Extreme Ultraviolet Frequency Combs Research Articles

Extreme-ultraviolet frequency combs for precision metrology and attosecond science

Femtosecond mode-locked lasers producing visible/infrared frequency combs have steadily advanced our understanding of fundamental processes in nature. For example, optical clocks employ frequency-comb techniques for the most precise measurements of time, permitting the search for minuscule drifts of natural constants. Furthermore, the generation of extreme-ultraviolet attosecond bursts synchronized to the electric field of visible/infrared femtosecond pulses affords real-time measurements of electron dynamics in matter. Cavity-enhanced high-order harmonic generation sources uniquely combine broadband vacuum- and extreme-ultraviolet spectral coverage with multimegahertz pulse repetition rates and coherence properties akin to those of frequency combs. Here we review the coming of age of this technology and its recent applications and prospects, including precision frequency-comb spectroscopy of electronic and potentially nuclear transitions, and low-space-charge attosecond-temporal-resolution photoelectron spectroscopy with nearly 100% temporal detection duty cycle. This Review covers the milestones for extreme-ultraviolet frequency combs and their applications. A future impact on the construction of nuclear-based optical clocks and multidimensional attosecond photoelectron spectroscopy of solids is remarked.

Extreme Ultraviolet Frequency Comb with More than 100 μW Average Power below 100nmSupported by the National Natural Science Foundation of China (Grant Nos. 11674356 and 11527807), and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB21010400).

Extreme ultraviolet (XUV) frequency comb is a powerful tool in precision measurement. It also brings many new opportunities to the field of strong field physics since high harmonic generation related phenomena can be studied with high repetition rate. We demonstrate the generation of an XUV frequency comb with the aid of intra-cavity high harmonic generation process. The setup is driven by a high power infrared frequency comb, and an average power of 4.5 kW is reached in the femtosecond enhancement cavity. With Xe gas as the working media, harmonics up to the 19th order are observed. Power measurement indicates that as much as 115.9 μW (1.3 mW) are generated at ∼94 nm (∼148 nm). The shortest wavelength we can reach is ∼55 nm. The coherence of the generated light is tested with an optical-heterodyne-based measurement of the third harmonic. The resulted line width is ∼3 Hz. In addition, with this system, we also observe a strong suppression of below threshold harmonics from O2 compared to that from Xe. These results suggest that the current system is ready for precision spectroscopic measurements with few-electron atomic and molecular systems in XUV region as well as the study of strong field physics with an unprecedented 100MHz repetition rate.

Tailoring the transverse mode of a high-finesse optical resonator with stepped mirrors

Enhancement cavities (ECs) seeded with femtosecond pulses have developed into the most powerful technique for high-order harmonic generation (HHG) at repetition rates in the tens of MHz. Here, we demonstrate the feasibility of controlling the phase front of the excited transverse eigenmode of a ring EC by using mirrors with stepped surface profiles, while maintaining the high finesse required to reach the peak intensities necessary for HHG. The two lobes of a mode of a 3.93 m long EC, seeded with a single-frequency laser, are delayed by 15.6 fs with respect to each other before a tight focus, and the delay is reversed after the focus. The tailored transverse mode exhibits an on-axis intensity maximum in the focus. Furthermore, the geometry is designed to generate a rotating wavefront in the focus when few-cycle pulses circulate in the EC. This paves the way to gating isolated attosecond pulses (IAPs) in a transverse manner (similarly to the attosecond lighthouse), heralding IAPs at repetition rates well into the multi-10 MHz range. In addition, these results promise high-efficiency harmonic output coupling from ECs in general, with an unparalleled power scalability. These prospects are expected to tremendously benefit photoelectron spectroscopy and extreme-ultraviolet frequency comb spectroscopy.

Extreme-ultraviolet frequency combs from high-order harmonic generation with few-cycle pulse trains

The spectrum of a high-repetition train of laser pulses consists of many equally spaced lines, forming an optical frequency comb which is useful for high-precision spectroscopy. By exposing atoms to a train of strong pulses, frequency combs reaching into the extreme ultraviolet may be produced via high-order harmonic generation. Here, we report a theoretical study of extreme-ultraviolet frequency-comb generation by trains of few-cycle pulses. We analyze the nontrivial comb structure arising from overlapping harmonic orders. The spacings of the comb lines and their dependence on the offset frequency of the incident pulse train are discussed.

Ultimate Limit in the Spectral Resolution of Extreme Ultraviolet Frequency Combs

We present the results of direct interferometric measurements on the pulse-to-pulse phase jitter of a metrological, fiber-based, infrared (IR) frequency comb. We show that the short-time evolution of such phase fluctuations, which cannot be actively controlled by any feedback system, imposes a stringent limit on the tooth linewidth of extreme ultraviolet (XUV) combs produced by high-order harmonic conversion, thus explaining the difference of 9 orders of magnitude between the coherence times of state-of-the-art IR and XUV frequency combs.

Cavity-enhanced field-free molecular alignment at a high repetition rate.

Extreme ultraviolet frequency combs are a versatile tool with applications including precision measurement, strong-field physics, and solid-state physics. Here we report on an application of extreme ultraviolet frequency combs and their driving lasers for studying strong-field effects in molecular systems. We perform field-free molecular alignment and high-order harmonic generation with aligned molecules in a gas jet at a repetition rate of 154 MHz using a high-powered optical frequency comb inside a femtosecond enhancement cavity. The cavity-enhanced system provides a means to reach suitable intensities to study field-free molecular alignment and enhance the observable effects of the molecule-field interaction. We observe modulations of the driving field, arising from the nature of impulsive stimulated Raman scattering responsible for coherent molecular rotations. We foresee the impact of this work on the study of molecule-based strong-field physics, with improved precision and a more fundamental understanding of the interaction effects on both the field and molecules.

Cavity-Enhanced High-Harmonic Generation with Spatially Tailored Driving Fields

We theoretically and experimentally investigate high-harmonic generation in a 78-MHz enhancement cavity with a transverse mode having on-axis intensity maxima at the focus and minima at an opening in the following mirror. We find that the conversion efficiency is comparable to that achievable with a Gaussian mode, whereas the output coupling efficiency can be significantly improved over any other demonstrated technique. This approach offers additional power scaling advantages and additional degrees of freedom in shaping the harmonic emission, paving the way to high-power extreme-ultraviolet frequency combs and the generation of multi-MHz repetition-rate-isolated attosecond pulses.

High Brightness XUV Frequency Combs via Intracavity High Harmonic Generation

We report the generation of high power extreme ultraviolet frequency combs at 154 MHz repetition rate. The XUV combs are characterized by conducting high resolution spectroscopy and observing the heterodyne beats between two independent systems

Extreme Nonlinear Optics in a Femtosecond Enhancement Cavity

Intrinsic to the process of high-order harmonic generation is the creation of plasma and the resulting spatiotemporal distortions of the driving laser pulse. Inside a high-finesse cavity where the driver pulse and gas medium are reused, this can lead to optical bistability of the cavity-plasma system, accumulated self-phase modulation of the intracavity pulse, and coupling to higher-order cavity modes. We present an experimental and theoretical study of these effects and discuss their implications for power scaling of intracavity high-order harmonic generation and extreme ultraviolet frequency combs.

Feasibility of coherent xuv spectroscopy on the1S−2Stransition in singly ionized helium

The $1S\text{\ensuremath{-}}2S$ two-photon transition in singly ionized helium is a highly interesting candidate for precision tests of bound-state quantum electrodynamics (QED). With the recent advent of extreme ultraviolet frequency combs, highly coherent quasi-continuous-wave light sources at 61 nm have become available, and precision spectroscopy of this transition now comes into reach for the first time. We discuss quantitatively the feasibility of such an experiment by analyzing excitation and ionization rates, propose an experimental scheme, and explore the potential for QED tests.

Surface-enhanced high-harmonic generation: a promising approach for extreme ultraviolet frequency combs

We propose a promising scheme to produce extreme ultraviolet frequency combs through high-harmonic generation with a surface-enhanced optical field. High harmonics are generated in a wavelength-scale spatial region and show a noticeable emission probability at an angle around 10 degrees relative to the surface. This can be further controlled with an additional static electric field or polarization-gated scheme, leading to enhanced energy conversion efficiency and extra even-order harmonic generation.

Extreme-ultraviolet frequency comb generation by polarization-gated surface-enhanced optical fields

We show that two synchronized counter-propagating femtosecond pulses could be controlled by adjusting their relative delay to excite surface-enhanced optical fields of time-gated linear polarization in contrast with intrinsic elliptic polarization excited by the conventional one-pulse incidence scheme. Such surface-enhanced optical fields can be used to generate efficient high harmonics and thus extreme-ultraviolet frequency combs. The energy conversion efficiency as well as the frequency span of the generated extreme-ultraviolet frequency combs can be significantly increased with controllable emission probabilities along different directions relative to the surface.

Extreme-ultraviolet frequency combs by surface-enhanced optical fields with diatomic molecules

An efficient and straightforward approach is proposed to produce extreme ultraviolet frequency combs by using high-order harmonic generation from diatomic molecules driven by surface-enhanced high-repetition-rate femtosecond pulses. For a nonpolar molecule, the maximum (minimum) energy conversion efficiency is observed as the molecule is oriented at an angle of $27\ifmmode^\circ\else\textdegree\fi{}$ $(108\ifmmode^\circ\else\textdegree\fi{})$ relative to the surface. For a polar molecule, the frequency components of the generated ultraviolet frequency combs are doubled as both odd- and even-order harmonics are generated, which shows different orientation dependence and shifts from the nonpolar molecule. The generated ultraviolet frequency combs are mainly emitted with angles smaller than $30\ifmmode^\circ\else\textdegree\fi{}$ close to the surface, while there is a noticeable emission probability around the directions perpendicular to the surface when the molecules are oriented with large angles.

Cavity-enhanced noncollinear high-harmonic generation for extreme ultraviolet frequency combs

We investigate an efficient scheme to generate and outcouple extreme ultraviolet frequency combs based on cavity-enhanced noncollinear high-harmonic generation. Our numerical results show that phase matching plays a crucial role for high energy conversion and output-coupling efficiencies, which strongly depend on the crossing angle, ionization probability, and initial atomic density.