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Abstract
We demonstrate a long-distance multi-frequency microwave distribution system over an optical fiber link with high phase stability based on transferring an optical frequency comb (OFC). The phase fluctuation induced by the transmission link variations is detected by applying a reference OFC and is then compensated with the proposed optical voltage-controlled oscillator (OVCO) by adjusting the phase of the repetition rate of the transmitted OFC. By applying the OVCO, we perform the OFC-based multi-frequency microwave distribution over a 100 km standard single-mode fiber. The performance of the transmission system can be exhibited by evaluating the repetition rate (10.015 GHz) and second harmonic frequency (20.03 GHz) signals achieved at the remote end. The residual phase noise of the 10.015 GHz and 20.03 GHz signal is −64 dBc/Hz and −58 dBc/Hz at 1 Hz frequency offset from the carrier, respectively. The fractional frequency instability is 1.4×10−16 and 2.4×10−16 at 10000 s averaging time, respectively. And the timing jitter in the frequency range from 0.01 Hz to 1 MHz reaches 88 fs and 87 fs, respectively. Based on the phase-locked loop theory, we conduct a simulation model of the transmission system and the simulated results match well with experiments. It shows that by detecting the phase fluctuation with higher harmonic frequency signals in the simulation system, the performance of the transmission system can be further improved.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
High-precision transfer of ultra-stable phase-locked multi-frequency microwaves are essential for many scientific and technical applications such as multi-band radars [1,2], distributed coherent aperture radar (DCAR) [3–5], channelized ultra-wide band receiver [6,7] and very long baseline interferometry (VLBI) [8,9]. For example, multi-band radars take advantage of multiple radar signals at different carrier frequencies simultaneously to enhance the performance in terms of sensitivity and resolution. The multi-frequency microwaves are desirable for each transmitter end of the multi-band radar systems to produce wideband waveform signals ranging up to the millimeter waveband, which significantly broaden the operation range of the radar systems. For the receiver ends, the multi-frequency microwaves are essential for converting the desired signals in certain frequency bands to a common intermediate frequency (IF) band, which reduces the bandwidth of the signal to be processed and enables the capability to receive multiple signals simultaneously. Furthermore, highly stable distribution of the multi-frequency microwaves is crucial for radar antennas at different sites to maintain the radar system coherency, which matches the urgent requirements of the fully coherent multiband radar e.g. in signals combining [1,2].
Due to the fiber link’s advantages of low attenuation, high reliability, and immunity to electromagnetic interference, there has been remarkable progress in the precise transfer and synchronization [10–12] of highly stable microwaves over optical fiber links in the last decades [13–15]. The transfer of microwave signals by optical frequency combs (OFCs), where the microwaves are encoded in the repetition rate, shows a superiority of providing the phase-locked fundamental repetition frequency and its harmonic frequencies simultaneously with low noise. Many researches about comb-based frequency distribution over fiber links have been conducted [16–18]. The transmission delay varies due to the mechanical perturbations and temperature variations along the optical fiber links, which would induce phase fluctuations of the received signals at remote ends [11,19]. Among numerous comb-based microwave signal distribution systems, it is important to detect and compensate for the excess phase fluctuations. The roundtrip delay correction mechanism is usually applied in the phase noise compensation system [20]. The fiber stretcher and the thermally controlled fiber spool have been widely investigated to compensate for the delay fluctuations [17–19]. Although their frequency-independent compensation enables the transfer of the OFC directly, the small compensation range will limit system’s transmission distance and long-term stability. Voltage-controlled oscillator (VCO) with infinite compensation range and fast frequency response has been widely used in long distance dissemination of microwave signals. As far as we know, some research on VCO-based dissemination systems mainly focus on the transmission of single frequency signals [21–23]. Recently, we have demonstrated a dissemination of the phase stabilized 100.02 GHz millimeter-wave (mm-wave) signal over optical fiber employing a photonic-generated mm-wave VCO where the phase noise is compensated based on pre-filtering and re-modulating the optical spectral lines of an OFC [24]. However, this scheme cannot support the dissemination of the multi-frequency microwaves simultaneously owing to the fact that the phase noises of the harmonic frequencies are different from each other. It is difficult to detect and compensate the phase fluctuations of the multi-frequency signals directly using conventional approaches with the photonic-generated VCO proposed in [24].
In this paper, we propose a highly stable phase-locked multi-frequency microwaves distribution system applying an optical voltage-controlled oscillator (OVCO) based on transferring an OFC. Comparing to our previous work in [24], a scheme using a reference OFC is employed, which permits the phase variations of the multi-frequency microwaves to be detected by the dual-heterodyne phase error transfer module. By pre-modulating the optical spectral lines with the OVCO, the phase of the repetition frequency of the transmitted OFC can be adjusted precisely. Thus, the phase noise of the harmonic frequencies induced by the fiber link variations can be compensated with the phase-locked loop (PLL). The highly stable phased-locked multi-frequency microwaves can be extracted simultaneously from the received OFC after optical-microwave conversion by employing a photo-detector (PD) at the remote end. We experimentally demonstrate the proposed multi-frequency microwaves distribution system over 100 km standard single mode fiber (SSMF) by transmitting an OFC with 10.015 GHz repetition frequency. A simulation indicates that more precise detection of the transmission time variations can be achieved by detecting the higher harmonic frequency signals.
2. Experimental setup for the multi-frequency microwaves distribution system based on an OVCO
Figure 1 illustrates the experimental setup of the OFC-based multi-frequency microwaves distribution system employing the proposed OVCO which compensates the fiber link induced phase noise by adjusting the repetition frequency () of the transmitted OFC. The transmission system can be divided into the local end, the remote end and the measurement module.
Fig. 1. Schematic of the experimental setup of the OFC-based multi-frequency microwaves dissemination system. T-OFC, transmitted optical frequency comb; R-OFC, reference optical frequency comb; OVCO, optical voltage-controlled oscillator; PM, phase modulator; IM, intensity modulator; TDM, tunable electrical delay module; DHPT, dual-heterodyne phase-error transfer; PMC, polarization-maintaining coupler; AOFS, acousto-optic frequency shifter; SSMF, standard single-mode fiber; C, circulator; SSBM, single sideband modulator; PFD, digital phase and frequency detector; LF, loop filter; VCO, voltage-controlled oscillator; PLL, phase-locked loop; EDFA, erbium-doped optical fiber amplifier; PD, photo detector; M, mixer; PT, polarization tracker.
The local end is composed of the proposed OVCO, the phase fluctuation detection module and the feed-back control module. The OVCO is applied to generate the pre-compensated multi-frequency microwave signals simultaneously. The scheme of the OVCO is described as follows. It includes an IF electrical VCO, a radio frequency (RF) microwave synthesizer, a single sideband modulator (SSBM), a transmitted OFC (T-OFC) and a laser. The VCO operating in megahertz range is tuned precisely according to the drive signal generating the phase correction. The SSBM is used to identically transfer the phase correction to RF drive signal of the T-OFC. Then the T-OFC is pre-modulated by adjusting the phase of the repetition rate with the RF drive signal, compensating the phase fluctuation induced by the one-trip fiber link. The laser with narrow linewidth is employed as the seed light source. Thus, the proposed OVCO permits low-frequency components in MHz region to precisely adjust the phase of the multi-frequency signals by pre-modulating the optical spectral lines of the T-OFC with GHz repetition rate. The pre-compensated multi-frequency microwave signals can be achieved.
In the multi-frequency transmission system, the local end and the remote end are connected by 100 km spooled SSMF. At both ends of the transmission link, the two optical circulators (C1, C2) are used to separate the forward and backward travelling OFCs. At the local end, the laser operating at 1550 nm is split into two branches and they are fed into two OFCs which are both produced by cascaded phase and intensity modulators. The 10 GHz microwave synthesizer (Keysight model E8267D), which is synchronized to a 10 MHz rubidium (Rb) oscillator, is divided into two branches. One branch is single-sideband modulated by the VCO (15 MHz) with the SSBM in the proposed OVCO generating the drive signal of the T-OFC which can be expressed as
At the remote end, an erbium-doped fiber amplifier (EDFA) is used to compensate for the power loss caused by the transmission link. To alleviate the polarization varying effect, two polarization trackers (General Photonics POS-002) are used at the remote and local ends before the detection. Then the T-OFC received at the remote end is frequency up-shifted 40 MHz by an acousto-optic frequency shifter (AOFS) to avoid the Rayleigh backscattering and distinguish the round-trip signal from the back-scattered signals. Afterwards, it is split into three parts by the PMCs. One part is used to obtain the multi-frequency microwave signals after optical-microwave conversion by the PD for the remote user. Another one is used to analyze the residual phase noise of the received multi-frequency microwave signals. The third one is sent back to the local end through the same transmission link to detect the fiber link variations. Since the received OFC suffers time-varying transmission delays ${\tau _{trans}}(t )$ passing through the same fiber link, the multi-frequency microwave signals achieved at the remote end can be described as
In order to achieve the phase stable multi-frequency microwaves at the remote end, the phase of the OVCO at the local end is controlled by the feed-back control module to pre-compensate the phase fluctuation induced by the fiber link. The compensation is realized as follows: Since the non-reciprocity of the transmission delays between the forward and backward directions can be ignored, the returned OFC experiences approximately the same fiber-induced phase noise as the forward one. Thus, $\textrm{2}\varphi_{v}(t )$ is needed to compensate the round-trip phase fluctuation corresponding to the remote achieved signals shown in Eq. (3). In the phase detection module at the local end, the round-trip OFC and the local R-OFC are beaten in a low-speed PD in the DHPT1. The scheme of the DHPT is described as followed. The phase fluctuation of the photonic-generated microwave signals, which is determined by the phase difference of the optical carriers, is transferred to an IF signal through the dual heterodyning and mixing operation. Thus, the phase variation of the microwave signal can be represented by the IF signal [24]. In the DHPT1, the generated 55 MHz and 70 MHz beating signals are filtered out by the electrical band-pass filters. And then a 40 MHz signal is generated by mixing the 55 MHz signal with the 15 MHz VCO signal. Subsequently, it is mixed with the 70 MHz signal to obtain the 30 MHz signal which can be expressed as
The ${I_{30MHz}}(t )$ after threefold divided are discriminated with the 10 MHz Rb oscillator by a digital phase and frequency detector (PFD) extracting the phase error signal which can be expressed as
where $\varphi_{Rb}$ is the phase of the Rb oscillator and is considered as a constant. Then the phase error signal is integrated in the loop filter and fed back to control the phase of the proposed OVCO. When the PLL is locked, the steady state error is zero, i.e., $E_{error}(t )\to \textrm{0}\textrm{.}$ Consequently, the received multi-frequency microwave signals can be expressed as3. Experimental results and analysis
Owing to the phase coherence of the OFC, the phase stability of the multi-frequency microwaves distribution system can be investigated with the arbitrary harmonic frequency signals received at the remote end [25]. Thus, the measurement is performed by testing the long-term residual phase noise of the received repetition rate (10.015 GHz) and the second harmonic frequency (20.03 GHz) signals of the remote OFC. As shown in the measurement module of Fig. 1, the received T-OFC is optical heterodyne with the R-OFC in the DHPT2 scheme achieving 15 MHz and 30 MHz beating signals by applying the appropriate electrical band-pass filters. According to the DHPT scheme, the residual phase noise and fractional frequency instability of the received 10.015 GHz and 20.03 GHz signals can be evaluated by measuring the achieved 15 MHz and 30 MHz beating signal with a phase noise analyzer (Symmetricom’s 5125A), respectively [23].
Figure 2 shows the measured single sideband (SSB) residual phase noise of the 10.015 GHz (a) and 20.03 GHz (b) signal after 100 km transmission link in conditions of free-running (without active phase compensation, VCO directly locked to the Rb oscillator), the phase locking, and the phase locked 1 m optical fiber transmission link. Moreover, to guarantee that the measurements are taken under the same conditions, the same loop bandwidth optimized approximately 230 Hz is used. The optical spectrum of the OFC received at the remote end is shown in the inset of Fig. 2(a). It can be observed that in the phase locked transmission system, the residual phase noise of the 10.015 GHz signal reaches −45 dBc/Hz and −64 dBc/Hz at 0.01 Hz and 1 Hz frequency offset from the carrier. And the residual phase noise of the 20.03 GHz signal is −35 dBc/Hz and −58 dBc/Hz at 0.01 Hz and 1 Hz frequency offset, respectively. The phase noise of the 20.03 GHz is increased by approximately 6 dB compared with the 10.015 GHz and the shapes of the phase noises are close to each other. The inherent coherence of different frequencies is preserved well [26]. When the noise cancellation is activated, the transmission link induced phase fluctuation is effectively suppressed within the loop bandwidth. The noise floor is measured with the transmission link replaced by the 1 m short fiber and an optical attenuator. Comparing the phase noise of the free-running and phase locked 100 km transmission system with repetition frequency and second harmonic signal, it can be seen the suppression of both the phase noise at 0.01 Hz offset frequencies are by up to 40 dB. The RMS timing jitter of the 10.015 GHz and 20.03 GHz signal in the phase locked 100 km transmission system is about 88 fs and 87 fs, respectively, which is calculated by integrating the phase noise over the frequency range from 0.01 Hz to 1 MHz. The RMS timing jitter of different harmonic frequency signals show approximately the same order of magnitude indicating the performance of the distribution system.
Fig. 2. Single sideband phase noise of the received 10.015 GHz signal (a) and 20.03 GHz signal (b) at the remote end in conditions of phase-locked 100 km fiber link, free running and phase locked 1 m short fiber (500 Hz measurement frequency bandwidth). The inset in the Fig. 2(a) shows the optical spectrum of the OFC received at the remote end.
The fractional frequency instability of the repetition frequency and second harmonic signal is shown in Fig. 3. The frequency instability of the 10.015 GHz and 20.03 GHz signal in the 100 km phase-locked transmission system achieves 1.4×10−16 and 2.4×10−16 at 10000 s averaging time, respectively. The approximately same magnitude of the achieved 10.015 GHz and 20.03 GHz signals indicates the high coherence between the signals [15]. The phase locked 100 km transmission system reduces the frequency instability by nearly three orders of magnitude compared with the free-running transmission system. The small difference of the frequency instability in the phase locked short fiber configuration and 100 km configuration is mainly caused by the delay self-heterodyne interferometric noise [22].
Fig. 3. Fractional frequency instability of received 10.015 GHz signal and 20.03 GHz signal at the remote end in conditions of phase-locked 100 km fiber link, free running and phase locked 1 m short fiber.
Figure 4 shows the timing drift of the 10.015 GHz and 20.03 GHz signal in the 100 km phase-locked, free-running transmission system and 1 m short fiber phase-locked transmission system. The transmission delay fluctuations of the 10.015 GHz and 20.03 GHz signal spans over about 1.2 ns and 4.2 ns in conditions of 100 km free-running transmission link. The difference of the delay fluctuations is mainly attributed to the variation of the environmental conditions. The magnified plots of the timing drift in the phase locked 100 km transmission system show that the timing drift of the 10.015 GHz and 20.03 GHz signal is confined well at the same magnitude below 0.58 ps and 0.75 ps, respectively. It can be observed that the proposed system effectively suppresses the phase noise introduced by the transmission delay fluctuations within the loop bandwidth, which exhibits the accurate phase-error-correction capability. The stability of the repetition frequency and second harmonic signal indicates that the system is capable of disseminating highly phase-stable multi-frequency signals based on transferring an OFC over long distance optical fiber. In fact, the proposed distribution system could be performed with the mode-locked laser (MLL) as the OFC potentially through adjusting the pump and cavity length with the error signal by employing a PLL.
Fig. 4. Timing drift of the received 10.015 GHz (a) and 20.03 GHz (b) signal at the remote end in 100 km phase-locked, free-running transmission system and 1 m short fiber phase-locked transmission system. The insets show the magnified plots of timing drift in the phase-locked transmission system.
To evaluate the performance of the distribution system, a simulation model based on the PLL theory is conducted and the transfer functions of the whole system are obtained. According to this model, the residual phase noise and fractional frequency instability of the 10.015 GHz, 20.03 GHz, 30.045 GHz, 40.06 GHz, 50.075 GHz and 100.15 GHz signals received at the remote end in the simulated phase-locked transmission system are evaluated. The results are shown in Fig. 5 by the solid lines. While the measured residual phase noise and fractional frequency instability of the received signals in the phase locked system are shown by dot dash lines, respectively. It can be observed that the measured results are close to the simulated results while the suppression is active. It is shown in Fig. 5(a) that the residual phase noise is increased by 6 dB when the frequency of the tested signal is doubled owing to the frequency multiplication [26]. And the Allan deviation which is normalized according to the frequency is shown the same magnitude with different frequencies. These results match well with the experimental results measured in the transmission system of 10.015 GHz and 20.03 GHz signals. The stability of the frequencies other than 10.015 GHz and 20.03 GHz can be predicted in the simulation system.
Fig. 5. Single sideband residual phase noise (a) and fractional frequency instability (b) of the received signals in 100 km phase-locked simulated (solid line: -s) and measured (dot dash line: -m) systems.
The performance of the transmission system can be improved by properly adjusting the experimental setup to change the repetition frequency of the T-OFC and R-OFC to 10.011 GHz and 10.01 GHz respectively. Actually, by detecting the phase fluctuation with the 10th harmonic frequency (100 GHz) signal, the signal-to-noise ratio of the time delay fluctuation detection can be improved. And the frequency division ratio of the PLL can be reduced to 2. Thus, the noise floor of the experimental setup can be reduced [27]. To investigate the potential of the adjusted transmission system, the corresponding simulation is carried out. The results are shown in Fig. 6 compared with the simulation results of 10 GHz detection frequency. The residual phase noise of the received 100 GHz signal in the 100 km phase-locked simulation system with 100 GHz detection frequency is reduced by 20 dB within the loop bandwidth compared with the simulation system with the repetition frequency (10 GHz) detection signal. And the fractional frequency instability of the received signal in the simulation system with 100 GHz detection frequency is reduced by more than an order of magnitude to 0.75×10−17 at 10000 s averaging time compared with the 10 GHz detection frequency. These results show that higher detection frequency enables more precise time delay variation detection of the transmission link, which significantly improve the performance of the transmission system. Although the use of extra electric components introducing more electrical noise into the modified distribution system, the influence could be limited by employing devices with low phase noise.
Fig. 6. Single sideband residual phase noise (a) and fractional frequency instability (b) of the received 100 GHz signal in 100 km phase-locked simulated systems with 10 GHz (blue line: -10) and 100 GHz (black line: -100) detection frequency.
4. Conclusion
In summary, a highly stable phase-locked multi-frequency microwaves distribution system based on the propagation of an OFC is presented. By applying a scheme with the reference OFC, the fiber link induced phase fluctuation is detected by the DHPT module. The phase noise of the transmitted multi-frequency microwave signals is compensated with the proposed OVCO. By pre-modulating the optical spectral lines of the OFC with the OVCO, the repetition rate of transmitted OFC can be adjusted precisely by applying the PLL. Thus, the highly stable multi-frequency microwaves can be achieved at the remote site. We demonstrate the multi-frequency microwaves dissemination over 100 km SSMF and the 10.015 GHz repetition frequency and 20.03 GHz second harmonic frequency signals are evaluated at the remote end. The residual phase noise of the 10.015 GHz and 20.03 GHz signal in the phase-locked 100 km fiber transmission system is measured to be −64 dBc/Hz and −58 dBc/Hz at 1 Hz frequency offset from the carrier, respectively. The fractional frequency instability is 1.4×10−16 and 2.4×10−16 at 10000 s averaging time, respectively. To further estimate the performance of the received signals with higher frequencies, a simulation model of the transmission system based on PLL theory is built. The phase noise and fractional frequency instability of the received signals are extrapolated to 100.05 GHz based on the model. The simulated results match well with the measured results. By detecting the phase fluctuation with higher harmonic frequency signals, the performance of the transmission system can be improved owing to the fact that higher detection frequency enables more precise time delay variation detection of the transmission link. The simulation is conducted with 10th harmonic frequency signal (100 GHz) and the fractional frequency instability of the received signal in the 100 km phase-locked simulation system is reduced to 0.75×10−17 at 10000 s averaging time. These results make it possible to enable the simultaneous dissemination of highly stable phase-locked microwave signals with affluent frequency components based on transmitting an OFC over long distance fiber link. Actually, the MLL could be used as the OFC potentially by adjusting the pump and cavity length with a PLL.
Funding
National Natural Science Foundation of China (61690193, 61827807, 61901039).
Disclosures
The authors declare no conflicts of interest.
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