Coherent optical frequency transfer via 972-km fiber link

We demonstrate coherent optical frequency dissemination over a distance of 972 km by cascading two spans where the phase noise is passively compensated for.Instead of employing a phase discriminator and a phase locking loop in the conventional active phase control scheme,the passive phase noise cancellation is realized by feeding double-trip beat-note frequency to the driver of the acoustic optical modulator at the local site.This passive scheme exhibits fine robustness and reliability,making it suitable for long-distance and noisy fiber links.An optical regeneration station is used in the link for signal amplification and cascaded transmission.The phase noise cancellation and transfer instability of the 972-km link is investigated,and transfer instability of 1.1×10^(-19)at 10^(4)s is achieved.This work provides a promising method for realizing optical frequency distribution over thousands of kilometers by using fiber links.

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/s^(2),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.

Determination of the orthometric height difference based on optical fiber frequency transfer technique

The development of remote frequency transfer techniques,especially the appearance of optical clocks with unprecedented stability,has prompted geoscientists to study their applications in geodesy.Using remote frequency transfer technique,by frequency comparison of two optical clocks at two points P and Q connected by optical fibers,one can measure the signal’s frequency shift between them,and the geopotential difference between them can be determined based on the gravity frequency shift equation.Given the orthometric height of P,the orthometric height of Q can be determined.Since the present stability of the optical clock has achieved 1×10^(-18) or better and comparing the frequency transfer via optical fiber provides stability at 10^(-19) level,the optical clock network enables determining the orthometric height at centimeter-level.This study provides a formulation to determine the height diffe rence at one-centimeter level between two points on the ground based on the optical fiber frequency transfer technique.

Microwave frequency transfer over a 112-km urban fiber link based on electronic phase compensation

We demonstrate the transmission of a microwave frequency signal at 10 GHz over a 112-km urban fiber link based on a novel simple-architecture electronic phase compensation system.The key element of the system is the low noise frequency divider by 4 to differentiate the frequency of the forward signal from that of the backward one,thus suppressing the effect of Brillouin backscattering and parasitic reflection along the link.In terms of overlapping Allan deviation,the frequency transfer instability of 4.2×10-15 at 1-s integration time and 1.6×10-18 at one-day integration time was achieved.In addition,its sensitivity to the polarization mode dispersion in fiber is analyzed by comparing the results with and without laser polarization scrambling.Generally,with simplicity and robustness,the system can offer great potentials in constructing cascaded frequency transfer system and facilitate the building of fiber-based microwave transfer network.

Numerical Prediction Methods for Clock Deviation Based on Two-Way Satellite Time and Frequency Transfer Data

Three functional models, polynomial, spectral analysis, and modified AR model, are studied and compared in fitting and predicting clock deviation based on the data sequence derived from two-way satellite time and frequency transfer. A robust equivalent weight is applied, which controls the significant influence of outlying observations. Some conclusions show that the prediction precision of robust estimation is better than that of LS. The prediction precision calculated from smoothed observations is higher than that calculated from sampling observations. As a count of the obvious period variations in the clock deviation sequence, the predicted values of polynomial model are implausible. The prediction precision of spectral analysis model is very low, but the principal periods can be determined. The prediction RMS of 6-hour extrapolation interval is Ins or so, when modified AR model is used.

Real-time frequency transfer system over ground-to-satellite link based on carrier-phase compensation at 10-16 level

We demonstrate a novel and stable frequency transfer scheme over ground-to-satellite link based on real-time carrier-phase detection and compensation.We performed a zero-baseline measurement with the designed system,an uninterrupted frequency standard signal is recovered in the reception station without additional post-correction of delay error caused in the route,which is because the phase error of the entire route is tracked and compensated continuously in real-time.To achieve this goal,we employed two carriers in the system and the differential signal is transferred in order to eliminate the instability results from the local oscillator at the satellite transponder as well as the common-mode noise induced in the transfer route and microwave components.The stability of 3×10^(-16) with an integration time of 1 day was achieved and the time fluctuation during one day was measured to be about±20 ps.Error sources and possible solutions are discussed.Our zero-baseline method shows a promising result for real-time satellite-based time and frequency transfer and deserves further research to find whether it works between long-baseline stations.

Passive phase noise compensation for fiber-optic radio frequency transfer with a nonsynchronized source

We propose a passive compensation fiber-optic radio frequency（RF） transfer scheme with a nonsynchronized RF stable source during a round-trip time, which can avoid high-precision phase-locking and efficiently suppress the effect of backscattering only using two wavelengths at the same time. A stable frequency signal is directly reproduced by frequency mixing at the remote site. The proposed scheme is validated by the experiment over a 40 km single mode fiber spool using nonsynchronized common commercial RF sources. The influence of the stability of nonsynchronized RF sources on the frequency transfer is investigated over different length fiber links.

Joint transfer of time and frequency signals and multi-point synchronization via fiber network

A system of jointly transferring time signals with a rate of 1 pulse per second （PPS） and frequency signals of 10 MHz via a dense wavelength division multiplex-based （DWDM） fiber is demonstrated in this paper. The noises of the fiber links are suppressed and compensated for by a controlled fiber delay line. A method of calibrating and characterizing time is described. The 1PPS is synchronized by feed-forward calibrating the fiber delays precisely. The system is experimen- tally examined via a 110 km spooled fiber in laboratory. The frequency stabilities of the user end with compensation are 1.8x 10-14 at 1 s and 2.0x 10-17 at 104 s average time. The calculated uncertainty of time synchronization is 13.1 ps, whereas the direct measurement of the uncertainty is 12 ps. Next, the frequency and 1PPS are transferred via a metropoli- tan area optical fiber network from one central site to two remote sites with distances of 14 km and 110 km. The frequency stabilities of 14 km link reach 3.0x 10-14 averaged in 1 s and 1.4x 10-17 in 104 s respectively; and the stabilities of 110 km link are 8.3 x 10-14 and 1.7 x 10-17, respectively. The accuracies of synchronization are estimated to be 12.3 ps for the 14 km link and 13.1 ps for the 110 km link, respectively.

Digital output compensation for precise frequency transfer over commercial fiber link

An ultra-highly precise and long-term stable frequency transmission system over 120 km commercial fiber link has been proposed and experimentally demonstrated. This system is based on digital output compensation technique to suppress phase fluctuations during the frequency transmission process. A mode-locked erbium-doped fiber laser driven by a hydrogen maser serves as an optical transmitter. Moreover, a dense wavelength division multiplexing system is able to separate forward and backward signals with reflection effect excluded. The ultimate fractional frequency instabilities for the long-distance frequency distributed system are up to 3.14×10^(-15) at 1 s and 2.96×10^(-19) at 10 000 s, respectively.

Coherent Transfer of Optical Frequency over 112 km with Instability at the 10^(-20) Level

We demonstrate optical-carrier transfer over a 112-km single-span urban fiber link, By actively compensating the phase noise induced along the fiber link, a noise suppression of 55 dB at 1 Hz is obtained. A fractional frequency instability of 2.5× 10^-16 at i s is achieved, and reaching 7.5× 10^-20 at 10000 s. The system is stable and able to run for a long time. This work will contribute to optical frequency distribution and remote comparison among atomic clocks.

Delay Effect on Coherent Transfer of Optical Frequency Based on a Triple-Pass Scheme

We demonstrate a triple-pass scheme for coherent transfer of optical frequency and the delay effect on the fiber phase noise compensation. It is theoretically proved that the delay effect consists of both fiber delay and servo delay. The delay effect confines the servo bandwidth within 1/8 and induces a residual fiber phase noise after noise compensation. For a 25-km-long fiber, the servo bandwidth is found to be around 1 k Hz, and the fiber phase noise is suppressed approaching to the theoretical limitation. The triple-pass scheme enables the simultaneous transfer of optical frequency to multiple remote users. The performance of noise compensator in the triple-pass scheme can achieve a similar level result compared with that in the double-pass scheme.

Fiber-based joint time and frequency dissemination via star-shaped commercial telecommunication network

A fiber-based, star-shaped joint time and frequency dissemination scheme is demonstrated. By working in cooperation with the existing commercial telecommunication network. Our scheme enables the frequency, time, and digital data networks to be integrated together and could represent an ideal option of interconnection among scientific institutions.The compensation functions of the time and frequency transfer scheme are set at the client nodes. The complexity of the central node is thus reduced, and future expansion by the addition of further branches will be accomplished more easily.During a performance test in which the ambient temperature fluctuation is 30℃/day, timing signal dissemination stability is achieved to be approximately ±50 ps along 25-km-long fiber spools. After calibration, a timing signal synchronization accuracy of 100 ps is also realized. The proposed scheme offers an option of the construction of large-scale fiber-based frequency and time transfer networks.

Application of Geodetic Receivers to Timing and Time Transfer

Two methods for smoothing pseudorange observable by Carrier and Doppler are discussed. Then the procedure based on the RINEX observation files is tested using the Ashtech Z-XII3T geodetic receivers driven by a stable external frequency at UNSO. This paper proposes to adapt this procedure for the links between geodetic receivers, in order to take advantage of the P codes available on L 1 and L 2. This new procedure uses the 30-second RINEX observations files, the standard of the International GPS Service (IGS), and processes the ionosphere-free combination of the codes P 1 and P 2; the satellite positions are deduced from the IGS rapid orbits, available after two days.

Portable Atmospheric Transfer of Microwave Signal Using Diode Laser with Timing Fluctuation Suppression

We demonstrate an atmospheric transfer of microwave signal over a 120 m outdoor free-space link using a compact diode laser with a timing fluctuation suppression technique.Timing fluctuation and Allan Deviation are both measured to characterize the instability of transferred frequency incurred during the transfer process.By transferring a 100 MHz microwave signal within 4500 s,the total root-mean-square(RMS)timing fluctuation was measured to be about 6 ps,with a fractional frequency instability on the order of 1×10-12 at 1 s,and order of 7×10-15 at 1000 s.This portable atmospheric frequency transfer scheme with timing fluctuation suppression can be used to distribute an atomic clock-based frequency over a free-space link.

Simultaneous transmission of time-frequency and data with co-amplification over urban fiber links

We demonstrate a simultaneous transmission of time-frequency and data over a 160-km urban business network in Shanghai.The signals are transmitted through a cascaded optical link consisting of 48 km and 32 km,which are connected by an optical relay.The metrological signals are inserted into the communication network using dense wavelength division multiplexing.The influence of the interference between different signals has been discussed.The experimental results demonstrate that the radio frequency(RF)instability can reach 2.1×10^(-14)at 1 s and 2.3×10^(-17)at 10,000 s,and the time interval transfer of one pulse per second(1 PPS)signal with less than 10 ps at 1 s is obtained.This work paves the way for the widespread dissemination of ultra-stable time and frequency signals over the communication networks.

Efficient structures for wideband digital receiver

Digital receivers have become more and more popular in radar, communication, and electric warfare for the advantages compared with their analog counterparts. But conventional digital receivers have been generally considered impractical for bandwidth greater than several hundreds MHz. To extend receiver bandwidth, decrease data rate and save hardware resources, three novel structures are proposed. They decimate the data stream prior to mixing and filtering, then process the multiple decimated streams in parallel at a lower rate. Consequently it is feasible to realize wideband receivers on the current ASIC devices. A design example and corresponding simulation results are demonstrated to evaluate the proposed structures.

Transfer of laser frequency from 729 nm to 1.5 μm with precision at the level of 10^(−20)

By using a self-reference transfer oscillator method,two individual 1560 nm lasers with about 1.2 GHz frequency difference were phase locked to a 729 nm ultra-stable laser at two preset ratios.By measuring the beat frequency of the two 1560 nm lasers,fractional instabilities of 2×10^(−17) at 1 s and 2×10^(−20) at 10,000 s averaging time were obtained,and the relative offset compared with the theoretical value was 4.2×10^(−21)±4.5×10^(−20).The frequency ratio of them was evaluated to a level of 1.3×10^(−20) in one day’s data acquisition.This work was a preparation for remote comparison of optical clocks through optical fiber links.The technique can also be used to synthesize ultra-stable lasers at other wavelengths.

On the low frequency characteristics of head-related transfer function

A method to correct the measured head-related transfer functions （HRTFs） at low frequency was proposed. By analyzing the HRTFs from the spherical head model at low frequency, it is proved that below the frequency of 400 Hz, magnitude of HRTF is nearly constant and the phase is a linear function of frequency both for the far and near field. Therefore, if the HRTFs above 400 Hz are accurately measured by experiment, it is able to correct the HRTFs at low frequency by the theoretical model. The results of calculation and subjective experiment show that the feasibility of the proposed method.