Beat Note Research Articles

A narrow linewidth terahertz dual-comb spectrometer with an all-fiber adaptive clock and a real-time feedback loop

Terahertz comb spectroscopy offers advantages of high-resolution in broadband THz regions. However, conventional implementations of terahertz comb spectrometers are difficult to simultaneously achieve high precision and long-term stability due to the residual timing jitter of the involved light sources. In this work, an adaptive-clock signal from optical beat note in optical region was extracted for real-time correcting the unstable sampling interval-time caused by the residual timing jitter and a loosely active frequency-stabilized scheme functioned as a real-time feedback. And finally, a long-term stable terahertz dual-comb spectrometer was constructed with a spectral resolution of 66.14 MHz, a comb linewidth of 1.9 kHz, a fractional precision of 1.7 × 10−9 and a long-term operation over 1200 h. This proved that the precise acquisition of THz pulses could be realized through the compensation of timing jitter for pumped optical pulses. The presented terahertz comb spectrometer is featured with enhanced robustness compared to previous schemes based on two fully stabilized mode-locked laser combs, which would thus facilitate field deployment outside the laboratories.

Mode-Locked Fiber Laser Sensors with Orthogonally Polarized Pulses Circulating in the Cavity

Intracavity phase interferometry is a powerful phase sensing technique using two correlated, counter-propagating frequency combs (pulse trains) in mode-locked lasers. Generating dual frequency combs of the same repetition rate in fiber lasers is a new field with hitherto unanticipated challenges. The large intensity in the fiber core, coupled with the nonlinear index of glass, result in a cumulative nonlinear index on axis that dwarfs the signal to be measured. The large saturable gain changes in an unpredictable way the repetition rate of the laser impeding the creation of frequency combs with identical repetition rate. The huge amount of phase coupling between pulses crossing at the saturable absorber eliminates the small signal response (deadband). Although there have been prior observation of gyroscopic response in mode-locked ring lasers, to our knowledge this is the first time that orthogonally polarized pulses were used to successfully eliminate the deadband and obtain a beat note.

Near-Full Current Dynamic Range THz Quantum Cascade Laser Frequency Comb.

The present study proposes a terahertz quantum cascade laser frequency comb (THz QCL FC) with a semi-insulated surface plasma waveguide characterized by a low threshold current density, high power and a wide current dynamic range. The gain dispersion value and the nonlinear susceptibility were optimized based on the combination of a hybrid bound-to-continuum active region with a semi-insulated surface plasmon waveguide. Without any extra dispersion compensator, stable frequency comb operation within a current dynamic range of more than 97% of the total was revealed by the intermode beat note map. Additionally, a total comb spectral emission of about 300 GHz centered around 4.6 THz was achieved for a 3 mm long and 150 µm wide device. At 10 K, a maximum output power of 22 mW was obtained with an ultra-low threshold current density of 64.4 A·cm-2.

Low threshold Kerr solitons.

Pumping a nonlinear optical cavity with continuous wave coherent light can result in generation of a stable train of short optical pulses. Pumping the cavity with a non-degenerate resonant coherent dichromatic pump usually does not produce a stable mode-locked regime due to competition of the oscillations at the pump frequencies. We show that generation of stable optical pulses is feasible in a dichromatically pumped cavity characterized with group velocity dispersion optimized in a way that the group velocity value becomes identical for the generated pulses and the beat note of the pump harmonics. The power threshold of the process drops nearly four times in this case and the produced pulses become sub-harmonically locked to the dichromatic pump harmonics. The process is useful for generation of broadband optical frequency combs and optical time crystals.

Temperature dependence of the absorption of the R(6) manifold of the 2ν3 band of methane in air in support of the MERLIN mission

Fifty nine high sensitivity spectra of the R(6) manifold of the 2ν3 band of methane in air, near 1.64 µm, have been recorded in support of the MERLIN mission. For this purpose, a cavity ring down spectrometer (CRDS) with a spectrally narrowed and stable (sub-kHz) laser source was coupled to a temperature regulated high-finesse optical cavity. The frequency scale of each spectrum was accurately determined from measurements of the beat note between a part of the laser light and the closest tooth of a frequency comb referenced to a rubidium clock. Series of spectra were recorded between 243 and 313 K with a 10 K temperature step. For each series, total pressure values of 50, 100, 250, 500 and 750 Torr were adopted. A multi-spectrum fitting procedure with the Hartmann-Tran (HT) line profile, including the first-order line-mixing parameter, has been used to derive the spectroscopic parameters for each of the six R(6) components, along with the temperature dependence of the line-shape parameters. The results show that the fitted effective model is able to reproduce the experimental spectra with a relative precision better than 0.2% for the entire R(6) manifold spectral region and better than 0.05% at the ON-line position of the MERLIN mission for the 250, 500 and 750 Torr spectra. The relative precision increases to 0.3% and the residuals at the ON-line position to 0.1% when including the 50 and 100 Torr spectra. Comparisons with ground-based atmospheric measurements show that these data significantly improve the modeling of methane absorption in this spectral region. The complete line list of the methane spectrum in the region of the R(6) manifold allowing notable improvement of the modeling of the absorption cross-section at the ON-line position of the MERLIN mission is provided as Supplementary Material.

All-fiber acetylene-referenced optical frequency comb

We demonstrated an all-fiber compact Erbium-doped optical frequency comb based on optical reference. Compared with the traditional RF reference, the whole system adopts the all-fiber design of optical reference. Comb stabilization is achieved by simultaneously locking the repetition rate (fr) to an RF reference and an optical comb tooth to a CW reference. The standard deviation of the fr frequency in 4.5 hours was recorded as 0.37 mHz, leading to a fraction instability of 4.3 ×10−12 at 1 s gate time and 2.8 ×10−13 at 10 s gate time. The locking of single comb tooth is achieved by locking the optical comb and the beat note of the CW laser. We used the P(16) overtone transition line of 13C2H2 as the CW reference and optimized the stabilization by choosing appropriate lock point on the Doppler-limited absorption transition. The comb was able to achieve stable locking for almost five hours. The short-term fraction instability of the optical frequency was measured to be 6.56 ×10−10 at 1 s gate time, which is mostly from the CW reference. Our approach of acetylene-stabilized fiber comb offers a feasible solution to help fiber combs move from laboratory to outdoors applications based on fiber sensing, laser stabilization and spectrum analysis.

Broadband coherently synthesized two-color electro-optic frequency combs with phase noise suppression

A coherently synthesized 1550/1560 nm two-color EO comb is generated by modulating two continuous-wave lasers with common EO modulators and phase-locking their beat note. Compared with a single-color EO comb, the phase noise of comb modes that accumulated from the RF synthesizer is effectively suppressed in our coherently synthesized two-color EO comb. Besides, a broader spectrum is demonstrated in a coherently synthesized 1535/1560 nm two-color EO comb, with a 60-nm total spectrum span. The coherently synthesized two-color EO combs are expected to be applied in coherent communication, spectroscopy, absolute distance measurement, etc.

Polarization-multiplexed dual-comb fiber laser based on an all-polarization-maintaining cavity configuration

In this study, we present a polarization-multiplexed, erbium-doped dual-comb fiber laser based on an all-polarization-maintaining cavity configuration. We observed that the dual-comb fiber laser easily realized the self-starting mode-locking operation due to the non-linear amplifying loop mirror (NALM) with a non-reciprocal phase shifter. Furthermore, owing to the sharing of the NALM part, the two outputs from this laser configuration had similar center wavelengths, with small different repetition rates (∆frep). In the free-running operation, the standard deviation of relative stability for Δfrep of 2.09 kHz was measured to be 1.59 Hz, and the full width at half-maximum of the relative beat note between the two frequency combs in the optical frequency domain was approximately 1 kHz. These results show that the two frequency combs from this laser configuration have high relative stability and mutual coherence.

Active Cancellation of Servo-Induced Noise on Stabilized Lasers via Feedforward

Many precision laser applications require active frequency stabilization. However, such stabilization loops operate by pushing noise to frequencies outside their bandwidth, leading to large ``servo bumps'' that can have deleterious effects for certain applications. The prevailing approach to filtering this noise is to pass the laser through a high-finesse optical cavity, which places constraints on the system design. Here, we propose and demonstrate a different approach where a frequency error signal is derived from a beat note between the laser and the light that passes through the reference cavity. The phase noise derived from this beat note is fed forward to an electro-optic modulator after the laser, carefully accounting for relative delay, for real-time frequency correction. With a hertz-line-width laser, we show $\ensuremath{\gtrsim}20\phantom{\rule{0.2em}{0ex}}\mathrm{dB}$ noise suppression at the peak of the servo bump (approximately $250\phantom{\rule{0.2em}{0ex}}\mathrm{kHz}$) and a noise-suppression bandwidth of approximately $5\phantom{\rule{0.2em}{0ex}}\mathrm{MHz}$---well beyond the servo bump. By simulating the Rabi dynamics of a two-level atom with our measured data, we demonstrate substantial improvements to the pulse fidelity over a wide range of Rabi frequencies. Our approach offers a simple and versatile method for obtaining a clean spectrum of a narrow-line-width laser, as required in many emerging applications of cold atoms, and is readily compatible with commercial systems that may even include wavelength conversion.

Frequency stabilisation and SI tracing of mid-infrared quantum-cascade lasers for precision molecular spectroscopy

The advancement of technologies for the precise interrogation of molecules offers exciting possibilities for new studies in the realms of precision spectroscopy and quantum technologies. Experiments in these domains often address molecular vibrations in the mid-infrared (MIR) spectral region, thus generating the need for spectrally pure and accurate MIR laser sources. Quantum-cascade lasers (QCLs) have emerged as flexible sources of coherent radiation available over a wide range of MIR frequencies. Here, we demonstrate a robust approach for the simultaneous linewidth narrowing, frequency stabilisation, and absolute frequency referencing of MIR QCLs all of which are prerequisites for precise spectroscopic experiments. Following upconversion of its radiation to the visible domain, we implement a phase lock of the QCL to a linewidth-narrowed optical frequency comb which is referenced to a remote SI-traceable primary frequency standard via a fibre link for absolute frequency calibration. To achieve a reliable frequency counting of the beat note between the QCL and the OFC, we employ redundant tracking oscillators and demonstrate a frequency instability of at 1 s and at 1000 s integration time, limited by the accuracy of our remote reference.

Feed-forward stabilization of a single-frequency, diode-pumped Pr:YLF-Cr:LiCAF laser operating at 813.42 nm.

We introduce a simple and compact diode-pumped Pr:YLF-Cr:LiCAF laser, operating at 813.42 nm and providing a 130-mW, single-frequency output tunable over a 3-GHz range. The laser has a short-term intrinsic linewidth estimated to be 700 Hz (β-separation method), while exhibiting a free-running wavelength stability of below 1 pm in one hour. Using a feed-forward technique we demonstrate the integration of the laser output into a fully stabilized, 1-GHz Ti:sapphire laser frequency comb, resulting in a heterodyne beat note between the laser and the comb with a bandwidth of 65 kHz. Combining feed-forward control with a low-bandwidth servo feedback loop permits stable long-term locking with an rms beat note variation of 15 kHz over 2 minutes. This performance makes the laser a potential candidate for the lattice laser in a 87Sr optical lattice clock.

Beyond the Petermann limit: Prospect of increasing sensor precision near exceptional points

Experiments near the lock-in region in maximally dissipative non-Hermitian systems, e.g., conventional laser gyroscopes near the deadband, have run up against the Petermann limit, where excess noise exactly cancels any scale-factor enhancement resulting in no overall enhancement in precision. As a result, one might be tempted to conclude that exceptional points (EPs) generally cannot be used to increase the precision of laser sensors. Indeed, using a linear eigenmode analysis we show that the Petermann limit applies not just to maximally dissipative systems, but for any type of EP, owing to the fact that EPs are rotationally invariant. It turns out, however, that this restriction comes from the assumption of linearity. We find that nonlinearity breaks the rotation symmetry such that the different types of EPs are no longer equivalent above threshold. In particular, EPs in conservatively coupled systems can lead to an increase in the fundamental precision beyond the Petermann limit as a result of gain saturation. Importantly, we find that only one mode lases under these conditions. We show that the beat note can be recovered by interference with an auxiliary mode, but that this has consequences for the quantum and classical noise that depend on the recovery scheme. Thus, it remains to be seen whether practical experiments can be designed that can take advantage of this enhancement.

Polarization multiplexed dissipative Kerr solitons in an on-chip micro-resonator.

We demonstrate polarization multiplexed dissipative Kerr solitons in an on-chip silicon nitride micro-resonator. In our experiment, TE- and TM-polarized solitons can be individually generated and controlled, thanks to their weak mutual interaction as the result of sufficiently different repetition rates and orthogonal polarization states. Furthermore, we find that TE- and TM-polarized solitons usually exhibit uncorrelated time jitters. Therefore, the frequency and phase coherence between the polarization multiplexed soliton microcombs change dramatically as a function of pump laser parameters, where by optimization, we achieve a narrow dual-microcomb beat note linewidth as small as 4.4 kHz. Potential applications of on-chip polarization multiplexed soliton microcombs include Kerr comb spectral expansion, dual-comb metrology, and measurement of quantum entanglements.

200-Hz longitudinal-mode linewidth found in a free-running mode-locked Yb:fiber laser.

We surveyed the longitudinal-mode linewidth of five homemade mode-locked Yb:fiber lasers by taking the beat note with a Hz-level narrow-linewidth CW laser. We systematically varied the resolution bandwidth of the spectrum analyzer and found that the linewidth can be as narrow as 200 Hz, which surpassed the records for free-running mode-locked lasers in the literature to our best knowledge. Based on the survey, we propose that making the cavity long and simple is a good working hypothesis for narrowing the linewidth and provide practical techniques to reduce the environmental fluctuations.

Modulation Transfer Spectroscopy of a four-level ladder system in atomic rubidium

We demonstrate Modulation Transfer Spectroscopy for a four-level ladder-configuration system in atomic rubidium that probes Rydberg states. Three lasers at wavelengths of 780 nm (probe), 1529 nm (dressing), and ∼700 nm (coupling) drive the 5S1/2→5P3/2→4D3/2→nF5/2 excitation path, with the first two lasers independently frequency-locked to their respective atomic resonances. To observe modulation transfer that involves the uppermost step, we apply frequency sidebands to the coupling laser with an electro-optic modulator before overlapping all three beams in a rubidium vapor cell. Within the cell, the probe beam efficiently acquires sidebands at the modulation frequency through a nonlinear mixing process that occurs when the coupling beam is tuned to atomic resonance. The transmitted probe beam is focused onto a fast photodiode; the phase of the resulting beat note exhibits a derivative-like response. We demonstrate that this response can be obtained with relatively low laser powers and use it as an error signal to limit the relative frequency drift of the coupling laser to ∼30 kHz on the timescale of hours.

Ultra-Stable Fiber Laser Based on Intracavity Dual Mode Self-Reference Mechanism

Ultra-stable lasers serve as the backbone for the most advanced optical metrology scientific experiments, enabling the ability to laser interferometry or atomic spectroscopy at the highest levels of precision, thanks to the rapid development of laser wavelength stabilization techniques based on optical or electrical feedback from an external reference such as absorption line or optical cavity. With the increasing interest in making these scientific systems portable and applying it outside of the laboratory, it still remains an open question as to how to realize a laser source that can reach the high wavelength stabilization and still remain sufficiently compact and portable for field use. Here, we describe a wavelength stabilization fiber laser with intracavity reference mechanism, by utilizing the beat note of dual modes inside the laser cavity as the laser wavelength drift reference signal. A laser wavelength drift less than 5 kHz and ADEV 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−13</sup> level at integration time scales from 0.01s to 1000s is achieved, which is to-date the best results for the laser wavelength stabilization without the external frequency reference. The outcome of this work presents a new way to achieve an ultra-stable laser with a simpler, lower cost feature. It offers new insights to promote the highest precision optical metrology scientific application outside of the laboratory, and also gives the possibilities of applying the ultra-stable laser source into a wider range of industrial application.

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).

CRDS measurements of air-broadened lines in the 1.6 µm band of 12CO2: Line shape parameters with their temperature dependence

The 12CO2 band at 1.6 µm is used for carbon dioxide monitoring in the Earth atmosphere. The targeted accuracy of these measurements motivates important efforts to improve the quality of the spectroscopic parameters in atmospheric conditions. In the present work, the line shapes of the R(6), R(12), R(16), R(18) and R(20) transitions of the 30013-00001 band of 12CO2 in air are studied with a cavity ring down spectrometer (CRDS). For each transition, high signal-to-noise ratio spectra (between 2000 and 20000) are recorded at different temperatures (250, 274, 285, 295 and 320 K) and total pressures (50, 100, 250, 500 and 750 Torr). To this end, a spectrally narrowed and stable (sub-kHz) laser source is coupled into a temperature regulated high-finesse optical cavity. The frequency scale of each spectrum is accurately determined from measurements of the frequency of the beat note between a part of the laser light and the closest tooth of a frequency comb referenced to a rubidium clock. A multi-spectrum fit procedure with quadratic speed dependent Nelkin-Ghatak profiles, including line-mixing effects, has been used to derive for each transition, the different spectroscopic parameters and their temperature dependence. Results are discussed in comparison with previous experimental data, HITRAN2020 database and values obtained from requantized classical molecular dynamics simulations (rCMDS).

Gradient Field Detection Using Interference of Stimulated Microwave Optical Sidebands.

We demonstrate that stimulated microwave optical sideband generation using parametric frequency conversion can be utilized as a powerful technique for coherent state detection in atomic physics experiments. The technique has advantages over traditional absorption or polarization rotation-based measurements and enables the isolation of signal photons from probe photons. We outline a theoretical framework that accurately models sideband generation using a density matrix formalism. Using this technique, we demonstrate a novel intrinsic magnetic gradiometer that detects magnetic gradient fields between two spatially separated vapor cells by measuring the frequency of the beat note between sidebands generated within each cell. The sidebands are produced with high efficiency using parametric frequency conversion of a probe beam interacting with ^{87}Rb atoms in a coherent superposition of magnetically sensitive hyperfine ground states. Interference between the sidebands generates a low-frequency beat note whose frequency is determined by the magnetic field gradient between the two vapor cells. In contrast to traditional gradiometers the intermediate step of measuring the magnetic field experienced by the two vapor cells is unnecessary. We show that this technique can be readily implemented in a practical device by demonstrating a compact magnetic gradiometer sensor head with a sensitivity of 25 fT/cm/sqrt[Hz] with a 4.4cm baseline, while operating in a noisy laboratory environment unshielded from Earth's field.

Synchronously Intracavity-Pumped Picosecond Optical Parametric Oscillators for Sensors.

The research and development of laser systems for intracavity phase interferometry is described. These systems are based on an intracavity synchronously pumped optical parametric oscillator (OPO), enabling the generation of two trains of picosecond pulses inside a single cavity. In such a configuration, it is possible to measure the beat note frequency between two pulses and to very precisely determine the phase difference between them. The pump source is a diode-pumped passively mode-locked Nd:YVO laser. A periodically poled magnesium-doped lithium niobate crystal is used as the optical parametric oscillator crystal coupling the pump and the signal cavities. We designed a synchronously pumped OPO in a linear and ring cavity configuration allowing generation in a dual-pulse regime. By a mutual detuning of both cavity lengths, the quasi-synchronous regime of pumping was achieved and high harmonics of repetition rate frequencies were generated. Such a system can be useful for applications such as pump-probe spectroscopy or for testing telecommunication systems. We also realized the subharmonic OPO cavity as a source of two independent trains of picosecond pulses suitable for intracavity phase interferometry; we also measured the beat note signal.