Cascaded Microwave Frequency Transfer Over 300-Km Fiber Link with Instability at the 10−18 Level
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remote sensing Article Cascaded Microwave Frequency Transfer over 300-km Fiber Link with Instability at the 10−18 Level Wenxiang Xue 1,2, Wenyu Zhao 1,2,*, Honglei Quan 1,2,3, Yan Xing 1,2 and Shougang Zhang 1,2 1 National Time Service Center, Chinese Academy of Sciences, Xi’an 710600, China; [email protected] (W.X.); [email protected] (H.Q.); [email protected] (Y.X.); [email protected] (S.Z.) 2 Key Laboratory of Time and Frequency Primary Standards, Chinese Academy of Sciences, Xi’an 710600, China 3 School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China * Correspondence: [email protected]; Tel.: +86-029-838-905-64 Abstract: Comparing and synchronizing atomic clocks between distant laboratories with ultra- stable frequency transfer are essential procedures in many fields of fundamental and applied science. Existing conventional methods for frequency transfer based on satellite links, however, are insufficient for the requirements of many applications. In order to achieve high-precision microwave frequency transfer over a thousand kilometers of fiber and to construct a fiber-based microwave transfer network, we propose a cascaded system for microwave frequency transfer consisting of three 100-km single-span spooled fiber links using an improved electronic phase compensation scheme. The × −14 × −18 transfer instability measured for the microwave signal reaches 1.1 10 at 1 s and 6.8 10 at 105 s, which agrees with the root-sum-square of each span contribution. It is feasible to extend the length of the fiber-based microwave frequency transfer up to 1200 km using 4 stages of our cascaded Citation: Xue, W.; Zhao, W.; Quan, H.; Xing, Y.; Zhang, S. Cascaded system, which is still sufficient to transfer modern cold atom microwave frequency standards. −15 −18 5 Microwave Frequency Transfer over Moreover, the transfer instability of 9.0 × 10 at 1 s and 9.0 × 10 at 10 s for a 100-MHz signal 300-km Fiber Link with Instability at is achieved. The residual phase noise power spectral density of the 300-km cascaded link measured the 10−18 Level. Remote Sens. 2021, 13, at 100-MHz is also obtained. The rejection frequency bandwidth of the cascaded link is limited by 2182. https://doi.org/10.3390/ the propagation delay of one single-span link. rs13112182 Keywords: fiber link; frequency transfer; cascaded system; transfer instability Academic Editor: Hugo Carreno-Luengo Received: 12 April 2021 1. Introduction Accepted: 25 May 2021 Published: 3 June 2021 Long-haul and high-precision frequency transfer between distant laboratories plays a crucial role in numerous fields of fundamental and applied science, such as time and Publisher’s Note: MDPI stays neutral frequency metrology [1,2], fundamental physics [3,4], and geodesy [5]. The synchronization with regard to jurisdictional claims in of distributed systems (such as phased-array radio telescopes [6–8], very long baseline published maps and institutional affil- interferometry (VLBI) [9,10], and multistatic radar systems [11,12]) are also applications. iations. At present, remote frequency comparison and synchronization is usually performed based on satellite links, including two-way satellite time and frequency transfer (TWSTT) as well as global positioning system (GPS) carrier-phase observations. However, owing to the non-reciprocity of links, these methods are limited by an instability of 10−15 after one day and do not provide the short-term stability necessary for synchronization applications [13]. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. Consequently, frequency transfer over satellite links is insufficient for many application This article is an open access article requirements. Fortunately, taking advantage of the low loss, high reliability and active distributed under the terms and phase stabilization potential of optical fiber, high stability has been demonstrated for conditions of the Creative Commons direct optical frequency transfer [14–17] and radio-frequency (RF) transmission using the Attribution (CC BY) license (https:// intensity modulation of an optical carrier [18–25] over fiber links. The instability of fiber- −20 4 creativecommons.org/licenses/by/ based optical frequency transfer reached the 10 level at 10 s over an urban fiber of more 4.0/). than 100 km [16,17], while microwave frequency transfer has presented an instability of Remote Sens. 2021, 13, 2182. https://doi.org/10.3390/rs13112182 https://www.mdpi.com/journal/remotesensing Remote Sens. 2021, 13, 2182 2 of 13 10−19 level at one day over an urban fiber of about 80 km [19,20]. In addition, simultaneous dissemination of time (1 PPS) and frequency (10/100 MHz) signals generated by atomic clocks over fiber have also demonstrated fairly low residual instability [26,27]. There are two main limitations to the achievable length of distance extension of fiber- based frequency transfer. In the first place, the bandwidth fc of the link noise compensation is limited by the propagation delay t of the fiber [28,29], which is simplified as fc < 1/4t. In the second place, frequency transfer instability is dominated by the signal-to-noise ratio (SNR) of the output-detected signal, which is limited by the attenuation of the fiber link. In particular, in the case of microwave frequency transmission using the intensity modulation of an optical carrier, the power of the microwave signal detected at the end of the fiber link is attenuated by twice of link attenuation (expressed in dB) [30], and the performance of link noise compensation is degraded by the chromatic dispersion and polarization mode dispersion (PMD) effect of fiber [19,31]. Therefore, compared with the single-span transfer, the cascaded transfer with independent link noise compensation for each short segment is more suitable for ultra-long-distance fiber-based microwave frequency transfer. The earliest reported study of cascaded microwave frequency transfer has demonstrated an instability of 6 × 10−14 at 1 s and 5 × 10−17 at one-half day over 204-km urban fiber link consisting of two single-span links [32]. In 2016, a 1-GHz signal was transferred through 430 km of urban fiber link with an instability of 1.94 × 10−13 at 1 s and 1.34 × 10−16 at 104 s using a cascaded system consisting of two single-span links, which is a record distance of fiber-based microwave frequency transfer [33]. The National Time Service Center (NTSC) of the Chinese Academy of Sciences (CAS) undertakes the task to generate, maintain, and transmit the national standard of time (Bei- jing Time), which has already demonstrated an ultra-stable microwave frequency transfer over a 112-km urban fiber link with an instability of 4.2 × 10−15 at 1 s and 1.6 × 10−18 at one day [25]. In this work, to achieve microwave frequency transfer with high precision over a thousand kilometers of fiber and construct fiber-based microwave transfer network, we first used fiber spools to perform a microwave frequency transfer experiment with a cascaded system. Subsequently, we investigated the ultra-stable microwave frequency transfer over a 300-km fiber link with the cascaded system, which is composed of three single-span links. The frequency transfer instability of each span, as well as of the cascaded link, is investigated. The 300-km cascaded link reached an instability of 1.1 × 10−14 at 1 s and 6.8 × 10−18 at 105 s. The residual phase noise of the entire link was also measured. The bandwidth of the link noise compensation was unaffected by the length of the entire link. 2. Materials and Methods 2.1. Principle of Frequency Transfer System In fiber-based microwave frequency transfer, two approaches of phase compensation exist: optical path compensation (OPC) and electronic phase compensation (EPC) [34]. Although the OPC approach can achieve better transfer instability, the compensation actuator, which consists of a piezo-electric fiber stretcher and thermally-controlled fiber spool [31,35], is complex and has small dynamic range, which is inconvenient for extensive applications. On the contrary, the EPC approach has strong adaptability and little PMD fluctuation effect due to the voltage-controlled oscillator (VCO) used as an actuator [25], except that the performance is slightly poorer than that of the OPC approach. Therefore, in order to broaden the application range of the fiber-based microwave frequency transfer system, we adopted the EPC scheme. For fiber-based frequency transfer, the phase noise induced by the fiber link was measured by comparing the round-trip signal with the reference signal and compensating it in real time. In a typical implementation of microwave transfer over fiber based on the EPC approach, the forward and backward signals have the same frequency, which leads to the transfer instability being limited by Brillouin backscattering and parasitic reflections along the link, especially for long-distance fiber with more connectors and splices. For this reason, to suppress the influence of the backscattering and parasitic reflections, an Remote Sens. 2021, 13, x 3 of 14 ing it in real time. In a typical implementation of microwave transfer over fiber based on Remote Sens. 2021, 13, 2182the EPC approach, the forward and backward signals have the same frequency, which 3 of 13 leads to the transfer instability being limited by Brillouin backscattering and parasitic re- flections along the link, especially for long-distance fiber with more connectors and splices. For this reason, to suppress the influence of the backscattering and parasitic re- flections, animproved improved frequency frequency transfer transfer system system based based on on the the EPC EPC approach approach was was designed de- with two signed with differenttwo different microwave microwave frequencies frequenc fories the for forward the forward and backward and backward signals.