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Abstract
We realize an ultra-stable microwave signal distribution system based on an optical phase-locked loop. The transmission delay jitter is accurately compensated with a piezoelectric fiber stretcher (PFS). For further eliminating the additional delay jitter originated from the polarization changes during the PFS stretching, we propose an orthogonal-polarized round-trip PFS structure. The transmission delay jitter of 24 GHz signals distributed to multiple remote ends using the proposed and the traditional PFS scheme are carefully compared and quantitively analyzed under various fiber types and lengths. With the proposed PFS structure, the relative delay jitter of two transmitted signals are decreased from 291.4 fs to merely 17.7 fs even via 200 m polarization maintaining fiber with considerable polarization mode dispersion, showing its remarkable superiority. This microwave signal distribution system can find its versatile applications in radio astronomy where multiple ultra-high relative stable microwave signals are highly desired in different locations.
© 2021 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Distribution of an ultra-stable frequency or time signal to different locations is a key technology in a variety of applications, such as the test of fundamental physical principles [1,2], development of next-generation accelerator-based x-ray sources [3], and long baseline coherent radio telescope arrays [4–6]. Taking advantage of the low loss, high reliability, and immunity to electromagnetic interference, the optical fiber link has been a promising candidate for the frequency and time signal distribution [7–12]. However, the fiber link usually suffers from environment perturbations, which will change the effective length of the link, thus deteriorating the phase stability of the signals at the remote end [13]. To compensate for this phase variation, several methods have been proposed, which can be classified into two categories: one is to properly adjust the phase of the transmitted signal [14–17] and the other is to change the effective length of the fiber link with an optical delay line which is usually considered to have higher stability and better control precision [18–20]. Generally, the controllable optical delay can be provided by the fiber-based delay line including the phase shifter and the piezoelectric fiber stretcher (PFS) [5], the motorized free-space delay line [7], the dispersive delay line with wavelength-dependent delay [21], the temperature-controlled fiber spool [22], and so on. Among all these delay lines, the fiber-based delay line has the fastest response, therefore, is considered to have the best compensation precision for a length-varied fiber link. Compared with the phase shifter that can only provide a delay of several optical wavelengths, a PFS with a stretching range of tens of ps is regarded as the most promising solution for ultra-high stable link length compensation, while other methods are usually only used for extending the compensation range of the PFS or solely used when the control precision requirement is not so high. However, the delay variation originating from the polarization changes during the PFS stretching known as polarization mode dispersion (PMD) still leads to the drift of the real propagation time of the transmitted signal even under the locking state [23,24]. It is challenging to either completely compensate this polarization related delay jitter or eliminate the polarization variation during the PFS stretching with the traditional structure, hindering the further improvement of the transmission stability.
Methods for mitigating the PMD induced transmission delay jitter have been greatly explored, especially in digital communications [25]. However, these bit coding based approaches are not applicable to the real-time frequency signal transmission. Currently, the common way to eliminate the PMD induced delay jitter in frequency signal transmission is using a polarization scrambler that averages the polarization related delay variations randomly [18]. But this is not suitable for the high-precision optical frequency coherence detection because it will cause rapid power variation when the scrambled signal beating with the reference wave at a fixed polarization state. To alleviate the PFS-induced polarization variation specifically, a feedback control system is proposed with a well-designed iterative searching algorithm to ensure that the optimal injected polarization state of the PFS can be achieved and fixed by tuning a polarization controller [26]. This method is effective, but the performance depends on the initial set point of the PFS, and the convergence time is usually as long as a few minutes. To shorten the iteration convergence time and improve the searching accuracy of the optimal state, a noniterative fast algorithm based on the Jones matrix Eigen-analysis has been proposed [26]. However, this fast algorithm requires heavy computation and has the risk that the compensator will lose track and end up in an unfavorable state or a suboptimal state. Moreover, both methods above still do not completely fix the output polarization state of the PFS, and the delay jitter originated from the PFS stretching still remains even in the tracking state. Until now, it is still a great challenge to eliminate the PMD related delay jitter caused by the PFS stretching.
In this paper, we present an ultra-stable microwave signal distribution system that transmits a 24 GHz single tone signal from a local end to different remote ends. The transmission delay jitter of each link is precisely detected with a round-trip Michelson interference structure and then accurately compensated with a PFS in a well-designed optical phase-locked loop (OPLL). To eliminate the delay jitter caused by the PFS stretching, we propose an orthogonal-polarized round-trip PFS structure assisted by a Faraday rotator mirror (FRM) to maintain the polarization state of the PFS input and output thereby ensuring the reciprocity of the forward and backward transmission link. The influence of the polarization changes related to the PFS stretching on the transmission delay jitter is analyzed in detail, and the performances of both the traditional PFS structure and the proposed scheme are compared carefully. Experimental results show that the proposed scheme can effectively fix the polarization state of the PFS output and suppress the delay jitter originated from the PFS stretching, resulting in a more stable transmission link. The feasibility of the scheme is further verified under different fiber lengths and fiber types with different PMD values. The relative root-mean-square (RMS) delay jitters of the transmitted signals in two different remote ends via 200 m single-mode (SM) fiber, 2 km SM fiber, and 200 m polarization maintaining (PM) fiber are 13.0 fs, 22.6 fs, and 17.7 fs within one hour, respectively. This microwave signal distribution system fits the applications in radio astronomy perfectly where multiple ultra-high relative stable microwave signals are required to be disseminated to different locations. The proposed PMD-free PFS structure is also highly desired in the systems that are sensitive to polarization variations.
2. Principle
To obtain an ultra-high stable microwave signal distribution system, any tiny transmission delay jitter of the signal at the remote end should be first detected and then compensated precisely. Benefitting from the high-frequency characteristic of the optical carrier, the phase variation of the optical carrier after the transmission can be measured with a precision as high as sub-femtosecond by using a round-trip Michelson interference structure. Meanwhile, in such a precise system, a PFS is often adopted for adjusting the fiber length with high control precision and considerable compensation range. Therefore, we adopt this round-trip Michelson interference structure with a PFS compensation module in a well-designed phase-locked loop.
The schematic diagram of the proposed microwave signal distribution system is shown in Fig. 1(a), consisting of a local end, a remote end, and the fiber link that connects the two parts. At the local end, a laser is first divided into the signal branch and the reference branch. In the signal branch, the microwave signal is modulated on the light by a Mach-Zehnder modulator (MZM). This optically carried microwave signal is split into multiple branches and then is transmitted to different remote ends. At the remote end, the frequency of the optical signal is shifted by an acousto-optic frequency shifter (AOFS). Then, this signal is divided into two parts, one of which is converted into a microwave signal by a receiver. Note that the Rayleigh backscattering has been avoided due to the usage of the AOFS at the remote end. The remaining part of the frequency-shifted optical signal is reflected back to the local end by an FRM, and then enters the delay control module together with the reference signal for phase discrimination and feedback control compensation to close the OPLL. Here, the 90-degree FRM guarantees a fixed polarization state of the returned signal at the local end [19]. Consequently, the two waves in the Michelson interferometer have always the same state of polarization, leading to a maximum beat-note signal without using any polarization controllers.
Fig. 1. The principle of the proposed microwave distribution system. (a) Schematic of the proposed distribution system. (b) Single compensation (SC) structure composed of a one-way PFS. (c) Roundtrip compensation (RC) structure composed of a PBS, a PFS, and an FRM. MZM: Mach-Zehnder modulator; OPLL: optical phase-locked loop; Com. structure: compensation structure; AOFS: acousto-optic frequency shifter; PBS: polarization beam splitter; PFS: piezoelectric fiber stretcher; FRM: Faraday rotator mirror.
As to the operation of the PFS-assisted control loop, the optically carried microwave signal is transferred to the remote end passing through the PFS and the optical fiber consecutively, while the optical carrier for phase locking is then retroreflected by an FRM and passes through the fiber and the PFS again back to the local end. The transmitted signal at the remote end can be expressed as
At the local end, the reflected and the reference optical waves for interference can be expressed as
It is worth noting that the optical interferometer system provides an ultra-sensitive measurement of transmission delay variation thanks to the high frequency of the optical carrier ${\mathrm{\omega }_{opt}}$. Equation (4) can be further simplified considering the practical conditions. First, since${\; }2{\mathrm{\omega }_{AOFS}}\; $is much smaller than ${\mathrm{\omega }_{opt}}$, the term $2{\mathrm{\omega }_{AOFS}}({{\tau_B} + {\tau_E} + {\tau_c} + {\tau_{BP}}} )$ is negligible. Second, ${\varphi _{opt}}({\textrm{t} - {\tau_{rou}}} )- {\varphi _{opt}}(\textrm{t} )$ is the difference between the transmitted and the local phase of the optical wave, which is also negligible if the laser frequency is stable enough. The phase variation of the IF signal is measured by comparing it with a stable reference signal in a phase frequency discriminator (PFD). The PFD output, as an error signal is used to drive the PFS, closing the control loop and maintaining the phase difference at a fixed value. When the control loop is locked, the transmission delay variation and the PFS induced delay for compensation can be expressed as
Figure 1(b) shows the traditional PFS compensation structure, where the optical signal directly passes through the PFS. We denote it as the single compensation (SC) structure. Due to the PFS stretching, the polarization state of the optical signal changes randomly in the PFS. This optical signal with a random polarization state (shown as green double-sided arrows) enters the transmission fiber afterward. As described above, the PMD of the PFS and the following fiber link transfer the random polarization variation to random transmission delay variation. Moreover, the delay variation for the forward and backward link (${\tau _{FP}}$ and ${\tau _{BP}}$) is different due to the different polarization evolution of the optical signal along the forward and backward trip. Thus, locking the round-trip delay still does not produce a phase-stable signal at the remote end with the SC structure. It has been verified in the previous work that the PFS induced delay jitter is tens of fs per millimeter stretch in real applications [24].
To eliminate this PMD related delay jitter produced by the PFS stretching, we propose an orthogonal-polarized round-trip PFS structure composed of a polarization beam splitter (PBS), a PFS, and an FRM as shown in Fig. 1(c). We denote it as the round-trip compensation (RC) structure. In this RC compensation structure, the optical signal is first injected into a PBS from one polarized port along the slow axis and then entirely passes through the following PFS. Unlike in the SC structure where the optical signal passes through the PFS only once with a random output polarization, here the optical signal is reflected back along the original path by the FRM. Due to the 90° polarization rotation, the backward signal passing through the PFS always experiences an orthogonal polarization evolution and finally reaches the PBS along the fast axis. Therefore, it gets out of the PBS entirely from another polarized port and enters the following transmission fiber in a fixed polarization state. Consequently, the delay jitter in the transmission fiber caused by the polarization change of the PFS output is eliminated, regardless of the PFS stretching. Meanwhile, considering the optical signal reflected back from the remote end, provided that the reflected signal reversely entering the RC structure has the same polarization state with the forward signal getting out of the RC structure (which can be realized easily as demonstrated in the next section), the polarization-related delay jitter in the PFS for the forward transmission link is exactly the same as for the backward link, even under drastic PFS stretching. These two facts fully ensure the validity of the adopted round-trip delay compensation scheme where ${\tau _{FP}}$ is equal to ${\tau _{BP}}$. Therefore, the PFS stretching induced polarization-related delay jitter both in the PFS itself and in the transmission fiber has been completely eliminated with this simple but effective orthogonal-polarized round-trip structure.
The proposed RC structure has evident advantages over the algorithm-based polarization control methods. It can not only fix the polarization state of the PFS output but also eliminate the difference of the polarization related delay jitter between the forward and backward transmission direction, which cannot be easily realized with the feedback polarization control. Furthermore, without any polarization control mechanism or complicated control algorithms, the proposed method is simple, cost-efficient yet with higher systematic stability. Additionally, the RC structure also doubles the delay compensation range, having the capability to cope with larger environmental variations. With the help of the proposed RC structure for eliminating the PMD related delay jitter induced by the PFS stretching, an ultra-high stability microwave signal distribution system can be finally realized.
3. Experiment and result
The experimental setup of the proposed stable microwave signal distribution system with 2 remote ends is shown in Fig. 2. It consists of a local end and two remote ends connected to the local end with 2 separate fiber links. In the local end, a stable fiber laser (NKT Koheras-BasiK-E15) operating around 1550 nm with a narrow linewidth (< 1 kHz) is firstly split into two parts by a 1:99 PM optical coupler. The 1% portion is further split into two parts, and each part becomes the reference arm of a Michelson interferometer. Here, the reference arm is buried in well-designed grooves that are filled with silica gel on an aluminum plate, thereby isolating the reference arm from potential temperature perturbations and mechanical vibrations. The arm length is also shortened to the minimum. The 99% portion is first modulated by a 24 GHz single tone signal generated from a vector network analyzer (VNA) in an MZM and then divided into two parts, injecting into two transmission links with a PFS-based delay control module by a 50:50 PM coupler. To verify the advantages of the proposed RC scheme over the traditional SC scheme, we set up two compensation structures for the delay control module. When the switch is on A, the 24 GHz signal first passes through a PM circulator and then enters the RC structure consisting of a PBS, a PFS, and an FRM. The adopted PFS has a stretching range of about 30 ps and a response bandwidth of several tens of kHz. As mentioned above, the optical signal entering and getting out of the RC structure both has a fixed polarization state. After the RC structure, the optical signal passes through a PM circulator and a PM PBS successively so that the signal reflected by an FRM at the remote end can reversely entering the RC structure with the same polarization state with the forward signal getting out of the RC structure, ensuring the reciprocity of the forward and backward transmission link. When the switch is on B, the 24 GHz signal merely passes through a PM PBS and then the SC structure. The following motorized optical delay line (MODL) induces determinate rapid link length variation for studying the PFS stretching related delay jitter in both compensation structures. 200 m SM fiber, 2 km SM fiber, and 200 m PM fibers with different PMD values are employed representing different transmission conditions.
Fig. 2. The experimental setup. Bias C: Bias control; MZM: Mach-Zehnder modulator; PBS: polarization beam splitter; PFS: piezoelectric fiber stretcher; FRM: Faraday rotator mirror; MODL: motorized optical delay line; OPLL: optical phase-locked loop; BPD: balanced photodetector; TIA: time interval analyzer; RSA: real-time spectrum analyzer; Mea. Sec.: measurement section; AOFS: acousto-optic frequency shifter; PA: power amplifier; VNA: vector network analyzer.
At the remote end, the optical signal is first frequency shifted by 40 MHz and then divided into two parts. One part is detected by a photodetector, obtaining the 24 GHz microwave signal. After amplified by a power amplifier, it is sent to the VNA for the evaluation of the relative delay jitter of the two signals at two remote ends. The other part is reflected back to the local end by an FRM. After beating with the local optical reference, the 80 MHz IF signal recording the relative delay variation of the signal arm is detected by a BPD. This IF signal then passes through a bandpass filter and enters the OPLL for phase discrimination with a 10 MHz reference signal. This 10 MHz reference signal is from an ultra-clean phase-locked oscillator which is locked to a cesium clock, leading to excellent short-term and long-term stability. The generated error signal is used to feedback control the PFS that adjusts the length of the fiber to compensate for the link delay variation, finally ensuring the stable microwave signal distribution over fiber.
The signal distribution stability is directly determined by the performance of the OPLL. To evaluate the performance of the OPLL in the proposed distribution system, the stability of the 80 MHz IF signal representing the stability of the 2 km transmission link is measured with and without phase locking both in the frequency domain and the time domain. Figure 3(a) shows the spectra of the 80 MHz IF signal measured by a real-time spectrum analyzer. The resolution bandwidth is 1 Hz, and the frequency span is 30 kHz. Compared with the unlocked link, significant noise suppression within a loop bandwidth of about 5 kHz is clearly observed when the loop is locked. The highly enhanced carrier-to-noise ratio reaches up to about 60 dB. The suppression of low-frequency noise indicates the long-term stability of the transmission link. In the time domain, the 80 MHz IF signal together with the 10 MHz reference signal is sent into a time interval analyzer (TIA) whose time resolution is 1 ps. In the TIA, the 80 MHz IF signal is first 8 divided to 10 MHz. Then the TIA records the specific time of all the zero-crossing points of this 10 MHz signal and the 10 MHz reference. By comparing the time interval of each pair of zero-crossing points, the phase variation of the 80 MHz IF signal has been obtained. Considering the frequency conversion from the optical carrier to the 80 MHz IF signal, the jitter detection precision is improved from 1 ps to 10 attoseconds (10−17 s). Figure 3(b) shows the round-trip transmission delay jitter deduced from the delay jitter of the in-loop IF signal within 1000 s. For the unlocked link, the delay variation caused by environmental disturbance is as large as 8 ps. This value is highly dependent on the range of the environmental variation. When the link is locked, however, the RMS delay jitter is merely 0.27 fs. Similar results are also observed for the 200 m PM fiber and the 200 m SM fiber link. It indicates that ultra-high precision delay jitter detection and compensation at the local end are obtained by using the well-designed OPLL.
Fig. 3. The stability evaluation of the 80 MHz IF signal at the local end under 2 km SM fiber link transmission with and without phase locking. (a) The spectra of IF signals in the frequency domain. (b) The round-trip transmission delay fluctuation deduced from the IF signal in the time domain.
Then, the PMD related delay jitter caused by the PFS stretching is carefully studied. The delay jitter of the signal at the remote end is directly measured by measuring the phase variation with a VNA. The RMS trace noise of the phase measurement is about 0.02°. Since the PFS will stretch only when the link length changes while under the locking state, we adopt an MODL to change the link length back and force repeatedly, triggering regular and constant PFS stretching. To ensure that the delay jitter is only related to the PMD effect, the PFS is driven at a rate of 0.1 mm/s (providing a single-trip link delay of about 0.5 ps/s), which is considerably faster than in the actual working state. Therefore, the instant delay variation is only caused by the PFS stretching. The interval between two times of length change is 100 s. The delay jitter of the round-trip link represented by the IF signal is measured both for the proposed RC scheme and the traditional SC scheme as shown in Fig. 4. Here, we use 200 m PM fiber to simulate the fiber link with a large PMD value. The constant delay change induced by the MODL is 24 ps and 9 ps for the RC and SC structure, respectively. Further increasing the delay change for the SC structure leads to an unstable locking state or even losing lock, while RC structure can cope with way larger link delay change, thanks to its PMD free characteristics and the doubled compensation range. The small delay fluctuation stems from the static loop locking error, which is limited by the precision of the phase discrimination. Note that this fluctuation is smaller in the RC structure, implying a smaller link delay variation and a more stable locking state. Meanwhile, large spikes in the SC structure have also been well suppressed. The delay jitters of the RC and SC structure remain 0.12 fs and 0.23 fs within 4000 s, respectively. It validates that the well-designed OPLL can still provide a high precision phase compensation with almost no error even for the large and fast PFS stretching with a large PMD value, ensuring the stability of the transmission link.
After verifying the validity of the loop locking state under larger PFS stretching conditions, the delay jitter of the transmitted signal at the remote end is carefully measured by a VNA. The fiber of different PMD values are employed, including 200 m SM fiber with small PMD, 2 km SM fiber with medium PMD, and 200 m PM fiber with large PMD, respectively as shown in Fig. 5. Several actions have been taken to ensure that the measured delay jitter is only related to the PMD effect caused by the PFS stretching. First, to fully eliminate the interference of the laser frequency drift, we adopt the relative delay jitter of RF signals at two remote ends to evaluate the PMD related jitter of one link. Since the two stable links share the same optical reference, the delay jitter related to the laser frequency drift can be fully canceled. Second, the two fiber links are placed in a soundproof box with vibration isolation to alleviate the polarization variation caused by the environmental disturbance. Third, the delay jitter caused by the group velocity change has been removed. Different from the fiber-based PFS, the free-space MODL can change the optical path without inducing evident signal polarization variation. However, due to the absence of the chromatic dispersion in the MODL and the phase locking of the optical carrier, the RF signal at the remote end experiences a determinate phase variation that is proportional to the delay variation induced by the MODL.
Fig. 5. The relative delay variation produced by fast PFS stretching with (a) 200 m SM fiber, (b) 2 km SM fiber, and (c) 200 m PM fiber.
Figure 5 shows the relative delay variation of the RF signal at the remote end through 200 m SM fiber, 2 km SM fiber, and 200 m PM fiber transmission with the SC and RC structure, respectively. Note that this relative delay variation includes both the PMD-related jitter and the determinate delay variation unintentionally caused by the MODL tuning. In 200 m SM fiber with a small PMD value, the constant link length variation induced by the MODL is set to 18 ps for both RC and SC structures. In the other two cases with larger PMD fiber, it is 24 ps and 9 ps for the RC and SC structure because the further increase of the delay change leads to an unstable locking state or even losing lock for the SC structure as mentioned above. It is clearly observed that for the RC structure, the relative delay variation keeps the same fixed value which is only determined by the fixed dispersion. As to the SC structure, however, the values of the relative delay variation have obvious random fluctuations. These fluctuations are owing to the random polarization changes caused by the PFS stretching that produces the difference between ${\tau _{FP}}$ and ${\tau _{BP}}$. Thus, the locking at the local ends cannot guarantee the stability of the signal at the remote end anymore. The increase of fluctuations is attributed to the increase of the PMD value for different fibers.
It is worth noting that the relative delay variation of the signal in Fig. 5 can not completely represent the PMD-related jitter due to the presence of the determinate delay variation unintentionally caused by the MODL tuning. To further analyze the delay jitter only related to the polarization evolution quantitatively, the constant delay variation caused by the fixed dispersion has been removed, and the remaining relative delay jitter is normalized to per picosecond delay variation of the link for fair comparison as shown in Fig. 6. Since the precise dispersion values of the 3 fiber links are unknown, we calculate them with the average delay fluctuation in the RC structure in each case, so that the mean value of the PMD related jitter in the RC structure is always zero. Thanks to the inherent PMD-free characteristics, the RMS of the PMD jitter for RC structure is always less than merely 1 fs even with 200 m PM fiber. For the traditional SC structure, however, the PMD related jitter varies with time, showing strong randomness. Abrupt jumps might occur even under some adjacent length changing. Generally, the PMD related jitter increases with the increase of the fiber PMD. However, the RMS jitters are not proportional to the PMD values of the SM and PM fiber we use, which are about $0.1\; \textrm{ps}/\sqrt {km} $ and $2.5\; \textrm{ps}/\textrm{m}$. This unpredictability is due to the unknown polarization state of the signal within the PFS and entering the following fiber link. The insets of Fig. 6(b) show the statistical distribution of the PMD related jitter for both structures during a 6.8 h measurement. For the RC structure, the Gaussian distribution of the PMD jitter is due to the delay variation from a very small portion of the link outside the control loop (pigtail of the photodetector and so on) as well as the measuring errors. For the SC structure, the jitter distribution appears to be random with a large mean value, corresponding to the random nature of the PMD effect. The comparison of all 3 different fiber links with different PMD values suggests that the RC structure can effectively eliminate the PMD related delay jitter which dramatically hinders the link stability in the SC structure.
Fig. 6. The PMD related jitter for the traditional SC and the proposed RC structures with (a) 200 m SM fiber, (b) 2 km SM fiber, and (c) 200 m PM fiber. Insets: the statistical distribution of the PMD related jitter of 2 km SM fiber.
Finally, the relative stability of the two links within 1 h is carefully measured under the RC structure. Figure 7(a) to 7(c) show the relative delay jitter of a 24 GHz signal transmitted to two remote ends via 200 m SM fiber, 2 km SM fiber, and 200 m PM fiber, respectively. After the elimination of the PMD related jitter caused by the PFS stretching, the RMS value of the relative delay jitter is as small as 13.0 fs, 22.6 fs, and 17.7 fs for the 3 cases. In contrast, the SC structure induces a 291.4 fs delay jitter for a 200 m PM fiber, which is 16 times as large as that for the RC structure. Actually, the value of relative delay jitter is random for the SC structure due to the stochastic characteristics of the PMD effect. In the experiment, we even observe huge delay variations in 200 m PM fiber when using the SC structure. It evidently proves the feasibility of the proposed RC PFS structure and also shows the high long-term stability of the demonstrated transmission link. Here, we only demonstrate a 1 hour period, however, a way longer stable period can be easily realized thanks to the stable locking state with the absence of the PMD related jitter and the doubled delay compensation range for the RC structure. The slight increase of the jitter in 2 km SM fiber is due to the larger accumulated noise along the link, especially the noise outside the loop bandwidth. Further optimization of the OPLL on the loop bandwidth, in-band gain, and the circuit noise level can further improve the system performance, which is the goal of our future work. This proposed RC PFS scheme itself can be used for very long standard SM fiber transmission with considerable accumulated PMD value, which has been indirectly verified with a 200 m PM fiber with a large PMD value. Nevertheless, the compensation range of the PFS we use is only about 30 ps. Despite doubled by using the RC structure, it still limits the transmission distance ultimately. Therefore, to realize an ultra-stable link with a longer distance, either the fiber is placed in a more stable environment or a PFS with a larger compensation range is required.
Fig. 7. The relative stability of the two links through (a) 200 m SM fiber with RC structure, (b) 2 km SM fiber with RC structure, and (c) 200 m PM fiber with RC structure (green line) and SC structure (red line).
4. Conclusion
We present an ultra-high stable microwave signal distribution system based on a round-trip Michelson interference structure and a PFS that is controlled by a well-designed OPLL. The relationship between the PFS stretching and the relative transmission delay jitter is theoretically and experimentally studied. To eliminate the delay jitter produced by the PFS stretching, an orthogonal-polarized round-trip compensation structure consisting of a PFS, a PBS, and an FRM is proposed. It can effectively fix the polarization state of the PFS output, thereby suppressing the delay jitter originate from the PFS stretching and leading to a stable signal transmission to the remote end. After eliminating the PMD related instability, the RMS relative delay jitters of the 24 GHz signal transmitted to the remote end are 13.0 fs, 22.6 fs, and 17.7 fs for the 200 m SM fiber, 2 km SM fiber, and 200 m PM fiber with different PMD values within 1 h, respectively. The proposed distribution system is highly desired in radio astronomy and distributed target detection where multiple ultra-high relative stable microwave signals are highly desired in different locations. The proposed PMD-free PFS structure can also be widely applied in systems that are sensitive to polarization variations.
Funding
National Natural Science Foundation of China (61690193, 61901039).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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