全固态飞秒光学频率梳研究进展及展望

自1999年至今,光学频率梳（Optical Frequency Comb,OFC）经历了二十多年的快速发展。基于飞秒激光的光学频率梳在频率计量学、超快光谱学、光学频率标准、阿秒脉冲的产生、多脉冲时域合成等众多前沿研究领域中发挥了不可替代的作用。特别是继飞秒钛宝石激光频率梳、飞秒光纤激光频率梳之后,基于二极管激光直接泵浦的全固态飞秒激光频率梳由于兼具钛宝石激光噪声低、重复频率高,光纤激光结构紧凑、电光效率高的共同优势,引起了许多研究组的兴趣,并取得系列有意义的进展。本文综述了全固态光学频率梳的发展和已取得的典型应用,并结合笔者所在课题组取得的研究成果,对全固态光学频率梳未来的发展方向进行展望,为促进全固态飞秒锁模振荡器的发展提供借鉴。     

Microwave interferometry: application to precision measurements and noise reduction techniques

A concept of interferometric measurements has been applied to the development of ultra-sensitive microwave noise measurement systems. These systems are capable of reaching a noise performance limited only by the thermal fluctuations in their lossy components. The noise floor of a real time microwave measurement system has been measured to be equal to -193 dBc/Hz at Fourier frequencies above 1 kHz. This performance is 40 dB better than that of conventional systems and has allowed the first experimental evidence of the intrinsic phase fluctuations in microwave isolators and circulators. Microwave frequency discriminators with interferometric signal processing have proved to be extremely effective for measuring and cancelling the phase noise in oscillators. This technique has allowed the design of X-band microwave oscillators with a phase noise spectral density of order -150 dBc/Hz at 1 kHz Fourier frequency, without the use of cryogenics. Another possible application of the interferometric noise measurements systems include “flicker noise-free” microwave amplifiers and advanced two oscillator noise measurement systems     

用差频腔产生覆盖633nm光谱的飞秒激光频率梳

飞秒激光频率梳被认为是连接光频和无线电频率的一个超精密齿轮,比较了自参考法锁相稳频飞秒激光频率梳和差频法单块结构飞秒激光频率梳的特点,前者光谱范围宽,但稳定性较差;后者稳定性较好,但光谱范围较窄。在差频腔单块结构飞秒激光频率梳的基础上,通过使用腔外压缩色散补偿方式压缩激光脉冲宽度,然后重新注入光子晶体光纤进行光谱扩展,获得了覆盖633nm波长的更宽的光谱范围,为633nm波长激光频率测量创造了条件。     

Secondary standard for PM and AM noise at 5, 10, and 100 MHz

A practical implementation of a portable secondary standard for phase modulation (PM) and amplitude modulation (AM) noise at 5, 10, and 100 MHz is described. The accuracy of the standard for both PM and AM noise is +0.14 dB, and the temperature coefficient is less than 0.02 dB/K. The noise floor S_φ (10 kHz) of the standard for PM noise measurements is less than -190 dBC relative to 1 rad²/Hz at 5, 10, and 100 MHz. The noise floor for AM measurements depends on the configuration. A calibrated level of PM and AM noise of approximately -130±0.2 dB relative to 1 rad² /Hz (for Fourier frequencies from approximately 1 Hz to 10% of the carrier frequency) is used to evaluate the accuracy versus Fourier frequency. Similar PM/AM noise standards are under test at 10 GHz. This new standard can also be used as an alternative to the normal method of calibrating the conversion sensitivity of the PM/AM detector for PM/AM measurements. Some types of time-domain measurement equipment can also be calibrated     

1/f frequency noise of 2-GHZ high-Q thin-film sapphire resonators

We present experimental results on intrinsic 1/f frequency modulation (FM) noise in high-overtone thin-film sapphire resonators that operate at 2 GHz. The resonators exhibit several high-Q resonant modes approximately 100 kHz apart, which repeat every 13 MHz. A loaded Q of approximately 20000 was estimated from the phase response. The results show that the FM noise of the resonators varied between S_y (10 Hz)=-202 dB relative (rel) to 1/Hz and -210 dB rel to 1/Hz. The equivalent phase modulation (PM) noise of an oscillator using these resonators (assuming a noiseless amplifier) would range from L(10 Hz)=-39 to -47 dBc/Hz     

Optical frequency standards and measurement

This paper celebrates the progress in optical frequency standards and measurement, won by the 40 years of dedicated work of world-wide teams working in frequency standards and frequency measurement. Amazingly, after this time interval, the field is now simply exploding with new measurements and major advances of convenience and precision, with the best fractional frequency stability and potential frequency accuracy now being offered by optical systems. The new "magic" technology underlying the RF/optical connection is the capability of using femtosecond (fs) laser pulses to produce optical pulses so short their Fourier spectrum covers an octave bandwidth in the visible. These "white light" pulses are repeated at stable rates (/spl sim/100 MHz to 1 GHz, set by design), leading to an optical "comb" of frequencies with excellent phase coherence and stability and containing some millions of stable coherent optical frequencies. Optical-heterodyned differences between comb lines provides a frequency-related RF or microwave output with remarkably low added phase noise, such that in an optically-based atomic clock, the phase noise of the standards-grade microwave frequency reference dominates over that of optical reference and the fs "gear-box".     

Phase noise performance of microwave analog frequency dividers: application to the characterization of oscillators up to the millimeter-wave range

The phase noise performance of two different microwave analog frequency dividers is characterized and compared with the values obtained using simple theories of noise in injection-locked systems. The direct measurement of the divider noise with a low phase noise synthesizer is not accurate enough, and the residual noise technique is used. The noise levels observed using this technique, between -120 and -155 dBc/Hz at a 10 kHz offset frequency, demonstrate that this divider noise is much lower than the phase noise of most microwave free running oscillators, even if this noise is still high with respect to the residual noise of amplifiers realized with the same active devices. The down conversion of microwave sources up to 40 GHz, is proposed as an application example.     

Noise properties of microwave signals synthesized with femtosecond lasers

We discuss various aspects of high resolution measurements of phase fluctuations at microwave frequencies. This includes methods to achieve thermal noise limited sensitivity, along with the improved immunity to oscillator amplitude noise. A few prototype measurement systems were developed to measure phase fluctuations of microwave signals extracted from the optical pulse trains generated by femtosecond lasers. This enabled first reliable measurements of the excess phase noise associated with optical-to-microwave frequency division. The spectral density of the excess phase noise was found to be -140 dBc/Hz at 100 Hz offset from the 10 GHz carrier which was almost 40 dB better than that of a high quality microwave synthesizer.     

Absolute frequency stability of a diode-laser-pumped Nd:YAG laser stabilized to a high-finesse optical cavity

We report the frequency stabilization of a diode-laser-pumped monolithic ring Nd:YAG laser locked to a high-finesse optical cavity. With an independent cavity as a frequency discriminator, the absolute frequency noise was measured to be as low as 2 × 10(-2) Hz/Hz(1/2) at the Fourier frequency of approximately 3 kHz. We also measured the heterodyne beat note between two lasers locked to the independent cavities. The beat linewidth is narrower than 30 Hz and the minimum root Allan variance is approximately 6 × 10(-14).     

Characterizing a fiber-based frequency comb with electro-optic modulator

We report on the characterization of a commercial- core fiber-based frequency comb equipped with an intracavity free-space electro-optic modulator (EOM). We investigate the relationship between the noise of the pump diode and the laser relative intensity noise (RIN) and demonstrate the use of a low-noise current supply to substantially reduce the laser RIN. By measuring several critical transfer functions, we evaluate the potential of the EOM for comb repetition rate stabilization. We also evaluate the coupling to other relevant parameters of the comb. From these measurements, we infer the capabilities of the femtosecond laser comb to generate very-low-phase-noise microwave signals when phase-locked to a high-spectral-purity ultra-stable laser.     

Low-phase-noise frequency synthesizer for the trapped atom clock on a chip

We report on the realization of a 6.834-GHz synthesis chain for the trapped atom clock on a chip (TACC) that is being developed at LNE-SYRTE. The chain is based on the frequency multiplication of a 100-MHz reference signal to obtain a signal at 6.4 GHz. It uses a comb generator based on a monolithic GaAs nonlinear transmission line. This is a novelty in the fabrication of high-stability microwave synthesizers. Measurements give a low flicker phase noise of -85 dBrad²/Hz at 1-Hz offset frequency and a white phase noise floor < -115 dBrad²/Hz. Based on these results, we estimate that the performance of the synthesizer is at least one order of magnitude better than the stability goal of TACC. This ensures that the synthesizer will not be limiting the clock performance.     

High capacity optical beam forming for phased arrays with fiber gratings and frequency conversion for beat noise control

A new wavelength division multiplexing grating-based beam-forming architecture for phased arrays that can achieve the minimum possible number of optical interconnects is presented. A reduction in interconnect hardware of 99.6% is obtained for a 512-beam array, which is, as far as we know, the lowest number of interconnects reported to date. Analysis of the ultimate beam capacity limit of the beam former shows that the beat noise interference limitation is the most important factor. We present a new hybrid frequency-converting optical beam former that removes the fundamental beat noise limitation. This frequency downconverts the rf signal to an intermediate frequency before performing the true-time-delay equalization in the optical domain. The resulting advantage of reduced optical bandwidth per channel enables more wavelengths to be used for a given wavelength span, resulting in an increased beam capacity. A greater than sevenfold increase in beam capacity is demonstrated through the use of the frequency conversion technique, with 960 beams synthesized at 12.4 GHz, showing a 99.8% reduction in required interconnects.     

Residual phase noise measurements of VHF, UHF, and microwavecomponents

The results of residual phase noise measurements on a number of VHF, UHF, and microwave amplifiers, both silicon (Si) bipolar junction transistor (BJT) and gallium arsenide (GaAs) field effect transistor (FET) based, electronic phase shifters, frequency dividers and multipliers, etc., which are commonly used in a wide variety of frequency source and synthesizer applications are presented. The measurement technique has also been used to evaluate feedback oscillator components, such as the loop and buffer amplifiers, which can play important roles in determining an oscillator's output phase noise spectrum (often in very subtle ways). While some information has previously been published related to component residual phase noise properties, it generally focused on the flicker noise levels of the devices under test, for carrier offset frequencies less than 10 kHz. The work reported herein makes use of an extremely low noise, 500 MHz surface acoustic wave resonator oscillator (SAWRO) test source for residual phase noise measurements, both close-to-and far-from-the-carrier. Using this SAWRO-based test source at 500 MHz, we have been able to achieve a measurement system phase noise floor of -184 dBc/Hz, or better, for carrier offset frequencies greater than 10 kHz, and a system flicker phase noise floor of -150 dBc/Hz, or better, at 1 Hz carrier offset. The paper discusses the results of detailed residual phase noise measurements performed on a number of components using this overall system configuration. Several interesting observations related to the residual phase noise properties of moderate to high power RF amplifiers, i.e., amplifiers with 1 dB gain compression points in the range of +20 to +33 dBm, are highlighted     

Dual-Comb Ranging

Absolute distance measurement is a fundamental technique in mobile and large-scale dimensional metrology. Dual-comb ranging is emerging as a powerful tool that exploits phase resolution and frequency accuracy for high-precision and fast-rate distance measurement. Using two coherent frequency combs, dual-comb ranging allows time and phase response to be measured rapidly. It breaks through the limitations related to the responsive bandwidth, ambiguity range, and dynamic measurement characteristics of conventional ranging tools. This review introduces dual-comb ranging and summarizes the key techniques for realizing this ranging tool. As optical frequency comb technology progresses, dual-comb ranging shows promise for various professional applications.     

A new compact circuit-level model of semiconductor lasers: investigation of relative intensity noise and frequency noise spectra

We introduce a new compact noise equivalent circuit model of semiconductor lasers (SLs) from the rate equation including Langevin noise sources. The noise sources are described in terms of the spectral properties of the relative intensity noise (RIN) and frequency/phase noise (FN). Unlike the previous noise equivalent circuit models, which are based on two different DC and small-signal circuit models, using only a single circuit model, the static and dynamic responses and also the noise characteristics of SLs, can be investigated. We examine the validity of the presented noise circuit model by comparing the simulated results with the analytical and numerical results available in the literatures.     

OFDM削波噪声迭代消除算法

高峰均功率比(PAPR)的OFDM信号通过功率放大器的时候会产生非线性干扰,同时降低了放大器的工作效率。传统削波算法可以降低信号的PAPR,但是会带来较大的频谱扩展。作为一种新的削波算法,误差削波可以在降低OFDM信号PAPR值的同时不带来任何频谱扩展。但是这种削波会给信号带来更大的带内干扰噪声。提出了一种OFDM削波噪声迭代估计和消除算法,它能有效的消除由于误差削波带来的噪声。新方法通过建立削波噪声模型,在接收端根据该噪声模型用迭代的方法重新产生削波噪声。仿真结果表明,使用削波噪声消除算法后,使得系统的误码率性能接近未削波信号的水平。     

Study of the excess noise associated with demodulation of ultra-short infrared pulses

The demodulation of ultra-short light pulses with photodetectors is accompanied by excess phase noise at the pulse repetition rate and harmonics in the spectrum of the photocurrent. The major contribution to this noise is power fluctuations of the detected pulse train that, if not compensated for, can seriously limit the stability of frequency transfer from optical to microwave domain. By making use of an infrared femtosecond laser, we measured the spectral density of the excess phase noise, as well as power-to-phase conversion for different types of InGaAs photodetectors. Noise measurements were performed with a novel type of dual-channel readout system using a fiber coupled beam splitter. Strong suppression of the excess phase noise was observed in both channels of the measurement system when the average power of the femtosecond pulse train was stabilized. The results of this study are important for the development of low-noise microwave sources derived from optical "clocks" and optical frequency synthesis.     

Diode laser phase noise influence on the ultimate performance of its frequency stabilization to a Mach-Zehnder interferometer fringe

We report a detailed investigation on the effect of semiconductor laser phase noise on the achievable frequency stability when locked to a Mach-Zehnder interferometer fringe. We show that the modulation-demodulation operation produces in the presence of laser phase noise two kinds of excess noise, which could be much above the shot noise limit, namely: conversion noise (PM-to-AM) and intermodulation noise. We show that in typical stabilization conditions, the frequency stability of the locked laser is limited by the intermodulation excess noise. This effect, reported initially in the microwave domain, can be considerably reduced by a convenient choice of the modulation frequency. To our knowledge, this is the first time such a phenomenon is reported in the optical domain.     

Analysis of light noise sources in a recycled Michelson interferometer with Fabry-Perot arms

We present a method by which the effect of laser field variations on the signal output of an interferometric gravitational wave detector is rigorously determined. Using the Laser Interferometer Gravitational Wave Observatory (LIGO) optical configuration of a power recycled Michelson interferometer with Fabry-Perot arm cavities as an example, we calculate the excess noise after the input filter cavity (mode cleaner) and the dependence of the detector strain sensitivity on laser frequency and amplitude noise, radio frequency oscillator noise, and scattered-light phase noise. We find that noise on the radio frequency sidebands generally limits the detector's sensitivity.     

Doppler-free spectroscopy using a continuous-wave optical frequency synthesizer

A continuous-wave (cw) optical frequency synthesizer is demonstrated by using a monolithic-type cw optical parametric oscillator (cw-OPO) and an optical frequency comb. The cw-OPO is phase locked to an optical frequency comb that is phase locked to an atomic clock. The output frequency of the cw-OPO is frequency shifted with an electro-optic modulator, which makes it possible to tune the frequency continuously over 10 GHz. Furthermore, Doppler-free spectroscopy is performed using the optical frequency synthesizer for a cesium D1 line at 895 nm. The observed linewidth of 5 MHz is the natural linewidth of cesium. The center frequency of the line is consistent with a previous report.