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We proposed a new primary calibration method of a laser Doppler vibrometer (LDV) using the optical modulated excitation of an electro-optical modulator and validated this approach by comparing mechanical modulated excitation with homodyne laser interferometer at the National Metrology Institute of Japan (NMIJ). The velocity sensitivity of the LDV was evaluated with the uncertainty budget at a high-frequency range up to 1 MHz, which is indicated as the upper limit of 50 kHz in ISO (International Organization for Standardization) 16063–41. As the results, we confirmed that velocity sensitivities between optical and mechanical modulated excitations are flat within their uncertainty from 100 Hz up to 1 MHz. Moreover, in order to evaluate the accurate phase shift of the accelerometer up to 20 kHz using optical modulated excitation, we also revealed the reliability of two time shifts between homodyne and heterodyne laser interferometers.

The new definition of the kilogram was implemented on May 20, 2019. The kilogram is presently defined by a fixed value of the Planck constant. On the basis of the new definition, the kilogram will be realized at the National Metrology Institute of Japan by the X-ray crystal density method using 28Si-enriched spheres. For the realization, the volume of 28Si-enriched spheres is measured by optical interferometry. The sphere surface characterization by X-ray photoelectron spectroscopy and ellipsometry is also performed. The relative standard uncertainty of the realization is estimated to be 2.4 × 10−8. Details of the realization and future dissemination of mass standards in Japan based on the 28Si-enriched spheres are described.

We search for ultralight scalar dark matter candidates that induce oscillations of the fine structure constant, the electron and quark masses, and the quantum chromodynamics energy scale with frequency comparison data between a ^{171}Yb optical lattice clock and a ^{133}Cs fountain microwave clock that span 298 days with an uptime of 15.4%. New limits on the couplings of the scalar dark matter to electrons and gluons in the mass range from 10^{-22} to 10^{-20} eV/c^{2} are set, assuming that each of these couplings is the dominant source of the modulation in the frequency ratio. The absolute frequency of the ^{171}Yb clock transition is also determined as 518 295 836 590 863.69(28) Hz, which is one of the important contributions toward a redefinition of the second in the International System of Units.

The International System of Units (SI) definition of the ‘second’ is likely to be redefined in the optical frequency region in the near future. Therefore, uncertainty reduction in the frequency link between 10 MHz, which is used in the frequency link with an artificial satellite, and the ultrastable laser for observing clock transitions in optical clocks, is an important issue for numerical determination in the new definition and for International Atomic Time operation after the redefinition. We have evaluated all the possible uncertainty factors in the frequency link with a femtosecond comb between 10 MHz and an optical frequency and obtained the lowest uncertainty yet reported of 3.9 × 10−18 by temperature-stabilizing RF multipliers and by using temperature insensitive coaxial cables. Furthermore, we have validated the uncertainty of the frequency link by simultaneously measuring an optical frequency of an identical laser using two femtosecond combs referenced to a common 10 MHz source and confirmed to be consistent with the evaluated uncertainty.

Phase noise induced by environmental disturbance was greatly reduced when the optical fiber was installed in an ultrastable environment. In this paper, the optical fiber length was 10 m, and the reduction in the phase noise power spectral density was approximately 70 and 30 dB at Fourier frequencies of 10 mHz and 10 Hz, respectively. To evaluate faint fiber noise, we developed a modified Mach–Zehnder heterodyne interferometer with reduced optical path length fluctuation. The Allan deviation calculated from the phase noise was $7 \times 10^{-20}$ at a 1-s averaging time and reached $2 \times 10^{-21}$ at a 10 000-s averaging time (measurement bandwidth: 500 Hz). In addition, we revealed the frequency bands in which fiber noise is reduced by selectively removing the environmental stabilization measures of evacuation, vibration isolation, acoustic shielding, and temperature stabilization from an ultrastable environment.

We carry out infrared-infrared double-resonance spectroscopy of the $2{\ensuremath{\nu}}_{3}{A}_{1}\text{\ensuremath{-}}{\ensuremath{\nu}}_{3}$ band of methane. Ten transitions of Q(1) to Q(4) are observed with an 88.5-THz difference-frequency-generation (DFG) source, while the lower levels are pumped through the ${\ensuremath{\nu}}_{3}$ band transition by another 90.5-THz DFG source phase-locked to an optical frequency comb (OFC). The transition frequencies are determined using the OFC with an uncertainty of 10 kHz, which is an improvement of 4 orders of magnitude compared with the previous studies.

Precise measurements of the geometrical thickness of a sample and its refractive index are important for materials science, engineering, and medical diagnosis. Among the possible non-contact evaluation methods, optical interferometric techniques possess the potential of providing superior resolution. However, in the optical frequency region, the ambiguity in the absolute phase-shift makes it difficult to measure these parameters of optically thick dispersive materials with sufficient resolution. Here, we demonstrate that dual frequency-comb spectroscopy can be used to precisely determine the absolute sample-induced phase-shift by analyzing the data smoothness. This method enables simultaneous determination of the geometrical thickness and the refractive index of a planar sample with a precision of five and a half digits and an ultra-wide dynamic range. The thickness and the refractive index at 193.414 THz of a silicon wafer determined by this method are 0.52047(3) mm and 3.4756(3), respectively, without any prior knowledge of the refractive index., Comment: 22 pages, 6 figures

We report improved frequency ratio measurement with $^{87}$Sr and $^{171}$Yb optical lattice clocks at the National Metrology Institute of Japan (NMIJ). The $^{87}$Sr optical lattice clock is enhanced with several major modifications and is re-evaluated with a reduced uncertainty of $1.1\times10^{-16}$. We employed a $^{171}$Yb optical lattice clock with an uncertainty of $4\times10^{-16}$ that was developed for contributing to International Atomic Time (TAI). The measurement result is $\nu_{\mathrm{Yb}}/\nu_{\mathrm{Sr}}$ = 1.207 507 039 343 338 58(49)$_{\mathrm{sys}}$(6)$_{\mathrm{stat}}$ with a fractional uncertainty of $4.1\times10^{-16}$, which is 3.4 times smaller than our previous measurement result., Comment: 8 pages, 6 figures, 1 table

Angle sensors based on the laser autocollimation are often employed to evaluate surface profiles of a target of interest. The authors have developed a femtosecond laser angle sensor, in which a spectrometer or an optical spectrum analyzer with a single-mode fiber is employed as the photodetector for simultaneous capturing of the multiple optical modes. In this paper, the concept of the femtosecond laser angle sensor is applied to evaluate the surface profile of a target of interest. An optical setup is designed in such a way that each mode in the spectrum of the mode-locked femtosecond is utilized as the laser beam to measure the local slope of a measurement target at each different point to evaluate the surface profile. Some basic experiments are carried out by using the developed optical setup with a mode-locked femtosecond laser source to evaluate basic performances of the developed optical setup as an optical angle sensor.

We report the status on an Yb optical lattice clock that was designed to run for a long-term operation towards contribution to the International Atomic Time (TAI) regularly. Nearly continuous operation of the Yb clock was realized with 90% uptime over several weeks. This enables to reduce the uncertainty in the link between the Yb clock and TAI to the low 10−16 level.

The new definition of the kilogram based on the Planck constant was implemented in May 2019. The National Metrology Institute of Japan (NMIJ) will realize the new kilogram by the X-ray crystal density method using a 28Si-enriched sphere. An international comparison of the realizations of the new kilogram by national metrology institutes was organized. As a participant in the comparison, the NMIJ realized the kilogram by the volume measurement and surface characterization of a 28Si-enriched sphere. Details of the measurement results and the uncertainty evaluation of the realization are described. The comparison of the realization results with previous realization results in 2016 is also provided.

The kilogram based on the Plank constant will be realized at the National Metrology Institute of Japan (NMIJ) by using the X-ray crystal density method. In this study, for the realization, the volume of a 28Si-enriched sphere, named AVO28-S5c, was measured. The volume was determined from diameter measurements taken in many directions using an optical interferometer. The apparent volume of the sphere, which does not consider the influence of the surface layers on the volume measurement, was determined with a relative standard uncertainty of $1.8\times 10^{-8}$ . The reproducibility of the kilogram realization is important for the reliable dissemination of the kilogram at the NMIJ. Therefore, the volume determined in this study was compared with that determined in 2016. These volumes were shown to agree with the uncertainty. This article provides details on the measurements, improvements of the interferometer, data analysis, and uncertainty evaluation.

We propose and demonstrate a novel technique for precisely and widely sweeping the frequency of a continuous-wave laser. One of the modulation sidebands of a slave laser generated with an electro-optic modulator is phase-locked to a master laser; in this situation, the slave carrier component can be swept by sweeping the modulation frequency. It does not require beat signal detection at varying and/or high frequency, thus providing a robust and reliable laser frequency sweep. Also, it requires neither a frequency comb for the sweep nor a large power loss. We successfully swept an 852 nm laser over 20 GHz; we confirmed that a second harmonic 426 nm laser could be continuously swept over 40 GHz.

We demonstrate a narrow linewidth electro-optic modulator based frequency comb with a simple modulator configuration. It was achieved by a servo control of a fragment of a high- frequency modulation signal through a low-frequency voltage-controlled oscillator.

We evaluate the uncertainty of our Sr optical lattice clock at the 10 -17 level, through robust clock operation with assistance of optical frequency combs. This clock will be operated for contribution to the International Atomic Time.

We introduce and experimentally apply “cosine similarity” as an index for quantitatively evaluating the degree of change in the spectra of optical frequency combs. The cosine similarity with the original spectrum increased or decreased as the amount of control applied to the combs increased or decreased; this is considered to be an appropriate indication of spectral similarity. Therefore, we apply this approach to an evaluation of the temporal spectral changes in polarization-maintaining (PM) and non-PM combs. The results suggest that there is no significant difference between the spectral stabilities of PM and non-PM combs, and reveal that the spectral sensitivity to the amount of control is a more effective factor.

The ν 1 + ν 3 vibration band of acetylene (C2H2) in the near infrared region was recorded with a dual-comb Fourier-transform spectrometer. We observed 56 transitions from P ( 26 ) to R ( 29 ) at six different column densities. The integral line intensity was determined for each recorded absorption line by fitting the line profile to Lambert-Beer’s law with a Voigt function. Thanks to the outstanding capability of dual-comb spectroscopy to cover a broad spectrum in a relatively short time with high resolution and high frequency precision, we determined the reliable line strength for each ro-vibrational transition as well as the transition dipole moment for this band.

Spectroscopic ellipsometry is a means of investigating optical and dielectric material responses. Conventional spectroscopic ellipsometry is subject to trade-offs between spectral accuracy, resolution, and measurement time. Polarization modulation has afforded poor performance because of its sensitivity to mechanical vibrational noise, thermal instability, and polarization-wavelength dependency. We combine spectroscopic ellipsometry with dual-comb spectroscopy, namely, dual-comb spectroscopic ellipsometry. Dual-comb spectroscopic ellipsometry (DCSE). DCSE directly and simultaneously obtains the ellipsometric parameters of the amplitude ratio and phase difference between s-polarized and p-polarized light signals with ultra-high spectral resolution and no polarization modulation, beyond the conventional limit. Ellipsometric evaluation without polarization modulation also enhances the stability and robustness of the system. In this study, we construct a polarization-modulation-free DCSE system with a spectral resolution of up to 1.2 × 10−5 nm throughout the spectral range of 1514–1595 nm and achieved an accuracy of 38.4 nm and a precision of 3.3 nm in the measurement of thin-film samples., Spectroscopic ellipsometry is an established technique to characterize the optical properties of a material. Here, Minamikawa et al. combine the method with dual-comb spectroscopy, which allows them to obtain ellipsometric parameters including the phase difference between s-polarized and p-polarized light.

To determine the Avogadro constant N A by the x-ray crystal density method, the density of a 28Si-enriched crystal was determined by absolute measurements of the mass and volume of a 1 kg sphere manufactured from the crystal. The mass and volume were determined by an optical interferometer and a vacuum mass comparator, respectively. The sphere surface was characterized by x-ray photoelectron spectroscopy and spectroscopic ellipsometry to derive the mass and volume of the Si core of the sphere excluding the surface layers. From the mass and volume, the density of the Si core was determined with a relative standard uncertainty of 2.3 × 10−8. By combining the Si core density with the lattice constant and the molar mass of the sphere reported by the International Avogadro Coordination (IAC) project in 2015, a new value of 6.022 140 84(15) × 1023 mol−1 was obtained for N A with a relative standard uncertainty of 2.4 × 10−8. To make the N A value determined in this work usable for a future adjustment of the fundamental constants by the CODATA Task Group on Fundamental Constants, the correlation of the new N A value with the N A values determined in our previous works was examined. The correlation coefficients with the values of N A determined by IAC in 2011 and 2015 were estimated to be 0.07 and 0.28, respectively. The correlation of the new N A value with the N A value determined by IAC in 2017 using a different 28Si-enriched crystal was also examined, and the correlation coefficient was estimated to be 0.21.

Ernst Haeckel (1834–1919), who is best known for his embryological principle that ontogeny recapitulates phylogeny, contributed not only to embryology but also to zoology, ecology, evolutionary the...

For the determination of the Avogadro constant by the x-ray crystal density method, an accurate volume measurement of 1 kg Si spheres is of primary importance. For this purpose, an optical interferometer was improved and used to measure the volumes of two 1 kg silicon spheres which were manufactured from a silicon crystal highly enriched in 28Si. The apparent volumes of the spheres, which do not take into account the influence of the surface layers on the volume measurement by interferometry, were determined with a relative standard uncertainty of as small as 2.0 × 10−8. The surface of the spheres was characterized by using an improved spectroscopic ellipsometer. By considering the influence of the surface layers, the core volumes of the spheres, which exclude the surface layers, were determined. These results were used for the determination of the Avogadro constant in 2015 as a framework organized by the International Avogadro Coordination project. This paper provides details on the measurements, the improvements made to the apparatus, the data analysis and the uncertainty evaluation.

We propose and demonstrate a polarization-sensitive dual-comb spectroscopy (DCS) technique that employs an electro-optic modulator for determining the anisotropic optical responses of materials. This straightforward extension of the typical DCS setup directly provides amplitudes and phases in two mutually orthogonal directions of the electric field of light. Using this method, we determined the optic axis direction and the anisotropy in the complex refractive index of a sample whose optical parameter is well defined. We estimate a birefringence of the sample to be 5.49(55)×10−5 at a comb tooth in the 780 nm region.

Dual-comb spectroscopy (DCS) is a modern method using two frequency combs with slightly different repetition rates [1,2]. The DCS down-converts a material response in the optical frequency domain to a rf signal that is easy to handle. It provides significant advantages over conventional spectroscopy such as high spectral resolution, broad spectral range, frequency precision, short measurement time, and so on. The DCS has mainly been applied to precise molecular gas spectroscopy [3]. There are several attempts to expand its application to solid state physics. One of the applications is the determination of complex refractive index of materials [4]. As changes in both the amplitude and phase inside the material can be measured by DCS, one can determine both the real and imaginary part of the refractive index without utilizing the Kramers-Kronig relation. In addition, we consider physically interesting materials such as low-dimensional nanostructures and polymers with polarization-dependent complex refractive index (optical anisotropy). For investigating their physical property, it is important to add polarization sensitiveness to the DCS. So far, we have developed a polarization-sensitive (PS) DCS using a rotating compensator polarimetry [5].

Frequency-stabilized lasers at the telecom wavelengths are of great interest for a wide range of applications, including wavelength standards for optical communication systems [1], and an absolute frequency marker of an optical frequency comb. Especially in astro-comb application [2], it is considered to be a good candidate of an optical frequency reference laser since it has a good frequency connection to a fiber-based frequency comb.

We report the status of our 171Yb optical lattice clock. The frequency stability of the Yb lattice clock is $1\times10^{-14}(\tau$/s)-1/2 where $\tau$ is an averaging time. The systematic uncertainty of the Yb lattice clock is evaluated to be $3.6\times10^{-16}$. Towards contribution to the International Atomic Time, some contrivances are incorporated in order for the Yb lattice clock to run for a long term. For example, automatic relocking schemes are recently prepared for phase locking and injection locking.

We report an uncertainty evaluation of an $^{171}$Yb optical lattice clock with a total fractional uncertainty of $3.6\times10^{-16}$, which is mainly limited by the lattice-induced light shift and the blackbody radiation shift. Our evaluation of the lattice-induced light shift, the density shift, and the second-order Zeeman shift is based on an interleaved measurement where we measure the frequency shift using the alternating stabilization of a clock laser to the $\mathrm{6s^{2}\,^{1}S_{0}-6s6p\,^{3}P_{0}}$ clock transition with two different experimental parameters. In the present evaluation, the uncertainties of two sensitivity coefficients for the lattice-induced hyperpolarizability shift $d$ incorporated in a widely-used light shift model by RIKEN and the second-order Zeeman shift $a_{\mathrm{Z}}$ are improved compared with the uncertainties of previous coefficients. The hyperpolarizability coefficient $d$ is determined by investigating the trap potential depth and the light shifts at the lattice frequencies near the two-photon transitions $\mathrm{6s6p^{3}P_{0}-6s8p^{3}P_{0}}$, $\mathrm{6s8p^{3}P_{2}}$, and $\mathrm{6s5f^{3}F_{2}}$. The obtained values are $d=-1.1(4)$ $\mathrm{\mu}$Hz and $a_{\mathrm{Z}}=-6.6(3)$ Hz/mT$^{2}$. These improved coefficients should reduce the total systematic uncertainties of Yb lattice clocks at other institutes.

A terahertz (THz) frequency synthesizer based on photomixing of two near-infrared lasers with a sub-THz to THz frequency offset is a powerful tool for spectroscopy of polar gas molecules due to its broad spectral coverage; however, its frequency accuracy and resolution are relatively low. To tune the output frequency continuously and widely while maintaining its traceability to a frequency standard, we developed a photomixing THz synthesizer phase-locked to dual optical frequency combs (OFCs). While the phase-locking to dual OFCs ensured continuous tuning within a spectral range of 120 GHz, in addition to the traceability to the frequency standard, use of a broadband uni-traveling carrier photodiode for photomixing enabled the generation of CW-THz radiation within a frequency range from 0.2 to 1.5 THz. We demonstrated THz frequency-domain spectroscopy of gas-phase acetonitrile CH3CN and its isotope CH3 13CN in the frequency range of 0.600–0.720 THz using this THz synthesizer. Their rotational transitions were assigned with a frequency accuracy of 8.42 × 10−8 and a frequency resolution of 520 kHz. Furthermore, the concentration of the CH3CN gas at 20 Pa was determined to be (5.41 ± 0.05) × 1014 molecules/cm3 by curve fitting analysis of the measured absorbance spectrum, and the mixture ratio of the mixed CH3CN/CH3 13CN gas was determined to be 1:2.26 with a gas concentration of 1014–1015 molecules/cm3. The developed THz synthesizer is highly promising for high-precision THz-FDS of low-pressure molecular gases and will enable the qualitative and quantitative analyses of multiple gases.

We describe frequency noise measurements for an optical frequency comb by using a delayed self-heterodyne method with a Michelson-type fiber-optic delay line interferometer without a low-noise reference laser. We measured the frequency noise power spectral densities (PSDs) for free-running and frequency-stabilized comb modes and estimated the uncertainties of the measurement results. For example, for the frequency-stabilized comb, the measured frequency noise PSD and its uncertainty were 23 dBHz2 Hz−2 and 0.66 dB, respectively, at a Fourier frequency of 10 kHz. We also measured the frequency noise PSDs of the comb modes by the conventional method using an ultrastable reference laser and compared the results with those that we measured with the delayed self-heterodyne method. The measurement results that we obtained with the two methods were consistent within their uncertainties, which shows that the delayed self-heterodyne method provides high reliability. This combined with its simplicity and user-friendliness suggest that the method has the potential to become a standard frequency noise measurement approach for frequency combs.

To improve the primary density standard of the National Metrology Institute of Japan (NMIJ), the absolute densities of two 1 kg silicon spheres, NMIJ-S4 and NMIJ-S5, were determined by measuring their masses and volumes. The volumes of the two spheres were measured by optical interferometry based on the primary length standard of NMIJ. For the accurate volume determination, the thicknesses of the surface layers on the spheres were determined by x-ray photoelectron spectroscopy (XPS). By combining the results of optical interferometry and XPS, the volumes of the two spheres at 20.000 °C and 0 Pa were determined with relative standard uncertainties of 3.0 × 10−8 and 2.9 × 10−8 for NMIJ-S4 and NMIJ-S5, respectively. From these results, the sphere volumes at 20.000 °C and 101.325 kPa were determined using the isothermal compressibility of silicon. The masses of the spheres in air were determined based on the national prototype of the kilogram of Japan. From the results of the volume and mass measurements, the densities of the two spheres at 20.000 °C and 101.325 kPa were determined with a relative standard uncertainty of 3.2 × 10−8. The density difference between the two spheres was estimated taking into account the correlation between the densities of the two spheres. The pressure-of-floatation method was also used to determine the density difference between the two spheres. The density differences determined by the two different methods agree with each other within their uncertainties.

We demonstrate two self-referencing optical frequency combs with a repetition rate of 19.8 MHz, which is the lowest ever reported, using nonlinear-polarization-evolution mode-locked Er:fiber lasers. The two combs are phase-locked with a common CW laser at 1.5 μm using high-speed feedback controls with servo bandwidths of 380 kHz. Over 40 absorption lines of the ν 1 + ν 3 vibration band of 13C2H2 are observed by dual-comb spectroscopy using those combs. We resolve the observed Doppler-limited lines with a 19.8 MHz frequency spacing (repetition rate), which is currently the smallest frequency spacing achieved, to the best of our knowledge.

We demonstrate the third harmonic generation of a 1542-nm laser using a dual-pitch periodically poled lithium niobate waveguide with a conversion efficiency of 66%/W2. The generated 514-nm light is used for saturation spectroscopy of molecular iodine and laser frequency stabilization. The achieved laser frequency stability is 1.1×10−12 at an average time of 1 s, which is approximately one order of magnitude better than the acetylene-stabilized laser at 1542 nm. Uncertainty evaluation and absolute frequency measurement are also performed. The developed frequency-stabilized laser can be used as a reliable frequency reference at the telecom wavelength for various applications including optical frequency combs and precision interferometric measurement.

This paper presents the development of a frequency comb using a mode-locked fiber laser as the light source for precision dimensional metrology. The mode-locked laser generates an optical pulse train with a central wavelength of approximately 1560 nm. The pulse train was amplified with an erbium-doped fiber amplifier, and its spectrum was broadened to the wavelength range from 1000 nm to 2000 nm. Furthermore, the carrier envelope offset beats were successfully detected by using a common-path f-2 f interferometer.

We report an uncertainty evaluation of an

We investigated phase noise induced in a piece of optical fiber installed in an ultra-stable environment. The ultra-stable environments were implemented by hermetically sealing, vacuuming, temperature stabilization, vibration isolation, and acoustic shielding. Moreover, in order to detect and evaluate such small fiber noise with high sensitivity, we employed the well-known self-heterodyne technique. The most stable environment drastically reduced the phase noise induced in a 10-m fiber; the noise corresponds to Allan deviation of $7\ \times {10^{-20}}$ at 1-s averaging time, and to $2 \times {10^{-21}}$ at 10000-s averaging time (measurement bandwidth: 500 Hz).