Jungwon Kim, Jonathan A. Cox, Jian J. Chen & Franz X. Kärtner. Department of Electrical Engineering and Computer Science and Research Laboratory

Transcription

1 1 Supplementary Information Drift-free femtosecond timing synchronization of remote optical and microwave sources with better than level stability Jungwon Kim, Jonathan A. Cox, Jian J. Chen & Franz X. Kärtner Department of Electrical Engineering and Computer Science and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 1. Timing-stabilized fibre links The fibre optic synchronization system operates by stabilizing the total group delay, or time-of-flight, of a dispersion-compensated single-mode fibre link with a motorized free-space delay and a piezoelectric fibre stretcher, as shown in Fig. 2a in the main paper. The 300-m long fibre link is comprised of ~40 m of dispersion-compensating fibre (DCF) and ~260 m of standard SMF-28 single-mode fibre. Since both opticaloptical synchronization and link stabilization rely on the cross-correlator, proper dispersion compensation of the entire link is necessary to get short input pulses for the cross-correlators to obtain high timing detection sensitivity. The single-crystal balanced cross-correlator, shown in Fig. 2a of the main paper, is based on the second-harmonic generation (SHG) and group delay shift between two orthogonal polarizations in the periodically-poled KTP (PPKTP) crystal. The combined input pulses (Pulse 1 and 2 in Fig. 2a) with orthogonal polarization states are transmitted through the dichroic beamsplitter (DBS in Fig. 2a) which transmits the input pulses but reflects the second harmonic component of the input pulses. The secondharmonic component generated by the forward input pulses through the PPTKP is

2 2 transmitted through the dichroic mirror (DM in Fig. 2a), which transmits the second harmonic component but reflects the input pulses, to one detector (PD in Fig. 2a) of the balanced photodetector. The remained input pulses are reflected back by the DM and generate the second-harmonic component through the PPKTP backward. This secondharmonic component is reflected by the DBS and detected by the other detector of the balanced photodetector. As the birefringence in the PPKTP crystal provides group delay between two input pulses, one can obtain the cross-correlation curve as shown in Fig. 3a inset of main paper, which allows locking the timing at the zero-crossing of the balanced cross-correlation where the intensity noise is cancelled. Note that the output is a smooth discriminator function due to a background-free type-ii phase-matched SHG process in the PPKTP crystal. More information on the design and implementation of this PPKTP cross-correlator can be found in Ref. S1. The result shown in Fig. 2b in the main paper is measured by balanced optical cross-correlation between the outputs from the two independently stabilized 300-m long fibre links. Figure S1 shows the schematic of this dual-link experimental setup. A ~100 fs pulse train from a 200-MHz erbium fibre laser (M-Comb-Custom from MenloSystems GmbH) is delivered across the two 300-m long fibre links. The closedloop bandwidth of this system is approximately 1 khz, which is sufficient to eliminate the vast majority of thermal and acoustic fibre fluctuations. In addition, a motor controller monitors the loop filter output and adjusts the free-space delay of a motorized retro-reflector mirror in order to keep the loop filter in range. To overcome the link loss and provide sufficient power for the optical cross-correlation, an in-loop erbium-doped fibre amplifier (EDFA) is inserted within the link. This amplifier amplifies both forward and backward propagating pulses.

3 3 Fibre Link Fibre Figure S1. A schematic of the dual timing link system with path length sensitive optics mounted in a symmetric fashion on temperature stabilized Invar breadboards. PBS, polarization beam splitter; PZT, piezo-electric transducer; EDFA, erbium-doped fibre amplifier; FRM, Faraday rotating mirror. Since the coefficient of thermal expansion for aluminium is about 0.7 fs/ºc/cm, a standard optics layout on the order of one metre in length will introduce significant timing uncertainty. Thermal drift of the optical path length of the pulse splitting optics, including the reference delay arms and the pulse recombination optics (in Fig. S1), directly affects the precision of the timing distribution and out-of-loop measurement accuracy. Therefore, it is necessary to construct the pulse splitting and recombination optics on a temperature-stabilized Invar breadboard. The temperature of these boards was held to ±0.1 ºC, providing a thermal stability of about ±4 as/cm. To further suppress unwanted thermal drifts in the optical components, the optics of both links were carefully arranged as symmetric mirror images. As a result, it is possible to accurately characterize the timing drift of one or more timing links over many days. Measurement of the timing stability between the outputs of the two links is performed with the out-of-loop PPKTP cross-correlator. The response of the crosscorrelator is calibrated against the time delay provided by the piezo fibre stretcher. The sensitivity was measured to be 20 mv/fs. We then conducted a measurement of the synchronization stability of the system over a 72-hour period of continuous, unaided

4 4 operation. Over a frequency interval from 35 µhz to 100 khz, we observed a total timing jitter of 3.3 fs (rms) between the two link outputs, as shown in Fig. S2. From 1 Hz to 100 khz, as measured with a commercial vector signal analyzer (Agilent 89410A), the timing jitter is 0.36 fs (rms). Much of this high-frequency jitter is the result of the sharp resonance of the piezo at 18 khz and shot noise, which can be improved with a faster piezo and greater conversion efficiency in the cross-correlator, respectively. The jitter from 35 µhz to 0.5 Hz was computed from the average spectral density of nine separate, eight-hour periods which were obtained by dividing the entire 72-hour time-domain measurement (shown in Fig. 2b in the main paper) into nine segments. Then, each eight-hour segment was shifted such that it began at zero drift, in order to simulate the beginning of a new experiment for each period. The standard deviation of the rms jitter of these nine, eight-hour intervals is 1.5 fs. Jitter Spectral Density (fs 2 /Hz) Integrated Jitter (fs rms) Frequency (Hz) Figure S2. The jitter spectral density measured between the two link outputs from 35 µhz to 100 khz (red solid curve). The total timing jitter, shown by the blue dashed curve, is 3.3 fs (rms). The jitter from 35 µhz to 0.5 Hz was computed from the average of nine separate, eight-hour periods from the entire 72-hour time-domain measurement.

5 5 Over the full 72-hour period of measurement, the temperature of the optical fibre, Invar breadboards, the positions of the motors and the optical power into the out-of-loop cross-correlator were continuously monitored (see Fig. S3). Care must be taken to ensure that the optical power into the out-of-loop cross-correlator does not substantially deviate over the measurement period, or the accuracy of the measurement can be compromised. The measurement was terminated when the birefringence of the fibre evolved sufficiently enough to reduce the optical power into the cross-correlator by a non-negligible amount. In addition, the free space delay imparted by the motorized delay stages in each fibre link reveal the timing error that would result had active stabilization not been employed. In addition, the thermal coefficient of expansion for the fibre link can be estimated from the fibre spool temperature and the free-space delay. For Link 2, the coefficient of thermal expansion for the fibre is found to be ~ , which is in good agreement with previously reported results S2. Since the optical layout is symmetrized and constructed on a highly temperature invariant breadboard, as described above, we believe the performance is now limited by the polarization mode dispersion (PMD) of SMF-28 fibre. With an upper limit on PMD (PMD Q ) of 60 fs/ km, one expects no more than 33 fs PMD per link, depending on the stress applied to the fibre S3. In fact, by rewinding the fibre spool for the second link in a looser fashion, we were able to reduce the PMD of Link 2 from ~370 fs/ km, where two separate ~500 fs pulses are clearly observable at the link output, to a level where only a single pulse was discernable. In addition, the looser winding reduced the fibre length drift of Link 2 by a factor of three, as revealed by the free-space delay imparted by the motors. Consequentially, we expect the performance of the system with standard single mode fibre (SMF) to be, in large part, limited by the PMD of the SMF and the physical stresses exerted upon it.

6 6 a Temperature T ( C) Out of Loop Invar In Loop Invar Fiber Spools time (hours) b Delay (ps) Freespace Delay Link 1 Link 2 c time (hours) Timing Drift Drift (fs) 0-5 d P/P time (hours) Out-of-Loop Power time (hours) Figure S3. a, The measured temperature of the optical fibre, as well as of the two invar breadboards on which the sensitive optics are mounted. b, The fibre length fluctuations, as revealed by the compensation imparted by the motors. c, The measured timing drift when the stabilization is used. d, The drift of optical power into the out-of-loop cross-correlator.

7 7 2. Optical-optical synchronization Figure S4 shows the schematic of the optical-optical synchronization experiment using a two-colour balanced optical cross-correlator S4. A 6-fs pulse from a Ti:sapphire laser and a 20-fs pulse from a Cr:forsterite laser are combined by a broadband 50:50 beamsplitter with matched group-delay dispersion (GDD). This beam-splitter has a constant 50:50 splitting ratio for the 600 nm 1500 nm wavelength range, with a GDD matched with 0.75 mm of fused silica for any input-output combinations (more information can be found in ref. S5). Half of the combined pulses are applied to the in-loop balanced cross-correlator for the synchronization; the other half of the combined pulses are the output from the synchronized lasers and applied to an out-of-loop cross-correlator for the measurement of synchronization performance. In the balanced cross-correlator, the 50:50 broadband beam-splitter is used again to split the combined pulses into the two beam paths. Here, keeping the same 50:50 splitting ratio for both Ti:sapphire and Cr:forsterite pulses is important for the long-term stable operation. If the splitting ratio is not exactly 50:50, optical power drifts in the input pulses can introduce an imbalance at the balanced detection output, which results in excess timing drift in the synchronization. For the nonlinear crystal, LBO crystals with 1-mm thickness are used for the sum-frequency generation (SFG) at 499 nm. The crystal is type-i SFG phase-matched between 830 nm from the Ti:sapphire laser and 1250 nm from the Cr:forsterite laser, that results in SFG at 499 nm (1/830nm + 1/1250nm = 1/499nm). Due to the difference in the input wavelengths, the output from the cross-correlator is a smooth discriminator function without fringes (as is shown in Fig. 3a inset). To generate a group delay offset of 48 fs between 830 nm and 1250 nm, a 3-mm thick fused silica window is used. Because the dependence of chromatic dispersion on temperature is very small (<1 as/k) S4, the timing offset is fixed at 48 fs without drift.

8 8 Figure S4. Experimental setup for the synchronization of the Ti:sapphire laser and the Cr:forsterite laser. BS, broadband 50:50 beam-splitter with matched group-delay dispersion S5 ; GD, 3-mm thick fused silica window providing 48 fs delay between the Ti:sapphire pulse and the Cr:forsterite pulse; NL, nonlinear crystal (LBOs for the in-loop cross-correlator; BBO for the out-of-loop crosscorrelator); BPF, bandpass optical filter at 500 nm; OC, output coupler of the Ti:sapphire laser; PD, Si-photodiode; PI1, proportional-integral controller for the fast feedback loop; PI2, proportional-integral controller for the slow feedback loop; PZT, piezo-electric transducer. The error signal from the balanced detector is applied to the loop filter. The loop filter has fast and slow signal paths. The fast signal output is a proportional-integral (PI) controller that controls the fast piezoelectric transducer (PZT). The fast PZT loop with ~100 khz bandwidth stabilizes the high frequency fluctuations. The slow signal output is applied to a slow PZT through a high voltage (1 kv) driver to compensate the timing drift over longer time scales. The bandwidth of the slow feedback loop is about 1 khz. These PZTs control the cavity length and the repetition rate of the Ti:sapphire laser. To further suppress noise in the low frequency (<1 khz), an additional lag compensation S6

9 9 RC-circuit is inserted in the slow loop. With the optimization of parameters (gains, positions of poles and zeros) in fast and slow loops, sub-femtosecond timing lock is obtained over 12 hours as shown in Fig. 3b in the main paper. In the frequency domain, optical-optical synchronization between lasers leads to identical repetition rates of the two lasers (that is, the spacing of the mode comb emitted by each laser is matched). Note that the carrier-envelope offset frequency of each laser is not controlled because the synchronization of the pulse train timing does not depend on the carrier-envelope offset frequency or phase. To evaluate the out-of-loop residual timing jitter between two lasers, an out-ofloop cross-correlator with a BBO crystal and a 2.3-MHz bandwidth photodetector is used. The residual timing jitter depends on the intensity noise of the Cr:forsterite laser and the locking conditions such as the gains and corner frequencies of the fast and slow feedback loops, and needs to be optimized at each time a new lock is obtained. As a result, the resulting residual timing jitter varies time to time. The typical timing jitter ranges between 0.3 fs and 0.5 fs. Figure S5 shows the representative out-of-loop timing jitter density when the two lasers are locked. The integrated timing jitter from 10 Hz to 1 MHz is 0.39 fs (rms). Most of the residual jitter originates from the peaks within ranges [300 Hz, 2 khz] and [100 khz, 200 khz]. This noise is mainly caused by the timing fluctuation converted from the intensity noise in the Cr:forsterite laser. This is especially true in the high frequency above 100 khz, where the feedback control is not effective and the residual timing noise follows that of the free-running lasers. The use of lower intensity noise lasers will allow even better synchronization below 0.1 fs.

10 10 Figure S5. Frequency-domain measurement result of the out-of-loop crosscorrelation. The voltage noise density of the cross-correlator output is measured with a vector signal analyzer, and then converted to the equivalent timing jitter density using the measured slope of the cross-correlation. 3. Optical-microwave synchronization To achieve the optical-microwave synchronization performance presented in this paper, major improvements both in the synchronization and in the characterization have been made. First, in order to reduce the excess noise in the synchronous detection, the same reference signal (with a frequency of ( n + 1/ 2) f ) is used both for driving the phase modulator and for the down-conversion (see Fig. 4a in the main paper). Previously, different signals were used for the modulator and the mixer (as shown in ref. S7), which introduced excess noise. In this experiment, we used a 500 MHz ( 2.5 f R ) signal, derived from the 200-MHz input optical pulse train, for the reference signal. The 500 MHz signal is used because it can be easily derived from the input pulse train (by detecting 1 GHz harmonic component and frequency division by two), and it is located in the frequency range where the laser intensity fluctuations are shot-noise limited. Note that R

11 11 the influence of noise in this reference signal is fully suppressed by the synchronous detection at the downconversion mixer, i.e., the perfectly correlated common-mode noise in the reference signal is cancelled when generating the baseband error signal by in-phase mixing. We also introduce a new out-of-loop timing characterization technique that enables long-term drift-free measurements. Previously, we used two independent optoelectronic phase-locked loops and compared the output microwave signals with a temperature-stabilized microwave mixer. As shown in refs. S8 and S9, the characterization using a microwave mixer involves uncontrolled timing drifts (more than 40 fs in an hour) even in the case that the mixer is well temperature stabilized. As a result, the long-term (e.g., more than an hour) measurement capability has been seriously compromised. To overcome this problem, we can use a balanced opticalmicrowave phase detector (BOM-PD), which is used for the synchronization, also for the out-of-loop timing characterization. Since it directly measures the timing error between the pulse train and the microwave signal without excess noise, we can now measure the timing jitter and drift over 10 hours as shown in Fig. 4b in the main paper. Figure S6 shows the schematic of the optical-microwave synchronization experiment using a BOM-PD. A MHz repetition rate optical pulse train is generated from a commercial Er-fibre laser (M-Comb-Custom, MenloSystems GmbH). Two almost identical but independent BOM-PDs were used to extract the timing error between the pulse train and the microwave signal. The first BOM-PD (BOM-PD 1 in Fig. S6) is used for synchronizing the optical pulse train with the GHz (the 51st harmonic of the fundamental repetition rate) microwave signal from the voltagecontrolled oscillator (VCO, DRO from PSI Ltd). The second BOM-PD (BOM- PD 2 in Fig. S6) is used to measure the out-of-loop relative timing jitter between the regenerated microwave signal and the optical pulse train.

12 12 Figure S6. Experimental setup for the optical-microwave synchronization using a balanced optical-microwave phase detector (BOM-PD). VCO, voltagecontrolled oscillator. The BOM-PD 1 is used for locking the microwave VCO to the pulse train. The BOM-PD 2 is used for characterizing the out-of-loop timing jitter and stability between the pulse train and the microwave signal. Figure S7a shows the out-of-loop single-sideband (SSB) phase noise density at GHz and the corresponding integrated timing jitter between the microwave signal and the optical pulse train. The timing jitter integrated from 1 Hz to 1 MHz is 4.4 fs (rms), and most of the jitter is concentrated in the high frequency range (above 100 khz) from the limited feedback loop bandwidth and the phase noise of the free-running VCO. The short-term timing jitter is improved compared to the result in Ref. S8, mainly due to the improved synchronous detection process. Figure S7b presents the relative timing stability of the microwave signal, calculated from the timing jitter measurement result in Fig. 4b in the main paper. When the measurement time is T, the relative timing stability is determined by the ratio of the integrated timing jitter ( t rms ) to the measurement time ( T ). Because the excess photodetection noise is not introduced in the microwave signal regeneration, the relative timing stability ( t rms / T ) improves 1 monotonically with an ideal ~ T slope, which reaches in 36,000 seconds.

13 13 Figure S7. a, Timing jitter density and the corresponding integrated timing jitter of the optical-microwave synchronization. b, The relative timing stability between the regenerated microwave signal and the optical pulse train, calculated from the timing jitter measurement result in Fig. 4b in the main paper. References S1. Kim, J. et al. Long-term femtosecond timing link stabilization using a single-crystal balanced cross-correlator. Opt. Lett. 32, (2007). S2. Lin, K.C., Lin, C.J. & Lee, W. Y. Effects of gamma radiation on optical fibre sensors. IEE Proc.-Optoelectron. 151, (2004). S3. Corning, Inc. Corning SMF-28e Optical Fiber Product Information (11/26/2007). (see also < S4. Schibli, T. R. et al. Attosecond active synchronization of passively mode-locked lasers using balanced cross correlation. Opt. Lett. 28, (2003). S5. Kim, J. et al. Ultrabroadband beamsplitter with matched group-delay dispersion. Opt. Lett. 30, (2005). S6. Franklin, G. F., Powell, J. D. & Emami-Naeini, A. Feedback Control of Dynamic Systems 3 rd edn (Addison Wesley, 1994).

14 14 S7. Kim, J., Kärtner, F. X. & Ludwig, F. Balanced optical-microwave phase detectors for optoelectronic phase-locked loops. Opt. Lett. 31, (2006). S8. Kim, J., Ludwig, F., Felber, M. & Kärtner, F. X. Long-term stable microwave signal extraction from mode-locked lasers. Opt. Express 15, (2007). S9. Lorbeer, B., Ludwig, F., Schlarb, H. & Winter, A. Noise and drift characterization of direct laser to rf conversion scheme for the laser based synchronization system for FLASH at DESY. in Proceedings of Particle Accelerator Conference (IEEE, Albuquerque, New Mexico, USA, 2007).