Erbium-doped-fiber-based broad visible range frequency comb with a 30 GHz mode spacing for astronomical applications.

We have realized a comb system with a 30 GHz mode spacing, 62 % available wavelength coverage in the visible region, and nearly 40 dB spectral contrast by combining a robust erbium-doped-fiber-based femtosecond laser, mode filtering with newly designed optical cavities, and broadband-visible-range comb generation using a chirped periodically-poled LiNbO3 ridge waveguide. Furthermore, it is suggested that this system produces a spectrum with little change over 29 months. These features of our comb will contribute to fields requiring broad-mode-spacing combs, including astronomical observations, such as exoplanet exploration and the verification of the cosmic accelerating expansion.

Search for Ultralight Dark Matter from Long-Term Frequency Comparisons of Optical and Microwave Atomic Clocks.

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.

Ultra-precise determination of thicknesses and refractive indices of optically thick dispersive materials by dual-comb spectroscopy.

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. The thickness and the refractive index at 193.414 THz (λ = 1550 nm) of a silicon wafer determined by this method are 0.5204737(19) mm and 3.475625(58), respectively, without any prior knowledge of the refractive index.

Cosine similarity for quantitatively evaluating the degree of change in an optical frequency comb spectra.

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.

40 GHz continuous, precise, and low power-loss laser frequency sweep using an electro-optic modulator.

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.

Iodine-stabilized laser at telecom wavelength using dual-pitch periodically poled lithium niobate waveguide.

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.

Polarization-sensitive dual-comb spectroscopy with an electro-optic modulator for determination of anisotropic optical responses of materials.

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.

Development of 8-branch Er:fiber frequency comb for Sr and Yb optical lattice clocks.

We demonstrate an 8-branch Er:fiber frequency comb with seven application ports, which can be individually optimized for applications with different wavelengths. The beat between the comb and a cw laser has a signal-to-noise ratio exceeding 30 dB at a resolution bandwidth of 300 kHz. The 8-branch frequency comb is used to perform frequency locking for four repumping and lattice lasers, and the frequency measurement of two clock lasers of strontium and ytterbium optical lattice clocks. We have achieved reliable optical lattice clock operation, thanks to the stable frequency locking and measurement obtained by using the 8-branch frequency comb. The developed frequency comb is a powerful experimental tool for various applications, including not only optical lattice clocks, but also research on quantum optics that use many frequency-stabilized lasers.

Uncertainty Evaluation of an 171Yb Optical Lattice Clock at NMIJ.

We report an uncertainty evaluation of an 171Yb optical lattice clock with a total fractional uncertainty of 3.6×10-16 , 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 6s2 1S0-6s6p 3P0 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 aZ 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 6s6p3P0-6s8p3P0, 6s8p3P2, and 6s5f3F2. The obtained values are d=-1.1(4) µ Hz and aZ=-6.6(3) Hz/mT2. These improved coefficients should reduce the total systematic uncertainties of Yb lattice clocks at other institutes.

Multi-branch fiber comb with relative frequency uncertainty at 10-20 using fiber noise difference cancellation.

In multi-branch combs, the comb outputs from the branches suffer from different fiber noises, which often limit the uncertainty of the combs referring a highly-stable optical frequency. To overcome this limitation, we introduced fiber noise difference cancellation to multi-branch fiber combs. We detected and phase-locked the beat notes between the branch outputs and a common 1542 nm continuous wave laser. A piezo-electric transducer-based fiber stretcher was installed in each branch except for the branch used as the cancellation reference. We fabricated two quasi-identical combs with this mechanism and confirmed the relative frequency uncertainty by comparing them. The cancellation improved the frequency uncertainty to a low level of 10-20 at a 100000-s averaging time.

Dual-comb spectroscopic ellipsometry.

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.

Ortho-Para-Dependent Pressure Effects Observed in the Near Infrared Band of Acetylene by Dual-Comb Spectroscopy.

We demonstrate that dual-comb spectroscopy, which allows one to record broadband spectra with high frequency accuracy in a relatively short time, provides a real advantage for the observation of pressure-broadening and pressure-shift effects. We illustrate this with the ν_{1}+ν_{3} vibration band of ^{12}C_{2}H_{2}. We observe transitions from P(26) to R(29), which extend over a 3.8 THz frequency range, at six pressures ranging up to 2654 Pa. Each observed absorption line profile is fitted to a Voigt function yielding pressure-broadening and pressure-shift coefficients for each rotation-vibration transition. The effectiveness of this technique is such that we are able to discern a clear dependence of the pressure-broadening coefficients on the nuclear spin state, i.e., on the ortho or para modification. This information, combined with the pressure-shift coefficients, can facilitate a detailed understanding of the mechanism of molecular collisions.

Generation of a frequency comb spanning more than 3.6 octaves from ultraviolet to mid infrared.

We have observed an ultra-broadband frequency comb with a wavelength range of at least 0.35 to 4.4 µm in a ridge-waveguide-type periodically poled lithium niobate device. The PPLN waveguide is pumped by a 1.0-2.4 µm wide frequency comb with an average power of 120 mW generated using an erbium-based mode-locked fiber laser and a following highly nonlinear fiber. The coherence of the extended comb is confirmed in both the visible (around 633 nm) and the mid-infrared regions.

Sub-Doppler resolution mid-infrared spectroscopy using a difference-frequency-generation source spectrally narrowed by laser linewidth transfer.

The spectral linewidth of a 3.28 µm difference-frequency-generation source has been reduced to 3.5 kHz using a laser linewidth transfer technique [Opt. Express21, 7891 (2013)]. We use an optical frequency comb with a broad servo bandwidth to transfer a narrow linewidth of a pump laser, a 1.06 µm Nd:YAG laser, to a signal laser, a 1.57 µm external-cavity laser diode. This source enables us to record the Lamb dip of the ν3 band R(2) E transition of methane with a molecular spectral linewidth of 21 kHz while the frequency axis is absolutely calibrated.

Compact iodine-stabilized laser operating at 531 nm with stability at the 10(-12) level and using a coin-sized laser module.

We demonstrate a compact iodine-stabilized laser operating at 531 nm using a coin-sized light source consisting of a 1062-nm distributed-feedback diode laser and a frequency-doubling element. A hyperfine transition of molecular iodine is observed using the light source with saturated absorption spectroscopy. The light source is frequency stabilized to the observed iodine transition and achieves frequency stability at the 10(-12) level. The absolute frequency of the compact laser stabilized to the a(1) hyperfine component of the R(36)32 - 0 transition is determined as 564074632419(8) kHz with a relative uncertainty of 1.4×10(-11). The iodine-stabilized laser can be used for various applications including interferometric measurements.

Adaptive sampling dual terahertz comb spectroscopy using dual free-running femtosecond lasers.

Terahertz (THz) dual comb spectroscopy (DCS) is a promising method for high-accuracy, high-resolution, broadband THz spectroscopy because the mode-resolved THz comb spectrum includes both broadband THz radiation and narrow-line CW-THz radiation characteristics. In addition, all frequency modes of a THz comb can be phase-locked to a microwave frequency standard, providing excellent traceability. However, the need for stabilization of dual femtosecond lasers has often hindered its wide use. To overcome this limitation, here we have demonstrated adaptive-sampling THz-DCS, allowing the use of free-running femtosecond lasers. To correct the fluctuation of the time and frequency scales caused by the laser timing jitter, an adaptive sampling clock is generated by dual THz-comb-referenced spectrum analysers and is used for a timing clock signal in a data acquisition board. The results not only indicated the successful implementation of THz-DCS with free-running lasers but also showed that this configuration outperforms standard THz-DCS with stabilized lasers due to the slight jitter remained in the stabilized lasers.

Real-time absolute frequency measurement of continuous-wave terahertz radiation based on dual terahertz combs of photocarriers with different frequency spacings.

Real-time measurement of the absolute frequency of continuous-wave terahertz (CW-THz) radiation is required for characterization and frequency calibration of practical CW-THz sources. We proposed a method for real-time monitoring of the absolute frequency of CW-THz radiation involving temporally parallel, i.e., simultaneous, measurement of two pairs of beat frequencies and laser repetition frequencies based on dual THz combs of photocarriers (PC-THz combs) with different frequency spacings. To demonstrate the method, THz-comb-referenced spectrum analyzers were constructed with a dual configuration based on dual femtosecond lasers. Regardless of the presence or absence of frequency control in the PC-THz combs, a frequency precision of 10(-11) was achieved at a measurement rate of 100 Hz. Furthermore, large fluctuation of the CW-THz frequencies, crossing several modes of the PC-THz combs, was correctly monitored in real time. The proposed method will be a powerful tool for the research and development of practical CW-THz sources, and other applications.

Near-infrared broadband dual-frequency-comb spectroscopy with a resolution beyond the Fourier limit determined by the observation time window.

We performed broadband dual-frequency-comb spectroscopy in the near-infrared region with a much higher resolution than the Fourier limit by using discrete Fourier transforms and spectral interleaving. We observed the resonant spectrum of a Fabry-Perot cavity over a spectral range of 187 to 218 THz using this technique, and measured its free spectral ranges and finesses. The recorded spectrum includes cavity resonance lines with widths of about 2 MHz, which is much narrower than the resolution of 48 MHz determined by the observation time window.

Frequency ratio measurement of 171Yb and 87Sr optical lattice clocks.

The frequency ratio of the (1)S(0)(F = 1/2)-(3)P(0)(F = 1/2) clock transition in (171)Yb and the (1)S(0)(F = 9/2)-(3)P(0)(F = 9/2) clock transition in (87)Sr is measured by an optical-optical direct frequency link between two optical lattice clocks. We determined the ratio (ν(Yb)/ν(Sr)) to be 1.207 507 039 343 341 2(17) fractional standard uncertainty of 1.4 × 10(-15) [corrected]. The measurement uncertainty of the frequency ratio is smaller than that obtained from absolute frequency measurements using the International Atomic Time (TAI) link. The measured ratio agrees well with that derived from the absolute frequency measurement results obtained at NIST and JILA, Boulder, CO using their Cs-fountain clock. Our measurement enables the first international comparison of the frequency ratios of optical clocks. The measured frequency ratio will be reported to the International Committee for Weights and Measures for a discussion related to the redefinition of the second.