Optical frequency combs [1,2,3] provide equidistant frequency markers in the infrared, visible and ultra-violet [4,5] and can link an unknown optical frequency to a radio or microwave frequency reference [6,7]. Since their inception frequency combs have triggered major advances in optical frequency metrology and precision measurements [6,7] and in applications such as broadband laser-based gas sensing [8] and molecular fingerprinting [9]. Early work generated frequency combs by intra-cavity phase modulation [10,11], while to date frequency combs are generated utilizing the comb-like mode structure of mode-locked lasers, whose repetition rate and carrier envelope phase can be stabilized [12]. Here, we report an entirely novel approach in which equally spaced frequency markers are generated from a continuous wave (CW) pump laser of a known frequency interacting with the modes of a monolithic high-Q microresonator [13] via the Kerr nonlinearity [14,15]. The intrinsically broadband nature of parametric gain enables the generation of discrete comb modes over a 500 nm wide span (≈ 70 THz) around 1550 nm without relying on any external spectral broadening. Optical-heterodyne-based measurements reveal that cascaded parametric interactions give rise to an optical frequency comb, overcoming passive cavity dispersion. The uniformity of the mode spacing has been verified to within a relative experimental precision of 7.3×10 −18 . In contrast to femtosecond mode-locked lasers[16] the present work represents an enabling step towards a monolithic optical frequency comb generator allowing significant reduction in size, cost and power consumption. Moreover, the present approach can operate at previously unattainable repetition rates [17] exceeding 100 GHz which are useful in applications where the access to individual comb modes is required, such as optical waveform synthesis [18], high capacity telecommunications or astrophysical spectrometer calibration [19].Optical microcavities [20] are owing to their long temporal and small spatial light confinement ideally suited for nonlinear frequency conversion, which has led to a dramatic improvement in the threshold of nonlinear optical light conversion [21]. In contrast to stimulated gain, parametric frequency conversion [22] does not involve coupling to a dissipative reservoir, is broadband as it does not rely on atomic or molecular resonances and constitutes a phase sensitive amplification process, making it uniquely suited for tunable frequency conversion. In the case of a material with inversion symmetry -such as silica -the non linear optical effects are dominated by the third order non linearity. The process is based on four-wave mixing among two pump photons (frequency ν P ) with a signal (ν S ) and idler photon (ν I ) and results in the emergence of (phase coherent) signal and idler sidebands from the vacuum fluctuations at the expense of the pump field (cf. Fig.1). The observation of parametric interactions requires two conditions to be satisfied. First momentum conservation...

The series of precisely spaced, sharp spectral lines that form an optical frequency comb is enabling unprecedented measurement capabilities and new applications in a wide range of topics that include precision spectroscopy, atomic clocks, ultracold gases, and molecular fingerprinting. A new optical frequency comb generation principle has emerged that uses parametric frequency conversion in high resonance quality factor (Q) microresonators. This approach provides access to high repetition rates in the range of 10 to 1000 gigahertz through compact, chip-scale integration, permitting an increased number of comb applications, such as in astronomy, microwave photonics, or telecommunications. We review this emerging area and discuss opportunities that it presents for novel technologies as well as for fundamental science.

Extremely narrow optical resonances in cold atoms or single trapped ions can be measured with high resolution. A laser locked to such a narrow optical resonance could serve as a highly stable oscillator for an all-optical atomic clock. However, until recently there was no reliable clockwork mechanism that could count optical frequencies of hundreds of terahertz. Techniques using femtosecond-laser frequency combs, developed within the past few years, have solved this problem. The ability to count optical oscillations of more than 1015 cycles per second facilitates high-precision optical spectroscopy, and has led to the construction of an all-optical atomic clock that is expected eventually to outperform today's state-of-the-art caesium clocks.

Comprehensive knowledge of the dynamic behaviour of electrons in condensed-matter systems is pertinent to the development of many modern technologies, such as semiconductor and molecular electronics, optoelectronics, information processing and photovoltaics. Yet it remains challenging to probe electronic processes, many of which take place in the attosecond (1 as = 10(-18) s) regime. In contrast, atomic motion occurs on the femtosecond (1 fs = 10(-15) s) timescale and has been mapped in solids in real time using femtosecond X-ray sources. Here we extend the attosecond techniques previously used to study isolated atoms in the gas phase to observe electron motion in condensed-matter systems and on surfaces in real time. We demonstrate our ability to obtain direct time-domain access to charge dynamics with attosecond resolution by probing photoelectron emission from single-crystal tungsten. Our data reveal a delay of approximately 100 attoseconds between the emission of photoelectrons that originate from localized core states of the metal, and those that are freed from delocalized conduction-band states. These results illustrate that attosecond metrology constitutes a powerful tool for exploring not only gas-phase systems, but also fundamental electronic processes occurring on the attosecond timescale in condensed-matter systems and on surfaces.

The amplitude and frequency of laser light can be routinely measured and controlled on a femtosecond (10(-15) s) timescale. However, in pulses comprising just a few wave cycles, the amplitude envelope and carrier frequency are not sufficient to characterize and control laser radiation, because evolution of the light field is also influenced by a shift of the carrier wave with respect to the pulse peak. This so-called carrier-envelope phase has been predicted and observed to affect strong-field phenomena, but random shot-to-shot shifts have prevented the reproducible guiding of atomic processes using the electric field of light. Here we report the generation of intense, few-cycle laser pulses with a stable carrier envelope phase that permit the triggering and steering of microscopic motion with an ultimate precision limited only by quantum mechanical uncertainty. Using these reproducible light waveforms, we create light-induced atomic currents in ionized matter; the motion of the electronic wave packets can be controlled on timescales shorter than 250 attoseconds (250 x 10(-18) s). This enables us to control the attosecond temporal structure of coherent soft X-ray emission produced by the atomic currents--these X-ray photons provide a sensitive and intuitive tool for determining the carrier-envelope phase.

We have used the frequency comb generated by a femtosecond mode-locked laser and broadened to more than an optical octave in a photonic crystal fiber to realize a frequency chain that links a 10 MHz radio frequency reference phase-coherently in one step to the optical region. By comparison with a similar frequency chain we set an upper limit for the uncertainty of this new approach to 5. 1x10(-16). This opens the door for measurement and synthesis of virtually any optical frequency and is ready to revolutionize frequency metrology.

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.

Optical frequency combs allow for the precise measurement of optical frequencies and are used in a growing number of applications. The new class of Kerr-frequency comb sources, based on parametric frequency conversion in optical microresonators, can complement conventional systems in applications requiring high repetition rates such as direct comb spectroscopy, spectrometer calibration, arbitrary optical waveform generation and advanced telecommunications. However, a severe limitation in experiments working towards practical systems is phase noise, observed in the form of linewidth broadening, multiple repetition-rate beat notes and loss of temporal coherence. These phenomena are not explained by the current theory of Kerr comb formation, yet understanding this is crucial to the maturation of Kerr comb technology. Here, based on observations in crystalline MgF 2 and planar Si 3 N 4 microresonators, we reveal the universal, platformindependent dynamics of Kerr comb formation, allowing the explanation of a wide range of phenomena not previously understood, as well as identifying the condition for, and transition to, low-phase-noise performance.O ptical frequency combs [1][2][3][4] have revolutionized the field of frequency metrology and spectroscopy and are enabling components in a range of applications 5 . Recently, a novel class of frequency comb generators has been discovered 6 by coupling a continuous-wave (c.w.) laser to a high-finesse fused silica microcavity, where the Kerr nonlinearity enables (cascaded) fourwave-mixing (FWM), resulting in an optical frequency comb. These Kerr combs could complement conventional frequency combs in applications where high power per comb line (typically .100 mW) and high repetition rate (.10 GHz spacing between the comb lines) are desirable 7 , such as in astronomical spectrometer calibration [8][9][10] , direct comb spectroscopy 11 , arbitrary optical waveform generation 12,13 and advanced telecommunications. The creation of Kerr combs using microresonators has been demonstrated in crystalline CaF 2 (refs 14,15) and MgF 2 (refs 16-18) resonators, fused-silica microspheres 19 , planar high-index silica 20 and Si 3 N 4 ring resonators 21,22 , and compact fibre cavities 23 . Over recent years, a significant advance in Kerr comb technology has been achieved by demonstrating a single and well-defined radiofrequency (RF) beat note between adjacent comb lines (corresponding to the equidistant comb spacing and required for stabilizing the comb) 6,14,24 , a fully phase-stabilized Kerr comb 24 , the generation of octave-spanning spectra (required for self-referencing the comb using the f-2f scheme) 25,26 , the detection and shaping of pulses 13 , and extension of spectral coverage towards the visible 27 and midinfrared spectral regimes 18 . In addition to these experimental advances, theoretical work 28,29 has also enabled an explanation of the power distribution of Kerr combs, particularly the first comb modes appearing not necessarily adjacent to the pump. Despite these advances,...