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.

Gigahertz frequency hopping in an optical phase-locked loop for Raman lasers

Raman lasers are essential in atomic physics,and the development of portable devices has posed requirements for time-division multiplexing of Raman lasers.We demonstrate an innovative gigahertz frequency hopping approach of a slave Raman laser within an optical phase-locked loop(OPLL),which finds practical application in an atomic gravimeter,where the OPLL frequently switches between near-resonance lasers and significantly detuned Raman lasers.The method merges the advantages of rapid and extensive frequency hopping with the OPLL’s inherent low phase noise,and exhibits a versatile range of applications in compact laser systems,promising advancements in portable instruments.

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.

Optical frequency comb technology: from ground to space

Optical frequency combs,as powerful tools for precision spectroscopy and research into optical frequency standards,have driven continuous progress and significant breakthroughs in applications such as time-frequency transfer,measurement of fundamental physical constants,and high-precision ranging,achieving a series of milestone results in ground-based environments.With the continuous maturation and evolution of femtosecond lasers and related technologies,optical frequency combs are moving from ground-based applications to astronomical and space-based applications,playing an increasingly important role in atomic clocks,exoplanet observations,gravitational wave measurements,and other areas.This paper,focusing on astronomical and space-based applications,reviews research progress on astronomical frequency combs,optical clock time-frequency networks,gravitational waves,dark matter measurement,dual-comb large-scale absolute ranging,and high-resolution atmospheric spectroscopy.With enhanced performance and their gradual application in the field of space-based research,optical frequency combs will undoubtedly provide more powerful support for astronomical science and cosmic exploration in the future.

Effects of initial frequency chirp on the linear propagation characteristics of the exponential optical pulse

In this paper, the linear propagation characteristics of the exponential optical pulse with initial linear and nonlinear frequency chirp are numerically studied in a single mode fibre for β2 〈 0. It can be found that the temporal full width at half maximum and time-bandwidth product of exponential pulse monotonically increase with the increase of propagation distance and decrease with the increase of linear chirp C for C 〈 0.5, go through an initial decreasing stage near ζ= 1, then increase with the increase of propagation distance and linear chirp C for C 〉 0.5. The broadening of pulses with negative chirp is faster than that with positive chirp. The exponential pulse with linear chirp gradually evolves into a near-Gaussian pulse. The effect of nonlinear chirp on waveform of the pulse is much greater than that of linear chirp. The temporal waveform breaking of exponential pulse with nonlinear chirp is first observed in linear propagation. Furthermore, the expressions of the spectral width and time-bandwidth product of the exponential optical pulse with the frequency chirp are given by use of the numerical analysis method.

A long-term frequency-stabilized erbium-fiber-laser-based optical frequency comb with an intra-cavity electro-optic modulator

We demonstrate an optical frequency comb based on an erbium-doped-fiber femtosecond laser with the nonlinear polarization evolution scheme. The repetition rate of the laser is about 209 MHz. By controlling an intra-cavity electro- optic modulator and a piezo-transducer, the repetition rate can be stabilized with a high-bandwidth servo in a frequency range of 3 kHz, enabling long-term repetition rate phase-locking. The in-loop frequency stability of repetition rate is about 1.6× 10-13 in an integration time of 1 s, limited by the measurement system; and it is inversely proportional to integration time in the short term. Furthermore, using a common path f-2f interferometer, the carrier envelope offset frequency of the comb is obtained with a signal-to-noise ratio of 40 dB in a 3-MHz resolution bandwidth. Stabilized cartier envelope offset frequency exhibits a deviation of 0.6 mHz in an integration time of 1 s.

Optical coherence transfer over 50-km spooled fiber with frequency instability of 2×10^(-17) at 1s

We demonstrate coherent transfer of an ultra-stable optical frequency at 192.8 THz over 50-km spooled fiber. Random phase noise induced by environmental disturbance through fiber is detected and suppressed by feeding a correctional signal into an acousto-optic modulator. After being compensated, the fiber-induced frequency instability is 2×10-17 at 1-s averaging time and reaches 8×10-20 after 16 h. The noise floor of the compensation system could be as low as 2×10-18 at 1-s averaging time.

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.

Tunable and broadband microwave frequency combs based on a semiconductor laser with incoherent optical feedback

Based on a semiconductor laser （SL） with incoherent optical feedback, a novel all-optical scheme for generating tunable and broadband microwave frequency combs （MFCs） is proposed and investigated numerically. The results show that, under suitable operation parameters, the SL with incoherent optical feedback can be driven to operate at a regular pulsing state, and the generated MFCs have bandwidths broader than 40 GHz within a 10 dB amplitude variation. For a fixed bias current, the line spacing （or repetition frequency） of the MFCs can be easily tuned by varying the feedback delay time and the feedback strength, and the tuning range of the line spacing increases with the increase in the bias current. The linewidth of the MFCs is sensitive to the variation of the feedback delay time and the feedback strength, and a linewidth of tens of KHz can be achieved through finely adjusting the feedback delay time and the feedback strength. In addition, mappings of amplitude variation, repetition frequency, and linewidth of MFCs in the parameter space of the feedback delay time and the feedback strength are presented.

Precise determination of characteristic laser frequencies by an Er-doped fiber optical frequency comb

Femtosecond optical frequency combs correlate the microwave and optical frequencies accurately and coherently.Therefore,any optical frequency in visible to near-infrared region can be directly traced to a microwave frequency.As a result,the length unit“meter”is directly related to the time unit“second”.This paper validates the capability of the national wavelength standards based on a home-made Er-doped fiber femtosecond optical frequency comb to measure the laser frequencies ranging from visible to near-infrared region.Optical frequency conversion in the femtosecond optical frequency comb is achieved by combining spectral broadening in a highly nonlinear fiber with a single-point frequencydoubling scheme.The signal-to-noise ratio of the beat notes between the femtosecond optical frequency comb and the lasers at 633,698,729,780,1064,and 1542 nm is better than 30 d B.The frequency instability of the above lasers is evaluated by using a hydrogen clock signal with a instability of better than 1×10^(-13)at 1-s averaging time.The measurement is further validated by measuring the absolute optical frequency of an iodine-stabilized 532-nm laser and an acetylenestabilized 1542-nm laser.The results are within the uncertainty range of the international recommended values.Our results demonstrate the accurate optical frequency measurement of lasers at different frequencies using the femtosecond optical frequency comb,which is not only important for the precise and accurate traceability and calibration of the laser frequencies,but also provides technical support for establishing the national wavelength standards based on the femtosecond optical frequency comb.

Plasma Uniformity in a Dual Frequency Capacitively Coupled Plasma Reactor Measured by Optical Emission Spectroscopy

Local measurement of plasma radial uniformity was performed in a dual frequency capacitively coupled argon plasma （DF-CCP） reactor using an optical probe. The optical probe collects the light emission from a small separate volume in plasma, thus enabling to diagnose the plasma uniformity for different experimental parameters. Both the gas pressure and the low- frequency （LF） power have apparent effects on the radial uniformity of argon plasma. With the increase in either pressure or LF power, the emission profiles changed from a bell-shaped to a double-peak distribution. The influence of a fused-silica ring around the electrodes on the plasma uniformity was also studied using the optical probe. Possible reasons that result in nonuniform plasmas in our experiments are discussed.

Optical temperature sensor based on up-conversion fluorescence emission in Yb^(3+):Er^(3+) co-doped ceramics glass

yb^3＋：Er^3＋ co-doped oxy-fluoride ceramics glass has been prepared. The mechanism of up-conversion emissions about Er^3＋ was discussed, and the temperature properties of green up-conversion fluorescence between 303 and 823 K were investigated. The results show that the sensitivity of this sample reaches its maximum value, about 0.0047 K^-1, when the temperature is 383 K, indicating that this kind of sample can be used as high temperature and high sensitivity optical temperature sensor.

First Evaluation and Frequency Measurement of the Strontium Optical Lattice Clock at NIM

An optical lattice clock based on 87Sr is built at National Institute of Metrology （NIM） of China. The systematic frequency shifts of the clock are evaluated with a total uncertainty of 2.3×10-16. To measure its absolute frequency with respect to NIM＇s cesium fountain clock NIM5, the frequency of a flywheel H-maser of NIM5 is transferred to the Sr laboratory through a 50-kin-long fiber. reference frequency of this H-maser, is used for the optical this Sr clock is measured to be 429228004229873.7（1.4）Hz. A fiber optical frequency comb, phase-locked to the frequency measurement. The absolute frequency of

Two-dimensional distributed strain sensing with an Archimedean spiral arrangement in optical frequency domain reflectometry

We demonstrate a distributed two-dimensional(2D)strain-sensing system in optical frequency domain reflectometry(OFDR)with an Archimedean spiral arrangement of the sensing fiber.The Archimedean spiral describes a simple relationship between the radial radius and polar angle,such that each circle(the polar angle from0 to 2π)can sense the 2D strain in all directions.The strain between two adjacent circles can also be easily obtained because an Archimedean spiral facilitates sensing of every angle covering the full 2D range.Based on the mathematical relation of Archimedean spirals,we deduce the relationship between the one-dimensional position of the sensing fiber and 2D distribution in polar coordinates.The results of the experiment show that an Archimedean spiral arrangement system can achieve 2D strain sensing with different strain load angles.

A diode laser spectrometer at 634 nm and absolute frequency measurements using optical frequency comb

This paper reports that two identical external-cavity-diode-laser （ECDL） based spectrometers are constructed at 634nm referencing on the hyperfine B-X transition R（80）8-4 of 127I2. The lasers are stabilized on the Doppler-free absorption signals using the third-harmonic detection technique. The instability of the stabilized laser is measured to be 2.8 × 10^-12 （after 1000 s） by counting the beat note between the two lasers. The absolute optical frequency of the transition is, for the first time, determined to be 472851936189.5 kHz by using an optical frequency comb referenced on the microwave caesium atomic clock. The uncertainty of the measurement is less than 4.9 kHz.

An Yb-fiber frequency comb phase-locked to microwave standard and optical reference

We present a fully stabilized Yb-fiber frequency comb locked to a microwave standard and an optical reference separately. The carrier-envelope offset frequency is generated by a standard f–2f interferometer with 40 dB signal-tonoise ratio. The offset frequency and the repetition rate are stabilized simultaneously to the radio frequency reference for more than 30 hours, and the fractional Allan deviation of the comb is the same as the microwave standard of 10^(-12) at 1 s.Alternatively, the comb is locked to an ultra-stable optical reference at 972 nm using an intracavity electro-optic modulator,exhibiting a residual integrated phase noise of 458 mrad(1 Hz–10 MHz) and an in-loop tracking stability of 1.77× 10^(-18) at 1 s, which is significantly raised by six orders comparing to the case locked to the microwave frequency standard.

Eigenvalue spectrum analysis for temporal signals of Kerr optical frequency combs based on nonlinear Fourier transform

Based on the nonlinear Schr?dinger equation(NLSE) with damping, detuning, and driving terms describing the evolution of signals in a Kerr microresonator, we apply periodic nonlinear Fourier transform(NFT) to the study of signals during the generation of the Kerr optical frequency combs(OFCs). We find that the signals in different states, including the Turing pattern, the chaos, the single soliton state, and the multi-solitons state, can be distinguished according to different distributions of the eigenvalue spectrum. Specially, the eigenvalue spectrum of the single soliton pulse is composed of a pair of conjugate symmetric discrete eigenvalues and the quasi-continuous eigenvalue spectrum with eye-like structure.Moreover, we have successfully demonstrated that the number of discrete eigenvalue pairs in the eigenvalue spectrum corresponds to the number of solitons formed in a round-trip time inside the Kerr microresonator. This work shows that some characteristics of the time-domain signal can be well reflected in the nonlinear domain.

Characteristic analysis of the optical delay in frequency response of resonant cavity enhanced (RCE) photodetectors

With consideration of the modulation frequency of the input lightwave itself, we present a new model to calculate the quantum efficiency of RCE p-i-n photodetectors （PD） by superimposition of multiple reflected lightwaves. For the first time, the optical delay, another important factor limiting the electrical bandwidth of RCE p-i-n PD excluding the transit time of the carriers and RCd response of the photodetector, is analyzed and discussed in detail. The optical delay dominates the bandwidth of RCE p-i-n PD when its active layer is thinner than several 10 nm. These three limiting factors must be considered exactly for design of ultra-high-speed RCE p-i-n PD.

Anisotropic optical feedback of single frequency intra-cavity He-Ne laser

This paper presents the anisotropic optical feedback of a single frequency intra-cavity He-Ne laser. A novel phenomenon was discovered that the laser output an elliptical polarized frequency instead of the initial linear polarized one. Two intensities with a phase difference were detected, both of which were modulated in the form of cosine wave and a fringe shift corresponds to a λ/2 movement of the feedback mirror. The phase difference can be continuously modulated by the wave plate in the external cavity. Frequency stabilization was used to stabilize the laser frequency so as to enlarge the measuring range and improve the measurement precision. This anisotropic optical feedback system offers a potential displacement measurement technology with the function of subdivision of λ/2 and in-time direction judgment. The three-mirror Fabry Perot cavity model is used to present the experimental results. Given the lack of need of lasing adjustment, this full intra-cavity laser can significantly improve the simplicity and stability of the optical feedback system.

Generation of Continuous-Wave 194 nm Laser for Mercury Ion Optical Frequency Standard

A 194-nm cw laser is an essential part in the mercury ion optical frequency standard. We report the generation of over 2mW continuous-wave radiation at 194nm in a beta barium borate crystal using a simple sum frequency mixing （SFM） system. One source beams at 718nm is resonantly enhanced with a cavity and the other at 266mn makes a single pass. Considering the walk-off effect in SFM, the source beam waists are designed to be elliptical, thus the conversion efficiency can be promoted. The 266-nm beam produced by frequency doubling of 532-nm laser is shaped close to the diffraction limit to achieve better mode matching.