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Abstract
We report on the realization of long-haul and high-precision millimeter-wave (mm-wave) transfer through a fiber-optic link based on balanced dual-heterodyne phase noise detection. The balanced dual-heterodyne detection is achieved by detecting the fiber phase noise superimposed two intermediate frequency (IF) signals without requiring a local synchronization signal and its output is used to compensate the fiber-induced phase noise by actuating the frequency of the one optical carrier. The proposed scheme can effectively get rid of the effect of the local reference, largely simplifying the configuration at the local site. Additionally, we model and experimentally study the noise contribution coming from the out-of-band, which can be effectively suppressed to the below of the system noise floor with a fractional frequency instability of 1.9 × 10−17 at 10,000 s by designing and implementing a high-precision temperature control module with a peak-to-peak temperature fluctuation of no more than 0.002 K. We experimentally demonstrate that a 100 GHz mm-wave signal to be transmitted over a 150 km fiber-optic link can achieve the fractional frequency instabilities of less than 3.4 × 10−14 at 1 s and 3.5 × 10−17 at 10,000 s.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical fiber link has been considered as an ideal medium for long-haul and high-precision frequency transfer, owing to its low attenuation, broad bandwidth, and immunity to electromagnetic interference. Thanks to the rapid development over the last decades, fiber-based millimeter-wave (mm-wave) dissemination plays a significant role for numerous scientific and technical applications involving very long baseline interferometry (VLBI) [1,2], particle accelerators [3,4] and distributed coherent aperture radar [5–7]. Unfortunately, the phase noise coming from the temperature variations and mechanical perturbations along the fiber link will severely deteriorate the mm-wave signal recovered at the remote site (RS) [8,9]. In order to attain an ultra-stable frequency signal at each RS, the phase noise detection and compensation techniques have been extensively investigated by many research groups [10–18].
The phase noise compensation schemes based on voltage-controlled oscillator (VCO) have the characteristics of fast response speed and unlimited compensation range, which have been widely applied in long-haul fiber-optic frequency distribution systems [13,19,20]. However, it is difficult to accurately detect and compensate the phase noise of the mm-wave signal due to limitations such as the restricted frequency bandwidth for phase noise detection and insufficient precision in compensating phase control in the traditional electronic approaches. Shillue et. al. proposed a fiber-optic mm-wave transfer scheme based on dual-heterodyne detection [21], which has successfully resolved the bandwidth limitation of the electronic devices. However, the mm-wave signal is generated by two optical carriers locked to each other. The performance of the optical phase-locked loop (OPLL) will significantly affect the quality of the mm-wave signal, which could be avoided by extracting two optical carriers from an electro-optic comb (EOC) [11,22]. Unfortunately, this scheme deteriorates the system’s long-term instability with additional phase noise caused by uncorrelated loose fiber links during mm-wave signal generation and control [11]. Deng et al. reported a long-haul mm-wave distribution over the fiber-optic link [12], where the impact of two carriers experiencing uncorrelated optical paths is solved by modulating the control signal onto the mm-wave signal by single side-band modulation, which improves the transfer distance and long-term performance. Nevertheless, the above-mentioned phase detection stage is strongly dependent on the local reference signal, which has to synchronize the transmitted mm-wave signal schemes [11,12]. For a typical example, as depicted in Fig. 1(a), the phase noise detection performance is extremely dependent on the local high-performance reference signal, which is not available for some high-precision mm-wave secures. For example, the frequency instability of mm-wave or terahertz signal generated based on the integrated microcomb photomixing can reach the level of $\sim 10^{-12}$/s, and its performance is continuously improving [23]. Pioneeringly, Yu et al. demonstrated a 108 GHz mm-wave signal transfer via a 10 km fiber link without any microwave reference at the local site (LS) [14]. Although this proposed scheme gets rid of the limitation of the local reference on the transfer system, the active phase noise compensation technique based on the fiber stretcher has a limited compensation range, and the maximum compensation range reported for the fiber stretcher (i.e., temperature-controlled fiber spools) is currently only 13 ns [24], which makes it challenging to realize long-haul mm-wave signal distribution. One intriguing question is how to design a high-precision and long-haul mm-wave transfer scheme that gets rid of the limitations imposed by phase-locked synchronization of the high-frequency signal with the local reference signal in a simple and efficient way.
Fig. 1. (a) Schematic diagram of the mm-wave transfer scheme based on unbalanced heterodyne detection [12]. (b) Schematic diagram of the proposed fiber-optic mm-wave transfer scheme. ANC: active phase noise compensation.
In this letter, we report on the realization of long-haul and high-precision mm-wave transfer through a fiber-optic link. As shown in Fig. 1(b), the proposed scheme utilizes a balanced dual-heterodyne detection technique to extract the phase noise induced by the fiber without the need of a local synchronized reference signal, making it an attractive technology for higher-precision mm-wave transfer via fiber-optic link. The phase noise introduced by the fiber-optic link is eliminated by acousto-optic modulator (AOM) based optical frequency shifting compensation technology, which has an infinite compensation range due to the adopt the approach of frequency tuning for phase noise compensation, making this scheme have the potential to realize long-haul mm-wave transfer. Moreover, we model and experimentally investigate the noise contribution originating from the out-of-band. To mitigate this noise, we have successfully developed and implemented a high-precision temperature control module. We experimentally demonstrated the scheme by transferring a 100 GHz mm-wave signal transfer via a 150 km fiber-optic link, achieving the fractional frequency instabilities of less than $3.4\times 10^{-14}$ and $3.5\times 10^{-17}$ at the integration times of 1 s and 10,000 s.
2. Principle
Figure 2 illustrates a schematic diagram of our proposed mm-wave transfer scheme based on balanced dual-heterodyne detection. The LS and RS are connected by a fiber-optic link consisting of single-mode fibers (SMFs). The transmitted mm-wave signal over the fiber-optic link is generated by extracting two optical carriers from an electro-optical comb (EOC) [22], which can be expressed as,
Fig. 2. (a) Schematic diagram of the proposed fiber-optic mm-wave transfer scheme. (b) Optical spectrum diagram produced by the electro-optic comb as the "1" indicated in (a). (c) Optical spectrum diagram of optically carried mm-wave signal extracted by the optical filter as the "$E_1$" indicated in (a). (d) Optical spectrum diagram of the signals to be processed at the balanced dual-heterodyne detection as the "2" indicated in (a). CWL: continuous wave laser, PM: phase modulator, PD: photodetector, WDM: wavelength division multiplexer, OC: optical coupler, OBPF: optical band-pass filter, AOM: acousto-optic modulator, FRM: Faraday mirror, EOC: electro-optical comb, FS: frequency standard, IF: intermediate frequency, VCO: voltage-controlled oscillator, BPF: band-pass filter, PS: power splitter, MIX: frequency mixer.
Most of the $E_3$ signal is reflected by a Faraday mirror and returned to the LS via the same fiber link. Subsequently, the round-trip signal is heterodynely detected against the local oscillator light to yield two IF signals ($E_5$ and $E_6$) that carry the phase noise caused by the fiber-optic link. $E_5$ and $E_6$ have expressions of,
Here, we assume that the phase noise introduced by the forward transmission signal via the same fiber link is the same as that of the backward transmission signal due to the high reciprocity of the forward and backward signal path [19]. The phase error is obtained by mixing the $E_5$ and $E_6$, resulting in,
When the active phase noise compensation module is activated, the phase error $V_e$ is canceled by tuning VCO, i.e., $V_e\rightarrow 0$. Equation (7) can be rewritten as,
By substituting Eq. (8) into Eq. (4), one can see that the stable mm-wave can be recovered at the RS, with the expression of cos($\omega _{mmw}t+\varphi _{mmw}$), which are independent of the fiber-induced phase fluctuations. Moreover, it can be seen from Eq. (8) that the dual-heterodyne phase noise detection and cancellation module can also eliminate the impact of the local IF auxiliary signal on the system by adjusting the frequency of the lower-branch AOM in real-time.
3. Experimental apparatus and results
3.1 Experimental Apparatus
The experimental apparatus of the proposed fiber-optic mm-wave transfer scheme is illustrated in Fig. 3. The optical carrier employs a narrow-linewidth optical source (NKT X15) working at a frequency near 193.4 THz with a linewidth of less than 100 Hz. At the LS, the frequency standard (Keysight Inc., N5183B) set at 25 GHz is fed into the phase modulator (EOSPACE Inc., PM-5VES-40) with an optical carrier together to generate the EOC signal. The tunable optical filter (FINISR Inc., WaveShaper 16000s) is adopted to extract the optically carried mm-wave signal with 100 GHz spacing from the EOC signal. The mm-wave signal to be transmitted consisting of two optical carriers is subsequently demultiplexed into two channels through the wavelength division multiplexer (WDM), namely C34, C35 according to the International Telecommunication Standardization. Although the AOMs adopted at the LS work at a fixed frequency with $\omega _{IF1}=\omega _{vco}=2\pi \times 80$ MHz (AOM1, AOM2, downshifted mode, −1 order), only the lower branch optical carrier plays a role of phase noise compensation in the proposed scheme. The AOM3 located at the RS working at upshifted mode with a fixed frequency shift $\omega _{IF2}=2\pi \times 45$ MHz.
Fig. 3. Experimental setup of the proposed fiber-optic mm-wave transfer scheme. CWL: continuous wave laser, PM: phase modulator, PD: photodetector, WDM: wavelength division multiplexer, OC: optical coupler, OBPF: optical band-pass filter, AOM: acousto-optic modulator, FRM: Faraday mirror, EOC: electro-optical comb, Bi-EDFA: bidirectional erbium-doped fiber amplifier, FS: frequency standard, IF: intermediate frequency, VCO: voltage-controlled oscillator, BPF: band-pass filter, PS: power splitter, MIX: frequency mixer.
The fiber-optic link consisting of 150 km SMFs (G.652) connects the LS and RS of the system. To boost the fading bidirectional optical signals, a home-made bidirectional erbium-doped fiber amplifier (Bi-EDFA) is placed into the 50 km +100 km fiber-optic link. Moreover, we select the PI controller (Newport Inc., LB1005) as the loop filter in the PLL unit. Principally, the performance of the mmW signal transfer system can be evaluated directly by comparing the two mm-wave signals at the local and remote sites with the help of large bandwidth optical-to-electrical conversion. In our case, we indirectly evaluate it by another dual heterodyne detection module as adopted in previous systems’ method [11]. In our configuration, the two IF signal with the angular frequency of 35 MHz recovered by additional PDs by heterodynely beating the compensated optical signals ($\omega _1$ and $\omega _2$) from the RS with the original optical signals ($\omega _1$ and $\omega _2$) from the LS, respectively, are used for the outloop verification. We measured a lower limit for the residual phase noise and ADEV of our transmission scheme by comparing the phase of these two IF signals with a phase noise measurement instrument (Symmetricom Inc., TSC-5120A) after passing them through a dual-mixer time difference module. Although this method of phase comparison did not measure the phase noise added during the optical to mm-wave conversion in the photodetector, we expect this noise to be negligible. Moreover, we design and implement a high-precision temperature control module, in order to experimentally study the noise contribution coming from the out-of-band. As shown in Fig. 3, optical couplers, Faraday mirrors, WDMs, AOMs, and a few short fiber-optic patch cords within the blue dotted line are housed in the active temperature control system.
3.2 Interferometer noise characteristics
The essence of balanced dual-heterodyne detection is a Michelson interferometer, which is commonly used in optical frequency and optical frequency comb transfer systems. Since the extra delay jitter introduced by the uncorrelated optical path of the two optical carriers on the interferometer cannot be eliminated by the compensation module, this part of the noise will have a more significant impact on the system as the transfer frequency increases [25]. Thus, the noise contribution coming from the out-of-band is an important factor limiting the performance of the fiber-optic mm-wave transfer system. The main work in this section is to analyze the impact of phase noise introduced by the interferometer on the mm-wave transfer system, and then design an experimental device to suppress this type of noise. Based on the optical frequency transfer theory [25,26], the residual out-of-loop propagation delay fluctuations $\delta \tau$ caused by interferometer noise in mm-wave transfer system can be expressed as,
From the Eq. (10), the phase noise originating from the interferometer is mainly related to the temperature fluctuations and the fiber mismatch length. Due to the fact that the out-of-band fiber mismatch length is fixed by highly integrated commercial optical components, the next step is to analyze the effect of temperature fluctuation on this type of noise. To facilitate the follow-up theoretical analysis, the ambient temperatures in Eq. (9)–(10) are deliberately set to an approximate sinusoidal fluctuation trend of the temperature. To verify the effectiveness of the noise model, as depicted in Fig. 4(a) and (b), the active temperature control system is approximately set in the working states of $\Delta T=0.8$ K, $T_c$=1000 s and $\Delta T=1.4$ K, $T_c=1500$ s. The purpose is to simulate the effect of interferometer noise on the system under different environments by changing the temperature control system. It can be clearly observed from Fig. 4(a) and (b) that the temperature fluctuation period and peak-to-peak value of the frequency deviation in the case of the 150 km stabilized link are almost consistent with the fluctuation law of the active temperature control system, demonstrating that the out-of-loop optical components directly affects system’s performance. The temperature data points recorded in the temperature control system are fitted as sine functions through the multiple regression fit. Substituting the fitted data with sinusoidal time-varying temperature into Eq. (10), we found that the long-term instability traces of the simulated results overlap with the experimental results as shown in Fig. 4(c), which confirms the effectiveness of our model.
Fig. 4. (a) and (b) are the temperature fluctuations and the 150 km stabilized link’s frequency deviations for the temperature fluctuation period of 1000 s (a) and 1500 s (b). (c) The measured and simulated fractional frequency instabilities caused by interferometer noise under different temperature conditions.
We further analyze the impact of the temperature fluctuations and the fiber mismatch length by simulation. When processing simulated results, each bump on the ADEV trace is considered as an envelope and fitted to the decline curve of $\sim \tau ^{-k}$ to intuitively characterize the influence of interferometer noise in the large-scale integration time. We set the period of temperature fluctuation to 3000 s, which is similar to the temperature fluctuation law in our laboratory, and analyze these two parts of the noise source on the system. It can be seen from Fig. 5 that both the fiber mismatch length and the peak-to-peak value of the temperature fluctuation are significant factors for the deterioration to the long-term instability of the system. Reasonably matching fiber length and making an accurate temperature control system can effectively suppress the influence of the interferometer noise, thereby improving the long-term performance of the mm-wave transfer system. Since the fiber mismatch length in the system cannot be changed, in the follow-up mm-wave transfer experiment, we stabilized the ambient temperature of the interferometer at 296 K, and the peak-to-peak temperature fluctuation does not exceed 0.002 K. Based on the simulation analysis, it can be known that the effect of the interferometer structure on the long-term performance of the mm-wave transfer system in this configuration is less than $3.2\times 10^{-18}$/10,000 s.
Fig. 5. The simulated results of fractional frequency instabilities at 10,000 s corresponding to the different fiber mismatch length $L_m$ and peak-to-peak value of temperature fluctuation $\Delta T$.
3.3 Long-haul millimeter wave transfer
The measured residual phase noise power spectral densities (PSDs) of the proposed scheme under different configurations are shown in Fig. 6(a). The back-to-back transfer configuration is measured by replacing 150 km SMFs with a short fiber patch, which is the phase noise floor of our experimental system. To better compare the performance of the compensated system, the 150 km free running link is also measured by transferring a 100 GHz mm-wave signal to the RS without the phase noise correction. All system configurations are measured under the condition that the low-noise active temperature control system operates at 296 K. We find that the phase noise PSD of our free running link is obviously higher than the 150 km stabilized link (about −35dBc at 0.1Hz, −43dBc at 1Hz) at the range of offset frequency less than 10 Hz, owing to the fiber-optic link propagation delay fluctuations coming from temperature variations. In the range of 0.02 Hz – 3 Hz, the phase noise PSD of the 150 km stabilized link is almost consistent with the back-to-back system noise floor (about −38dBc at 0.1Hz, −43dBc at 1Hz), indicating that the phase noise caused by the fiber link is efficiently suppressed by our active compensation technique. In the range of offset frequency greater than 3 Hz, there is a large deviation in the phase noise of the system noise floor and 150 km stabilized link, which is mainly affected by the different PID parameters of the compensated system, delayed self-interferometry, non-reciprocal noise, etc [27,28].
Fig. 6. Residual phase noise PSDs (a) and Allan deviation (b) measured for different system configurations: 150 km stabilized link (red curve), 150 km free running link (green curve) and the back-to-back system noise floor (black curve).
Complementary to the frequency-domain feature, we used fractional frequency instability in our experiments to describe the performance of the transfer system in the time-domain. As shown in Fig. 6(b), we measured the fractional frequency instabilities, commonly referred to the ADEV for different system configurations. On can observe that the 150 km stabilized system has obtained transfer frequency instability less than $3.4\times 10^{-14}$ at 1 s, $3.5\times 10^{-17}$ at 10,000 s. The long-term instability of $1.1\times 10^{-13}$ at the integration time of 10,000 s is achieved for the 150 km free running link, which is nearly deteriorated four orders of magnitude in comparison with 150 km stabilized link. The fractional frequency instability of 150 km stabilized is slightly higher than the back-to-back system noise floor ($2.9\times 10^{-14}$ at 1 s, $1.9\times 10^{-17}$ at 10,000 s) due to the degradation of the system’s signal-to-noise ratio (SNR), the reduction of the delay-limited bandwidth and the non-reciprocal noise of the fiber link [29].
We have conducted a series of experiments by changing the distance of the transmission link. It can be seen from Fig. 7 that the fractional frequency instabilities of the system at 1 s and 100 s under the different transmission distances are close to the system noise floor, indicating that the system noise floor limits the system’s short-term instability under long-haul transfer. Thus, in the follow-up research work, the high-precision mm-wave transfer should focus on solving the problem that the short-term instability of the transfer system is limited by the back-to-back system noise floor. As a supplement to the characteristics of fractional frequency instability and phase noise, we also performed an evaluation of the frequency accuracy in the case of the 150 km stabilized link, which cannot be captured in the instability evaluation. The data points of frequency deviation are recorded with a 1 s gate time. The inset of Fig. 7 shows that the mean frequency is shifted by 16.9 ${\mathrm{\mu} {\rm{Hz}}}$ ($1.7\times 10^{-16}$) and the standard deviation is 5.5 mHz ($5.5\times 10^{-14}$).
Fig. 7. The fractional frequency instabilities measured at different transmission links. The inset shows the frequency deviation of the 150 km stabilized link.
4. Conclusions
In conclusion, we present a long-haul and high-precision mm-wave transfer scheme. The proposed scheme utilizes a balanced dual-heterodyne detection technique to extract the phase noise induced by the fiber without requiring a local synchronization signal, making it an attractive technology for higher-precision mm-wave transfer via fiber-optic link. The phase noise introduced by the fiber-optic link is eliminated by AOM-based optical frequency shifting compensation technology with unlimited compensation range, making this scheme has the potential to realize long-haul mm-wave transmission. Furthermore, we model and experimentally study the noise contribution originating out-of-band, which can be effectively suppressed to the below of the system noise floor with a instability of $1.9\times 10^{-17}$ at 10,000 s by designing and implementing a high-precision temperature control module with a peak-to-peak temperature fluctuation of no more than 0.002 K. We experimentally demonstrated the scheme by transferring a 100 GHz mm-wave signal transfer via a 150 km fiber-optic link, achieving the fractional frequency instabilities of less than $3.4\times 10^{-14}$ and $3.5\times 10^{-17}$ at the averaging times of 1 s and 10,000 s.
Funding
Natural Science Foundation of Shanghai (22ZR1430200); National Natural Science Foundation of China (62120106010); Zhejiang provincial Key Research and Development Program of China (2022C01156).
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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