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Abstract
We demonstrated a sub-picosecond laser-based underwater frequency transfer with an optical phase compensation. With this transfer technique, a highly-stable 500 MHz radio-frequency (RF) signal was disseminated over a 5-m underwater link for 5000 s, and the characteristic of the timing fluctuation and instability for the transfer was analyzed and measured. The experimental results show the total root-mean-square (RMS) timing fluctuation of the transferred RF signal with compensation is about 162 fs with a fractional frequency instability on the order of 2.8 × 10−13 at 1 s and 2.7 × 10−16 at 1000 s. The laser-based underwater frequency transfer proposed in this paper has a potential application of transferring atomic clock in water environment as its instability is less than the currently-used commercial Cs or H-master clocks.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In the past years, transfer of optical signal in water environment [1–3] has been widely used in the field of underwater communication. This underwater optical transmission is more flexible and efficient than the traditional underwater communication methods, for example, submarine optical fiber communication [4,5], sonar underwater communication [6,7], and microwave method [8]. Although the submarine optical fiber network can provide a high-bandwidth communication, it can only be used in the case of static objects in the water. Current available acoustic scheme which launches the acoustic waves in water can reach a long distances (ranging larger than few hundred meters). However, it is still limited by the high attenuation, low bandwidth, time varying multipath propagation, and high latency. The transmission of microwave have a high-bandwidth and high propagation speed. However, the microwave signal is highly attenuated by the water, which significantly limits the distance of the underwater communication (ranging only few meters). Therefore, as the most potential technique in underwater communication, the underwater transfer of optical signal has received a substantial development.
Many experiments have shown that the high-bandwidth underwater optical communication with green diode lasers had been achieved [9–16]. With the development of the underwater optical communication, dissemination of time and frequency between the sites in the water environment is becoming more and more important, which can be widely used in the underwater metrology [17,18] such as submersible synchronization, underwater navigation, and underwater sensing. In the past years, the direct optical transfer of time and frequency signal has been realized over the atmospheric links [19–24]. However, for underwater links, the optical transfer of time and frequency signals was barely reported thus far. A prior work shows that a modulated green laser is used to transfer a 100 MHz radio-frequency (RF) signal over a underwater transmisstion link [25], where the timing fluctuation introduced by the water turbulace is been suppressed by an electronic phase compensation technique. However, in that technque, the residual timing drift between the two phase shifters and the low frequency of the transmitted mircrowave limit the resolution of the phase compenstion, which constrains the RMS timing fluctuation to picosecond-level.
In this paper, a novel transfer of RF signal over underwater link is demonstrated with an optical phase compensation technique. In our underwater frequency transfer experiment, we disseminated a 500 MHz RF signal over a 5-m underwater link. The experimental results show that the RMS timing drifts of the transferred frequency signals without and with phase compensation are 7.3 ps and 162 fs in 5000 s, respectively; and the relative fractional frequency instabilities of the transmission links without and with phase compensation reaches on the order of 2.5 × 10−12 for 1 s and 1 × 10−14 for 1000 s, and the order of 2.8 × 10−13 for 1 s and 2.7 × 10−16 for 1000 s, respectively.
2. Scheme of underwater frequency transfer with optical phase compensation
In the underwater optical transfer of a RF signal from one site to another, the most convenient method is to directly modulate the signal to a laser and then transfer the light to the remote site. In this process, the quality of the signal transmitted over the underwater transmission link could be degraded by the timing fluctuation introduced by water turbulence and temperature drift [26–31]. From the investigation of literatures, there is as such no specific mathematical model to characterize the effect of water turbulence. However, the classical Kolmogorov spectrum model of atmospheric optical transmission can be used to the case of underwater link. Because the physical mechanism of the water turbulence is similar to the atmospheric transmission link.
A study shows that the turbulence induces variation in the refractive index of water [27], which could directly lead to excess phase noise or timing fluctuation attributed to the transmitted frequency signal. Here, the power spectrum density (PSD) of the phase noise related to refractive index affected by underwater turbulence can be expressed briefly as [30,31], $\Phi _n^k(\kappa )= {K_3}{\kappa ^{ - 11/3}}$, where K3=Χε-1/3 (Χ denotes the strength of the temperature gradient and ε is defined as the kinetic energy dissipation rate) is a constant that represents the strength of water turbulence. For an underwater environment, the value of K3 ranges from 10−14 to 10−8 m-2/3. Note that κ is the scalar spatial frequency (in rad/m). Equation above shows that the excess timing fluctuation of transmitted frequency signal is inevitably introduced by the water turbulence. To improve the quality of the transmitted frequency signal, the timing fluctuations should be suppressed. In our prior study, we proposed an electronic phase compensation technique to suppress the timing fluctuation introduced by the water turbulence in a laser-based underwater RF transfer experiment. However, the level of the fluctuation suppression with the proposed technique was just limited to a few picoseconds due to the two problems. One is the residual timing drift between the two phase shifters. This is becusae the parameters of the phase shifters are not totally identical, slightly different timing delays between them exist, which has been discused in a literature [32]. The other one is just the low frequency of the transmitted mircrowave (only 100 MHz). This is because the lower frequency microwave produces lower phase-discrimination resolution. In this paper, to break the limitation, we propose a novel laser-based underwater transfer of RF signal with an optical phase compenstion technique.
Figure 1 shows the schematic of our laser-based underwater frequency transfer with optical phase compensation. On the transmitter, the optical source is a 520-nm diode laser that is modulated by a microwave signal. The laser beam goes through a half-wave plate, a polarization beam splitter (PBS), and a quarter-wave plate, and then is sent to an optical delay line (ODL), where the modulated light has an extra phase delay. After that, the beam is launched into a water tank. When the light goes through the underwater transmission link, half of the transmitted beam is reflected by a half mirror on the receiver, and the remaining beam is converted into a RF signal via a high-speed silicon photodiode (PD1). On the transmitter, the returning beam that travels the identical underwater optical path is separated from the PBS, and converted to another RF signal via another high-speed silicon photodiode (PD2) on the receiver. Note that, water turbulence introduces an identical timing fluctuation to the forward and backward beams since they have same underwater optical transmission path. With a phase detector, the detected RF signal from PD2 is phase-compared with the reference frequency source signal. An error signal is generated from the phase detector, and it includes the information of timing fluctuation affected by water turbulence. With the help of a proportional-integral (PI) servo controller, the error signal is fed-back to the ODL to change the phase delay. When the loop is closed, the timing fluctuations are corrected, thus achieves the phase compensation. Next, the mechanism of the passive phase correction will be explained in detail below.
Fig. 1. Schematic of underwater RF transfer with optical phase compensation. PBS: polarization beam splitter, PD: photodiode, HM: half-mirror, PI: proportional-integral controller.
As shown in Fig. 1, we assume that RF signal generated by the frequency source has an initial phase φ0. Consequently, the initial phase of the modulated laser beam is φ0. This beam is then phase-shifted with φc by the ODL before it is launched to water tank. In the underwater area, the phase fluctuation of the forward transmission link caused by the water turbulence is assumed as φp. Hence the recovered RF signal from PD1 on the receiver has a total phase delay of φtotal=φ0+φc+φp. The reflected beam goes through the same optical link from receiver to transmitter, and therefore, an identical timing fluctuation φp is introduced. Here, the phase delay of the returned beam which reaches the transmitter is φtotal=φ0+φc+φp. By introducing another phase delay φc via the ODL, the returned beam is detected PD2, and the converted RF signal has a final phase delay φreturned=φ0+2φc+2φp. The RF signal is phase-compared with the reference frequency source on a phase detector to eliminate the initial phase φ0 and generated an error signal which includes the information of 2(φc+φp). With the PI servo controller, the error signal is fed-back to the ODL to compensate the phase delay φp caused by the water turbulence. When the servo loop is active, the error signal equals zero as 2(φc+φp) = 0. In this case, the timing fluctuation could be corrected as φc = -φp. Thanks to this optical phase compensation, the underwater frequency transfer will achieved a significant improvement in terms of high resolution of phase compensation, compared to our previous underwater transfer scheme with electronic phase compensation technique. To estimate the performance of the underwater frequency transfer with optical phase compensation, an actual indoor laser-based frequency transfer experiment has been built.
3. Experimental setup
Figure 2 shows the experimental setup of the proposed laser-based underwater frequency transfer with optical phase compensation. We built a glass water tank (3.1-m length and 0.35 m width) for the underwater light transmission. The entire experiment setup, including the tank and the photonics components, was built in a laboratory with opened-windows. Based on the research of optical underwater communication, it is shown that green light has a lower loss than other lights in the water environment. Therefore, we used a 520-nm diode laser as the optical source whose power is about 30 mW. With an amplitude modulation (AM) technique, a highly-stable 500 MHz RF signal produced by a microwave generator (RS, SMB100A) was directly loaded to the laser. On the transmitter, the laser beam went through a half-wave plate, a polarization beam splitter (PBS), a quarter-wave plate and a two-stages ODL. The first-stage ODL was driven by a motor with a low bandwidth (about 10 Hz) and long adjustable length (about 10 mm). The second-stage ODL was driven by a piezoelectric transducer (PZT) with a high bandwidth (about 10 kHz) and short adjustable length (about 100μm). The motor-based ODL and PZT-based ODL both provided a timing delay to the laser beam. With a lens-based collimator, the beam was then launched into the water tank directly, where the beam size was about 2 mm before it was transmitted by the collimator. A silver-coated two-inch mirror (M1) was settled at 2.5-m far away remote site to reflect the beam to the receiver, which formed a 5-m underwater transmission link.
Fig. 2. Experimental setup of our atmospheric OFC-based frequency transfer with phase conjunction correction. OFC: optical frequency comb, OC: optical coupler, CM: collimator, PD: photodiode, PI: proportional-integral controller, AMP: amplifier, BPF: band-pass filter, HM: half-mirror.
At the end of the 5-m transmission link in the water tank, half of the beam was reflected to the transmitter along with the same optical link by a half-mirror (M2). On the transmitter, the reflected beam went through the ODL and quarter-wave plate again, and was separated from the PBS. This separated beam which has a power of ∼0.5mW was detected by a Si photodetector. The converted 500 MHz RF signal with twice timing fluctuations was amplified and phase-compensated with the reference signal to produce a phase error. The error signal was fed-back to the ODL via a PI controller (The fast control signal was sent to PZT-based ODL and the slow one was sent to the motor-based ODL), to compensate the timing fluctuation affected by water turbulence. Here, a switch was inserted between the PI controller and ODL, and therefore, the compensation loop can be closed or opened via it. To estimate the timing fluctuation and stability of the transmitted RF signal, the other half of beam from M2 which has a power of ∼4 mW was collected and detected by another Si photodetector on the receiver via another collimator, where the beam size was about 3 mm after it went through the collimator. By phase-comparing the converted RF signal with the frequency reference source, a DC error signal was produced. We sent it to a digital voltage meter (Keysight, 34461A) and a dynamic signal analyzer (HP, HP35665), for data recording and FFT analysis.
4. Experimental results and discussion
The underwater frequency transfer experiment with optical phase compensation was conducted in a normal day. Figure 3 shows a real photo of the experiment for underwater frequency transfer. Before we started the experiment, the cover of the tank was removed and the windows of the room were all opened. In this case, the wind flow and temperature drift will introduce a significant impact on the transferred frequency signal in the water. With the optical phase compensation technique, we believe the quality of the transferred RF signal should be improved, compared to our previous experiment with the electronic phase compensation.
In the experiment, we measured the timing fluctuations of the transferred RF signal at two time scales, one is the timing jitter PSD at short-term scale, and another is the timing drift at long-term scale. Figure 4 shows the experimental results of the timing jitter PSD. Curve (i) and (ii) are the timing jitter PSD data without and with phase compensation when the switch is off and on, respectively. Curve (iii) shows a timing jitter for a direct link when the laser beam is blocked. This is just attributed from the electronics noise, and can be considered as the background noise floor of our setup. From Curve (i) and (ii), we can see the timing jitter PSD was suppressed below 10 Hz offset frequency. This indicates the short-term timing fluctuation in 10 Hz offset frequency can be suppressed with our phase compensation. There is a hike in Curve (ii) around 100 Hz. We believe this is because the bandwidth of the PI-based closed loop is about 100 Hz, which causes a slight servo bump in the timing jitter PSD around 100 Hz. In addition, the bottoms of Curve (i) and (ii) are limited by the shot noise, which is shown as Curve (iv) in Fig. 3. Note that there are spikes for all Curves at 50 Hz and its harmonics. We estimate that this was attributed by the effect of the 50 Hz AC power supplier on our photonic systems.
Fig. 4. Timing jitter PSD results for the underwater RF transfer. Curve (i): Phase compensation is turned on. Curve (ii): Phase compensation is turned off. Curve (iii): The measurement floor attributed by the electronic noise for direct link.
Figure 5 shows the experimental results of timing drift, and each curve data had been for recorded 5000 seconds. Curve (i) shows the timing drift of the 500 MHz RF signal recovered from the photodetector on the receiver without phase compensation when the switch is off, and its RMS timing drift is approximately 7.3 ps. Curve (ii) shows the timing drift of the 500 MHz RF signal recovered from the photodetector with phase compensation when the switch is on, and its RMS timing drift is reduced to about 162 fs within 5000 s. Here, we also measured the timing drift for the direct link as the measurement floor. Curve (iii) shows the timing drift of measurement floor, and its RMS timing drift is approximately 70 fs. The comparison between the transfer without and with phase compensation demonstrates that the optical phase compensation had effectively suppressed the long-term timing fluctuation.
Fig. 5. Timing drift results for the underwater RF transfer. Curve (i): Phase compensation is turned on. Curve (ii): Phase compensation is turned off. Curve (iii): The measurement floor attributed by the electronic noise for direct link. Sample rate is 1 point/second for all curves.
To estimate the instability of the underwater RF transfer, the Allan deviations were calculated based on the timing drift data. Figure 6 shows the instability results of the transferred RF signal. Curve (i) is the relative Allan deviations of the transferred signal without phase compensation, and it shows that the uncompensated transmission link has a instability of 2.5 × 10−12 for 1 s and 1 × 10−14 for 1000 s. Curve (ii) is the relative Allan deviation of the transferred signal with phase compensation, and it shows that the compensated link has an instability of 2.8 × 10−13 for 1 s and 2.7 × 10−16 for 1000 s. From the two Curves, it indicates that the instability of the compensated underwater frequency transmission link is reduced approximately one order of magnitude at 1 s and one and half order of magnitude at 1000 s thanks to the phase compensation. Curve (iii) shows the measurement floor obtained via the direct link. Note that, curve (iii) is merely the lower bound of instability for our system. This measurement floor is just limited by the electronic noises of our setup. By comparing the instability of our underwater frequency transmission link to the commercial Cs clock (5071A) [33] and H-master clock (MHM-2010) [34], we found that the instability of our frequency transfer system is superior to those commercial clocks. Therefore, we believe the underwater frequency transfer technique proposed in this paper provides a potential tool which can disseminates a Cs or H-maser clock signal between sites in water environment without stability deterioration.
Fig. 6. Instability results for underwater frequency transfer, (i) Relative Allan deviation of the uncompensated transmission link; (ii) Relative Allan deviation of the compensated transmission link; (iii) Allan deviation for the direct link as measurement floor.
In our experiment, the distance of the underwater frequency transfer is about 5 meters, which is mainly limited by the laser power. As shown in the Section of Experimental setup, the direct loss of the power between transmitter and receiver is about 10 dB. Therefore, it is hard to achieve a longer underwater frequency transfer with current laser device. With a higher power laser diode, longer transmission (for example above 10 meters) is very promising.
5. Conclusions
We have demonstrated a sub-picosecond laser-based underwater frequency transfer with an optical phase compensation. A highly-stable 500 MHz RF signal over a 5-m underwater link had been disseminated for 5000 seconds in a transfer experiment, and the characteristic of the timing jitter, timing drift and instability for the transfer is analyzed and measured. The experimental results shows that the RMS timing drift of the transferred RF signal with phase compensation was measured to be approximately 162 fs with a fractional frequency instability on the order of 2.8 × 10−13 at 1 s and of 2.7 × 10−16 at 1000 s. In particular, the instability of the underwater transmission link achieved here is less than the currently-used Cs and H-master clocks, which indicated that the atomic clocks can be disseminated over underwater links with the transfer technique proposed in this paper. In the future, we will attempt to build an underwater RF transmission link with a lower short-time timing fluctuation and a longer distance by loading a microwave of higher frequency and using a diode laser with higher power.
Funding
National Natural Science Foundation of China (61601084, 61871084, 91836301); Applied Basic Research Program of Sichuan Province (2019YJ0200); State Key Laboratory of Advanced Optical Communication Systems and Networks.
Disclosures
The author declares no conflicts of interest.
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