A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

Dual-comb spectroscopy is an emerging new spectroscopic tool that exploits the frequency resolution, frequency accuracy, broad bandwidth, and brightness of frequency combs for ultrahigh-resolution, high-sensitivity broadband spectroscopy. By using two coherent frequency combs, dual-comb spectroscopy allows a sample’s spectral response to be measured on a comb tooth-by-tooth basis rapidly and without the size constraints or instrument response limitations of conventional spectrometers. This review describes dual-comb spectroscopy and summarizes the current state of the art. As frequency comb technology progresses, dual-comb spectroscopy will continue to mature and could surpass conventional broadband spectroscopy for a wide range of laboratory and field applications.

Dual-comb spectroscopy

In the past decade we have witnessed remarkable advances associated with the frequency stabilization of the comb present in the output of a mode-locked femtosecond laser. While proving itself to be fantastically successful in its role as the “gears” of optical atomic clocks, the optical frequency comb has further evolved into a valuable tool for a wide range of applications, including ultraviolet and infrared spectroscopy, frequency synthesis, optical and microwave waveform generation, astronomical spectrograph calibration, and attosecond pulse generation, to name a few. In this review, I will trace several of these developments while attempting to offer perspective on the challenges and opportunities for frequency combs that might lie ahead in the next decade.

The evolving optical frequency comb [Invited]

By coupling a high-power, high-repetition-rate near-infrared frequency comb to a femtosecond optical cavity, a frequency comb operating in the extreme-ultraviolet spectral range has been produced, by high harmonic generation, and provides high-resolution spectroscopy in this spectral region. Laser-based optical frequency combs, so called because they emit evenly spaced spectral lines, are used in precision spectroscopy and other applications requiring accurate measurements, such as atomic clocks. Efforts to extend this capability to shorter wavelengths in the extreme ultraviolet — which would open up exciting new applications, including searches for variation in fundamental constants — have lacked sufficient power for the purpose until now. Jun Ye and co-workers demonstrate a new approach, using a high-power, high-repetition pulsed infrared laser coupled into an optical cavity, to produce an improved extreme UV comb. In a first precision spectroscopy demonstration, they use direct frequency comb spectroscopy to determine argon and neon atomic transitions with ultra-high precision. The development of the optical frequency comb (a spectrum consisting of a series of evenly spaced lines) has revolutionized metrology and precision spectroscopy owing to its ability to provide a precise and direct link between microwave and optical frequencies1,2. A further advance in frequency comb technology is the generation of frequency combs in the extreme-ultraviolet spectral range by means of high-harmonic generation in a femtosecond enhancement cavity3,4. Until now, combs produced by this method have lacked sufficient power for applications, a drawback that has also hampered efforts to observe phase coherence of the high-repetition-rate pulse train produced by high-harmonic generation, which is an extremely nonlinear process. Here we report the generation of extreme-ultraviolet frequency combs, reaching wavelengths of 40 nanometres, by coupling a high-power near-infrared frequency comb5 to a robust femtosecond enhancement cavity. These combs are powerful enough for us to observe single-photon spectroscopy signals for both an argon transition at 82 nanometres and a neon transition at 63 nanometres, thus confirming the combs’ coherence in the extreme ultraviolet. The absolute frequency of the argon transition has been determined by direct frequency comb spectroscopy. The resolved ten-megahertz linewidth of the transition, which is limited by the temperature of the argon atoms, is unprecedented in this spectral region and places a stringent upper limit on the linewidth of individual comb teeth. Owing to the lack of continuous-wave lasers, extreme-ultraviolet frequency combs are at present the only promising route to extending ultrahigh-precision spectroscopy to the spectral region below 100 nanometres. At such wavelengths there is a wide range of applications, including the spectroscopy of electronic transitions in molecules6, experimental tests of bound-state and many-body quantum electrodynamics in singly ionized helium and neutral helium7,8,9, the development of next-generation ‘nuclear’ clocks10,11,12 and searches for variation of fundamental constants13 using the enhanced sensitivity of highly charged ions14.

Direct frequency comb spectroscopy in the extreme ultraviolet

The extremely precise extraction of the proton radius obtained by Pohl et al. from the measured energy difference between the 2P and 2S states of muonic hydrogen disagrees significantly with that extracted from electronic hydrogen or elastic electron–proton scattering. This discrepancy is the proton radius puzzle. In this review, we explain the origins of the puzzle and the reasons for believing it to be very significant. We identify various possible solutions of the puzzle and discuss future research needed to resolve the puzzle.

https://www.annualreviews.org/doi/pdf/10.1146/annurev-nucl-102212-170627

Muonic Hydrogen and the Proton Radius Puzzle

The remarkable precision of frequency-comb (FC) lasers is transferred to the extreme ultraviolet (XUV, wavelengths shorter than 100 nm), a frequency region previously not accessible to these devices. A frequency comb at XUV wavelengths near 51 nm is generated by amplification and coherent up-conversion of a pair of pulses originating from a near-infrared femtosecond FC laser. The phase coherence of the source in the XUV is demonstrated using helium atoms as a ruler and phase detector. Signals in the form of stable Ramsey-like fringes with high contrast are observed when the FC laser is scanned over P states of helium, from which the absolute transition frequency in the XUV can be extracted. This procedure yields a (4)He ionization energy at h×5 945 204 212(6)  MHz, improved by nearly an order of magnitude in accuracy, thus challenging QED calculations of this two-electron system.

/pdf/extreme-ultraviolet-frequency-comb-metrology-1z27l4rp70.pdf

Extreme Ultraviolet Frequency Comb Metrology

The application of White Rabbit precision time protocol (WR-PTP) in long-distance optical fiber links has been investigated. WR-PTP is an implementation of PTP in synchronous Ethernet optical fiber networks, originally intended for synchronization of equipment within a range of 10 km. This paper discusses the results and limitations of two implementations of WR-PTP in the existing communication fiber networks. A 950-km WR-PTP link was realized using unidirectional paths in a fiber pair between Espoo and Kajaani, Finland. The time transfer on this link was compared (after initial calibration) against a clock comparison by GPS precise point positioning (PPP). The agreement between the two methods remained within ${\pm }{2}\; \text{ns}$ over three months of measurements. Another WR-PTP implementation was realized between Delft and Amsterdam, the Netherlands, by cascading two links of 137 km each. In this case, the WR links were realized as bidirectional paths in single fibers. The measured time offset between the starting and end points of the link was within 5 ns with an uncertainty of 8 ns, mainly due to the estimated delay asymmetry caused by chromatic dispersion.

White Rabbit Precision Time Protocol on Long-Distance Fiber Links

The operation of a frequency comb at extreme ultraviolet (xuv) wavelengths based on pairwise amplification and nonlinear upconversion to the 15th harmonic of pulses from a frequency-comb laser in the near-infrared range is reported. It is experimentally demonstrated that the resulting spectrum at 51 nm is fully phase coherent and can be applied to precision metrology. The pulses are used in a scheme of direct-frequency-comb excitation of helium atoms from the ground state to the 1s4p and 1s5p 1 P 1 states. Laser ionization by auxiliary 1064 nm pulses is used to detect the excited-state population, resulting in a cosine-like signal as a function of the repetition rate of the frequency comb with a modulation contrast of up to 55%. Analysis of the visibility of this comb structure, thereby using the helium atom as a precision phase ruler, yields an estimated timing jitter between the two upconverted-comb laser pulses of 50 attoseconds, which is equivalent to a phase jitter of 0.38(6) cycles in the xuv at 51 nm. This sets a quantitative figure of merit for the operation of the xuv comb and indicates that extension to even shorter wavelengths should be feasible. The helium metrology investigation results in transition frequencies of 5740806993(10) and 5814248672(6) MHz for excitation of the 1s4p and 1s5p 1 P1 states, respectively. This constitutes an important frequency measurement in the xuv, attaining high accuracy in this windowless part of the electromagnetic spectrum. From the measured transition frequencies an eight-fold-improved 4 He ionization energy of 5945204212(6) MHz is derived. Also, a new value for the 4 He ground-state Lamb shift is found of 41247(6) MHz. This experimental value is in agreement with recent theoretical calculations up to order mα 6 and m 2 /Mα 5 , but with a six-times-higher precision, therewith providing a stringent test of quantum electrodynamics in bound two-electron systems.

/pdf/xuv-frequency-comb-metrology-on-the-ground-state-of-helium-28ukg69vjn.pdf

XUV frequency comb metrology on the ground state of helium

Results of optical frequency transfer over a carrier-grade dense-wavelength-division-multiplexing (DWDM) optical fiber network are presented. The relation between soil temperature changes on a buried optical fiber and frequency changes of an optical carrier through the fiber is modeled. Soil temperatures, measured at various depths by the Royal Netherlands Meteorology Institute (KNMI) are compared with observed frequency variations through this model. A comparison of a nine-day record of optical frequency measurements through the 2×298  km fiber link with soil temperature data shows qualitative agreement. A soil temperature model is used to predict the link stability over longer periods (days-months-years). We show that optical frequency dissemination is sufficiently stable to distribute and compare, e.g., rubidium frequency standards over standard DWDM optical fiber networks using unidirectional fibers.

/pdf/effect-of-soil-temperature-on-optical-frequency-transfer-1nlbezwnck.pdf

Effect of soil temperature on optical frequency transfer through unidirectional dense-wavelength-division-multiplexing fiber-optic links.

We propose a Y splitter in a two-dimensional photonic crystal with a triangular lattice of air holes suitable for mechano-optical switching. Full switching between the two output ports can be achieved at a certain wavelength owing to the presence of a resonant central cavity with well-chosen symmetry. Experimental results confirm the operation of the device and its potential as an ultracompact mechanical switch.

T. J. Pinkert

Papers

Extreme Ultraviolet Frequency Comb Metrology

White Rabbit Precision Time Protocol on Long-Distance Fiber Links

XUV frequency comb metrology on the ground state of helium

Effect of soil temperature on optical frequency transfer through unidirectional dense-wavelength-division-multiplexing fiber-optic links.

Photonic Crystal Cavity-Based Y Splitter for Mechano-Optical Switching