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Abstract
We propose a novel scheme that uses only a single passive phase compensation device to achieve stable optical and radio frequency joint transfer. The phase noises of optical and radio frequency can be simultaneously compensated by passively embedding their phase information on the two optical carrier sidebands generated by an electro-optical modulator without using the phase discrimination and active servo controller. As a result, this scheme has many advantages, such as high spectral purity, short settling time and infinite compensation accuracy. We experimentally demonstrate the joint transfer of optical and 1 GHz RF over 120 km fiber spools. The optical frequency stability achieves 6.9 × 10−17 at 1 s and 7.03 × 10−19 at 10000 s, while the 1 GHz RF is 6.47 × 10−13 at 1 s and 3.96 × 10−16 at 10000 s.
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1. Introduction
The state-of-the-art optical clock and RF clocks have facilitated many science and technology fields such as geodesy [1], radio astronomy [2], optical clock comparison [3], general relativity effect verification [4], and precise testing of fundamental physical constants [5]. To drastically utilize these ultra-stable references, hundreds of clocks all over the world are linked. They are either used to compare with each other to access their weight factors, which is the origin of International Atomic Time, or for dark matter research [6], earthquakes detection using submarine fibers [7], etc. As a result, many methods have been investigated for the dissemination of either optical frequency or radio frequency (RF) to remote users over optical fiber networks [8–17]. In order to make full use of the fiber network and meet the needs of increasing variety of applications, the optical and RF joint transmission system has been developed, which can be broadly divided into three categories. The first category is dual optical frequencies transfer [18,19]. This scheme is achieved by stabilizing two optical frequencies separately, and the frequency interval of two optical frequencies is the RF signal that needs to be transmitted. The second category is the hybrid frequency transfer solution [20,21]. It combines optical and radio frequency transfer techniques through wavelength division multiplexing (WDM) and uses separate phase noise compensation systems for the different frequencies being transmitted. The third category is optical frequency comb transfer [22,23]. The entire structure of the optical frequency comb is precisely transmitted to the remote site, then it is equivalent to realizing the simultaneous transmission of multiple RF and optical frequency signals.
The hybrid frequency transfer is the most commonly used optical and radio frequency joint transfer technique. However, it occupies many fiber channels and increases the asymmetry of the system and the complexity of the central site. For dual optical frequencies transfer, although the method occupies only one fiber channel, uncommon-mode phase noise is generated at the stable RF because two optical frequencies pass through different optical paths of the local site [18] and the two independent phase noise compensation devices are used [18,19]. The National Physical Laboratory (NPL) has demonstrated transmitting the full structures of an optical frequency comb [24]. However, the problem of how to accurately maintain the optical comb structure over long fiber lengths has not been properly addressed so far, limited by issues such as dispersion, amplification of the transmitted pulses and so on. Moreover, all three methods require multiple active phase stabilization devices to compensate the phase noises introduced by optical fiber. The active approach needs complex circuits to extract the phase error and drive the devices for phase correction in real-time, so the frequency transfer systems are affected by compensation bandwidth, speed, accuracy and others [25,26].
Different from active approach, the passive frequency transfer technology requires neither phase discrimination devices nor active servo controller. It can achieve high spectral purity, short settling time and infinite compensation accuracy [25,26]. There are some passive frequency transfer schemes for optical frequency [25,26] or RF [27,28] that have been proposed. However, to the best of our knowledge, the feasibility and adaptability of the optical frequency and RF simultaneous transmission system based on passive phase compensation technique have not been theoretically and experimentally reported. This novel optical and RF joint transfer scheme potentially provides better performance without the above-mentioned problems caused by active phase compensation technique.
In this paper, we propose a novel stable optical and RF joint transfer method based on passive phase compensation. The phase noises of optical and radio frequency can be simultaneously compensated by passively embedding their phase information on the two optical carrier sidebands generated by the electro-optical modulator (EOM) without the phase discrimination and active servo controller. In addition, a special passive phase stabilization frame is designed to distinguish the forward and backward optical frequencies and RFs, so that the phase noises of optical and RF can be compensated by using a single optical phase stabilization device, which highly simplifies the complexity and improves the stability of the system. The experimental results show that the proposed scheme reaches in the order of 10−19 for optical frequency and 10−16 for RF via 120 km fiber spools in a laboratory.
2. Principle of implementation
Figure 1 shows a schematic diagram of stable optical and radio frequency joint transfer based on passive phase compensation. This scheme uses the EOM as a passive feedback actuator, and the local and remote acousto-optic modulators (AOMs) as a fixed set of frequency shifts to distinguish the reflected light by Faraday Mirror (FM) from stray light on the fiber link [8]. The detailed working principle is as follows.
Fig. 1. Schematic diagram of stable optical and radio frequency joint transfer based on passive phase compensation. EOM: electro-optic modulator, OC: optical circulator, AOM: acousto-optic modulator, BI-EDFA: bidirectional erbium-doped fiber amplifier, PD: photodetector, PC: power combiner, DDS: direct-digital synthesizer, BPF: band-pass filter, FM: Faraday mirror.
The electric field of the optical signal ${\textrm{E}_0} \propto \cos ({\omega _0}\textrm{t})$ generated by the narrow linewidth laser is fed into the EOM biased at ${\textrm{V}_\pi }/2$. Here ${\omega _0}$ is the angular frequency of the optical carrier. For convenience, we ignore the amplitude and initial phase here and in the following. At the remote site, the AOM can distinguish the round-trip signal from the spurious reflections along the fiber link. The optical signal ${\nu _\textrm{R}}$ at the remote site can be expressed as:
The ${\nu _\textrm{L}}$ is divided by a factor of 2 to get the ${\nu _{\textrm{L,error}}}$ with the phase error of unidirectional link.
The ${\nu _{\textrm{L,error}}}$ is mixed with the local reference frequency ${\Omega _1}$ to obtain the phase-conjugated signal ${\nu _{\textrm{L,conj}}}$.
The ${\nu _{\textrm{L,conj}}}$ is injected into the EOM and then reloaded on the optical carrier sidebands. At this time, a stable optical frequency signal ${\nu _{\textrm{R,stable}}}$ by passive phase stabilization is available at the remote site.
Here we note the existence of residual phase noise $- {\Omega _1}\varDelta \tau + {\Omega _\textrm{a}}\varDelta \tau + 2{\Omega _\textrm{b}}\varDelta \tau$ for optical frequency. Since this residual phase noise is six orders of magnitude smaller than the phase noise ${\omega _0}\varDelta \tau$ introduced by the optical fiber link, its effect on the optical frequency stability is negligible [19].
At the remote site, the optical signal is split into three paths, one part is reflected by the FM, another part beats with the reference optical frequency at the PD2, and the third part is used for stability assessment of RF (will be mentioned later).
As for RF, the output optical signal from the EOM contains an amplitude modulation with an angular frequency of ${\Omega _2}$. The electric field of output optical signal can be expressed as (only the upper sidebands are considered for clarity, the cancellation of phase noise also works for the lower sideband):
The ${\textrm{E}_1}$ is fed into the optical fiber link through the optical circulator, then the modulated optical signal at the remote site becomes:
At the remote site, the reflected optical signals follow the same fiber link back to the local site and beat against reference optical frequency at the PD1. The round-trip signal received by PD1 becomes:
The ${\textrm{E}_3}$ is divided into two parts, both parts pass through band-pass filter with angular frequencies $2({\Omega _\textrm{a}} + {\Omega _\textrm{b}})$ and ${\Omega _2} + 2({\Omega _\textrm{a}} + {\Omega _\textrm{b}})$, respectively. Then the two parts (the first and second terms of ${\textrm{E}_3}$) are mixed to obtain the ${\textrm{E}_4}$ with phase noise introduced by fiber link. It can be expressed as:
It should be noted that since the forward RF signal has the same angular frequency as the backward one on the same optical wavelength, ${\textrm{E}_4}$ cannot be obtained by direct detection to avoid backward scattering [29]. In order to avoid backward scattering, we add the RF signals to the optical carrier sidebands by amplitude modulation using EOM, so that when the optical signals pass through the AOM, the optical carrier and its sidebands can be shifted by the AOM at the same time. The above special passive phase stabilization frame is designed to distinguish the forward and backward optical frequencies and RFs, so that the phase noises of optical frequency and RF can be compensated by the phase correction of a single optical actuator in one phase stabilization device, which simplifies the complexity and improves the stability of the system.
To assist in acquiring the phase-conjugated RF signal, we need to generate the third harmonic of ${\Omega _2}$:
Mixing ${\textrm{E}_5}$ and ${\textrm{E}_4}$, taking the low-frequency components and the phase-conjugated RF signal ${\textrm{E}_6}$ is obtained:
Similarly, we use the power combiner to feed the ${\textrm{E}_6}$ into EOM, the stable RF signal is then available on PD3 at the remote site.
As mentioned above, the proposed scheme compensates for the phase noise of optical frequency and RF introduced by fiber link, respectively.
3. Optical frequency and RF joint transfer over 120km fiber spools
To verify the principle of the proposed scheme, the stable optical and radio frequency joint transfer based on passive phase compensation via 120 km fiber spools is demonstrated. NKT BASIK X15 narrow linewidth laser is used to generate a 1550.12 nm optical carrier. The bias point of EOM with 10 GHz bandwidth is set at ${\textrm{V}_\pi }/2$, and its insertion loss is about 9 dBm (due to the aging of the EOM). Moreover, we control the temperature variation of the EOM to minimize the influence of thermal noise on the frequency stability of optical frequency and RF transmission. The temperature variation is controlled within ±50mk. The optical signal power launched into the fiber link is kept at a low level (0 dBm in our example) to avoid Brillouin scattering and nonlinear effects [30]. In this experiment, we use the direct-digital synthesizer (Holzworth HS9004B) to generate ${\Omega _1}$= 40 MHz, ${\Omega _2}$= 500 MHz and ${\textrm{E}_5}$= 1500 MHz as the RF reference input signals of the proposed scheme, and the stable 1 GHz RF signal (${\textrm{E}_7} = \cos (2{\Omega _2}\textrm{t})$) will be obtained in our experiment results. The AOMs (downshift mode, −1 order) are operated at the driving frequency ${\Omega _\textrm{a}}$ = ${\Omega _\textrm{b}}$ = 75 MHz. The bidirectional erbium-doped fiber amplifiers (Bi-EDFA) are used to compensate for fiber link loss. Since the return optical signals need to pass through the FM and optical coupler, the Bi-EDFA is placed at the end of the entire 120km fiber to exert its amplification performance. To facilitate the evaluation of the system performance, the local and remote sites are placed together so that the frequency stability of the optical frequency and RF could be measured simultaneously. We use frequency counter Keysight 53230A and phase noise analyzer Microsemi TSC 5125A to measure the stability of optical frequency and RF, respectively. The frequency divider is used to divide 1 GHz RF by the factor of 10, so that it can be measured using Microsemi TSC 5125A. The 10 MHz RF signal from REFGEN 10292 is the reference frequency source for all experimental devices.
For the fractional frequency stability of optical frequency, we use a frequency counter with the gate time 1s (Λ-counting) to measure the result [31,32]. By beating the stable optical frequency signal ${\nu _{\textrm{R,stable}}}$ with the reference optical frequency on the PD2, we obtain the ${\nu _{\textrm{R,beat}}}$.
The residual noise of ${\nu _{\textrm{R,beat}}}$ reflects the performance of the optical frequency transfer. As for the frequency stability of 1 GHz RF (${\textrm{E}_7}$), it can be measured using a phase noise analyzer.
The frequency stability of optical frequency and RF are shown in Fig. 2. With the implementation of proposed scheme, we achieve optical frequency and RF stable joint transfer over the 120 km fiber spools. As shown in Fig. 2(a), optical frequency stability at 1 s is improved by three orders of magnitude, and the optical frequency transfer reaches the fractional frequency stability of 6.9 × 10−17 at the integral time of 1 s and 7.03 × 10−19 at 10000 s. In Fig. 2(b), the frequency stability of 1 GHz RF is 6.47 × 10−13 at 1 s and 3.96 × 10−16 at 10000 s, and the long-term stability of RF reaches good performance. We also measure the frequency stability noise floor of optical frequency and RF transfer by replacing the 120 km fiber spools with a 1 m fiber. They are 5.75 × 10−18 at 1 s and 1.77 × 10−19 at 10000 s for optical frequency transfer and 6.28 × 10−13 at 1 s and 3.54 × 10−16 at 10000 s for RF transfer as shown in Fig. 2. Moreover, we have to note that the experimental results of RF stability are significantly different from conventional RF transmission by amplitude modulating a continuous wave laser, the main cause may be limited by the crosstalk phase noise effect or the experimental environment [19]. In the future, increasing the isolation between signals may effectively improve the frequency stability of RF signals.
Fig. 2. The results of optical frequency and RF joint transfer. (a) Measured fractional frequency stability of the free-running optical frequency (cyan triangle) and the stabilized optical frequency (red plaid). (b) Measured frequency stability of the free-running RF (cyan triangle) and the stabilized RF (red plaid). The measured noise floor of the optical frequency and RF transfer are also shown (black circle).
In addition, the phase noise PSD of passive and active optical frequency transfer schemes are shown in Fig. 3 over 120 km fiber spools, respectively. The phase noise PSD of active optical frequency transfer via the same fiber length is used as a comparison with the passive optical frequency transfer to illustrate the difference between them. The active optical frequency transfer scheme is that the phase discrimination is used to extract the error signal of the round-trip optical signal with fiber link phase noise, and the servo controller is used to regulate the AOM at the local site. It uses doppler noise suppression technology to achieve stable optical frequency transmission. In Fig. 3(a), when the passive optical frequency transfer device works, the optical frequency phase noise PSD within the feedback bandwidth of 416 Hz ($1/4\tau$) [11] shows a power-law dependence of f-1 from 5 Hz to 416 Hz and a power-law dependence of f° from 1 Hz to 5 Hz, which confirms that the stabilized optical frequency phase noise reaches the theoretical one [25]. In Fig. 3(b), the optical frequency phase noise of active stabilization scheme is also roughly consistent with the theoretical phase noise limitation [11]. More importantly, we also observe that the apparent servo bump in Fig. 3(b) for active stabilization scheme disappears in Fig. 3(a) for passive stabilization scheme, which indicates that optical frequency transfer with passive stabilization scheme has better spectral purity and system stability than the active one [33]. We note that the phase noise PSD measured by the active method does not fit the theoretical case well compared to the passive method. That can be explained as the servo impact of active method will create a phase jump of the stable optical frequency during the experimental measurement process.
Fig. 3. Phase noise PSD of passive and active optical frequency transfer scheme over 120 km fiber spools. (a) Measured the phase noise PSD of passive optical frequency transfer for stabilized case (red curve), the free-running case (black curve) and the theoretical prediction (green curve Ref. [25]). (b) Measured the phase noise PSD of active optical frequency transfer for stabilized case (red curve), the free-running case (black curve) and the theoretical prediction (green curve Ref. [11]).
4. Conclusion
We first propose a new scheme of stable optical and radio frequency joint transfer based on passive phase compensation. The proposed scheme demonstrates the feasibility and compatibility of optical frequency and RF simultaneous transmission based on passive phase stabilization techniques. Since the phase noise is not affected by servo bump, the optical frequency jitter is reduced and the robustness of the system is improved. The absence of active electronics shortens the response time of the compensation device and phase recovery time, which reaches the same sensitivity as in the conventional optical frequency transfer techniques. The RF stability, however, is not yet excellent, which may need to be solved by reducing the crosstalk between signals. Moreover, the stable optical frequency output at the remote site also has a frequency offset. In the future, a clean optical frequency signal can be achieved by adding an AOM with the opposite frequency shift at the remote site. The experimental result shows that the frequency stability of optical frequency and RF can meet the demand of stable optical frequency and RF simultaneous transmission in most cases. The novel technique provides an alternative phase compensation technique besides the active phase compensation technique, which is important to complement the existing frequency simultaneous transmission scheme. It also may be further applied in distributed (multiple users) ultra-long distance time and frequency transfer systems to improve their performance.
Funding
National Key Research and Development Program of China (2020YFB0408300); National Natural Science Foundation of China (62175246); Natural Science Foundation of Shanghai (22ZR1471100); Youth Innovation Promotion Association of the Chinese Academy of Sciences (YIPA2021244).
Disclosures
The authors declare no competing interests.
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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