Coherently averaged dual-comb spectroscopy with a low-noise and high-power free-running gigahertz dual-comb laser: erratum.

This erratum corrects a typographical error in equation (8) of our published paper [Opt. Express31, 7103 (2023)10.1364/OE.479356]. All the calculations used the correct equation, so all the results and conclusions remain unchanged.

Coherently averaged dual-comb spectroscopy with a low-noise and high-power free-running gigahertz dual-comb laser.

We present a new type of dual optical frequency comb source capable of scaling applications to high measurement speeds while combining high average power, ultra-low noise operation, and a compact setup. Our approach is based on a diode-pumped solid-state laser cavity which includes an intracavity biprism operated at Brewster angle to generate two spatially-separated modes with highly correlated properties. The 15-cm-long cavity uses an Yb:CALGO crystal and a semiconductor saturable absorber mirror as an end mirror to generate more than 3 W average power per comb, below 80 fs pulse duration, a repetition rate of 1.03 GHz, and a continuously tunable repetition rate difference up to 27 kHz. We carefully investigate the coherence properties of the dual-comb by a series of heterodyne measurements, revealing several important features: (1) ultra-low jitter on the uncorrelated part of the timing noise; (2) the radio frequency comb lines of the interferograms are fully resolved in free-running operation; (3) we validate that through a simple measurement of the interferograms we can determine the fluctuations of the phase of all the radio frequency comb lines; (4) this phase information is used in a post-processing routine to perform coherently averaged dual-comb spectroscopy of acetylene (C2H2) over long timescales. Our results represent a powerful and general approach to dual-comb applications by combining low noise and high power operation directly from a highly compact laser oscillator.

Efficient pump-probe sampling with a single-cavity dual-comb laser: Application in ultrafast photoacoustics.

Ultrafast pump-probe measurements are used to characterize various samples, such as biological cells, bulk, and thin-film structures. However, typical implementations of the pump-probe apparatus are either slow or complex and costly hindering wide deployment. Here we combine a single-cavity dual-comb laser with a simple experimental setup to obtain pump-probe measurements with ultra-high sensitivity, fast acquisition, and high timing precision over long optical delay scan ranges of 12.5 ns that would correspond to a mechanical delay of about 3.75 m. We employ digital signal balancing to obtain shot-noise-limited detection compatible with pump-probe microscopy deployment. Here we demonstrate ultrafast photoacoustics for thin-film sample characterization. We measured a tungsten layer thickness of (700 ± 4) Å with shot-noise-limited detection. Such single-cavity dual-comb lasers can be used for any pump-probe measurements and are especially well-suited for ultrafast photoacoustic studies such as involving ultrasonic echoes, Brillouin oscillations, surface acoustic waves and thermal dynamics.

Dual-comb optical parametric oscillator in the mid-infrared based on a single free-running cavity.

We demonstrate a free-running single-cavity dual-comb optical parametric oscillator (OPO) pumped by a single-cavity dual-comb solid-state laser. The OPO ring cavity contains a single periodically-poled MgO-doped LiNbO3 (PPLN) crystal. Each idler beam has more than 245-mW average power at 3550 nm and 3579 nm center wavelengths (bandwidth 130 nm). The signal beams are simultaneously outcoupled with more than 220 mW per beam at 1499 nm and 1496 nm center wavelength. The nominal repetition rate is 80 MHz, while the repetition rate difference is tunable and set to 34 Hz. To evaluate the feasibility of using this type of source for dual-comb applications, we characterize the noise and coherence properties of the OPO signal beams. We find ultra-low relative intensity noise (RIN) below -158 dBc/Hz at offset frequencies above 1 MHz. A heterodyne beat note measurement with a continuous wave (cw) laser is performed to determine the linewidth of a radio-frequency (RF) comb line. We find a full-width half-maximum (FWHM) linewidth of around 400 Hz. Moreover, the interferometric measurement between the two signal beams reveals a surprising property: the center of the corresponding RF spectrum is always near zero frequency, even when tuning the pump repetition rate difference or the OPO cavity length. We explain this effect theoretically and discuss its implications for generating stable low-noise idler combs suitable for high-sensitivity mid-infrared dual-comb spectroscopy (DCS).

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.

Complex Field-Induced States in Linarite PbCuSO4(OH)2 with a Variety of High-Order Exotic Spin-Density Wave States.

Low-temperature neutron diffraction and NMR studies of field-induced phases in linarite are presented for magnetic fields H∥b axis. A two-step spin-flop transition is observed, as well as a transition transforming a helical magnetic ground state into an unusual magnetic phase with sine-wave-modulated moments ∥H. An effective J[over ˜]_{1}-J[over ˜]_{2} single-chain model with a magnetization-dependent frustration ratio α_{eff}=-J[over ˜]_{2}/J[over ˜]_{1} is proposed. The latter is governed by skew interchain couplings and shifted to the vicinity of the ferromagnetic critical point. It explains qualitatively the observation of a rich variety of exotic longitudinal collinear spin-density wave, SDW_{p}, states (9≥p≥2).

Magnetic frustration in a quantum spin chain: the case of linarite PbCuSO4(OH)2.

We present a combined neutron diffraction and bulk thermodynamic study of the natural mineral linarite PbCuSO4(OH)2, this way establishing the nature of the ground-state magnetic order. An incommensurate magnetic ordering with a propagation vector k=(0,0.186,1/2) was found below T(N)=2.8 K in a zero magnetic field. The analysis of the neutron diffraction data yields an elliptical helical structure, where one component (0.638µ(B)) is in the monoclinic ac plane forming an angle with the a axis of 27(2)°, while the other component (0.833µ(B)) points along the b axis. From a detailed thermodynamic study of bulk linarite in magnetic fields up to 12 T, applied along the chain direction, a very rich magnetic phase diagram is established, with multiple field-induced phases, and possibly short-range-order effects occurring in high fields. Our data establish linarite as a model compound of the frustrated one-dimensional spin chain, with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. Long-range magnetic order is brought about by interchain coupling 1 order of magnitude smaller than the intrachain coupling.