Preliminary design of a femtosecond timing system for large accelerator facilities

Preliminary design of a femtosecond timing system for large accelerator facilities 1 corresp first-author Corresponding author. E-mail address: liuming@sinap.ac.cn Corresponding author. E-mail address: liuming@sinap.ac.cn liuming@sinap.ac.cn 1 1 1 2 Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China University of Chinese Academy of Sciences, Beijing 100049, China University of Chinese Academy of Sciences, Beijing 100049, China Large accelerator facilities require clocks and triggers with high accuracy to synchronize equipment and devices. A new femtosecond timing system was designed to meet the demands of new facilities. In this system, the radio-frequency signal is modulated in a continuous-wave laser carrier with frequency stabilization, and timing events are distributed in the same fiber. The phase drift is detected precisely, based on the principle of the Michelson interferometer. The phase drift is compensated with coarse and fine correctors afterward. We aim to realize the stable transmission of the RF signal and timing events for a long distance and duration, with the phase drift and additive jitter in femtoseconds. After the extension, the system will become a complete solution for the clock-and-trigger distribution of synchrotron radiation facilities, free electron lasers, and other accelerators. The physics design, simulation analysis, and preliminary results are included in the paper. Timing system Large accelerator facilities Synchronization in femtoseconds 1. Introduction 1 In a large accelerator facility, a timing system with high accuracy is required to synchronize various equipment and devices located at different points around the facility. A traditional event timing system transmits triggers and clocks [ 1 1 ]. The pulse width and delay of the transmitted signals are adjustable to different accuracies from nanoseconds to picoseconds, and the jitter of the transmitted signals is in picoseconds. The performance of the event system meets the requirements of third-generation light sources [ 2 2 – 4 4 2–4 ], electron-positron colliders [ 5 5 ], and other kinds of large accelerator facilities. Along with the development of an experimental methodology for the beamlines of synchrotron radiation facilities, the traditional electronic timing system has gradually fallen behind the demands of scientists. For new pump-probe experiments in synchrotron radiation facilities, beamline users demand a timing accuracy that is higher than picoseconds [ 6 6 – 8 8 6–8 ]. In the new generation of light source facilities, such as free electron lasers, highly stable radio-frequency (RF) clocks are transmitted as timing benchmarks. Moreover, highly stable timing triggers are utilized to synchronize electron guns, laser devices, and experimental equipment. The accuracy of the clocks and triggers is required to reach 10–100 fs [ 9 9 – 13 13 9–13 ]. The method of pure electronics cannot achieve the goal. Generally, there are two technical routes to realize a transmission with high accuracy. Both of them are based on optical technologies. One method makes use of a mode-locked laser as the reference. The delay fluctuation of the transmission time is sensed by an optical cross-correlator, and then it is compensated by an optical feedback approach. The other method makes use of a continuous-wave laser as the reference. The delay fluctuation of the transmission time is sensed by the optical fiber system based on the principle of the Michelson interferometer, and it is compensated by an electronic feedback approach. Scientists from Massachusetts Institute of Technology (MIT) originated the first method [ 14 14 ], and it is implemented in free-electron lasers such as Free-electron LASer in Hamburg (FLASH) [ 15 15 ] and Pohang Accelerator Laboratory X-ray Free-Electron Laser (PAL-XFEL) [ 16 16 ]. In this method, the output voltage from the optical cross-correlator is measured to calculate the value of the delay fluctuation. The stability of the method reaches a degree of femtoseconds or subfemtoseconds. However, the transmission of optical signals in free space is unavoidable for the laser source and the optical cross-correlator. Consequently, it is difficult to make the system compact, and furthermore, the system is easily affected by mechanical vibration and air disturbance. Scientists from Lawrence Berkeley National Laboratory (LBNL) originated the second method [ 17 17 ], and it is implemented in Linac Coherent Light Source (LCLS) at Stanford Linear Accelerator Center (SLAC) [ 18 18 ]. The stability of the method reaches a degree of femtoseconds. Owing to its all-fiber network, the system is compact, easy to extend, and immune to mechanical vibration and air disturbance. Nevertheless, the method is applicable to RF clocks but not trigger pulses. The system in our design aims to improve the structure of the topology and extend the functionality in the second method. Based on the principle of the Michelson interferometer, the phase of the laser carrier is converted one-to-one to the phase of the beat frequency. Therefore, the optical system senses very fine fluctuations in the transmission delay. After that, the optical delay line and the fiber stretcher compensate the phase of the transmitted signal. We expect to stabilize the short-term jitter of the transmitted S-band RF signal to 0.01º in a 100-kHz bandwidth, i.e., 10 fs, and the long-term drift to 100 fs for 24 h. In addition, the traditional event timing system is integrated with the same optical fiber network. Thus, it is beneficial for the timing triggers to decrease the effect of the ambient temperature drift. 2. System design 1 In the system, the transmitter covers most of the functions, including detection and compensation of the phase drift of the transmitted signal. Therefore, the transmitter is much more complex than the receiver, as illustrated in Fig. 1. Fig. 1. The gray blocks are optical components, and the white blocks are electronic components. Only single-mode fibers are used in the optical part of the system. The structure is different from the original design from LBNL. In our design, the function of phase detection was implemented in the transmitter, so the receiver was simplified drastically. For practical applications, we will design compact receiver modules on standard platforms such as Micro Telecommunications Computing Architecture (MTCA). Considering the reference distribution topology in large accelerator facilities, we believe that the new layout will enhance the scalability of the system. The transmitter is comprised of an optical part and an electronic part. Available commercial products are utilized to form the optical part, including a continuous-wave laser, analog modulator (AM), acoustic-optic frequency shifter (AOFS), Faraday rotator mirror (FRM), and optical delay modules. The transmitted RF signal is modulated in a continuous-wave laser carrier. The AOFS, FRM, and fiber connection serve as one arm of the Michelson interferometer. By means of Michelson heterodyne interference, we obtain the beat frequency signal, which is further used to calculate the optical path variation from the transmitter to the receiver in the electronic part. The optical delay line (ODL) and the fiber stretcher are the execution components of the phase compensation. The two modules are for coarse and fine correction, respectively. In addition, a wavelength division multiplexer (WDM) multiplexes the event stream and the modulated RF signal into a single fiber. In the electronic part, the beat frequency signal is recovered in the photodiode. Then, we evaluate the optical path variation by measuring the phase of the beat frequency signal, and calculate the feedback quantities by using a Proportion Integration Differentiation (PID) algorithm. Because the phase of the laser carrier is converted one-to-one to the phase of the beat frequency, a variation of 360º in the beat frequency corresponds to approximately 5 fs. In other words, the precision of the measurement is very high. After the phase measurement, all functions are accomplished digitally, which does not introduce additional noise. The digital output of the controller is used to drive the optical delay modules. The receiver serves as the other arm of the Michelson interferometer. Moreover, it recovers the received signal and demultiplexes it to the RF signal and the event codes. The critical modules of the transmitter and the receiver should be temperature controlled, including the AOFS, FRMs, photodiodes, and core components of the electronics, so that no additional phase drift is introduced. 2.1. Signal modulation and transmission 2 It is assumed that a continuous-wave laser generates an ideal monochromatic linearly polarized light. After modulation by the RF signal and transmission along the optic fiber, the optical signal is sensed by the photodiode at the receiver. The wave function of the electric vector of the beam is <math display="block" id="M1"><mrow><msub><mi>E</mi><mrow><mtext>d</mtext><mn>1</mn></mrow></msub><mrow><mo>(</mo><mrow><mi>t</mi><mo>,</mo><mi>l</mi></mrow><mo>)</mo></mrow><mo>=</mo><mrow><mo>[</mo><mrow><mn>1</mn><mo>+</mo><mi>b</mi><mi>cos</mi><mrow><mo>(</mo><mrow><msub><mi>ω</mi><mrow><mtext>rf</mtext></mrow></msub><mi>t</mi><mo>−</mo><msub><mi>β</mi><mrow><mtext>rf</mtext></mrow></msub><mi>l</mi></mrow><mo>)</mo></mrow></mrow><mo>]</mo></mrow><mi>cos</mi><mrow><mo>(</mo><mrow><msub><mi>ω</mi><mrow><mtext>op</mtext></mrow></msub><mi>t</mi><mo>−</mo><msub><mi>β</mi><mrow><mtext>op</mtext></mrow></msub><mi>l</mi></mrow><mo>)</mo></mrow><mo>,</mo></mrow></math> where b is the modulation index; <math id="M2"><mrow><msub><mi>ω</mi><mrow><mtext>rf</mtext></mrow></msub></mrow></math> and <math id="M3"><mrow><msub><mi>ω</mi><mrow><mtext>op</mtext></mrow></msub></mrow></math> are the angular frequencies of the RF signal and the laser carrier, respectively; and l is the length of the fiber from the transmitter to the receiver. The angular wavenumbers of the RF signal are <math id="M4"><mrow><mtext> </mtext><msub><mi>β</mi><mrow><mtext>rf</mtext></mrow></msub><mo>=</mo><msub><mi>ω</mi><mrow><mtext>rf</mtext></mrow></msub><mfrac><mi>n</mi><mi>c</mi></mfrac></mrow></math> , and the angular wavenumbers of the laser carrier are <math id="M5"><mrow><msub><mi>β</mi><mrow><mtext>op</mtext></mrow></msub><mo>=</mo><msub><mi>ω</mi><mrow><mtext>op</mtext></mrow></msub><mfrac><mi>n</mi><mi>c</mi></mfrac></mrow></math> . n is the refractive index of the optical fiber, and c is the velocity of light in a vacuum. The amplitudes and the initial phases of all signals are intentionally omitted in order to simplify the formulae in this paper. The RF signal is the envelope of the laser signal. Since the bandwidth of the selected photodiode is far lower than the frequency of the laser carrier, the photodiode records the average of the light intensity during a sampling interval. After filtering the DC and harmonic components, the output of the photodiode at the receiver is <math display="block" id="M6"><mrow><msub><mi>I</mi><mrow><mtext>d</mtext><mn>1</mn></mrow></msub><mo>=</mo><mi>cos</mi><mrow><mo>(</mo><mrow><msub><mi>ω</mi><mrow><mtext>rf</mtext></mrow></msub><mi>t</mi><mo>−</mo><msub><mi>β</mi><mrow><mtext>rf</mtext></mrow></msub><mi>l</mi></mrow><mo>)</mo></mrow><mo>.</mo></mrow></math> Compared with the length of the fiber, the change in the refractive index contributes much more to the optical path variation when the temperature changes. [ 19 19 ] Therefore, the phase drift of the RF signal is <math display="block" id="M7"><mrow><mfrac><mrow><mo>∂</mo><msub><mi>ϕ</mi><mrow><mtext>rf</mtext></mrow></msub></mrow><mrow><mo>∂</mo><mi>T</mi><mo>∂</mo><mi>z</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mo>∂</mo><mrow><mo>(</mo><mrow><msub><mi>β</mi><mrow><mtext>rf</mtext></mrow></msub><mi>l</mi></mrow><mo>)</mo></mrow></mrow><mrow><mo>∂</mo><mi>T</mi><mo>∂</mo><mi>z</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mtext>d</mtext><msub><mi>β</mi><mrow><mtext>rf</mtext></mrow></msub></mrow><mrow><mtext>d</mtext><mi>T</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mi>ω</mi><mrow><mtext>rf</mtext></mrow></msub></mrow><mi>c</mi></mfrac><mo>⋅</mo><mfrac><mrow><mtext>d</mtext><mi>n</mi></mrow><mrow><mtext>d</mtext><mi>T</mi></mrow></mfrac><mo>.</mo></mrow></math> Assuming that <math id="M8"><mrow><msub><mi>ω</mi><mrow><mtext>rf</mtext></mrow></msub><mo> </mo></mrow></math> = 2π × 2856 MHz, c ≈ 3 × 10 5 km/s, and d n / d T ≈ 9 × 10 -6 /°C at or near room temperature, the phase drift in the unit distance and unit temperature is about 0.17 π rad/km/°C. The corresponding time is about 30 ps/km/°C. 2.2. Phase drift detection and correction 2 It is a feature of the system to accomplish both the detection and correction of the phase drift at the transmitter. The phase detection is based on the principle of the Michelson interferometer. One arm of the interference is the modulated laser signal that passes through the AOFS twice and is reflected by the FRM at the transmitter. <math display="block" id="M9"><mrow><msub><mi>E</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>[</mo><mrow><mn>1</mn><mo>+</mo><mi>b</mi><mi>cos</mi><msub><mi>ω</mi><mrow><mtext>rf</mtext></mrow></msub><mi>t</mi></mrow><mo>]</mo></mrow><mi>cos</mi><mrow><mo>(</mo><mrow><msub><mi>ω</mi><mrow><mtext>op</mtext></mrow></msub><mi>t</mi><mo>+</mo><mn>2</mn><msub><mi>ω</mi><mrow><mtext>fs</mtext></mrow></msub><mi>t</mi></mrow><mo>)</mo></mrow><mo>,</mo></mrow></math> where <math id="M10"><mrow><msub><mi>ω</mi><mrow><mtext>fs</mtext></mrow></msub></mrow></math> is the angular frequency of the AOFS. The other arm of the interference is the modulated laser signal reflected from the receiver to the transmitter. <math display="block" id="M11"><mrow><msub><mi>E</mi><mn>3</mn></msub><mrow><mo>(</mo><mrow><mi>t</mi><mo>,</mo><mn>2</mn><mi>l</mi></mrow><mo>)</mo></mrow><mo>=</mo><mrow><mo>[</mo><mrow><mn>1</mn><mo>+</mo><mi>b</mi><mi>cos</mi><mrow><mo>(</mo><mrow><msub><mi>ω</mi><mrow><mtext>rf</mtext></mrow></msub><mi>t</mi><mo>−</mo><mn>2</mn><msub><mi>β</mi><mrow><mtext>rf</mtext></mrow></msub><mi>l</mi></mrow><mo>)</mo></mrow></mrow><mo>]</mo></mrow><mi>cos</mi><mrow><mo>(</mo><mrow><msub><mi>ω</mi><mrow><mtext>op</mtext></mrow></msub><mi>t</mi><mo>−</mo><mn>2</mn><msub><mi>β</mi><mrow><mtext>op</mtext></mrow></msub><mi>l</mi></mrow><mo>)</mo></mrow><mo>.</mo></mrow></math> The signals in Eq.(4) and Eq. (5) interfere and form the beat frequency signal, which is received by the photodiode at the transmitter. Since <math id="M12"><mrow><msub><mi>ω</mi><mrow><mtext>op</mtext></mrow></msub><mo>≫</mo><msub><mi>ω</mi><mrow><mtext>rf</mtext></mrow></msub></mrow></math> , we neglect the phase infinitesimals with <math id="M13"><mrow><msub><mi>ω</mi><mrow><mtext>rf</mtext></mrow></msub></mrow></math> and filter the DC and harmonic components higher than <math id="M14"><mrow><mn>2</mn><msub><mi>ω</mi><mrow><mtext>fs</mtext></mrow></msub></mrow></math> in the beat frequency signal. Then, the filtered output of the photodiode at the transmitter is <math display="block" id="M15"><mrow><msub><mi>I</mi><mrow><mtext>d</mtext><mn>2</mn></mrow></msub><mo>=</mo><mi>cos</mi><mrow><mo>(</mo><mrow><mn>2</mn><msub><mi>ω</mi><mrow><mtext>fs</mtext></mrow></msub><mi>t</mi><mo>+</mo><mn>2</mn><msub><mi>β</mi><mrow><mtext>op</mtext></mrow></msub><mi>l</mi></mrow><mo>)</mo></mrow><mo>=</mo><mi>cos</mi><mrow><mo>(</mo><mrow><mn>2</mn><msub><mi>ω</mi><mrow><mtext>fs</mtext></mrow></msub><mi>t</mi><mo>+</mo><mfrac><mrow><mn>2</mn><msub><mi>ω</mi><mrow><mtext>op</mtext></mrow></msub><mi>l</mi></mrow><mi>c</mi></mfrac><mi>n</mi></mrow><mo>)</mo></mrow><mo>,</mo></mrow></math> where the phase of the laser carrier <math id="M16"><mrow><mfrac><mrow><mn>2</mn><msub><mi>ω</mi><mrow><mtext>op</mtext></mrow></msub><mi>l</mi></mrow><mi>c</mi></mfrac><mi>n</mi></mrow></math> is converted one-to-one to the frequency domain of the AOFS. A very fine change of the refractive index n will cause a very large phase change of the beat frequency signal, since <math id="M17"><mrow><msub><mi>ω</mi><mrow><mi>o</mi><mi>p</mi></mrow></msub></mrow></math> is usually 10 6 higher than <math id="M18"><mrow><msub><mi>ω</mi><mrow><mi>f</mi><mi>s</mi></mrow></msub></mrow></math> . The ratio between the phase change <math id="M19"><mrow><mi>Δ</mi><msub><mi>ϕ</mi><mrow><mtext>bf</mtext></mrow></msub></mrow></math> <math id="M20"><mrow/></math> of the beat frequency signal and the phase change <math id="M21"><mrow><mi>Δ</mi><msub><mi>ϕ</mi><mrow><mi>r</mi><mi>f</mi></mrow></msub></mrow></math> of the transmitted RF signal is <math display="block" id="M22"><mrow><mfrac><mrow><msub><mi>ϕ</mi><mrow><mtext>bf</mtext></mrow></msub></mrow><mrow><mi>Δ</mi><msub><mi>ϕ</mi><mrow><mtext>rf</mtext></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>Δ</mi><mrow><mo>(</mo><mrow><mn>2</mn><msub><mi>β</mi><mrow><mtext>op</mtext></mrow></msub><mi>l</mi></mrow><mo>)</mo></mrow></mrow><mrow><mi>Δ</mi><mrow><mo>(</mo><mrow><msub><mi>β</mi><mrow><mtext>rf</mtext></mrow></msub><mi>l</mi></mrow><mo>)</mo></mrow></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><msub><mi>ω</mi><mrow><mtext>op</mtext></mrow></msub></mrow><mrow><msub><mi>ω</mi><mrow><mtext>rf</mtext></mrow></msub></mrow></mfrac><mo>.</mo></mrow></math> Assuming that <math id="M23"><mrow><msub><mi>ω</mi><mrow><mtext>op</mtext></mrow></msub><mo> </mo></mrow></math> = 2π × 200 THz and <math id="M24"><mrow><msub><mi>ω</mi><mrow><mtext>rf</mtext></mrow></msub><mo> </mo></mrow></math> = 2π × 2856 MHz, it is estimated that the detection sensitivity of the phase drift is improved by five orders of magnitude. In order to detect a 0.01º phase drift of the RF signal, we only need to detect four periods’ phase drift of the laser signal, i.e., 20 fs. The method of the heterodyne interference effectively improves the measuring precision. Compensation of the phase drift is accomplished at the transmitter as well. The electronic part at the transmitter acquires the phase drift. After calculating the control quantities by the PID algorithm, the customized controller outputs them to the motorized variable optical delay line and the optic fiber stretcher to correct the phase drift coarsely and finely, respectively. It is supposed that the two execution components suppress the phase drift from a range of hundreds of picoseconds to the level of femtoseconds. 2.3. Frequency stabilization of laser 2 The system adopts the output of a continuous-wave distributed feedback (DFB) fiber laser module as the carrier of the RF signal. The frequency stability of the laser module is of great importance to the performance of the system. From the aspect of short-term stability, the length of the wave train should be larger than that of the round-way optical path in order to make the signals in the two arms of the Michelson interferometer coherent. We assume that the length of the optical fiber is 1 km from the transmitter to the receiver. The round way of the optical path is about 2.92 km in consideration of the refractive index of 1.46. The wavelength of the laser signal <math id="M25"><mrow><mo> </mo><mi>λ</mi></mrow></math> ≈ 1560 nm. According to the formula that the coherent length is <math id="M26"><mrow><mi>L</mi><mo>=</mo><msup><mi>λ</mi><mn>2</mn></msup><mo>/</mo><mtext>Δ</mtext><mi>λ</mi></mrow></math> , the linewidth of the laser module should be less than 100 kHz. From the aspect of long-term stability, a change in ambient temperature causes a slow drift of the laser frequency. The slow drift is about tens of MHz/°C, which introduces a systematic error to the phase detection. If the angular frequency of the laser signal <math id="M27"><mrow><msub><mi>ω</mi><mrow><mtext>op</mtext></mrow></msub></mrow></math> deviates by <math id="M28"><mrow><mi>Δ</mi><msub><mi>ω</mi><mrow><mtext>op</mtext></mrow></msub></mrow></math> , the phase change of the beat frequency signal is <math id="M29"><mrow><mi>Δ</mi><msub><mi>ϕ</mi><mrow><mtext>bf</mtext></mrow></msub><mo>=</mo><mfrac><mrow><mi>Δ</mi><msub><mi>ω</mi><mrow><mtext>op</mtext></mrow></msub></mrow><mrow><msub><mi>ω</mi><mrow><mtext>op</mtext></mrow></msub></mrow></mfrac><mo>·</mo><mn>2</mn><msub><mtext>β</mtext><mrow><mtext>op</mtext></mrow></msub><mi>l</mi></mrow></math> , according to Eq. (6). We also assume that the length of the optical fiber is 1 km from the transmitter to the receiver. In order to make the phase drift less than 0.01º, <math id="M30"><mrow><mfrac><mrow><mi>Δ</mi><msub><mi>ω</mi><mrow><mtext>op</mtext></mrow></msub></mrow><mrow><msub><mi>ω</mi><mrow><mtext>op</mtext></mrow></msub></mrow></mfrac></mrow></math> , which describes the stability of the laser frequency, should be better than 2 × 10 -9 over the long term. According to the results calculated above, the selection of a low-linewidth laser module is of the most importance. Then, the wave train of the laser signal is long enough, which guarantees that the signals in the two arms of the interferometer interfere in the fiber. Preventing the frequency of the laser from drifting slowly is in the second place. The sophisticated solution to the issue is to lock the frequency of the laser to a saturated absorption line of a certain element [ 20 20 ]. The system will lock the wavelength of the laser to 1560.49 nm, which is the second harmonic of the rubidium absorption line, by a feedback mechanism. In this way, the long-term stability of the laser frequency is guaranteed. 2.4. Dispersion compensation 2 In the optical fiber, the laser carrier travels at a phase velocity <math id="M31"><mrow><msub><mi>v</mi><mtext>p</mtext></msub><mo>=</mo><mtext>c</mtext><mo>/</mo><mi>n</mi></mrow></math> , while the modulated RF signal travels at a group velocity <math id="M32"><mrow><msub><mi>v</mi><mtext>g</mtext></msub><mo>=</mo><mtext>c</mtext><mo>/</mo><mi>N</mi></mrow></math> , where N is the group refractive index. Since the frequency of the laser module is in the normal dispersion region of the fiber, the laser carrier transmits faster than the RF signal. In a fiber with a length of l , the transmission time of the RF signal is <math display="block" id="M33"><mrow><mi>τ</mi><mo>=</mo><mfrac><mi>l</mi><mrow><msub><mi>v</mi><mtext>g</mtext></msub></mrow></mfrac><mo>=</mo><mfrac><mi>l</mi><mrow><msub><mi>v</mi><mtext>p</mtext></msub></mrow></mfrac><mo>+</mo><mtext>Δ</mtext><mi>τ</mi><mo>=</mo><mfrac><mi>l</mi><mrow><msub><mi>v</mi><mtext>p</mtext></msub></mrow></mfrac><mo>+</mo><mi>D</mi><mo>⋅</mo><mi>l</mi><mo>⋅</mo><mtext>Δ</mtext><mi>λ</mi><mo>,</mo></mrow></math> where D is the dispersion coefficient, and <math id="M34"><mrow><mtext>Δ</mtext><mi>λ</mi></mrow></math> is the linewidth of the laser carrier in nanometers. In Eq.(8), the first term is the transmission time of the laser carrier, whose fluctuation can be measured and corrected by the method in Sect. 2.2, and the second term <math id="M35"><mrow><mtext>Δ</mtext><mi>τ</mi></mrow></math> is the group delay, which is the delay of the envelope center relative to the constant phase front of the carrier. The group delay fluctuates owing to thermal changes. The delay fluctuation can be mostly corrected by allocating dispersion compensation fibers along the transmission path. Dispersion compensation fibers have a negative dispersion coefficient D’ and a total length l’ to make <math id="M36"><mrow><mi>D</mi><mo>⋅</mo><mi>l</mi><mo>+</mo><msup><mi>D</mi><mo>′</mo></msup><mo>⋅</mo><msup><mi>l</mi><mo>′</mo></msup><mo>≈</mo><mn>0</mn></mrow></math> . The remaining part of the fluctuation can be measured and corrected by the optical delay modules. The group delay discussed above is the first-order effect of the dispersion, and the group velocity dispersion is the second-order effect of the dispersion. Since the linewidth of the laser signal is narrow enough, the envelope distortion caused by the group velocity dispersion is negligible. 2.5. Transmission of event stream and RF clock in one fiber 2 We designed an entire set of the event timing system based on electronics that distributed the event sequence around the accelerator facility to synchronize various equipment and devices. This system has already been applied in many large accelerator facilities successfully [ 21 21 – 24 24 21–24 ]. Nevertheless, it cannot meet the requirements of next-generation light sources owing to the inherent defects of the electronic system. In our new design, the traditional event timing system is integrated with the femtosecond timing system. In this way, timing information with diverse accuracy is distributed to the devices with diverse timing demands. Specifically, the RF signal is modulated in the laser carrier with a wavelength of 1560 nm, while the event stream is modulated in the laser carrier with a wavelength of 1310 nm. Two wavelength division multiplexers (WDM) combine and separate the two signals at the transmitter and at the receiver, respectively. Therefore, they transmit in a single fiber. At the receiver, the recovered event codes are aligned by the compensated RF signal. Thus, the effect of the fiber temperature change on the timing triggers is eliminated. However, the effect of temperature changes in the electronic devices still remains. 3. Simulation 1 We conducted a simulation with the software OptiSystem 14 Evaluation Version. The structure of the simulated optical part is illustrated in Fig. 2. Fig. 2. The RF signal with a frequency of 2856 MHz was modulated in one laser carrier with a wavelength of 1560.49 nm. The ideal frequency converter was a crude substitute for the AOFS in Fig. 1 Fig. 1 , and the frequency shift was 50 MHz. An 8-bit sequence 01011100, as the event code to be transmitted, was modulated in the other laser carrier with a wavelength of 1310.00 nm. One WDM device multiplexed the two signals onto a single fiber at the transmitter, while another WDM device demultiplexed them. The first signal was received to recover the RF signal at the receiver, and it was also reflected to the transmitter as one arm of the interference. The second signal was received to recover the event stream. The simulated results are as follows. It was confirmed that the RF signal was recovered at the receiver, as illustrated in Fig. 3 Fig. 3 . Figure 3(a) Figure 3(a) illustrates the signal in the time domain, and Fig. 3(b) Fig. 3(b) illustrates it in the frequency domain. It is observed that the recovered signal at the photodiode contained not only the fundamental frequency but also harmonic components. Therefore, a band-pass filter will be necessary in future experiments. It was also confirmed that the beat frequency signal was generated at the transmitter, as illustrated in Fig. 3 Fig. 3 . Figure 3(c) Figure 3(c) illustrates the signal in the time domain, and Fig. 3(d) Fig. 3(d) illustrates the signal in the frequency domain. It is observed that the envelope of the signal was at double the frequency of the AOFS, i.e., 100 MHz. The simulated signal also contained harmonic components of the RF signal and corresponding double sideband signals of 100 MHz. Therefore, we need a band-pass filter to obtain the pure beat frequency signal. Then, we can detect the phase of the beat frequency signal. The event code 01011100 was recovered at the receiver, as illustrated in Fig. 4. Fig. 4. It was confirmed that multiplexing and demultiplexing did not affect the transmission of the event stream. 4. Preliminary results 1 A prototype of the optical part was designed and tested in the laboratory, as illustrated in Fig. 5 Fig. 5 . We aimed to verify basic functions of the optical part qualitatively by using the prototype, including the modulation and demodulation of the RF signal in the laser carrier, the generation of the beat frequency signal and transmission of the RF signal, and the event sequence along the same fiber. We also built a simple feedback loop with the help of an oscilloscope and MATLAB. The wavelength of the DFB fiber laser module was 1560 nm. The frequency of the AOFS was 50 MHz. A Rohde & Schwarz SMA 100A signal generator output an RF signal with a frequency of 2856 MHz. A Tektronix TDS 694C oscilloscope and an Agilent E4440A PSA Series spectrum analyzer were used to observe the signals in the time domain and frequency domain, respectively. The recovered RF signals in the time domain and frequency domain are illustrated in Fig. 6(a) Fig. 6(a) and Fig. 6(b) Fig. 6(b) , respectively. It is observed that it was locked to the input RF signal at the transmitter in the upper part. In the demodulation process, DC and harmonic components were generated, which should be filtered in subsequent designs. The generated beat frequency signals in the time domain and frequency domain are illustrated in Fig. 6(c) Fig. 6(c) and Fig. 6(d) Fig. 6(d) , respectively. It is observed that the signal modulated the RF signal. The 100-MHz double sideband signal suggested by the simulation was experimentally realized. Unwanted components should be filtered in subsequent designs. After that, the phase of the beat frequency signal can be measured precisely. Regardless of the contribution of noise, the results in Fig. 7 Fig. 7 and Fig. 8 Fig. 8 agree with the simulation in Sect. 3. The RF signal and the timing trigger were recovered at the receiver, as illustrated in Fig. 7 Fig. 7 . Since the event timing system is only capable of utilizing the RF signal with a frequency of several hundreds of MHz as the reference, 500 MHz rather than 2856 MHz was chosen as the frequency of the RF signal for convenience. The RF signal was generated in the Agilent E4400B signal generator. A WDM module at the transmitter and another at the receiver were used to multiplex and demultiplex two laser carriers with different wavelengths. The signal in Ch2 was the RF signal from the signal generator at the transmitter. The signal in Ch4 was the RF signal recovered at the receiver. The signal in Ch3 was the timing trigger mapped from the transmitted event code, which was recovered at the receiver as well. It is observed that the event stream and the RF signal could be transmitted in a single fiber, and the event code was still locked to the RF signal after being demodulated at the receiver. A preliminary test of the phase stability of the transmitted RF signal was conducted in the laboratory, as illustrated in Fig. 8. Fig. 8. The laser was stabilized with a saturated absorption line of rubidium. A 2-km optical fiber was used to transmit the signal. The oscilloscope picked up the signal of the photodiode. The Simulink program in MATLAB read the waveforms at a sampling rate of 100 Hz from the oscilloscope, calculated the phase of the signal, and output the feedback quantity to a mechanical optical delay line. The PID algorithm was also implemented in Simulink. It is observed in Fig. 8(a) Fig. 8(a) that the phase of the RF signal was stabilized in 0.84 ps (r.m.s.) within a temperature range of 0.6 °C. The quantity of the phase variation here covered only the wander part but not the jitter part. The threshold between the wander and jitter is 10 Hz, which is defined by the International Telecommunication Union (ITU). [ 25 25 ] By contrast, the temperature coefficient of the phase delay was about 150 ps/°C for the unstabilized signal, as illustrated in Fig. 8(b) Fig. 8(b) . This value is considerably larger because the group delay fluctuation caused by thermal changes also contributed to the total phase drift of the RF signal. An initial analysis is as follows. The software of calculation and execution decreased the feedback frequency. The mechanical optical delay line did not have enough accuracy to compensate precisely. Optimization of the PID parameters was still required. 5. Discussion 1 According to the simulation and the preliminary test, the prototype of the optical part was realized. However, we still need to improve the prototype in three aspects for further evaluation. First, the mechanical optical delay line is not enough to compensate the phase drift precisely. Execution components with higher adjusting accuracy, i.e., a fiber stretcher, will be added to the system. Second, the detection and correction of the phase including the PID algorithm will be implemented in hardware to increase the bandwidth of the feedback loop. Third, core components of the optical part, such as the AOFS and the photodiodes, are easily affected by the ambient temperature. An evaluation of the effect will be carried out to decide whether temperature controllers are necessary in the future. In the next step of our work, we plan to design the electronic part of the system. The main functions are to acquire the phase of the beat frequency signal, to calculate the feedback control quantities using the PID algorithm, and to output the quantities to the execution components of the optical delay. In order to distribute the RF signal and timing triggers with high stability to equipment and devices around large accelerator facilities, we plan to design a fanout module to extend the system. The parameters of different components affect the overall performance of the system. On the basis of the test in Section 4, the contributions of different components to the system performance will be evaluated quantitatively. After that, we will match the remedy to the case, and solve every problem to improve the overall performance. 6. Conclusion 1 In this paper, we described the preliminary design of a femtosecond timing system. The simulation and the initial test of the optical prototype were demonstrated. In addition, the transmission of the RF signal and the event stream in a single fiber was realized. We aimed to suppress the short-term jitter of the transmitted RF signal to 0.01º in a bandwidth of 100 kHz and the long-term drift to 100 fs for 24 h. 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Definitions and Terminology for Synchronization Networks . International Telecommunication Union , ITU-T Recommendation G.810 , 1996 . Definitions and Terminology for Synchronization Networks 10.1007/s41365-018-0369-1 The project was supported by the Youth Innovation Promotion Association CAS (No. 2016238) and the National Natural Science Foundation of China (No.11305246). 2017-08-17 2017-11-23 2017-12-26 2018-02-19 2018-03-01 2021-04-11 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2018 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-018-0369-1 http://dx.doi.org/10.1007/s41365-018-0369-1 . 2018 Nuclear Science and Techniques 03 29