Precision phase control of an ultrawide-bandwidth femtosecond laser: a network of ultrastable frequency marks across the visible spectrum

We demonstrate that the stability of the current optical frequency comb generated by a Kerr-lens mode-locked femtosecond laser is limited by the microwave reference used for phase locking the comb spacing. Hence we implement precision frequency/phase control of the entire comb to the fundamental and second-harmonic frequencies of a stable cw laser without any external microwave reference. The stability of a cw iodine-stabilized laser is transferred to millions of comb lines (with an instability of 3 x 10(-13)) covering more than one octave of the optical frequency spectrum. In addition, the mode spacing of the comb can be used as a stable microwave frequency derived directly from a stable optical oscillator.     

Tunable optical frequency comb with a crystalline whispering gallery mode resonator

We report on the experimental demonstration of a tunable monolithic optical frequency comb generator. The device is based on four-wave mixing in a crystalline calcium fluoride whispering gallery mode resonator. The frequency spacing of the comb is given by an integer number of the free spectral range of the resonator. We select the desired number by tuning the frequency of the pumping laser with respect to the corresponding resonator mode. We also observe a rich variety of optical combs and high-frequency hyperparametric oscillation, depending on the experimental conditions. A potential application of the comb for generating tunable narrow band frequency microwave signals is demonstrated.     

Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb

We demonstrate a great simplification in the long-standing problem of measuring optical frequencies in terms of the cesium primary standard. An air-silica microstructure optical fiber broadens the frequency comb of a femtosecond laser to span the optical octave from 1064 to 532 nm, enabling us to measure the 282 THz frequency of an iodine-stabilized Nd:YAG laser directly in terms of the microwave frequency that controls the comb spacing. Additional measurements of established optical frequencies at 633 and 778 nm using the same femtosecond comb confirm the accepted uncertainties for these standards.     

Widely tunable THz synthesizer

The generation of cw-THz radiation by photomixing is particularly suited to the high resolution spectroscopy of gases; nevertheless, until recently, it has suffered from a lack of frequency metrology. Frequency combs are a powerful tool that can transfer microwave frequency standards to optical frequencies and a single comb has permitted accurate (10⁻⁸) THz frequency synthesis with a limited tuning range. A THz synthesizer composed of three extended cavity laser diodes phase locked to a frequency comb has been constructed and its utility for high resolution gas phase spectroscopy demonstrated. The third laser diode allows a larger tuning range of up to 300 MHz to be achieved without the need for large frequency excursions, while the frequency comb provides a versatile link to be established from any traceable microwave frequency standard. The use of a single frequency comb as a reference for all of the cw-lasers eliminates the dependency of synthesized frequency on the carrier envelope offset frequency. This greatly simplifies the frequency comb stabilization requirements and leads to a reduced instrument complexity.     

Stabilization of femtosecond lasers for optical frequency metrology and direct optical to radio frequency synthesis

We have actively stabilized the comb of frequencies from a mode-locked femtosecond laser using a Fabry-Perot reference cavity. This technique offers the ability to synthesize a comb of highly stable radio frequencies directly from optical transitions. The measured fractional frequency instability of the components of the frequency comb relative to the reference cavity was <5x10(-13) in 0.1 sec. The variation of the optical mode spacing versus frequency of the reference cavity was also directly measured using this technique.     

1.6-W self-referenced frequency comb at 2.06 μm using a Ho:YLF multipass amplifier

A high-power optical frequency comb at 2.06 μm has been generated using a Ho:YLF multipass amplifier seeded by the long wavelength supercontinuum tail of an octave-spanning Er:fiber comb source. The Ho:YLF amplifier showed a net gain larger than 30 dB from 2048 to 2068 nm, allowing the generation of a 20 nm bandwidth comb with a mode spacing of 100 MHz and a power per mode ranging from 20 to 370 μW. In the time domain, the amplified comb corresponds to a pulse train with 1.6 W total power and 508 fs transform-limited pulse duration. Using a self-referencing f-2f interferometer and a phase-locking loop, spectral narrowing of the offset frequency down to less than 17 Hz has been achieved.     

Optical generation of a precise microwave frequency comb by harmonic frequency locking

A semiconductor laser under negative optoelectronic feedback is applied to the generation of a microwave frequency comb through the nonlinear dynamics. The laser system is operated in a harmonic frequency-locked pulsing state, where its power spectrum is a microwave frequency comb that consists of multiples of a locking frequency. Every frequency component of the comb can be simultaneously stabilized by simply injecting an external microwave modulation at any component of the comb. This phenomenon can be viewed as a kind of microwave injection locking of the laser dynamics.     

光梳主动滤波放大实现锶原子光钟二级冷却光源

提出一种结合注入锁定技术的主动滤波放大方法,将光梳直接注入锁定至光栅外腔半导体激光器,产生窄线宽激光光源,该光源可以用于锶原子光钟二级冷却.实验中,将中心波长为689 nm,带宽为10 nm的光梳种子光源注入689 nm光栅式外腔半导体激光器,通过半导体增益光谱与半导体光栅外腔,从飞秒光梳的多个纵模梳齿中挑选出一个纵模模式来进行增益放大,再通过模式竞争,实现单纵模连续光输出;同时,光梳的重复频率锁定在线宽为赫兹量级的698 nm超稳激光光源上,因此,注入锁定后输出的窄线宽激光也继承了超稳激光光源的光谱特性.利用得到的输出功率为12 mW的689 nm窄线宽激光光源实现了88Sr原子光钟的二级冷却过程,最终获得温度为3μK,原子数约为5×10~6的冷原子团.该方法可拓展至原子光钟其他光源的获得,从而实现原子光钟的集成化和小型化.     

Optical frequency counter based on two mode-locked fiber laser combs

This work demonstrates a semi-automatic optical frequency counter based on two mode-locked fiber laser combs. The mode number of the comb line involved in the optical frequency measurement is determined by operating the two laser combs at three different repetition rates, with two of them similar enough to have the same mode number of the beating comb lines. The determination of the mode number is independent of the frequency fluctuation of the laser under measurement. The whole measurement process was automated, except for the frequency stabilization of the laser combs and the optimization of the beat signal–to–noise ratio.     

光学频率标准与光钟的实现

综述了时间频率标准的发展过程.对构成光学频率标准的四个要素,即激光冷却、激光稳频、离子捕陷和光学频率梳进行了系统的介绍.详细描述了光钟的原理与系统构成,并对光学频率标准与光钟的应用前景进行了展望.     

光学频率梳空间光谱分辨精度研究

光学频率梳的高精度光谱整形在微波光子学、光谱学及通信光学等学科领域具有广泛应用. 为了描述和评价光学频率梳光谱整形系统的光谱分辨精度, 使用光线追迹的方法对单光栅、平行光栅对、单光栅透镜变换和反平行光栅 对透镜变换四种结构的空间色散能力进行了理论建模和分析, 得到了输出面上不同波长的光斑间距和光斑大小, 设立判据得到系统的光谱空间分离能力. 计算结果表明, 使用后面两种色散结构更容易实现高精度光谱分离和整形; 波长较长、纵模间距较大、光斑尺寸较大的光学频率梳更适合作为光谱整形系统的光源; 光栅刻线密度高、入射角小、多次通过色散系统有利于得到更高的光谱分辨精度. 本文的分析和计算过程具有普遍适用性, 对基于光学频率梳的高精度光谱整形系统的实验和评价具有指导意义.     

基于双环混频光电振荡器的可调谐微波频率梳产生

随着无线通信的速率提升和微蜂窝趋势,光载微波技术已经成为重要的发展趋势,而光生多载波系统是光载微波的最重要的技术之一.本文提出了一种基于双环混频光电振荡器（OEO）的可调谐光载微波频率梳产生方案,可同时实现多频段微波信号产生,从而高效低成本地为无线节点提供光生微波载波.方案采用混频双环OEO系统,通过工作在增益开关状态的直调激光器,利用其非线性动态特性产生多频率光载微波频率梳信号,并采用双路微波滤波器分别滤出两个相邻频率的微波信号,并利用二者的差频反馈注入直调激光器构成光电谐振.利用偏振双环结构抑制长谐振腔引起的边模问题,提高了输出信号的噪声特性.经过实验分析,得到了低相噪的多路微波信号,并最终实现了间隔797.4 MHz的稳定的微波频率梳信号,一阶载波相位噪声低于-101.7 dBc/Hz@10 kHz,-115.2 dBc/Hz@50 kHz.因此该方案产生的光载微波频率梳信号具有低噪声的优点,适用于光载微波通信系统.     

Phase-locked, erbium-fiber-laser-based frequency comb in the near infrared

A phase-locked frequency comb in the near infrared is demonstrated with a mode-locked, erbium-doped, fiber laser whose output is amplified and spectrally broadened in dispersion-flattened, highly nonlinear optical fiber to span from 1100 to >2200 nm. The supercontinuum output comprises a frequency comb with a spacing set by the laser repetition rate and an offset by the carrier-envelope offset frequency, which is detected with the standard f-to-2f heterodyne technique. The comb spacing and offset frequency are phase locked to a stable rf signal with a fiber stretcher in the laser cavity and by control of the pump laser power, respectively. This infrared comb permits frequency metrology experiments in the near infrared in a compact, fiber-laser-based system.     

Einstein Lecture – Passion for precision

Optical frequency combs from mode‐locked femtosecond lasers have link optical and microwave frequencies in a single step, and they provide the long missing clockwork for optical atomic clocks. By extending the limits of time and frequency metrology, they enable new tests of fundamental physics laws. Precise comparisons of optical resonance frequencies of atomic hydrogen and other atoms with the microwave frequency of a cesium atomic clock are establishing sensitive limits for possible slow variations of fundamental constants. Optical high harmonic generation is extending frequency comb techniques into the extreme ultraviolet, opening a new spectral territory to precision laser spectroscopy. Frequency comb techniques are also providing a key to attosecond science by offering control of the electric field of ultrafast laser pulses. In our laboratories at Stanford and Garching, the development of new instruments and techniques for precision laser spectroscopy has long been motivated by the goal of ever higher resolution and measurement accuracy in optical spectroscopy of the simple hydrogen atom which permits unique confrontations between experiment and fundamental theory. This lecture recounts these adventures and the evolution of laser frequency comb techniques from my personal perspective.     

Ultra-stable microwave generation with a diode-pumped solid-state laser in the 1.5-μm range

We demonstrate the first ultra-stable microwave generation based on a 1.5-μm diode-pumped solid-state laser (DPSSL) frequency comb. Our system relies on optical-to-microwave frequency division from a planar-waveguide external cavity laser referenced to an ultra-stable Fabry–Perot cavity. The evaluation of the microwave signal at ~10 GHz uses the transportable ultra-low-instability signal source ULISS^®, which employs a cryo-cooled sapphire oscillator. With the DPSSL comb, we measured ?125 dBc/Hz phase noise at 1 kHz offset frequency, likely limited by the photo-detection shot-noise or by the noise floor of the reference cryo-cooled sapphire oscillator. For comparison, we also generated low-noise microwave using a commercial Er:fiber comb stabilized in similar conditions and observed >20 dB lower phase noise in the microwave generated from the DPSSL comb. Our results confirm the high potential of the DPSSL technology for low-noise comb applications.     

Demonstration of a HeNe/CH4-based optical molecular clock

We implement a simple optical clock based on the F2(2) [P(7), v3] optical transition in methane. A single femtosecond laser's frequency comb undergoes difference frequency generation to provide an IR comb at 3.39 microm with a null carrier-envelope offset. This IR comb provides a phase-coherent link between the 88-THz optical reference and the rf repetition rate. Comparison of the repetition rate signal with a second femtosecond comb stabilized to molecular iodine shows an instability of 1.2 x 10(-13) at 1 s, limited by microwave detection of the repetition rates. The single-sideband phase noise of the microwave signal, normalized to a carrier frequency of 1 GHz, is below -93 dBc/Hz at 1-Hz offset.     

Photonic generation of high quality frequency-tunable millimeter wave and terahertz wave

A scheme for the photonic generation of frequency-tunable millimeter wave and terahertz wave signals based on a highly flat optical frequency comb is proposed and demonstrated experimentally.The frequency comb is generated using two cascaded phase modulators(PMs)and an electro-absorption modulator(EAM).The frequency comb covers a 440-GHz frequency range,with 40-GHz comb spacing and less than 2-dB amplitude variation.By filtering out two of the comb lines with 50 dB out of the band suppression ratio,high frequency-purity and low phase noise millimeter wave or terahertz wave signals are successfully generated,with frequencies ranging from 40 to 440 GHz.     

A Reconfigurable Microwave Photonic Channelized Receiver Based on Dense Wavelength Division Multiplexing Using an Optical Comb

A photonic approach to implementing a microwave channelized receiver based on dense wavelength division multiplexing using an optical comb is proposed. In the approach, a flat optical comb with 11 comb lines is generated using two cascaded Mach-Zehnder modulators. Frequency analysis of a microwave signal with multiple-frequency components is realized by using the optical comb together with an optical etalon with a periodic transfer function, a wavelength division multiplexer (WDM) and a photodetector array. The system is investigated numerically. Frequency measurement of a multi-frequency signal with a measurement range from 0.5-11.5 with an accuracy of ± 0.5 GHz is achieved. The reconfigurability of the system realized by tuning the comb-line spacing and the peak positions of the etalon is also evaluated. The improvement of the dynamic range of the system using an optimized periodic filter is also discussed.     

Frequency comb generation using femtosecond pulses and cross-phase modulation in optical fiber at arbitrary center frequencies

A technique is presented for generating optical frequency combs centered at arbitrary wavelengths by use of cross-phase modulation (XPM) between a femtosecond pulse train and a cw laser beam by copropagating these signals through an optical fiber. We report results from use of this method to place a 90-MHz frequency comb on an iodine-stabilized Nd:YAG laser at 1064 nm and on a frequency-doubled Nd:YVO(4) laser at 532 nm. XPM is verified to be the comb-generating process, and the width of the frequency comb is measured and compared with theory. The spacing of the frequency comb is compared with the femtosecond source, and a frequency measurement with this comb is demonstrated.     

Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation

The shortest pulses periodically emitted directly from a mode-locked Ti:sapphire laser are approaching the two-optical-cycle range. In this region, the phase of the optical carrier with respect to the pulse envelope becomes important in nonlinear optical processes such as high-harmonic generation. Because there are no locking mechanisms between envelope and carrier inside a laser, their relative phase offset experiences random fluctuations. Here, we propose several novel methods to measure and to stabilize this carrier-envelope offset (CEO) phase with sub-femtosecond uncertainty. The stabilization methods are an important prerequisite for attosecond pulse generation schemes. Short and highly periodic pulses of a two-cycle laser correspond to an extremely wide frequency comb of equally spaced lines, which can be used for absolute frequency measurements. Using the proposed phase-measurement methods, it will be possible to phase-coherently link any unknown optical frequency within the comb spectrum to a primary microwave standard. Experimental studies using a sub-6-fs Ti:sapphire laser suggesting the feasibility of carrier-envelope phase control are presented. Received: 19 August 1999 / Published online: 8 September 1999