Optical Frequency Transfer Research Articles

Correction: Wang et al. Optical Frequency Transfer on the Order of 10−19 Fractional Frequency Instability over a 64 m Free-Space Link. Photonics 2024, 11, 587

In the original publication [...]

Robust Transfer of Optical Frequency over 500km Fiber Link with Instability of 10−21

Abstract Our primary objective is to mitigate the adverse effects of temperature fluctuations on the optical frequency transmission system by reducing the length of the interferometer. Following optimization, the phase-temperature coefficient of the optical system is reduced to approximately 1.35 fs/K. By applying a sophisticated temperature control to the remained “out-of-loop” optics fiber, the noise floor of the system has been effectively lowered to 10−21 level. Based on this performance-enhanced transfer system, we demonstrate coherent transmission of optical frequency through 500-km spooled fiber link. After being actively compensated, the transfer instability of 4.5 × 10−16 at the averaging time of 1 s and 5.6 × 10−21 at 10000 s is demonstrated. The frequency uncertainty of received light at remote site relative to that of the origin light at local site is achieved to be 1.15 × 10−19. This enhanced system configuration is particularly well suited for future long-distance frequency transmission and comparison of the most advanced optical clock signals.

Dual optical frequency transfer through wavelength-division and polarization multiplexing in an 184-meter fiber link

Stabilized dual optical frequency transfer is demonstrated through wavelength-division or polarization multiplexing in a 184-meter long polarization-maintaining fiber link. The latter is stabilized at a primary frequency in the telecom C-band using the established Doppler cancellation technique. Simultaneously, a secondary optical frequency is transferred in the same fiber. Out-of-loop characterization demonstrates an indirect Doppler cancellation for the secondary optical frequency. Compared to an unstabilized link, at 1000 seconds integration time we measure an 11.5 dB stability improvement for wavelength-division multiplexing and a 16 dB improvement for polarization multiplexing. Taking advantage of a stabilized link to distribute other wavelengths is useful for applications in frequency metrology. As an example, we are using a cavity-stabilized 1560 nm laser to stabilize the fiber link while a 1556.2 nm two-photon rubidium clock laser is being distributed.

Integrated optical frequency transfer and optical physical layer key distribution with enhanced link reciprocity detection

Integrated optical frequency transfer and optical physical layer key distribution with enhanced link reciprocity detection

Optical Frequency Transfer on the Order of 10−19 Fractional Frequency Instability over a 64 m Free-Space Link

High-precision time–frequency is widely used in time measurement, satellite navigation, scientific research, and other fields. With the rapid development of optical clock technology, the fractional frequency instability and uncertainty of optical clock have reached 10−18 orders of magnitude, which is expected to contribute to generating the International Atomic Time and may even be used to redefine the “second” in the future. Therefore, the long-distance transfer of time–frequency signals between optical atomic clocks is of great significance. Free-space optical frequency transfer technology is one of the important technologies for solving the space-based optical clock comparison because of its high transfer precision and easy networking characteristics. In order to solve the long-distance space-based optical clock comparison, this paper investigates a free-space active phase noise compensation method using an Acousto-Optic Modulator (AOM), based on the traditional optical fiber phase noise compensation scheme. This new method is more flexible and scalable than the optical fiber time–frequency transfer technology. The optical frequency transfer over a 64 m free-space link is demonstrated. The fractional frequency transfer instability during free running is 9.50 × 10−16 at 1 s, and 4.44 × 10−16 at 2000 s, and the fractional frequency instability after compensation is 7.10 × 10−17 at 1 s, 3.07 × 10−19 at 2000 s, which is about 1–3 orders of magnitude better than that in free running, and provides a feasible scheme for space-based optical clock comparison.

Optical frequency transfer link with remote site compensation

Optical frequency transfer link with remote site compensation

Phase-Noise Characterization in Stable Optical Frequency Transfer over Free Space and Fiber Link Testbeds

Time and frequency metrology depends on stable oscillators in both radio-frequency and optical domains. With the increased complexity of the highly precise oscillators also came the demand for delivering the oscillators’ harmonic signals between delocalized sites for comparison, aggregation, or other purposes. Besides the traditional optical fiber networks, free-space optical links present an alternative tool for disseminating stable sources’ output. We present a pilot experiment of phase-coherent optical frequency transfer using a free-space optical link testbed. The experiment performed on a 30 m long link demonstrates the phase-noise parameters in a free-space optical channel under atmospheric turbulence conditions, and it studies the impact of active MEMS mirror stabilization of the received optical wave positioning on the resulting transfer’s performance. Our results indicate that a well-configured MEMS mirror beam stabilization significantly enhances fractional frequency stability, achieving the−14th-order level for integration times over 30 s.

Analysis and Reduction of Nonlinear Effects in Optical Fiber Frequency Transfer

Nonlinear effects in optical fiber frequency transfer have a significant impact on the precision of frequency transfer. We investigate the main nonlinear effects, including the Brillouin scattering and the Raman scattering, in optical fiber frequency transfer through theoretical and simulation calculations in detail. The calculation results show that the threshold powers of the Brillouin scattering and the Raman scattering decrease with the increase in the fiber length; however, the fiber length has little to no impact on the threshold powers when the fiber length is greater than 10 km. The threshold powers, including the Brillouin scattering and the Raman scattering, increase as the attenuation coefficient increases. Conversely, when it comes to the gain coefficients, the outcomes exhibit a reverse trend. When the linewidth Δvlaser of the laser source is from 1 Hz to 1 MHz, the linewidth Δvlaser does not affect the threshold powers of the Brillouin scattering. This study seeks to offer design guidance aimed at mitigating nonlinear effects in optical fiber frequency transfer. The calculated results hold considerable potential in guiding various applications reliant on Brillouin and Raman scattering properties, such as laser technology and optical fiber sensing.

Robust free-space optical frequency transfer in time-varying link distances conditions

Future inter-satellite clock comparison on high orbit will require optical time and frequency transmission technology between moving objects. Here, we demonstrate robust optical frequency transmission under the condition of variable link distance. This variable link is accomplished by the relative motion of a single telescope fixed on the experimental platform to a corner-cube reflector (CCR) installed on a sliding guide. Two acousto–optic modulators with different frequencies are used to separate forward signal from backward signal. With active phase noise suppression, when the CCR moves back and forth at a constant velocity of 20 cm/s and an acceleration of 20 cm/s2, we achieve the best frequency stability of 1.9 × 10−16 at 1 s and 7.9 × 10−19 at 1000 s indoors. This work paves the way for future studying optical frequency transfer between ultra-high-orbit satellites.

Remote Residual Instability Evaluation of Comb-Based Precise Frequency Transmission for Optical Clock

Optical clocks can be used as the absolute frequency reference due to their high accuracy and stability. In a precise optical clock transmission system, the instability loss of the link is usually evaluated by beating the remote optical signal with the reference clock, which is not suitable for real frequency distribution applications. Therefore, it is necessary to assess the performance directly at the remote site for the optical frequency transfer, because the two sites of the link are usually not co-located. In this paper, we proposed a comb-based remote residual instability evaluation scheme. Two coherent optical combs with different wavelengths were extracted from a frequency stable comb and transmitted after multiplexing. The residual instability was evaluated directly at the remote site by measuring the phase fluctuation difference between the two combs. We achieved 8.61 × 10−19 at 40,000 s over a 10 km fiber link, reaching the instability of optical clocks. These results revealed that our scheme can evaluate optical clock frequency transmission directly at the remote site, which made the method truly practical.

Multiple-Branch Optical Frequency Transfer Without the Frequency Allocation Constraints

We report on the realization of a multiple-branch optical frequency transfer method, which can be adopted to deliver an optical reference to multiple independent remote sites. In comparison with the previous techniques, the proposed technique mitigates the frequency allocation constraints of the driving frequencies for the acousto-optic modulators (AOMs) at the remote sites by adding a short loop fiber link at the local site. The end-to-end optical path phase noise detection and compensation for each remote site is simultaneously performed at the remote site, which significantly simplifies the configuration at the local site, and can improve the signal-to-noise ratio (SNR) and reduce the cycle slip rate. We also conduct theoretical analysis for the effect of frequency aliasing from the perspective of different refractive index in triple-pass optical frequency transfer, analyze the effect of the SNR and cycle slips on the fractional frequency instability, and present a comprehensive equation for calculating noise contributions from end-to-end optical frequency transfer over the multiple-branch fiber network, demonstrating that the implementation of the fiber noise cancellation (FNC) for the each branch consisting of two fiber topologies with the single FNC setup is practical. This technique paves the way to integrate the optical frequency networks into the existing fiber communication networks with the higher compatibility and reliability.

Stabilized free space optical frequency transfer using digitally enhanced heterodyne interferometry.

Free-space continuous-wave laser interferometry using folded links has applications in precision measurement for velocimetry, vibrometry, optical communications, and verification of frequency transfer for metrology. However, prompt reflections from the transceiver optics degrade the performance of these systems, especially when the power of the returning signal is equal to or less than the power of the prompt reflections. We demonstrate phase stabilized free-space continuous-wave optical frequency transfer that exploits the auto-correlation properties of pseudo-random binary sequences to filter out prompt reflections. We show that this system significantly improves the stability and robustness of optical frequency transfer over a 750 m turbulent free-space channel, achieving a best fractional frequency stability of 8 × 10-20 at an integration time of τ = 512 s, and cycle-slip-free periods up to 162 min.

Towards optical frequency geopotential difference measurements via a flying drone.

Geopotential and orthometric height differences between distant points can be measured via timescale comparisons between atomic clocks. Modern optical atomic clocks achieve statistical uncertainties on the order of 10-18, allowing height differences of around 1 cm to be measured. Frequency transfer via free-space optical links will be needed for measurements where linking the clocks via optical fiber is not possible, but requires line of sight between the clock locations, which is not always practical due to local terrain or over long distances. We present an active optical terminal, phase stabilization system, and phase compensation processing method robust enough to enable optical frequency transfer via a flying drone, greatly increasing the flexibility of free-space optical clock comparisons. We demonstrate a statistical uncertainty of 2.5×10-18 after 3 s of integration, corresponding to a height difference of 2.3 cm, suitable for applications in geodesy, geology, and fundamental physics experiments.

Modelling and design of ultra-high stable Fabry–Pérot cavity

Lasers having sub-Hz linewidth and long-term stability better than a few parts in 1016 is an unavoidable requisite to achieve unprecedented accuracy in the optical atomic clocks, intercomparing distributed atomic clocks and their networking, establishing coherent optical fibres, precision time & frequency transfer, production of optical qubits, and many more. For these wide ranges of applications, ultrastable Fabry–Pérot (FP) cavities, which act as the reference optical resonator, have got lots of attention. Designing such a FP cavity is a challenge due to the requirements of suppressing instabilities from all the thermo-mechanical noise sources at the highest degree. In this article, we report a comprehensive study to elucidate detailed design steps and associated numerical analysis procedures to build such a FP cavity. For this, we considered all sources of noises arising from: improper optical and opto-mechanical settings, ground vibrations transmitted to the cavity, deformations due to self-weight as it worsens the stability due to acoustic noise coupled to it, and temperature fluctuation. We present quantitative assessments of the instabilities for different shapes, geometries, and constituent materials of the cavities. In order to model the vibration-induced instability, we developed a novel forced-vibration based technique for accurate estimation of the instabilities, that reciprocates the experimental results reported in the literature, and the method is found to be superior compared to the other approaches, therefore estimating the overall cavity stability more accurately. We found in short term (¡ 10 s), the instability of the cavity is limited by temperature fluctuation, and in the long term (¿ 10 s), Brownian noise dominates the instability, therefore demands adequate precautions to reach the desired level of stability. Through systematic simulations, we have identified the best criteria for minimization of all these noises and obtain stabilities of 8.5×10−17 and 5.1×10−17 using dielectric and crystalline mirror coatings, respectively, which are similar to the best-reported results among its homologue cavities.

Residual timing jitter in the free-space optical two-way time and frequency transfer caused by atmospheric turbulence

Free-space optical two-way time and frequency transfer (FSO-TWTFT) will play an important role in the establishment of optical clock network, enabling the improvement of communication and navigation. In this paper, the model of residual timing jitter caused by the atmospheric turbulence is built for the FSO-TWTFT, where the spatial and temporal turbulence variation are both considered. The power spectrum density (PSD) of the residual timing jitter is derived and verified by comparing with the reported experimental results. The impacts of atmospheric turbulence on the comb-based FSO-TWTFT technique and the FSO-based optical frequency transfer technique are further analyzed for the satellite-to-ground links. The PSD at different satellite heights and elevation angles are presented. The results show the influence of temporal turbulence variation will be higher than that of spatial turbulence variation when the satellite is over 2000 km due to the large link delay. The residual timing jitters of the two FSO-TWTFT techniques are less than 6.4 fs in most orbit zones under medium turbulence intensity. In particular, for the comb-based FSO-TWTFT technique, there is a special orbit zone where the Doppler frequency shift approaches the repetition frequency difference of linear optical sampling and then the residual timing jitter increases dramatically.

Optical frequency transfer with below 10−21 uncertainty using a DFB–laser-based fiber Brillouin amplifier

Exploiting the outstanding performance of optical atomic clocks for improved timekeeping, relativistic geodesy, and fundamental physics beyond the standard model demands comparing distant state-of-the-art optical clocks. Interferometric optical fiber links have been demonstrated as an eminent method for such frequency comparisons over distances up to thousands of kilometers. However, for such distances, the optical fiber attenuation mandates signal amplification. Fiber Brillouin amplification (FBA) has been proven as an efficient amplification technique for coherent frequency transfer. Demonstrated FBA schemes have been designed based on costly narrow-linewidth pump lasers and analog pump-to-signal phase locking schemes. Furthermore, the high pump power requirement of these FBAs hinders the integration of FBA-based frequency dissemination on fiber connections for shared telecommunication signals in the C-band. In this paper, we propose and experimentally demonstrate a novel FBA module (FBAM) employing cost-effective distributed feedback (DFB) pump lasers assisted by a digital phase locking scheme based on a field programmable gated array. The new FBAM is compact, cost-effective, and directly applicable to different bands, which opens up new opportunities to establish a frequency metrology infrastructure within existing telecommunication fiber networks. Additionally, the small-footprint of the DFB-FBAM allows for frequent amplification stages with lower pump power to reach continental scale optical metrology links with an optimized signal-to-noise ratio. We characterized the DFB-FBAM’s frequency transfer uncertainty using a two-way layout over an in-lab 100 km long optical fiber link and reach a fractional frequency instability of 9.3 × 10−22 at a 10 ks integration time. The DFB-FBAM characterizations show uncertainty contributions of (−2.1 ± 3.3) × 10−22 and below for averaging times >100 ks. For the first time, we assess the temporal Brillouin frequency shift variations in an underground fiber link and implement a scheme to track these changes in a remote FBAM.

Highly vibration-resistant sub-Hertz ultra-stable laser passing over 1700 km transport test

We present a compact ultra-stable laser at 1550 nm with a line-width of 0.57 Hz, achieved using a 50-mm length cubic optical cavity. With the help of elaborate investigation of the vibration behavior of the cavity in three directions, its physical structure was optimized for significantly improved insensitivity to vibration by increasing the first-order resonance frequency almost twice that of the previous setup. The anti-vibration capability of the ultra-stable laser was then verified in the long-distance highway transport test over more than 1700 km, which shows nearly unchanged performance compared to that before transport. A fractional frequency instability of ∼ 2.6 × 10−15 was observed at 1–10 s, approaching the thermal noise floor. To our knowledge, this is the longest-distance transport vibration test for a practical transportable laser to date. The presented system will act as the local optical oscillator for high-precision remote optical frequency transfer, and the design strategy is valuable for space-borne laser applications.

High-precision optical frequency transfer over a 96 km urban fiber link.

We demonstrated the optical frequency transfer over a 96km urban business network in Shanghai. The key factors affecting the optical frequency transmission system, such as fiber link quality, feedback compensation strength, and out-of-loop fiber temperature variation, are studied for the urban fiber link characteristics. The effective suppression technique of complex urban fiber link noise with different feedback compensation parameters is studied. With active phase noise suppression, the optical frequency stability can reach 1.9×10-16 at 1s and 2.2×10-18 at 10,000s over a 96km urban fiber link. This work potentially plays an important role in optical clock frequency comparison, and it makes a good foundation for future research on long-distance optical frequency transfer over an urban business network.

Frequency transfer of an optically detected magnetic resonance and observation of the Hanle effect in a nonzero magnetic field

The method of transferring the frequency of an optically detected magnetic resonance both up and down by an arbitrary value is implemented in a single-beam optical pumping scheme by modulating the linearly polarized beam component. The possibility of observing the Hanle resonance in a magnetic field virtually zeroed upon transition to a rotating coordinate system is demonstrated. A model experiment was carried out, confirming the fundamental feasibility and effectiveness of the method. Keywords: Optically detectable magnetic resonance, optical resonance frequency transfer, Hanle effect, Bell-Bloom scheme, quantum magnetometer.

High-Precision Optical Fiber Time and Frequency Transfer Method Based on Wavelength Division Multiplexing

High-Precision Optical Fiber Time and Frequency Transfer Method Based on Wavelength Division Multiplexing