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

1. Introduction

Oscillator instabilities are a fundamental concern for any system that receives or transmits a signal [1]. As the building block for modern information and communication technology, electronic oscillators typically generate clock signals with picosecond timing jitter. This jitter level can be further reduced to a few femtoseconds by using cryogenic sapphire oscillator [1] or optoelectronic oscillators [1,2]. Recently, passively mode-locked lasers have drawn increasing attention as a candidate for ultralow jitter optical oscillator. It has been known that passively mode-locked lasers emit uniformly spaced femtosecond laser pulse trains with extremely good short term stability [3–6]. The quantum limited timing jitter of a low cost femtosecond Er-fiber laser working at room temperature easily reaches hundreds of attoseconds at high Fourier frequency [3,7]. By phase locking to an optical/rf reference, the mode-locked laser thus serves as an optical master oscillator [8]. Recently, ultralow jitter mode-locked lasers have shown great potential for a number of high precision applications, such as high speed analog digital conversion (ADC) [9], large-scale timing synchronization [8], time-of-flight laser ranging [10,11], coherent optical pulse synthesis [12], and high spectral purity rf signal generation [13], to name a few. Precise timing jitter characterization of mode-locked lasers is fundamental for the advances in all the fields.

Timing jitter of mode-locked lasers can be simply characterized by direct high-speed photodetection of laser pulse train and a subsequent repetition rate phase noise analysis by using standard rf techniques [14–17]. However, excess phase noise in the photodetection process limits timing resolution to a few femtoseconds. Although it is sufficient to characterize technical jitters at low Fourier frequencies, this method is not capable of measuring sub-femtosecond quantum limited timing jitter of passively mode-locked lasers. The resolution limit of rf techniques has been overcome by optical cross-correlation methods [18–20], which make use of inherent steep rising edge of femtosecond laser pulses as highly sensitive timing error discriminator. Particularly, a balanced optical cross-correlation (BOC) [19,20] setup is most commonly used, which secures amplitude noise insensitive timing information extraction. A record-low timing jitter of 13 as (from DC to Nyquist frequency) from Kerr-lens mode-locked Ti:sapphire lasers generating 10 fs pulses has been demonstrated by using BOC method [4]. Besides well-established BOC method, novel optical heterodyne methods based on comb-line interference [21,22] provides highly sensitive timing discrimination signal as well, enabling attosecond precision timing jitter characterization. Details on the rapidly evolving timing jitter measurement techniques towards attosecond precision can be found in a recent review article [23].

The existing methods mostly measure timing jitter power spectral density (PSD) for mode-locked lasers. As a complementary approach to spectral analysis, eye diagram analysis has been extensively used for electronic systems as well, where signal timing behavior is visualized in an oscilloscope or digitizer, providing a straightforward online diagnosis in time domain. In this letter, we demonstrate a novel time domain timing jitter characterization method, which is an optical equivalent to eye diagram analysis used at rf frequencies. It essentially takes advantage of an asynchronous optical sampling (ASOPS) approach [24,25], which is capable of linearly stretching ultrafast processes in time such that sub-femtosecond period jitter of optical pulse stream is visible to fast data acquisition electronics. Here, ASOPS is implemented by optical cross-correlation between a pair of passively mode-locked Er-fiber lasers with a fixed or flexible offset repetition rate. The period jitter of one mode-locked Er-fiber laser serving as laser under test (LUT) is resolved with 350 as resolution. This number can be reduced to tens of attoseconds by decreasing the offset repetition rate, which effectively magnifies the time-stretch ratio.

2. Measurement principle

The concept is based on direct sub-femtosecond precision pulse timing determination by ASOPS, as depicted in Fig. 1. Two mode-locked lasers with repetition periods (repetition rates) of Tr (fr) and Tr+ΔTr (frΔfr) serve as LUT and local oscillator (LO), respectively. The LUT sends an ultrashort pulse stream to a free space pulse interleaver which divides a single laser pulse into a pulse pair. Here, the timing for the front pulse peak is set as origin, while the timing for the rear pulse peak is tp. The LUT pulse pairs are sampled against LO for high precision rear pulse timing acquisition. Every repetition period (Tr), the LO pulse shifts by ΔTr relative to the LUT pulses, and samples a slightly different portion of the LUT pulse pair. An entire scan of the LUT pulse pair is updated every TupdateTr2/ΔTr, corresponding to an update rate of Δfr=1/Tupdate. The so called ASOPS process effectively stretches real femtosecond timescale by a factor of N=Tr/ΔTr. As a result, the timing for the rear pulse peak can be determined by Tp/N, where Tp is the acquired rear pulse timing in the magnified timescale. Ideally, the consecutively acquired Tp would be invariant, determined by the differential optical path length between the two arms of the pulse interleaver. Nevertheless, ASOPS process will inevitably introduce uncertainty in Tp in the presence of timing jitter. Suppose the LO is noise free, while the LUT is quantum limited, meaning that the LUT emits an optical pulse train undergoing random walk. The optical period jitter δi, defined by the deviation from the ideal time interval between the ith and the (i+1)th pulse, exhibits normal distribution with variance of σ02. Given that a LO pulse exactly overlaps the peak of LUT front pulse, the sample of rear pulse peak is expected after M repetition periods with M[Tp/Tr]. During this time interval, the random walk of LUT pulse train will bring a summed timing error i=1Mδi with variance σM2=Mσ02. As a result, the consecutively acquired Tp in the magnified timescale will fluctuate following a normal distribution with variance

σ2=N2(Mσ02)tpfr 4Δfr 3σ02,
which is exactly a magnified period jitter variance of LUT. Here, we define σ2 as visual timing jitter variance, which can be routinely quantified by standard jitter statistics in rf domain. The period jitter variance σ02 of LUT can thus be mapped back into the original femtosecond or even attosecond timescale as long as the magnification factors of M and N are determined in advance.

 figure: Fig. 1

Fig. 1 Concept of timing jitter measurement based on ASOPS in time domain. The solid (dotted) pulses illustrate the ASOPS process without (with) LUT timing jitter.

Download Full Size | PPT Slide | PDF

3. Numerical simulation

We test the concept by a numerical model used in Ref [11]. A noise free Gaussian shaped LO pulse train with pulse duration of 100 fs and repetition rate of 100 MHz is generated at first. With the same pulse shape and a pulse duration of 1 ps, a LUT pulse train having a lower repetition rate of 99.999 MHz is constructed in the following. A Gaussian white period jitter δk with variance of σ02=1 fs2 is added to the kth pulse of LUT, thereby inducing a lumped temporal shift of m=1kδm with respect to its ideal timing position. By this means, the LUT pulse train takes on a random walk character. A copy of this pulse train is delayed by tp=~667 ps and is combined with the original pulse train, representing the interleaved LUT. Finally, a sum frequency generation (SFG) based intensity cross-correlation between LO and interleaved LUT and a subsequent square law photo-detection [11,26] produce repetitive pulse pairs in a stretched timescale.

The waveforms of a series of 4000 stretched pulse pairs are superimposed such that the front pulses are aligned, as displayed in Fig. 2. This is analogous to creating an eye diagram with an oscilloscope or digitizer in a long-persistence display mode. The density of waveforms reflects a timing error histogram, as shown in the inset of Fig. 2. A visual timing jitter variance of σ2= 65.45 ns2 can be directly derived and the retrieved period jitter variance is σ02=0.982 fs2 considering M=6666 and N = 105. This number matches well with variance of white period jitter added on LUT in advance.

 figure: Fig. 2

Fig. 2 Superimposed waveforms of a series of 4000 stretched pulse pairs aligned by the front pulses. The inset shows the cross section of the overlapped rear pulses, revealing timing error histogram.

Download Full Size | PPT Slide | PDF

4. Experiment with stabilized ultrafast lasers

4.1 Experimental setup

This method has been applied to characterize period jitter of a passively mode-locked fiber laser. The experimental setup is shown in Fig. 3. Two NPR mode-locked Er-fiber lasers working at 1550 nm serve as LUT and LO, respectively. Both LUT and LO operate with a close-to-zero cavity dispersion, delivering an output pulse duration of 905 fs and 440 fs, respectively. Longer pulse duration from LUT is attributed to an 8 nm bandpass filter just before the output. The limited output laser bandwidth is necessary to prevent aliasing in the following ASOPS stage [10]. Note that, the intracavity filtering also changes the pulse dynamics of LUT from stretched pulse regime to dissipative soliton formation, bearing an increased timing jitter [27]. Under this situation, LO timing jitter is negligible in comparison with LUT. The repetition rates of the two lasers are ~100 MHz. The LUT repetition rate fr and offset repetition rate Δfr are referenced to external rf standards by feedback control on piezo mirror actuators in LUT and LO, respectively. The locking bandwidth is ~300 Hz. Therefore, magnification factor of M and N would keep constant and thus be precisely determined. A Michelson-based pulse interleaver is used to produce reference pulse pairs, which are combined with LO on a PBS for type-II periodically poled KTiOPO4 (PPKTP) crystal based SFG. The generated intensity cross-correlation signals are received by an avalanche photodetector (Thorlabs, APD120A), low-pass filtered, and then continuously sampled by a 14 bit 100 MHz digitizer (National Instrument, PXIe-5122), thus accomplishing ASOPS. Inset in Fig. 3 shows a full sample of reference pulse pair by using ASOPS. The individual pulses are fitted with Gaussian functions and the retrieved peak-to-peak time interval accounted for the measured Tp.

 figure: Fig. 3

Fig. 3 Schematic of the timing jitter measurement based on ASOPS in time domain. The repetition rates are ~100 MHz. The 5th harmonic of repetition rate in LUT is photo-detected and phase-locked to signal generator 1 (SG1), while the offset repetition rate between the 10th harmonic of the two lasers are phase locked to signal generator 2 (SG2). The inset shows a full LUT pulse pair acquired by digitizer in a stretched timescale. BPF, band pass filter; HWP, half wavelength plate; LPF, low pass filter; PBS, polarizing beam splitter; QWP, quarter wavelength plate.

Download Full Size | PPT Slide | PDF

4.2 Experimental results

Figure 4 summarizes the experimental results at a fixed offset repetition rate of 2 kHz, where tp is scanned from 7 ps to 93 ps by adjusting the displacement of the movable mirror in the Michelson pulse interleaver from 1 mm to 14 mm. Accordingly, Tp reads from 0.35 μs to 4.65 μs considering a time-stretch factor of N = 50000 by ASOPS. Note that, in the microsecond acquisition time, the impact of technical noise can be ignored, and the mode-locked lasers are regarded as quantum noise limited. The obtained standard deviation (STDEV) of visual timing jitter versus tp is plotted in Fig. 4(a). Each data point is acquired from histogram analysis based on 5500 successive Tpmeasurements. The inset gives one histogram at an arbitrary ~4.68 mm movable mirror displacement, agreeing well with a normal distribution. The constant visual timing jitter STDEV of σe = 0.35 ns for tp <25 ps (corresponds to a 3.75 mm movable mirror displacement) reflects the sensitivity of electronic data acquisition system, mainly determined by the limited signal noise ratio (SNR) of the photo-detected cross-correlation signals as well as the uncertainty of Gaussian-fit based pulse timing extraction. Visual timing jitter STDEV increases versus tp for tp >25 ps, see the red-dashed guide curve in Fig. 4(a), in accordance with Eq. (1). Obviously, increased temporal delay tp is favorable for an enhanced timing jitter measurement sensitivity.

 figure: Fig. 4

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.

Download Full Size | PPT Slide | PDF

Real period jitter STDEV has been obtained when the measured visual timing jitter STDEV is divided by NM. A period jitter STDEV of 0.626 fs with uncertainty of 16 as has been retrieved based on the measurements for tp > 25 ps, as shown in Fig. 4(b). When period jitter STDEV is measured, the diffusion constant B for pulse timing can be directly obtained by B=σ02×fr and we can predict a timing jitter PSD, shown as red line in the insert of Fig. 4(b). The grey area in the insert of Fig. 4(b) shows the estimated jitter PSD according to the analytical model in Ref [7]. The laser parameters are from LUT used in experiment, where the reference pulse width τ0 is 480 fs, the saturated gain g is 0.46 calculated from a roundtrip pulse energy attenuation of ~60%, the gain bandwidth Ωg is 1.57 × 1013 rad/s, the 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.

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 tp 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.

 figure: Fig. 5

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.

Download Full Size | PPT Slide | PDF

Taking into account the impact of both tp and Δfr, the ultimate resolvable optical period jitter STDEV in the presence of electronic limited measurement sensitivity (σe) can be expressed as

σ0r=σe×1tp×Δfr3fr4
Figure 5(b) maps the resolvable optical period jitter STDEV by altering Δfr and tp at the present σe = 0.35 ns. Under a 2 kHz offset repetition rate, the lowest measurable period jitter at tp = 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 tp invariant.

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 fr and Δfr 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 Δfr 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 fr. 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 Δfr. 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.

 figure: Fig. 6

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.

Download Full Size | PPT Slide | PDF

Note that, digitizers require large data storage depth for jitter measurement based on free running lasers because the measurement of Δfr relies on uninterrupted collection of samples. While, by phase-locking both fr and Δfr, 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.

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.

References and links

1. E. Rubiola, Phase Noise and Frequency Stability in Oscillators, The Cambridge RF and Microwave Engineering Series (Cambridge University, 2009).

2. X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13(8), 1725–1735 (1996). [CrossRef]  

3. T. K. Kim, Y. Song, K. Jung, C. Kim, H. Kim, C. H. Nam, and J. Kim, “Sub-100-as timing jitter optical pulse trains from mode-locked Er-fiber lasers,” Opt. Lett. 36(22), 4443–4445 (2011). [CrossRef]   [PubMed]  

4. J. Benedick, J. G. Fujimoto, and F. X. Kärtner, “Optical flywheels with attosecond jitter,” Nat. Photonics 6(2), 97–100 (2012). [CrossRef]  

5. E. Portuondo-Campa, R. Paschotta, and S. Lecomte, “Sub-100 attosecond timing jitter from low-noise passively mode-locked solid-state laser at telecom wavelength,” Opt. Lett. 38(15), 2650–2653 (2013). [CrossRef]   [PubMed]  

6. N. Kuse, J. Jiang, C. C. Lee, T. R. Schibli, and M. E. Fermann, “All polarization-maintaining Er fiber-based optical frequency combs with nonlinear amplifying loop mirror,” Opt. Express 24(3), 3095–3102 (2016). [CrossRef]   [PubMed]  

7. S. Namiki and H. A. Haus, “Noise of the stretched pulse fiber lasers: Part I-Theory,” IEEE J. Quantum Electron. 33(5), 649–659 (1997). [CrossRef]  

8. J. Kim, J. A. Cox, J. Chen, and F. X. Kärtner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2(12), 733–736 (2008). [CrossRef]  

9. A. Khilo, S. J. Spector, M. E. Grein, A. H. Nejadmalayeri, C. W. Holzwarth, M. Y. Sander, M. S. Dahlem, M. Y. Peng, M. W. Geis, N. A. DiLello, J. U. Yoon, A. Motamedi, J. S. Orcutt, J. P. Wang, C. M. Sorace-Agaskar, M. A. Popović, J. Sun, G. R. Zhou, H. Byun, J. Chen, J. L. Hoyt, H. I. Smith, R. J. Ram, M. Perrott, T. M. Lyszczarz, E. P. Ippen, and F. X. Kärtner, “Photonic ADC: overcoming the bottleneck of electronic jitter,” Opt. Express 20(4), 4454–4469 (2012). [CrossRef]   [PubMed]  

10. I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009). [CrossRef]  

11. H. Shi, Y. Song, F. Liang, L. Xu, M. Hu, and C. Wang, “Effect of timing jitter on time-of-flight distance measurements using dual femtosecond lasers,” Opt. Express 23(11), 14057–14069 (2015). [CrossRef]   [PubMed]  

12. J. A. Cox, W. P. Putnam, A. Sell, A. Leitenstorfer, and F. X. Kärtner, “Pulse synthesis in the single-cycle regime from independent mode-locked lasers using attosecond-precision feedback,” Opt. Lett. 37(17), 3579–3581 (2012). [CrossRef]   [PubMed]  

13. F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Jiang, and S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36(16), 3260–3262 (2011). [CrossRef]   [PubMed]  

14. R. P. Scott, C. Langrock, and B. H. Kolner, “High-dynamic-range laser amplitude and phase noise measurement techniques,” IEEE J. Sel. Top. Quantum Electron. 7(4), 641–655 (2001). [CrossRef]  

15. O. Prochnow, R. Paschotta, E. Benkler, U. Morgner, J. Neumann, D. Wandt, and D. Kracht, “Quantum-limited noise performance of a femtosecond all-fiber ytterbium laser,” Opt. Express 17(18), 15525–15533 (2009). [CrossRef]   [PubMed]  

16. C. Ouyang, P. Shum, H. Wang, J. Haur Wong, K. Wu, S. Fu, R. Li, E. J. R. Kelleher, A. I. Chernov, and E. D. Obraztsova, “Observation of timing jitter reduction induced by spectral filtering in a fiber laser mode locked with a carbon nanotube-based saturable absorber,” Opt. Lett. 35(14), 2320–2322 (2010). [CrossRef]   [PubMed]  

17. H. Byun, D. Pudo, J. Chen, E. P. Ippen, and F. X. Kärtner, “High-repetition-rate, 491 MHz, femtosecond fiber laser with low timing jitter,” Opt. Lett. 33(19), 2221–2223 (2008). [CrossRef]   [PubMed]  

18. L. A. Jiang, S. T. Wong, M. E. Grein, E. P. Ippen, and H. A. Haus, “Measuring timing jitter with optical cross correlations,” IEEE J. Quantum Electron. 38(8), 1047–1052 (2002). [CrossRef]  

19. T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen, and F. X. Kaertner, “Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation,” Opt. Lett. 28(11), 947–949 (2003). [CrossRef]   [PubMed]  

20. J. Kim, J. Chen, J. Cox, and F. X. Kärtner, “Attosecond-resolution timing jitter characterization of free-running mode-locked lasers,” Opt. Lett. 32(24), 3519–3521 (2007). [CrossRef]   [PubMed]  

21. D. Hou, C.-C. Lee, Z. Yang, and T. R. Schibli, “Timing jitter characterization of mode-locked lasers with <1 zs/√Hz resolution using a simple optical heterodyne technique,” Opt. Lett. 40(13), 2985–2988 (2015). [CrossRef]   [PubMed]  

22. K. Jung and J. Kim, “All-fibre photonic signal generator for attosecond timing and ultralow-noise microwave,” Sci. Rep. 5, 16250 (2015). [CrossRef]   [PubMed]  

23. J. Kim and Y. J. Song, “Ultralow-noise mode-locked fiber lasers and frequency combs: principles, status, and applications,” Adv. Opt. Photonics 8(3), 465–540 (2016). [CrossRef]  

24. P. A. Elzinga, R. J. Kneisler, F. E. Lytle, Y. Jiang, G. B. King, and N. M. Laurendeau, “Pump/probe method for fast analysis of visible spectral signatures utilizing asynchronous optical sampling,” Appl. Opt. 26(19), 4303–4309 (1987). [CrossRef]   [PubMed]  

25. R. Gebs, G. Klatt, C. Janke, T. Dekorsy, and A. Bartels, “High-speed asynchronous optical sampling with sub-50fs time resolution,” Opt. Express 18(6), 5974–5983 (2010). [CrossRef]   [PubMed]  

26. H. Zhang, H. Wei, X. Wu, H. Yang, and Y. Li, “Absolute distance measurement by dual-comb nonlinear asynchronous optical sampling,” Opt. Express 22(6), 6597–6604 (2014). [CrossRef]   [PubMed]  

27. P. Qin, Y. Song, H. Kim, J. Shin, D. Kwon, M. Hu, C. Wang, and J. Kim, “Reduction of timing jitter and intensity noise in normal-dispersion passively mode-locked fiber lasers by narrow band-pass filtering,” Opt. Express 22(23), 28276–28283 (2014). [CrossRef]   [PubMed]  

References

  • View by:

  1. E. Rubiola, Phase Noise and Frequency Stability in Oscillators, The Cambridge RF and Microwave Engineering Series (Cambridge University, 2009).
  2. X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13(8), 1725–1735 (1996).
    [Crossref]
  3. T. K. Kim, Y. Song, K. Jung, C. Kim, H. Kim, C. H. Nam, and J. Kim, “Sub-100-as timing jitter optical pulse trains from mode-locked Er-fiber lasers,” Opt. Lett. 36(22), 4443–4445 (2011).
    [Crossref] [PubMed]
  4. J. Benedick, J. G. Fujimoto, and F. X. Kärtner, “Optical flywheels with attosecond jitter,” Nat. Photonics 6(2), 97–100 (2012).
    [Crossref]
  5. E. Portuondo-Campa, R. Paschotta, and S. Lecomte, “Sub-100 attosecond timing jitter from low-noise passively mode-locked solid-state laser at telecom wavelength,” Opt. Lett. 38(15), 2650–2653 (2013).
    [Crossref] [PubMed]
  6. N. Kuse, J. Jiang, C. C. Lee, T. R. Schibli, and M. E. Fermann, “All polarization-maintaining Er fiber-based optical frequency combs with nonlinear amplifying loop mirror,” Opt. Express 24(3), 3095–3102 (2016).
    [Crossref] [PubMed]
  7. S. Namiki and H. A. Haus, “Noise of the stretched pulse fiber lasers: Part I-Theory,” IEEE J. Quantum Electron. 33(5), 649–659 (1997).
    [Crossref]
  8. J. Kim, J. A. Cox, J. Chen, and F. X. Kärtner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2(12), 733–736 (2008).
    [Crossref]
  9. A. Khilo, S. J. Spector, M. E. Grein, A. H. Nejadmalayeri, C. W. Holzwarth, M. Y. Sander, M. S. Dahlem, M. Y. Peng, M. W. Geis, N. A. DiLello, J. U. Yoon, A. Motamedi, J. S. Orcutt, J. P. Wang, C. M. Sorace-Agaskar, M. A. Popović, J. Sun, G. R. Zhou, H. Byun, J. Chen, J. L. Hoyt, H. I. Smith, R. J. Ram, M. Perrott, T. M. Lyszczarz, E. P. Ippen, and F. X. Kärtner, “Photonic ADC: overcoming the bottleneck of electronic jitter,” Opt. Express 20(4), 4454–4469 (2012).
    [Crossref] [PubMed]
  10. I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
    [Crossref]
  11. H. Shi, Y. Song, F. Liang, L. Xu, M. Hu, and C. Wang, “Effect of timing jitter on time-of-flight distance measurements using dual femtosecond lasers,” Opt. Express 23(11), 14057–14069 (2015).
    [Crossref] [PubMed]
  12. J. A. Cox, W. P. Putnam, A. Sell, A. Leitenstorfer, and F. X. Kärtner, “Pulse synthesis in the single-cycle regime from independent mode-locked lasers using attosecond-precision feedback,” Opt. Lett. 37(17), 3579–3581 (2012).
    [Crossref] [PubMed]
  13. F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Jiang, and S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36(16), 3260–3262 (2011).
    [Crossref] [PubMed]
  14. R. P. Scott, C. Langrock, and B. H. Kolner, “High-dynamic-range laser amplitude and phase noise measurement techniques,” IEEE J. Sel. Top. Quantum Electron. 7(4), 641–655 (2001).
    [Crossref]
  15. O. Prochnow, R. Paschotta, E. Benkler, U. Morgner, J. Neumann, D. Wandt, and D. Kracht, “Quantum-limited noise performance of a femtosecond all-fiber ytterbium laser,” Opt. Express 17(18), 15525–15533 (2009).
    [Crossref] [PubMed]
  16. C. Ouyang, P. Shum, H. Wang, J. Haur Wong, K. Wu, S. Fu, R. Li, E. J. R. Kelleher, A. I. Chernov, and E. D. Obraztsova, “Observation of timing jitter reduction induced by spectral filtering in a fiber laser mode locked with a carbon nanotube-based saturable absorber,” Opt. Lett. 35(14), 2320–2322 (2010).
    [Crossref] [PubMed]
  17. H. Byun, D. Pudo, J. Chen, E. P. Ippen, and F. X. Kärtner, “High-repetition-rate, 491 MHz, femtosecond fiber laser with low timing jitter,” Opt. Lett. 33(19), 2221–2223 (2008).
    [Crossref] [PubMed]
  18. L. A. Jiang, S. T. Wong, M. E. Grein, E. P. Ippen, and H. A. Haus, “Measuring timing jitter with optical cross correlations,” IEEE J. Quantum Electron. 38(8), 1047–1052 (2002).
    [Crossref]
  19. T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen, and F. X. Kaertner, “Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation,” Opt. Lett. 28(11), 947–949 (2003).
    [Crossref] [PubMed]
  20. J. Kim, J. Chen, J. Cox, and F. X. Kärtner, “Attosecond-resolution timing jitter characterization of free-running mode-locked lasers,” Opt. Lett. 32(24), 3519–3521 (2007).
    [Crossref] [PubMed]
  21. D. Hou, C.-C. Lee, Z. Yang, and T. R. Schibli, “Timing jitter characterization of mode-locked lasers with <1 zs/√Hz resolution using a simple optical heterodyne technique,” Opt. Lett. 40(13), 2985–2988 (2015).
    [Crossref] [PubMed]
  22. K. Jung and J. Kim, “All-fibre photonic signal generator for attosecond timing and ultralow-noise microwave,” Sci. Rep. 5, 16250 (2015).
    [Crossref] [PubMed]
  23. J. Kim and Y. J. Song, “Ultralow-noise mode-locked fiber lasers and frequency combs: principles, status, and applications,” Adv. Opt. Photonics 8(3), 465–540 (2016).
    [Crossref]
  24. P. A. Elzinga, R. J. Kneisler, F. E. Lytle, Y. Jiang, G. B. King, and N. M. Laurendeau, “Pump/probe method for fast analysis of visible spectral signatures utilizing asynchronous optical sampling,” Appl. Opt. 26(19), 4303–4309 (1987).
    [Crossref] [PubMed]
  25. R. Gebs, G. Klatt, C. Janke, T. Dekorsy, and A. Bartels, “High-speed asynchronous optical sampling with sub-50fs time resolution,” Opt. Express 18(6), 5974–5983 (2010).
    [Crossref] [PubMed]
  26. H. Zhang, H. Wei, X. Wu, H. Yang, and Y. Li, “Absolute distance measurement by dual-comb nonlinear asynchronous optical sampling,” Opt. Express 22(6), 6597–6604 (2014).
    [Crossref] [PubMed]
  27. P. Qin, Y. Song, H. Kim, J. Shin, D. Kwon, M. Hu, C. Wang, and J. Kim, “Reduction of timing jitter and intensity noise in normal-dispersion passively mode-locked fiber lasers by narrow band-pass filtering,” Opt. Express 22(23), 28276–28283 (2014).
    [Crossref] [PubMed]

2016 (2)

N. Kuse, J. Jiang, C. C. Lee, T. R. Schibli, and M. E. Fermann, “All polarization-maintaining Er fiber-based optical frequency combs with nonlinear amplifying loop mirror,” Opt. Express 24(3), 3095–3102 (2016).
[Crossref] [PubMed]

J. Kim and Y. J. Song, “Ultralow-noise mode-locked fiber lasers and frequency combs: principles, status, and applications,” Adv. Opt. Photonics 8(3), 465–540 (2016).
[Crossref]

2015 (3)

2014 (2)

2013 (1)

2012 (3)

2011 (2)

2010 (2)

2009 (2)

O. Prochnow, R. Paschotta, E. Benkler, U. Morgner, J. Neumann, D. Wandt, and D. Kracht, “Quantum-limited noise performance of a femtosecond all-fiber ytterbium laser,” Opt. Express 17(18), 15525–15533 (2009).
[Crossref] [PubMed]

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

2008 (2)

J. Kim, J. A. Cox, J. Chen, and F. X. Kärtner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2(12), 733–736 (2008).
[Crossref]

H. Byun, D. Pudo, J. Chen, E. P. Ippen, and F. X. Kärtner, “High-repetition-rate, 491 MHz, femtosecond fiber laser with low timing jitter,” Opt. Lett. 33(19), 2221–2223 (2008).
[Crossref] [PubMed]

2007 (1)

2003 (1)

2002 (1)

L. A. Jiang, S. T. Wong, M. E. Grein, E. P. Ippen, and H. A. Haus, “Measuring timing jitter with optical cross correlations,” IEEE J. Quantum Electron. 38(8), 1047–1052 (2002).
[Crossref]

2001 (1)

R. P. Scott, C. Langrock, and B. H. Kolner, “High-dynamic-range laser amplitude and phase noise measurement techniques,” IEEE J. Sel. Top. Quantum Electron. 7(4), 641–655 (2001).
[Crossref]

1997 (1)

S. Namiki and H. A. Haus, “Noise of the stretched pulse fiber lasers: Part I-Theory,” IEEE J. Quantum Electron. 33(5), 649–659 (1997).
[Crossref]

1996 (1)

1987 (1)

Bartels, A.

Benedick, J.

J. Benedick, J. G. Fujimoto, and F. X. Kärtner, “Optical flywheels with attosecond jitter,” Nat. Photonics 6(2), 97–100 (2012).
[Crossref]

Benkler, E.

Byun, H.

Chen, J.

Chernov, A. I.

Coddington, I.

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

Cox, J.

Cox, J. A.

J. A. Cox, W. P. Putnam, A. Sell, A. Leitenstorfer, and F. X. Kärtner, “Pulse synthesis in the single-cycle regime from independent mode-locked lasers using attosecond-precision feedback,” Opt. Lett. 37(17), 3579–3581 (2012).
[Crossref] [PubMed]

J. Kim, J. A. Cox, J. Chen, and F. X. Kärtner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2(12), 733–736 (2008).
[Crossref]

Dahlem, M. S.

Dekorsy, T.

Diddams, S. A.

DiLello, N. A.

Elzinga, P. A.

Fermann, M. E.

Fortier, T. M.

Fu, S.

Fujimoto, J. G.

Gebs, R.

Geis, M. W.

Gopinath, J. T.

Grein, M. E.

Haur Wong, J.

Haus, H. A.

L. A. Jiang, S. T. Wong, M. E. Grein, E. P. Ippen, and H. A. Haus, “Measuring timing jitter with optical cross correlations,” IEEE J. Quantum Electron. 38(8), 1047–1052 (2002).
[Crossref]

S. Namiki and H. A. Haus, “Noise of the stretched pulse fiber lasers: Part I-Theory,” IEEE J. Quantum Electron. 33(5), 649–659 (1997).
[Crossref]

Holzwarth, C. W.

Hou, D.

Hoyt, J. L.

Hu, M.

Ippen, E. P.

Janke, C.

Jiang, J.

Jiang, L. A.

L. A. Jiang, S. T. Wong, M. E. Grein, E. P. Ippen, and H. A. Haus, “Measuring timing jitter with optical cross correlations,” IEEE J. Quantum Electron. 38(8), 1047–1052 (2002).
[Crossref]

Jiang, Y.

Jung, K.

Kaertner, F. X.

Kärtner, F. X.

Kelleher, E. J. R.

Khilo, A.

Kim, C.

Kim, H.

Kim, J.

J. Kim and Y. J. Song, “Ultralow-noise mode-locked fiber lasers and frequency combs: principles, status, and applications,” Adv. Opt. Photonics 8(3), 465–540 (2016).
[Crossref]

K. Jung and J. Kim, “All-fibre photonic signal generator for attosecond timing and ultralow-noise microwave,” Sci. Rep. 5, 16250 (2015).
[Crossref] [PubMed]

P. Qin, Y. Song, H. Kim, J. Shin, D. Kwon, M. Hu, C. Wang, and J. Kim, “Reduction of timing jitter and intensity noise in normal-dispersion passively mode-locked fiber lasers by narrow band-pass filtering,” Opt. Express 22(23), 28276–28283 (2014).
[Crossref] [PubMed]

T. K. Kim, Y. Song, K. Jung, C. Kim, H. Kim, C. H. Nam, and J. Kim, “Sub-100-as timing jitter optical pulse trains from mode-locked Er-fiber lasers,” Opt. Lett. 36(22), 4443–4445 (2011).
[Crossref] [PubMed]

J. Kim, J. A. Cox, J. Chen, and F. X. Kärtner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2(12), 733–736 (2008).
[Crossref]

J. Kim, J. Chen, J. Cox, and F. X. Kärtner, “Attosecond-resolution timing jitter characterization of free-running mode-locked lasers,” Opt. Lett. 32(24), 3519–3521 (2007).
[Crossref] [PubMed]

T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen, and F. X. Kaertner, “Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation,” Opt. Lett. 28(11), 947–949 (2003).
[Crossref] [PubMed]

Kim, T. K.

King, G. B.

Kirchner, M. S.

Klatt, G.

Kneisler, R. J.

Kolner, B. H.

R. P. Scott, C. Langrock, and B. H. Kolner, “High-dynamic-range laser amplitude and phase noise measurement techniques,” IEEE J. Sel. Top. Quantum Electron. 7(4), 641–655 (2001).
[Crossref]

Kolodziejski, L. A.

Kracht, D.

Kuse, N.

Kuzucu, O.

Kwon, D.

Langrock, C.

R. P. Scott, C. Langrock, and B. H. Kolner, “High-dynamic-range laser amplitude and phase noise measurement techniques,” IEEE J. Sel. Top. Quantum Electron. 7(4), 641–655 (2001).
[Crossref]

Laurendeau, N. M.

Lecomte, S.

Lee, C. C.

Lee, C.-C.

Leitenstorfer, A.

Lemke, N.

Li, R.

Li, Y.

Liang, F.

Ludlow, A. D.

Lyszczarz, T. M.

Lytle, F. E.

Maleki, L.

Morgner, U.

Motamedi, A.

Nam, C. H.

Namiki, S.

S. Namiki and H. A. Haus, “Noise of the stretched pulse fiber lasers: Part I-Theory,” IEEE J. Quantum Electron. 33(5), 649–659 (1997).
[Crossref]

Nejadmalayeri, A. H.

Nenadovic, L.

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

Neumann, J.

Newbury, N. R.

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

Obraztsova, E. D.

Orcutt, J. S.

Ouyang, C.

Paschotta, R.

Peng, M. Y.

Perrott, M.

Petrich, G. S.

Popovic, M. A.

Portuondo-Campa, E.

Prochnow, O.

Pudo, D.

Putnam, W. P.

Qin, P.

Quinlan, F.

Ram, R. J.

Sander, M. Y.

Schibli, T. R.

Scott, R. P.

R. P. Scott, C. Langrock, and B. H. Kolner, “High-dynamic-range laser amplitude and phase noise measurement techniques,” IEEE J. Sel. Top. Quantum Electron. 7(4), 641–655 (2001).
[Crossref]

Sell, A.

Shi, H.

Shin, J.

Shum, P.

Smith, H. I.

Song, Y.

Song, Y. J.

J. Kim and Y. J. Song, “Ultralow-noise mode-locked fiber lasers and frequency combs: principles, status, and applications,” Adv. Opt. Photonics 8(3), 465–540 (2016).
[Crossref]

Sorace-Agaskar, C. M.

Spector, S. J.

Sun, J.

Swann, W. C.

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

Tandon, S. N.

Taylor, J. A.

Thorpe, M. J.

Wandt, D.

Wang, C.

Wang, H.

Wang, J. P.

Wei, H.

Wong, S. T.

L. A. Jiang, S. T. Wong, M. E. Grein, E. P. Ippen, and H. A. Haus, “Measuring timing jitter with optical cross correlations,” IEEE J. Quantum Electron. 38(8), 1047–1052 (2002).
[Crossref]

Wu, K.

Wu, X.

Xu, L.

Yang, H.

Yang, Z.

Yao, X. S.

Yoon, J. U.

Zhang, H.

Zhou, G. R.

Adv. Opt. Photonics (1)

J. Kim and Y. J. Song, “Ultralow-noise mode-locked fiber lasers and frequency combs: principles, status, and applications,” Adv. Opt. Photonics 8(3), 465–540 (2016).
[Crossref]

Appl. Opt. (1)

IEEE J. Quantum Electron. (2)

L. A. Jiang, S. T. Wong, M. E. Grein, E. P. Ippen, and H. A. Haus, “Measuring timing jitter with optical cross correlations,” IEEE J. Quantum Electron. 38(8), 1047–1052 (2002).
[Crossref]

S. Namiki and H. A. Haus, “Noise of the stretched pulse fiber lasers: Part I-Theory,” IEEE J. Quantum Electron. 33(5), 649–659 (1997).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

R. P. Scott, C. Langrock, and B. H. Kolner, “High-dynamic-range laser amplitude and phase noise measurement techniques,” IEEE J. Sel. Top. Quantum Electron. 7(4), 641–655 (2001).
[Crossref]

J. Opt. Soc. Am. B (1)

Nat. Photonics (3)

J. Benedick, J. G. Fujimoto, and F. X. Kärtner, “Optical flywheels with attosecond jitter,” Nat. Photonics 6(2), 97–100 (2012).
[Crossref]

J. Kim, J. A. Cox, J. Chen, and F. X. Kärtner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2(12), 733–736 (2008).
[Crossref]

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

Opt. Express (7)

H. Shi, Y. Song, F. Liang, L. Xu, M. Hu, and C. Wang, “Effect of timing jitter on time-of-flight distance measurements using dual femtosecond lasers,” Opt. Express 23(11), 14057–14069 (2015).
[Crossref] [PubMed]

O. Prochnow, R. Paschotta, E. Benkler, U. Morgner, J. Neumann, D. Wandt, and D. Kracht, “Quantum-limited noise performance of a femtosecond all-fiber ytterbium laser,” Opt. Express 17(18), 15525–15533 (2009).
[Crossref] [PubMed]

A. Khilo, S. J. Spector, M. E. Grein, A. H. Nejadmalayeri, C. W. Holzwarth, M. Y. Sander, M. S. Dahlem, M. Y. Peng, M. W. Geis, N. A. DiLello, J. U. Yoon, A. Motamedi, J. S. Orcutt, J. P. Wang, C. M. Sorace-Agaskar, M. A. Popović, J. Sun, G. R. Zhou, H. Byun, J. Chen, J. L. Hoyt, H. I. Smith, R. J. Ram, M. Perrott, T. M. Lyszczarz, E. P. Ippen, and F. X. Kärtner, “Photonic ADC: overcoming the bottleneck of electronic jitter,” Opt. Express 20(4), 4454–4469 (2012).
[Crossref] [PubMed]

N. Kuse, J. Jiang, C. C. Lee, T. R. Schibli, and M. E. Fermann, “All polarization-maintaining Er fiber-based optical frequency combs with nonlinear amplifying loop mirror,” Opt. Express 24(3), 3095–3102 (2016).
[Crossref] [PubMed]

R. Gebs, G. Klatt, C. Janke, T. Dekorsy, and A. Bartels, “High-speed asynchronous optical sampling with sub-50fs time resolution,” Opt. Express 18(6), 5974–5983 (2010).
[Crossref] [PubMed]

H. Zhang, H. Wei, X. Wu, H. Yang, and Y. Li, “Absolute distance measurement by dual-comb nonlinear asynchronous optical sampling,” Opt. Express 22(6), 6597–6604 (2014).
[Crossref] [PubMed]

P. Qin, Y. Song, H. Kim, J. Shin, D. Kwon, M. Hu, C. Wang, and J. Kim, “Reduction of timing jitter and intensity noise in normal-dispersion passively mode-locked fiber lasers by narrow band-pass filtering,” Opt. Express 22(23), 28276–28283 (2014).
[Crossref] [PubMed]

Opt. Lett. (9)

T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen, and F. X. Kaertner, “Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation,” Opt. Lett. 28(11), 947–949 (2003).
[Crossref] [PubMed]

J. Kim, J. Chen, J. Cox, and F. X. Kärtner, “Attosecond-resolution timing jitter characterization of free-running mode-locked lasers,” Opt. Lett. 32(24), 3519–3521 (2007).
[Crossref] [PubMed]

D. Hou, C.-C. Lee, Z. Yang, and T. R. Schibli, “Timing jitter characterization of mode-locked lasers with <1 zs/√Hz resolution using a simple optical heterodyne technique,” Opt. Lett. 40(13), 2985–2988 (2015).
[Crossref] [PubMed]

E. Portuondo-Campa, R. Paschotta, and S. Lecomte, “Sub-100 attosecond timing jitter from low-noise passively mode-locked solid-state laser at telecom wavelength,” Opt. Lett. 38(15), 2650–2653 (2013).
[Crossref] [PubMed]

T. K. Kim, Y. Song, K. Jung, C. Kim, H. Kim, C. H. Nam, and J. Kim, “Sub-100-as timing jitter optical pulse trains from mode-locked Er-fiber lasers,” Opt. Lett. 36(22), 4443–4445 (2011).
[Crossref] [PubMed]

C. Ouyang, P. Shum, H. Wang, J. Haur Wong, K. Wu, S. Fu, R. Li, E. J. R. Kelleher, A. I. Chernov, and E. D. Obraztsova, “Observation of timing jitter reduction induced by spectral filtering in a fiber laser mode locked with a carbon nanotube-based saturable absorber,” Opt. Lett. 35(14), 2320–2322 (2010).
[Crossref] [PubMed]

H. Byun, D. Pudo, J. Chen, E. P. Ippen, and F. X. Kärtner, “High-repetition-rate, 491 MHz, femtosecond fiber laser with low timing jitter,” Opt. Lett. 33(19), 2221–2223 (2008).
[Crossref] [PubMed]

J. A. Cox, W. P. Putnam, A. Sell, A. Leitenstorfer, and F. X. Kärtner, “Pulse synthesis in the single-cycle regime from independent mode-locked lasers using attosecond-precision feedback,” Opt. Lett. 37(17), 3579–3581 (2012).
[Crossref] [PubMed]

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Jiang, and S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36(16), 3260–3262 (2011).
[Crossref] [PubMed]

Sci. Rep. (1)

K. Jung and J. Kim, “All-fibre photonic signal generator for attosecond timing and ultralow-noise microwave,” Sci. Rep. 5, 16250 (2015).
[Crossref] [PubMed]

Other (1)

E. Rubiola, Phase Noise and Frequency Stability in Oscillators, The Cambridge RF and Microwave Engineering Series (Cambridge University, 2009).

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1 Concept of timing jitter measurement based on ASOPS in time domain. The solid (dotted) pulses illustrate the ASOPS process without (with) LUT timing jitter.
Fig. 2
Fig. 2 Superimposed waveforms of a series of 4000 stretched pulse pairs aligned by the front pulses. The inset shows the cross section of the overlapped rear pulses, revealing timing error histogram.
Fig. 3
Fig. 3 Schematic of the timing jitter measurement based on ASOPS in time domain. The repetition rates are ~100 MHz. The 5th harmonic of repetition rate in LUT is photo-detected and phase-locked to signal generator 1 (SG1), while the offset repetition rate between the 10th harmonic of the two lasers are phase locked to signal generator 2 (SG2). The inset shows a full LUT pulse pair acquired by digitizer in a stretched timescale. BPF, band pass filter; HWP, half wavelength plate; LPF, low pass filter; PBS, polarizing beam splitter; QWP, quarter wavelength plate.
Fig. 4
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 T p . (b). The retrieved period jitter STDEV of LUT versus tp. The inset shows the estimated jitter PSD and the comparison with analytical model.
Fig. 5
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.
Fig. 6
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 T p . (b). The retrieved period jitter STDEV of LUT versus tp.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

σ 2 = N 2 ( M σ 0 2 ) t p f r   4 Δ f r   3 σ 0 2 ,
σ 0 r = σ e × 1 t p × Δ f r 3 f r 4

Metrics