Spectrally interleaved, comb-mode-resolved spectroscopy using swept dual terahertz combs

Jitter correction for asynchronous optical sampling terahertz spectroscopy using free-running pulsed lasers

We demonstrate a jitter correction method for asynchronous optical sampling (ASOPS) terahertz (THz) time-domain spectroscopy using two free-running oscillators. This method simultaneously records the THz waveform and a harmonic of the laser repetition rate difference, Δ f _r, to monitor the jitter information for software jitter correction. By suppressing the residual jitter below 0.1 ps, the accumulation of the THz waveform is achieved without losing the measurement bandwidth. Our measurement of water vapor successfully resolves the absorption linewidths below 1 GHz, demonstrating a robust ASOPS with a flexible, simple, and compact setup without any feedback control or additional continuous-wave THz source.

Precision dual-comb spectroscopy using wavelength-converted frequency combs with low repetition rates

Precision spectroscopy contributed significantly to the development of quantum mechanics in its early stages. In the twenty-first century, precision spectroscopy has played an important role in several fields, including fundamental physics, precision measurement, environmental monitoring, and medical diagnostics. An optical frequency comb is indispensable in determining the frequency axis in precision spectroscopy and it is useful as a light source for spectroscopy. Dual-comb spectroscopy uses two frequency combs with slightly different repetition rates and has the potential to surpass conventional Fourier-transform infrared spectrometers. The resolution of dual-comb spectroscopy is limited by the frequency spacing of the comb components, that is, the repetition rate of the comb. We demonstrate dual-comb spectroscopy in the visible-wavelength region using wavelength-converted frequency combs from Er-doped fiber combs. The repetition rates of the combs are relatively low at 19.8 MHz, resulting in relatively high resolution in the dual-comb spectroscopy. The observed spectral shape in dual-comb spectroscopy agrees well with the fitting result based on the hyperfine structure of molecular iodine. The realized dual-comb spectroscopy using wavelength-converted Er-doped fiber combs is reliable (maintenance free) and applicable in other experiments at visible wavelengths.

Dual chirped microcomb based parallel ranging at megapixel-line rates

Laser-based ranging (LiDAR) - already ubiquitously used in industrial monitoring, atmospheric dynamics, or geodesy - is a key sensor technology. Coherent laser ranging, in contrast to time-of-flight approaches, is immune to ambient light, operates continuous-wave allowing higher average powers, and yields simultaneous velocity and distance information. State-of-the-art coherent single laser-detector architectures reach hundreds of kilopixel per second sampling rates, while emerging applications - autonomous driving, robotics, and augmented reality - mandate megapixel per second point sampling to support real-time video-rate imaging. Yet, such rates of coherent LiDAR have not been demonstrated. Recent advances in photonic chip-based microcombs provide a route to higher acquisition speeds via parallelization but require separation of individual channels at the detector side, increasing photonic integration complexity. Here we overcome the challenge and report a hardware-efficient swept dual-soliton microcomb technique that achieves coherent ranging and velocimetry at megapixel per second line scan measurement rates with up to 64 optical channels. Multiheterodyning two synchronously frequency-modulated microcombs yields distance and velocity information of all individual ranging channels on a single receiver alleviating the need for individual separation, detection, and digitization. The reported LiDAR implementation is compatible with photonic integration and demonstrates the significant advantages of acquisition speed afforded by the convergence of optical telecommunication and metrology technologies.

Photonic integrated systems can be harnessed for fast and efficient optical telecommunication and metrology technologies. Here the authors develop a dual-soliton microcomb technique for massively parallel coherent laser ranging that requires only a single laser and a single photoreceiver.

Unlocking synchrotron sources for THz spectroscopy at sub-MHz resolution

Synchrotron radiation (SR) has proven to be an invaluable contributor to the field of molecular spectroscopy, particularly in the terahertz region (1-10 THz) where its bright and broadband properties are currently unmatched by laboratory sources. However, measurements using SR are currently limited to a resolution of around 30 MHz, due to the limits of Fourier-transform infrared spectroscopy. To push the resolution limit further, we have developed a spectrometer based on heterodyne mixing of SR with a newly available THz molecular laser, which can operate at frequencies ranging from 1 to 5.5 THz. This spectrometer can record at a resolution of 80 kHz, with 5 GHz of bandwidth around each molecular laser frequency, making it the first SR-based instrument capable of sub-MHz, Doppler-limited spectroscopy across this wide range. This allows closely spaced spectral features, such as the effects of internal dynamics and fine angular momentum couplings, to be observed. Furthermore, mixing of the molecular laser with a THz comb is demonstrated, which will enable extremely precise determinations of molecular transition frequencies.

Carrier-envelope offset frequency dynamics of a 10-GHz modelocked laser based on cascaded quadratic nonlinearities

Cascaded quadratic nonlinearities from phase-mismatched second-harmonic generation build the foundation for robust soliton modelocking in straight-cavity laser configurations by providing a tunable and self-defocusing nonlinearity. The frequency dependence of the loss-related part of the corresponding nonlinear response function causes a power-dependent self-frequency shift (SFS). In this paper, we develop a simple analytical model for the SFS-induced changes on the carrier-envelope offset frequency (f_CEO) and experimentally investigate the static and dynamic f_CEO dependence on pump power. We find good agreement with the measured dependence of f_CEO on laser output power, showing a broad f_CEO tuning capability from zero up to the pulse repetition rate. Moreover, we stabilize the relative intensity noise to the -157 dBc/Hz level leading to a tenfold reduction in f_CEO-linewidth.

Interleaved electro-optic dual comb generation to expand bandwidth and scan rate for molecular spectroscopy and dynamics studies near 1.6 µm

A chirped-pulse interleaving method is reported for generation of dual optical frequency combs based on electro-optic phase modulators (EOM) in a free-running all-fiber based system. Methods are discussed to easily modify the linear scan rate and comb resolution by more than three orders of magnitude and to significantly increase the spectral bandwidth coverage. The agility of the technique is shown to both capture complex line shapes and to magnify rapid passage effects in spectroscopic and molecular dynamics studies of CO₂. These methods are well-suited for applications in the areas of remote sensing of greenhouse gas emissions, molecular reaction dynamics, and sub-Doppler studies across the wide spectral regions accessible to EOMs.

Optical image amplification in dual-comb microscopy

Dual-comb microscopy (DCM), based on a combination of dual-comb spectroscopy (DCS) with two-dimensional spectral encoding (2D-SE), is a promising method for scan-less confocal laser microscopy giving an amplitude and phase image contrast with the confocality. However, signal loss in a 2D-SE optical system hampers increase in image acquisition rate due to decreased signal-to-noise ratio. In this article, we demonstrated optical image amplification in DCM with an erbium-doped fiber amplifier (EDFA). Combined use of the image-encoded DCS interferogram and the EDFA benefits from not only the batch amplification of amplitude and phase images but also significant rejection of amplified spontaneous emission (ASE) background. Effectiveness of the optical-image-amplified DCM is highlighted in the single-shot quantitative nanometer-order surface topography and the real-time movie of polystyrene beads dynamics under water convection. The proposed method will be a powerful tool for real-time observation of surface topography and fast dynamic phenomena.

Plasmonic heterodyne spectrometry for resolving the spectral signatures of ammonia over a 1-4.5 THz frequency range

We present a heterodyne terahertz spectrometry platform based on plasmonic photomixing, which enables the resolution of narrow spectral signatures of gases over a broad terahertz frequency range. This plasmonic heterodyne spectrometer replaces the terahertz mixer and local oscillator of conventional heterodyne spectrometers with a plasmonic photomixer and a heterodyning optical pump beam, respectively. The heterodyning optical pump beam is formed by two continuous-wave, wavelength-tunable lasers with a broadly tunable terahertz beat frequency. This broadly tunable terahertz beat frequency enables spectrometry over a broad bandwidth, which is not restricted by the bandwidth limitations of conventional terahertz mixers and local oscillators. We use this plasmonic heterodyne spectrometry platform to resolve the spectral signatures of ammonia over a 1-4.5 THz frequency range.

All-polarization-maintaining, polarization-multiplexed, dual-comb fiber laser with a nonlinear amplifying loop mirror

We developed an all-polarization-maintaining, polarization-multiplexed, dual-comb fiber laser with a nonlinear amplifying loop mirror (NALM) mode-locking mechanism. Owing to the use of the slow and fast axes of a polarization-maintaining fiber (PMF), the dual-frequency combs with slightly different repetition rates from the single-laser cavity are generated at the same center wavelength without extra-cavity nonlinear spectral broadening. The narrow relative beat note between the two frequency combs is obtained with a full-width-at-half-maximum of ~1 kHz in the optical frequency domain. The two frequency combs have high relative stability and mutual coherence owing to passive common-mode noise cancellation.

High-coherence ultra-broadband bidirectional dual-comb fiber laser

Dual-comb spectroscopy has emerged as an attractive spectroscopic tool for high-speed, high-resolution, and high-sensitivity broadband spectroscopy. It exhibits certain advantages when compared to the conventional Fourier-transform spectroscopy. However, the high cost of the conventional system, which is based on two mode-locked lasers and a complex servo system with a common single-frequency laser, limits the applicability of the dual-comb spectroscopy system. In this study, we overcame this problem with a bidirectional dual-comb fiber laser that generates two high-coherence ultra-broadband frequency combs with slightly different repetition rates (f_rep). The two direct outputs from the single-laser cavity displayed broad spectra of > 50 nm; moreover, an excessively small difference in the repetition rate (< 1.5 Hz) was achieved with high relative stability, owing to passive common-mode noise cancellation. With this slight difference in the repetition rate, the applicable optical spectral bandwidth in dual-comb spectroscopy could attain ~479 THz (~3,888 nm). In addition, we successfully generated high-coherence ultra-broadband frequency combs via nonlinear spectral broadening and detected high signal-to-noise-ratio carrier-envelope offset frequency (f_CEO) beat signals using the self-referencing technique. We also demonstrated the high relative stability between the two f_CEO beat signals and tunability. To our knowledge, this is the first demonstration of f_CEO detection and frequency measurement using a self-referencing technique for a dual-comb fiber laser. The developed high-coherence ultra-broadband dual-comb fiber laser with capability of f_CEO detection is likely to be a highly effective tool in practical, high-sensitivity, ultra-broadband applications.

Electro-optic THz dual-comb architecture for high-resolution, absolute spectroscopy

An absolute-frequency terahertz (THz) dual-frequency comb spectrometer based on electro-optic modulators for tunable, high-resolution, and real-time rapid acquisition is presented. An optical line of a master frequency comb (filtered via optical injection locking) serves as the seed to electro-optically generate a pair of new frequency combs (probe and local oscillator). Photomixing both combs with another coherent line from the same original master comb generates a narrow linewidth THz dual-comb with teeth frequencies that can be referenced to a radio-frequency standard. The system is validated with a proof-of-principle measurement of a microwave filter in the W-band.

Fast MHz spectral-resolution dual-comb spectroscopy with electro-optic modulators

Frequency-agile dual-comb spectroscopy (DCS) with electro-optic modulators (EOMs) promises to facilitate the implementation of DCS in many environmental applications. In this Letter, we demonstrate a 1 MHz resolution electro-optic dual-comb system with a measurement speed of 20 kHz. We generate an electro-optic frequency comb (EOFC) consisting of 50000 teeth with 1 MHz line spacing. Each comb tooth is well resolved by another EOFC with 2.5 GHz line spacing. We record transmittances of high Q-factor resonators within milliseconds. Our figure of merit is shown to be 36 times more sensitive than a configuration that would beat two combs of 1 MHz spacing.

Self-triggered Asynchronous Optical Sampling Terahertz Spectroscopy using a Bidirectional Mode-locked Fiber Laser

We report a self-triggered asynchronous optical sampling terahertz spectroscopy system based on a single bidirectional mode-locked fiber laser and plasmonics-enhanced photoconductive nanoantennas. The fiber laser generates two optical mutually coherent pulse trains with a stable repetition rate difference, enabling time-domain terahertz spectroscopy without using any mechanical delay line, stabilization electronics, or external trigger. The resolved terahertz spectra over a 0.1-2 THz frequency range and a 30-second measurement time show more than a 70-dB dynamic range, revealing water absorption lines matching the HITRAN database, through a light-weight and compact spectroscopy setup.

Arbitrary energy-preserving control of the line spacing of an optical frequency comb over six orders of magnitude through self-imaging

Spectral self-imaging (SI) is an efficient technique for controlling the line spacing (LS) of optical frequency combs (OFC). However, the degree of control is relatively limited, since the LS of the output comb must be set to be an integer sub-multiple of the input one. This technique can be extended to achieve arbitrary control of the comb LS by pre-conditioning the input comb with a properly designed spectral phase mask. This way, the output LS can be set to be any desired integer or fractional multiple of the input one. This generalized spectral SI process is intrinsically energy-preserving, which enables passive amplification of individual spectral lines of the comb when the scheme is designed for LS increase. Here we demonstrate the unique capabilities of generalized spectral SI in a simple dedicated fiber-optics platform, based on a frequency-shifting recirculating loop. When seeded with an external CW laser, the loop delivers a frequency comb with an arbitrary and reconfigurable quadratic spectral phase. We report lossless arbitrary control of the LS of the generated OFCs over six orders of magnitude, from the kHz to the GHz range, including passive amplification of individual comb lines by factors as high as 17 dB. The LS control is produced without modifying the features of the frequency comb. Practical applications of this LS control method are discussed.

Dual terahertz comb spectroscopy with a single free-running fibre laser

Dual terahertz (THz) comb spectroscopy enables high spectral resolution, high spectral accuracy, and broad spectral coverage; however, the requirement for dual stabilized femtosecond lasers hampers its versatility. We here report the first demonstration of dual THz comb spectroscopy using a single free-running fibre laser. By tuning the cavity-loss-dependent gain profile with an intracavity Lyot filter together with precise management of the cavity length and dispersion, dual-wavelength comb light beams with slightly detuned repetition frequencies are generated in a single laser cavity. Due to sharing of the same cavity, such comb light beams suffer from common-mode fluctuation of the repetition frequency, and hence the corresponding frequency difference between them is passively stable around a few hundred hertz within millihertz fluctuation. While greatly reducing the size, complexity, and cost of the laser source by use of a single free-running fibre laser, the dual THz comb spectroscopy system maintains a spectral bandwidth and dynamic range of spectral power comparable to a system equipped with dual stabilized fibre lasers, and can be effectively applied to high-precision spectroscopy of acetonitrile gas at atmospheric pressure. The demonstrated results indicate that this system is an attractive solution for practical applications of THz spectroscopy and other applications.

Hybrid dual-comb interferometer with easily established mutual coherence and a very high refresh rate

In this Letter, we propose a hybrid dual-comb interferometer (DCI) with a free-running mode-locked laser and an electro-optic frequency comb. The mutual coherence of this DCI is achieved by using an injection locking technique without any complicated phase-locking loops or post data processing algorithms. The proposed architecture is validated by resolving more than 10,000 comb lines of 250 MHz spacing with a refresh rate of 500 kHz. This combination of two kinds of optical frequency comb sources is suitable for wideband spectroscopic applications, where moderate spectral resolutions as well as high refresh rates are necessary.

Measurement of absolute frequency of continuous-wave terahertz radiation in real time using a free-running, dual-wavelength mode-locked, erbium-doped fibre laser

A single, free-running, dual-wavelength mode-locked, erbium-doped fibre laser was exploited to measure the absolute frequency of continuous-wave terahertz (CW-THz) radiation in real time using dual THz combs of photo-carriers (dual PC-THz combs). Two independent mode-locked laser beams with different wavelengths and different repetition frequencies were generated from this laser and were used to generate dual PC-THz combs having different frequency spacings in photoconductive antennae. Based on the dual PC-THz combs, the absolute frequency of CW-THz radiation was determined with a relative precision of 1.2 × 10⁻⁹ and a relative accuracy of 1.4 × 10⁻⁹ at a sampling rate of 100 Hz. Real-time determination of the absolute frequency of CW-THz radiation varying over a few tens of GHz was also demonstrated. Use of a single dual-wavelength mode-locked fibre laser, in place of dual mode-locked lasers, greatly reduced the size, complexity, and cost of the measurement system while maintaining the real-time capability and high measurement precision.

Gas-phase broadband spectroscopy using active sources: progress, status, and applications

Broadband spectroscopy is an invaluable tool for measuring multiple gas-phase species simultaneously. In this work we review basic techniques, implementations, and current applications for broadband spectroscopy. We discuss components of broad-band spectroscopy including light sources, absorption cells, and detection methods and then discuss specific combinations of these components in commonly-used techniques. We finish this review by discussing potential future advances in techniques and applications of broad-band spectroscopy.

Tunable resolution terahertz dual frequency comb spectrometer

Terahertz dual frequency comb spectroscopy (THz-DFCS) yields high spectral resolution without compromising bandwidth. Nonetheless, the resolution of THz-DFCS is usually limited by the laser repetition rate, which is typically between 80 MHz and 1 GHz. In this paper, we demonstrate a new method to achieve sub-repetition rate resolution in THz-DFCS by adaptively modifying the effective laser repetition rate using integrated Mach-Zehnder electro-optic modulators (MZ-EOMs). Our results demonstrate that it is possible to improve the 100 MHz resolution of a terahertz frequency comb by at least 20x (down to 5 MHz) across the terahertz spectrum without compromising the average output power, and to a large extent, its bandwidth. Our approach can augment a wide range of existing THz-DFCS systems to provide a significant and easily adaptable resolution improvement.

Dual-comb spectroscopy with a phase-modulated probe comb for sub-MHz spectral sampling

We present a straightforward and efficient method to reduce the mode spacing of a frequency comb based on binary pseudo-random phase modulation of its pulse train. As a proof of concept, we use such a densified comb to perform dual-comb spectroscopy of a long-delay Mach-Zehnder interferometer and a high-quality-factor microresonator with sub-MHz spectral sampling. Since this approach is based on binary phase modulation, it combines all the advantages of other densification techniques: simplicity, single-step implementation, and conservation of the initial comb's power.

Applications using high-Tc superconducting terahertz emitters

Using recently-developed THz emitters constructed from single crystals of the high-T_c superconductor Bi₂Sr₂CaCu₂O_8+δ, we performed three prototype tests of the devices to demonstrate their unique characteristic properties for various practical applications. The first is a compact and simple transmission type of THz imaging system using a Stirling cryocooler. The second is a high-resolution Michelson interferometer used as a phase-sensitive reflection-type imaging system. The third is a system with precise temperature control to measure the liquid absorption coefficient. The detailed characteristics of these systems are discussed.

Thermal tuning of Kerr frequency combs in silicon nitride microring resonators

Microresonator based Kerr frequency comb generation has many attractive features, including ultrabroad spectra, chip-level integration, and low power consumption. Achieving precise tuning control over the comb frequencies will be important for a number of practical applications, but has been little explored for microresonator combs. In this paper, we characterize the thermal tuning of a coherent Kerr frequency comb generated from an on-chip silicon nitride microring. When the microring temperature is changed by ~70 °C with an integrated microheater, the line spacing and center frequency of the comb are tuned respectively by -253 MHz (-3.57 MHz/°C) and by -175 GHz (-2.63 GHz/°C); the latter constitutes 75% of the comb line spacing. From these results we obtain a shift of 25 GHz (362.07 MHz/°C) in the comb carrier-envelope offset frequency. Numerical simulations are performed by taking into account the thermo-optic effects in the waveguide core and cladding. The temperature variation of the comb line spacing predicted from simulations is close to that observed in experiments. The time-dependent thermal response of the microheater based tuning scheme is characterized; time constants of 30.9 μs and 0.71 ms are observed.

Dual-comb spectroscopy

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.

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.

Parameter optimization of a dual-comb ranging system by using a numerical simulation method

Dual-comb system parameters have significant impacts on the ranging accuracy. We present a theoretical model and a numerical simulation method for the parameter optimization of a dual-comb ranging system. With this method we investigate the impacts of repetition rate difference, repetition rate, and carrier-envelope-offset frequency on the ranging accuracy. Firstly, the simulation results suggest a series of discrete zones of repetition rate difference in an optimal range, which are consistent with the experimental results. Secondly, the simulation results of the repetition rate indicate that a higher repetition rate is very favorable to improve the ranging accuracy. Finally, the simulation results suggest a series of discrete optimal ranges of the carrier-envelope-offset frequency for the dual-comb system. The simulated results were verified by our experiments.

Self-heterodyne interference spectroscopy using a comb generated by pseudo-random modulation

We present an original instrument designed to accomplish high-speed spectroscopy of individual optical lines based on a frequency comb generated by pseudo-random phase modulation of a continuous-wave (CW) laser. This approach delivers efficient usage of the laser power as well as independent control over the spectral point spacing, bandwidth and central wavelength of the comb. The comb is mixed with a local oscillator generated from the same CW laser frequency-shifted by an acousto-optic modulator, enabling a self-heterodyne detection scheme. The current configuration offers a calibrated spectrum every 1.12 µs. We demonstrate the capabilities of the spectrometer by producing averaged, as well as time-resolved, spectra of the D1 transition of cesium with a 9.8-MHz point spacing, a 50-kHz resolution and a span of more than 3 GHz. The spectra obtained after 1 ms of averaging are fitted with complex Voigt profiles that return parameters in good agreement with expected values.

A decade-spanning high-resolution asynchronous optical sampling terahertz time-domain and frequency comb spectrometer

We present the design and capabilities of a high-resolution, decade-spanning ASynchronous OPtical Sampling (ASOPS)-based TeraHertz Time-Domain Spectroscopy (THz-TDS) instrument. Our system employs dual mode-locked femtosecond Ti:Sapphire oscillators with repetition rates offset locked at 100 Hz via a Phase-Locked Loop (PLL) operating at the 60th harmonic of the ∼80 MHz oscillator repetition rates. The respective time delays of the individual laser pulses are scanned across a 12.5 ns window in a laboratory scan time of 10 ms, supporting a time delay resolution as fine as 15.6 fs. The repetition rate of the pump oscillator is synchronized to a Rb frequency standard via a PLL operating at the 12th harmonic of the oscillator repetition rate, achieving milliHertz (mHz) stability. We characterize the timing jitter of the system using an air-spaced etalon, an optical cross correlator, and the phase noise spectrum of the PLL. Spectroscopic applications of ASOPS-THz-TDS are demonstrated by measuring water vapor absorption lines from 0.55 to 3.35 THz and acetonitrile absorption lines from 0.13 to 1.39 THz in a short pathlength gas cell. With 70 min of data acquisition, a 50 dB signal-to-noise ratio is achieved. The achieved root-mean-square deviation is 14.6 MHz, with a mean deviation of 11.6 MHz, for the measured water line center frequencies as compared to the JPL molecular spectroscopy database. Further, with the same instrument and data acquisition hardware, we use the ability to control the repetition rate of the pump oscillator to enable THz frequency comb spectroscopy (THz-FCS). Here, a frequency comb with a tooth width of 5 MHz is generated and used to fully resolve the pure rotational spectrum of acetonitrile with Doppler-limited precision. The oscillator repetition rate stability achieved by our PLL lock circuits enables sub-MHz tooth width generation, if desired. This instrument provides unprecedented decade-spanning, tunable resolution, from 80 MHz down to sub-MHz, and heralds a new generation of gas-phase spectroscopic tools in the THz region.

High density terahertz frequency comb produced by coherent synchrotron radiation

Frequency combs have enabled significant progress in frequency metrology and high-resolution spectroscopy extending the achievable resolution while increasing the signal-to-noise ratio. In its coherent mode, synchrotron radiation is accepted to provide an intense terahertz continuum covering a wide spectral range from about 0.1 to 1 THz. Using a dedicated heterodyne receiver, we reveal the purely discrete nature of this emission. A phase relationship between the light pulses leads to a powerful frequency comb spanning over one decade in frequency. The comb has a mode spacing of 846 kHz, a linewidth of about 200 Hz, a fractional precision of about 2 × 10(-10) and no frequency offset. The unprecedented potential of the comb for high-resolution spectroscopy is demonstrated by the accurate determination of pure rotation transitions of acetonitrile.

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.

Decade-spanning high-precision terahertz frequency comb

The generation and detection of a decade-spanning terahertz (THz) frequency comb is reported using two Ti:sapphire femtosecond laser oscillators and asynchronous optical sampling THz time-domain spectroscopy. The comb extends from 0.15 to 2.4 THz, with a tooth spacing of 80 MHz, a linewidth of 3.7 kHz, and a fractional precision of 1.8×10^{-9}. With time-domain detection of the comb, we measure three transitions of water vapor at 10 mTorr between 1-2 THz with an average Doppler-limited fractional accuracy of 6.1×10^{-8}. Significant improvements in bandwidth, resolution, and sensitivity are possible with existing technologies.

High-resolution terahertz spectroscopy with a single tunable frequency comb

We report an improvement of three orders of magnitude in the spectral resolution of a recently proposed single-comb terahertz spectroscopy [Opt. Lett.39, 5669 (2014)]. The improvement is achieved by using a femtosecond optical pulse train with a tunable repetition rate. Terahertz comb with tunable spectral line spacing generated by the train is detected via nonlinear mixing with a harmonic of a CW signal from a microwave frequency synthesizer. By applying this technique to the low-pressure gas spectroscopy, we achieved a 100 kHz spectral resolution in measuring separate absorption lines of the rotational manifold of fluoroform (CF₃H).

Coherent dual-comb interferometry with quasi-integer-ratio repetition rates

We demonstrate a generalized method for dual-comb interferometry that involves the use of two frequency combs with quasi-integer-ratio repetition rates. We use a 16.67 MHz comb to probe an 80-cm-long ring cavity and a 100 MHz comb to asynchronously sample its impulse response. The resulting signal can be seen as six time-multiplexed independent interferograms. We perform a deconvolution of the photodetector's impulse response to prevent any crosstalk between these multiplexed data sets. The measurement is then demultiplexed and corrected with referencing signals. We obtain a measurement with a spectral point spacing of 16.67 MHz and a spectral SNR of 55 dB by averaging 15,000 interferograms, corresponding to a measurement time of 500 s. Compared to conventional dual-comb spectroscopy, this generalized technique allows to either reduce the spectral point spacing or the acquisition time by changing the repetition rate of only one of the combs.

Phase-slope and phase measurements of tunable CW-THz radiation with terahertz comb for wide-dynamic-range, high-resolution, distance measurement of optically rough object

Phase measurement of continuous-wave terahertz (CW-THz) radiation is a potential tool for direct distance and imaging measurement of optically rough objects due to its high robustness to optical rough surfaces. However, the 2π phase ambiguity in the phase measurement of single-frequency CW-THz radiation limits the dynamic range of the measured distance to the order of the wavelength used. In this article, phase-slope measurement of tunable CW-THz radiation with a THz frequency comb was effectively used to extend the dynamic range up to 1.834 m while maintaining an error of a few tens µm in the distance measurement of an optically rough object. Furthermore, a combination of phase-slope measurement of tunable CW-THz radiation and phase measurement of single-frequency CW-THz radiation enhanced the distance error to a few µm within the dynamic range of 1.834 m without any influence from the 2π phase ambiguity. The proposed method will be a powerful tool for the construction and maintenance of large-scale structures covered with optically rough surfaces.