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

Highly coherent hybrid dual-comb spectrometer

Dual comb spectroscopy (DCS) is a broadband technique offering high resolution and fast data acquisition. Current state-of-the-art designs are based on a pair of fiber or solid-state lasers, which allow broadband spectroscopy but require a complicated stabilization setup. Semiconductor lasers are tunable, cost-effective, and easily integrable while limited by a narrow bandwidth. This motivates a hybrid design combining the advantages of both systems. However, establishing sufficiently long mutual coherence time remains challenging. This work describes a hybrid dual-comb spectrometer comprising a broadband fiber laser (FC) and an actively mode-locked semiconductor laser (MLL) with a narrow but tunable spectrum. A high mutual coherence time of around 100 seconds has been achieved by injection locking the MLL to a continuous laser (CW), which is locked on a single line of the FC. We have also devised a method to directly stabilize the entire spectrum of FC to a high finesse cavity. This results in a long term stability of 5 × 10^-12 at 1 second and 5 × 10^-14 at 350 seconds. Additionally, we have addressed the effect of cavity dispersion on the locking quality, which is important for broadband comb lasers.

Ultra-rapid dual-comb ranging with an extended non-ambiguity range

In this Letter, we report a scheme that combines time-of-flight (ToF) ranging detection of multi-repetition-rate pulses with asymmetric dual-comb ranging (DCR) measurement. Notably, this combination extends the non-ambiguity range (NAR) of the DCR method without sacrificing its refresh rate and distance precision. With this scheme, we demonstrate absolute distance measurement of moving targets with an NAR of 1.5 km, which is 5× larger than that allowed solely by the DCR method for a given refresh rate at 500 kHz. The ranging precision in a single measurement of 2 µs reaches 10 µm at an effective distance of 571 m (down to 60 nm in 0.1 s). This combined scheme benefits remote sensing of high-speed objects.

Linear optical sampling enabled soliton nonlinear frequency spectrum classification

Nonlinear Fourier transform (NFT) is a powerful tool for characterizing optical soliton dynamics, which, however, suffers from fundamental limitations that ultra-wide bandwidth photodetectors and ultra-high sampling rate analog-to-digital converters should be used when accessing the full-field information of an ultrafast optical pulse. Herein, we report on the experimental demonstration of the linear optical sampling (LOS) enabled nonlinear frequency spectrum classification of ultrashort optical pulses, which could break this limitation. Instead of traditional coherent detection, the LOS overcomes the ultra-wide bandwidth constraint of commercially available optoelectrical devices. By finely adjusting the repetition rate difference between the soliton to be characterized and the sampling pulsed source, a 55.56-TSa/s equivalent sampling rate arising in the LOS can be secured, where only 400-MHz balanced photodetectors and 5-GSa/s analog-to-digital converter are used. Meanwhile, according to the nonlinear frequency spectrum calculated from the accurate full-field information, the promising concept of soliton distillation has been experimentally verified for the first time. The LOS-enabled NFT technique provides an alternative and efficient characterization tool for ultrafast fiber lasers, which facilities comprehensive insight into soliton dynamics.

Timing jitter characterization of free-running dual-comb laser with sub-attosecond resolution using optical heterodyne detection

Pulse trains emitted from dual-comb systems are designed to have low relative timing jitter, making them useful for many optical measurement techniques such as optical ranging and spectroscopy. However, the characterization of low-jitter dual-comb systems is challenging because it requires measurement techniques with high sensitivity. Motivated by this challenge, we developed a technique based on an optical heterodyne detection approach for measuring the relative timing jitter of two pulse trains. The method is suitable for dual-comb systems with essentially any repetition rate difference. Furthermore, the proposed approach allows for continuous and precise tracking of the sampling rate. To demonstrate the technique, we perform a detailed characterization of a single-mode-diode pumped Yb:CaF₂ dual-comb laser from a free-running polarization-multiplexed cavity. This new laser produces 115-fs pulses at 160 MHz repetition rate, with 130 mW of average power in each comb. The detection noise floor for the relative timing jitter between the two pulse trains reaches 8.0 × 10^-7 fs²/Hz (∼ 896 zs/Hz), and the relative root mean square (rms) timing jitter is 13 fs when integrating from 100 Hz to 1 MHz. This performance indicates that the demonstrated laser is highly compatible with practical dual-comb spectroscopy, ranging, and sampling applications. Furthermore, our results show that the relative timing noise measurement technique can characterize dual-comb systems operating in free-running mode or with finite repetition rate differences while providing a sub-attosecond resolution, which was not feasible with any other approach before.

Phase-stable repetition rate multiplication of dual-comb spectroscopy based on a cascaded Mach-Zehnder interferometer

In this Letter, we demonstrate a passive all-fiber pulse delay method for repetition rate multiplication of dual-comb spectroscopy. By combining a cascaded Mach-Zehnder interferometer and digital error correction, a mode-resolved spectrum with improved acquisition speed and sensitivity can be obtained. This technique has the strengths of compact, broadband, high energetic efficiency, and low complexity. Due to the use of an adaptive post-processing algorithm, sophisticated closed-loop feedback electronics are not required, which provides a simple and effective scheme to break through the physical limitation of the repetition frequency of the frequency comb for phase-stable dual-comb applications.

Achieving Precise Spectral Analysis and Imaging Simultaneously with a Mode-Resolved Dual-Comb Interferometer

In this paper, we report a scheme providing precise spectral analysis and surface imaging, simultaneously, based on a high-coherence dual-comb interferometer. With two tightly phase-locking frequency combs, we demonstrate a high-coherence dual-comb interferometer (DCI) covering 188 to 195 THz (1538.5 to 1595.7 nm) with comb-tooth resolution and a max spectral signal-to-noise ratio (SNR) of 159.7. The combination of the high-coherence dual-comb spectrometer and a reference arm simultaneously enables gas absorption spectroscopy and for the absolute distance information to be obtained in one measurement. As a demonstration, we measure the spectrum of CO2 and CO. From the same interferograms, we demonstrate that distance measurement, by time-of-flight (TOF), can be resolved with an rms precision of 0.53 μm after averaging 140 images and a measurement time of 1 s. Finally, we demonstrate that non-contact surface imaging, using 2D mechanical scanning, reaches lateral resolution of 40 μm. The longitudinal precision is 0.68 μm with a measurement time of 0.5 s. It verifies that DCS has the potential to be applied in standoff detection, environmental pollution monitors, and remote sensing.

Time-expanded phase-sensitive optical time-domain reflectometry

Phase-sensitive optical time-domain reflectometry (ΦOTDR) is a well-established technique that provides spatio-temporal measurements of an environmental variable in real time. This unique capability is being leveraged in an ever-increasing number of applications, from energy transportation or civil security to seismology. To date, a wide number of different approaches have been implemented, providing a plethora of options in terms of performance (resolution, acquisition bandwidth, sensitivity or range). However, to achieve high spatial resolutions, detection bandwidths in the GHz range are typically required, substantially increasing the system cost and complexity. Here, we present a novel ΦOTDR approach that allows a customized time expansion of the received optical traces. Hence, the presented technique reaches cm-scale spatial resolutions over 1 km while requiring a remarkably low detection bandwidth in the MHz regime. This approach relies on the use of dual-comb spectrometry to interrogate the fibre and sample the backscattered light. Random phase-spectral coding is applied to the employed combs to maximize the signal-to-noise ratio of the sensing scheme. A comparison of the proposed method with alternative approaches aimed at similar operation features is provided, along with a thorough analysis of the new trade-offs. Our results demonstrate a radically novel high-resolution ΦOTDR scheme, which could promote new applications in metrology, borehole monitoring or aerospace.

Gain-switched semiconductor lasers with pulsed excitation and optical injection for dual-comb spectroscopy

In this work we demonstrate the capability of two gain-switched optically injected semiconductor lasers to perform high-resolution dual-comb spectroscopy. The use of low duty cycle pulse trains to gain switch the lasers, combined with optical injection, allows us to obtain flat-topped optical frequency combs with 350 optical lines (within 10 dB) spaced by 100 MHz. These frequency combs significantly improve the spectral resolution reported so far on dual-comb spectroscopy with gain-switched laser diodes. We evaluate the performance of our system by measuring the transmission profile of an absorption line of H¹³CN at the C-band, analyzing the attainable signal-to-noise ratio for a range of averaging times.

Broadband and high-resolution electro-optic dual-comb interferometer with frequency agility

We propose a broadband and high-resolution dual-comb interferometer (DCI) realized with dense electro-optic frequency combs (EOFCs), which are generated with two-stage electro-optic modulation and nonlinear fiber spectral broadening. The broadband coarse comb is generated in the first-stage modulation and the space between neighboring combs is filled with a dense electrical comb in the second-stage modulation. The spectral resolution of the DCI can be flexibly changed from 10 MHz to 1 GHz easily as required, and electro-optic DCIs with 10-MHz, 100-MHz, and 1-GHz frequency resolutions are experimentally realized. Meanwhile, DCI working in the quasi-integer-ratio mode is easily implemented in this system for the increased refresh rate and improved figure of merit especially for high resolution. As a demonstration, 150000 comb lines with 10 MHz frequency interval are resolved in the experiment.

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.

Calculating the Effective Center Wavelength for Heterodyne Interferometry of an Optical Frequency Comb

Heterodyne interferometry based on an optical frequency comb (OFC) is a powerful tool for distance measurement. In this paper, a method to calculate the effective center wavelength of wide spectrum heterodyne interference signal was explored though both simulation and experiment. Results showed that the effective center wavelength is a function of the spectra of the two interfered beams and time-delay of the two overlapped pulses. If the product of the spectra from two arms is symmetric, the effective center wavelength does not change with time-delay of the two pulses. The relative difference between the simulation and experiment was less than 0.06%.

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.

Synthetic wavelength interferometry of an optical frequency comb for absolute distance measurement

We present a synthetic-wavelength based heterodyne interferometer of optical frequency combs with wide consecutive measurement range for absolute distance measurement. The synthetic wavelength is derived from two wavelengths obtained by two band-pass filters. The interferometric phase of the synthetic wavelength is used as a marker for the pulse-to-pulse alignment, which greatly improves the accuracy of traditional peak finding method. The consecutive measurement range is enlarged by using long fiber to increase the path length difference of the reference and measurement arms. The length of the long fiber is stabilized according to the interferometric phase of a CW laser. The experimental results show the present system can realize an accuracy of 75 nm in 350 mm consecutive measurement range.

Dense electro-optic frequency comb generated by two-stage modulation for dual-comb spectroscopy

An electro-optic frequency comb enables frequency-agile comb-based spectroscopy without using sophisticated phase-locking electronics. Nevertheless, dense electro-optic frequency combs over broad spans have yet to be developed. In this Letter, we propose a straightforward and efficient method for electro-optic frequency comb generation with a small line spacing and a large span. This method is based on two-stage modulation: generating an 18 GHz line-spacing comb at the first stage and a 250 MHz line-spacing comb at the second stage. After generating an electro-optic frequency comb covering 1500 lines, we set up an easily established mutually coherent hybrid dual-comb interferometer, which combines the generated electro-optic frequency comb and a free-running mode-locked laser. As a proof of concept, this hybrid dual-comb interferometer is used to measure the absorption and dispersion profiles of the molecular transition of H¹³CN with a spectral resolution of 250 MHz.

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.

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.

Coherent radio-frequency detection for narrowband direct comb spectroscopy

We demonstrate a scheme for coherent narrowband direct optical frequency comb spectroscopy. An extended cavity diode laser is injection locked to a single mode of an optical frequency comb, frequency shifted, and used as a local oscillator to optically down-mix the interrogating comb on a fast photodetector. The high spectral coherence of the injection lock generates a microwave frequency comb at the output of the photodiode with very narrow features, enabling spectral information to be further down-mixed to RF frequencies, allowing optical transmittance and phase to be obtained using electronics commonly found in the lab. We demonstrate two methods for achieving this step: a serial mode-by-mode approach and a parallel dual-comb approach, with the Cs D1 transition at 894 nm as a test case.

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.

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.