


σ 0r =σ e ×

1 ∆f r3 × t p f r4

(2)

Figure 5(b) maps the resolvable optical period jitter STDEV by altering ∆f r and t p at the present σ e = 0.35 ns. Under a 2 kHz offset repetition rate, the lowest measurable period jitter at t p = 80 ps reads 0.35 fs. This number can be reduced to 43.75 as by lowering the offset repetition rate to 500 Hz while keeping t p invariant.

Fig. 5. The measurement results obtained under 1.5 kHz and 2 kHz offset repetition rate. (a) The measured visual timing jitter STDEV (upper) and the calculated optical period jitter (bottom) versus tp. (b) The lowest measurable period jitter versus various Δfr and tp when σe = 0.35 ns.

5. Experiment with free running ultrafast lasers The above measurements require actively repetition-rate-locked ultrafast lasers for the sake of a fixed time-stretch ratio. In fact, the same measurement can be conducted with free running ultrafast lasers as long as f r and ∆f r can be updated in real time. This will significantly simplify the measurement setup and results in a practical sub-femtosecond jitter analysis device since the complex phase-locked loop is not necessary. The experimental setup is based on Fig. 3, while the phase-locked loops are removed. By tuning the offset repetition rate to roughly 2 kHz, stream of ASOPS waveforms can be observed by an oscilloscope and recorded by a digitizer. The offset repetition rate ∆f r is readily determined by recording update period ( Τupdate ), which is no more than the time interval of neighboring repetitive ASOPS waveforms. A frequency counter (Agilent, 53220A) is used to measure the LUT repetition rate f r . The counter’s gate time is set to one second (1 Hz update rate) for the sake of a 14-digit resolution. Note that, this update rate is much slower than that of ∆f r . In order to evaluate the impact of slow update of frequency counter on jitter measurement precision, we characterize the repetition rate stability of the LUT. The measured repetition rate Allan deviation of the free running LUT at 1 second observation time is merely 285 mHz. According to Eq. (1), this uncertainty will impose negligible impact on the precision of the acquired optical period jitter. A jitter measurement experiment is conducted when the digitizer and frequency counter are referenced to the same frequency standard. The measured results based on ~3700 frames of ASOPS waveforms are depicted in Fig. 6. The acquired STDEV of optical period jitter is 0.579 fs with 20 as uncertainty. The slight


difference from the result with repetition rate phase-locking is due to a slight variation in mode-locking condition between the two experiments. Note that, digitizers require large data storage depth for jitter measurement based on free running lasers because the measurement of ∆f r relies on uninterrupted collection of samples. While, by phase-locking both f r and ∆f r , we only need to record the sample data within Tp during each ASOPS period ( Tupdate ). Considering the limited data storage depth of digitizer, more sample frames can be acquired for jitter statistics by using stabilized lasers. The slight fluctuations of the retrieved optical period jitter versus tp in Fig. 6 is merely due to shortage of sample frames. It can be more severe when offset repetition rate is further decreased, thus limits the obtainable jitter measurement resolution.

Fig. 6. Experimental results by using free running lasers at a flexible offset repetition rate of ~2 kHz. (a). The obtained STDEV of visual timing jitter versus tp. The inset shows a typical jitter histogram of the measured Tp . (b). The retrieved period jitter STDEV of LUT versus tp.

6. Conclusion In conclusion, we directly characterize the quantum limited timing jitter of femtosecond lasers in time domain with ASOPS method, enabling real-time visualization of attosecond period jitter of mode-locked lasers based on histogram analysis. In comparison with the routinely used BOC technique, the measurement is less dependent on LUT pulse duration since the measurement resolution is mainly determined by time-stretch ratio. Attosecond sensitivity can be preserved even with picosecond laser pulses, which effectively enlarge the measurement dynamics range as well. Particularly, jitter measurement can be conducted without complex phase-locking loops, which is indispensable for most of existing attosecond resolution jitter measurement techniques. As a result, this simple setup is expected to become a routine approach to attosecond precision jitter measurement for ultrafast optical pulse trains, analogous to eye diagram analysis for digital signals.


Funding National Natural Science Foundation of China (NSFC) (11274239, 11527808, 61535009); Program for Changjiang Scholars and Innovative Research Team in University (IRT13033); National High Technology Research and Development Program of China (2013AA122602). Acknowledgments We acknowledge fruitful discussions with Prof. Jungwon Kim from Korea Advanced Institute of Science and Technology (KAIST), South Korea.