Removing biases in dual frequency comb spectroscopy due to digitizer nonlinearity.

Operation of any dual-comb spectrometer requires digitization of the interference signal before further processing. Nonlinearities in the analog-to-digital conversion can alter the apparent gas concentration by multiple percent, limiting both precision and accuracy of this technique. This work describes both the measurement of digitizer nonlinearity and the development of a model that quantitatively describes observed concentration bias over a range of conditions. We present hardware methods to suppress digitizer-induced bias of concentration retrievals below 0.1%.

Quantum-limited optical time transfer for future geosynchronous links.

The combination of optical time transfer and optical clocks opens up the possibility of large-scale free-space networks that connect both ground-based optical clocks and future space-based optical clocks. Such networks promise better tests of general relativity1-3, dark-matter searches4 and gravitational-wave detection5. The ability to connect optical clocks to a distant satellite could enable space-based very long baseline interferometry6,7, advanced satellite navigation8, clock-based geodesy2,9,10 and thousandfold improvements in intercontinental time dissemination11,12. Thus far, only optical clocks have pushed towards quantum-limited performance13. By contrast, optical time transfer has not operated at the analogous quantum limit set by the number of received photons. Here we demonstrate time transfer with near quantum-limited acquisition and timing at 10,000 times lower received power than previous approaches14-24. Over 300 km between mountaintops in Hawaii with launched powers as low as 40 µW, distant sites are synchronized to 320 attoseconds. This nearly quantum-limited operation is critical for long-distance free-space links in which photons are few and amplification costly: at 4.0 mW transmit power, this approach can support 102 dB link loss, more than sufficient for future time transfer to geosynchronous orbits.

The time-programmable frequency comb and its use in quantum-limited ranging.

Two decades after its invention, the classic self-referenced frequency comb laser is an unrivalled ruler for frequency, time and distance metrology owing to the rigid spacing of its optical output1,2. As a consequence, it is now used in numerous sensing applications that require a combination of high bandwidth and high precision3-5. Many of these applications, however, are limited by the trade-offs inherent in the rigidity of the comb output and operate far from quantum-limited sensitivity. Here we demonstrate an agile programmable frequency comb where the pulse time and phase are digitally controlled with ±2-attosecond accuracy. This agility enables quantum-limited sensitivity in sensing applications as the programmable comb can be configured to coherently track weak returning pulse trains at the shot-noise limit. To highlight its capabilities, we use this programmable comb in a ranging system, reducing the required power to reach a given precision by about 5,000-fold compared with a conventional dual-comb system. This enables ranging at a mean photon per pulse number of 1/77 while retaining the full accuracy and precision of a rigid frequency comb. Beyond ranging and imaging6-12, applications in time and frequency metrology1,2,5,13-23, comb-based spectroscopy24-32, pump-probe experiments33 and compressive sensing34,35 should benefit from coherent control of the comb-pulse time and phase.

Collinear opto-optical loss modulation for carrier-envelope offset stabilization of a fiber frequency comb.

Opto-optical loss modulation (OOM) for stabilization of the carrier-envelope offset (CEO) frequency of a femtosecond all-fiber laser is performed using a collinear geometry. Amplitude-modulated 1064 nm light is fiber coupled into an end-pumped semiconductor saturable absorber mirror (SESAM)-mode-locked all-polarization-maintaining erbium fiber femtosecond laser, where it optically modulates the loss of the SESAM resulting in modulation of the CEO frequency. A noise rejection bandwidth of 150 kHz is achieved when OOM and optical gain modulation are combined in a hybrid analog/digital loop. Collinear OOM provides a simple, all-fiber, high-bandwidth method for improving the CEO frequency stability of SESAM mode-locked fiber lasers.

External serrodyne modulation for the suppression of low-frequency noise in quadrature interferometry.

In interferometry, reaching a high signal-to-noise ratio at low frequencies can be challenging when the additive noise is nonstationary. Although this problem is typically solved by inserting a frequency shifter into one of the arms, in some cases, the interferometer cannot or should not be modified in this way. This Letter presents an alternative solution, based on external serrodyne frequency modulation, which is comparable to the typical approach in terms of complexity and performance yet does not require the modification of a passive interferometer. We demonstrate a prototype that achieves frequency shifting at 500 kHz with 89% power efficiency, leading to the wideband suppression of low-frequency additive noise by more than 19 dB. This enables a fully passive measurement of the thermoconductive noise of a 100 m single-mode fiber.

Amplified noise nonstationarity in a mode-locked laser based on nonlinear polarization rotation.

Beat note measurements between a mode-locked (ML) and a continuous-wave laser, as well as between two ML sources, were used to demonstrate that the sub-threshold, cavity filtered, amplified spontaneous emission is not stationary, even when a fast mode-locking mechanism, such as nonlinear polarization rotation, is used to generate short pulses. A relatively small gain modulation of a few percent created by high-intensity pulses can produce a significant modulation of the amplified noise once synchronously accumulated over several cavity round-trips, even if the repetition rate is faster than the gain dynamics.

Dual electro-optic frequency comb spectroscopy using pseudo-random modulation.

An approach for dual-comb spectroscopy using electro-optic (EO) phase modulation is reported. Maximum-length pseudo-random binary sequences allow for energy-efficient and flexible comb generation. Self-correction of interferograms is shown to remove relative comb drifts and improve mutual coherence, even for EO combs derived from the same laser source. Methane spectroscopy is reported over a ∼10 GHz spectral range, limited by the modulators' bandwidth. The potential of a simple EO comb instrument is demonstrated to rapidly quantify atmospheric methane emissions with ppb precision over 1 km.

Measuring the nonlinear phase shift in a mode-locked laser.

The spectrum of a mode-locked laser (MLL) is down-mixed to electrical frequencies using a tunable continuous-wave laser. By characterizing the sub-threshold low-intensity emission relative to the laser mode positions, one can measure the nonlinear phase shift of the MLL while in operation.

Femtosecond time synchronization of optical clocks off of a flying quadcopter.

Future optical clock networks will require free-space optical time-frequency transfer between flying clocks. However, simple one-way or standard two-way time transfer between flying clocks will completely break down because of the time-of-flight variations and Doppler shifts associated with the strongly time-varying link distances. Here, we demonstrate an advanced, frequency comb-based optical two-way time-frequency transfer (O-TWTFT) that can successfully synchronize the optical timescales at two sites connected via a time-varying turbulent air path. The link between the two sites is established using either a quadcopter-mounted retroreflector or a swept delay line at speeds up to 24 ms-1. Despite 50-ps breakdown in time-of-flight reciprocity, the sites' timescales are synchronized to < 1 fs in time deviation. The corresponding sites' frequencies agree to ~ 10-18 despite 10-7 Doppler shifts. This work demonstrates comb-based O-TWTFT can enable free-space optical networks between airborne or satellite-borne optical clocks for precision navigation, timing and probes of fundamental science.

An open and flexible digital phase-locked loop for optical metrology.

This paper presents an open and flexible digital phase-locked loop optimized for laser stabilization systems. It is implemented on a cheap and easily accessible FPGA-based digital electronics platform (Red Pitaya) running a customizable open-source firmware. A PC-based software interface allows controlling the platform and optimizing the loop parameters remotely. Several tools are included to allow measurement of quantities of interest smoothly and rapidly. To demonstrate the platform's capabilities, we built a fiber noise canceller over a 400 m fiber link. Noise cancellation was achieved over a 30 kHz bandwidth, a value limited mainly by the delays introduced by the actuator and by the round-trip propagation over the fiber link. We measured a total latency of 565 ns for the platform itself, limiting the theoretically achievable control bandwidth to approximately 225 kHz.

Comparing Optical Oscillators across the Air to Milliradians in Phase and 10

We demonstrate carrier-phase optical two-way time-frequency transfer (carrier-phase OTWTFT) through the two-way exchange of frequency comb pulses. Carrier-phase OTWTFT achieves frequency comparisons with a residual instability of 1.2×10^{-17} at 1 s across a turbulent 4-km free space link, surpassing previous OTWTFT by 10-20 times and enabling future high-precision optical clock networks. Furthermore, by exploiting the carrier phase, this approach is able to continuously track changes in the relative optical phase of distant optical oscillators to 9 mrad (7 as) at 1 s averaging, effectively extending optical phase coherence over a broad spatial network for applications such as correlated spectroscopy between distant atomic clocks.

Self-corrected chip-based dual-comb spectrometer.

We present a dual-comb spectrometer based on two passively mode-locked waveguide lasers integrated in a single Er-doped ZBLAN chip. This original design yields two free-running frequency combs having a high level of mutual stability. We developed in parallel a self-correction algorithm that compensates residual relative fluctuations and yields mode-resolved spectra without the help of any reference laser or control system. Fluctuations are extracted directly from the interferograms using the concept of ambiguity function, which leads to a significant simplification of the instrument that will greatly ease its widespread adoption and commercial deployment. Comparison with a correction algorithm relying on a single-frequency laser indicates discrepancies of only 50 attoseconds on optical timings. The capacities of this instrument are finally demonstrated with the acquisition of a high-resolution molecular spectrum covering 20 nm. This new chip-based multi-laser platform is ideal for the development of high-repetition-rate, compact and fieldable comb spectrometers in the near- and mid-infrared.

Improving the signal-to-noise ratio of the beat note between a frequency comb and a tunable laser using a dynamically tracking optical filter.

An acousto-optic filter is locked to a tunable continuous wave (CW) laser so that a frequency comb can be dynamically filtered around the wavelength of the CW source. The signal-to-noise ratio (SNR) of the heterodyne beat note between the comb and the CW laser is improved by a factor of up to 19 dB. Furthermore, a SNR of more than 56 dB in 100 kHz is obtained over an 85 nm wavelength span. This technique could enable wideband, agile, and cycle-slip-free phase tracking of a beat note across a full comb spectrum.

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.

Tight real-time synchronization of a microwave clock to an optical clock across a turbulent air path.

The ability to distribute the precise time and frequency from an optical clock to remote platforms could enable future precise navigation and sensing systems. Here we demonstrate tight, real-time synchronization of a remote microwave clock to a master optical clock over a turbulent 4-km open air path via optical two-way time-frequency transfer. Once synchronized, the 10-GHz frequency signals generated at each site agree to 10-14 at one second and below 10-17 at 1000 seconds. In addition, the two clock times are synchronized to ±13 fs over an 8-hour period. The ability to phase-synchronize 10-GHz signals across platforms supports future distributed coherent sensing, while the ability to time-synchronize multiple microwave-based clocks to a high-performance master optical clock supports future precision navigation/timing systems.

Synchronization of Clocks Through 12 km of Strongly Turbulent Air Over a City.

We demonstrate real-time, femtosecond-level clock synchronization across a low-lying, strongly turbulent, 12-km horizontal air path by optical two-way time transfer. For this long horizontal free-space path, the integrated turbulence extends well into the strong turbulence regime corresponding to multiple scattering with a Rytov variance up to 7 and with the number of signal interruptions exceeding 100 per second. Nevertheless, optical two-way time transfer is used to synchronize a remote clock to a master clock with femtosecond-level agreement and with a relative time deviation dropping as low as a few hundred attoseconds. Synchronization is shown for a remote clock based on either an optical or microwave oscillator and using either tip-tilt or adaptive-optics free-space optical terminals. The performance is unaltered from optical two-way time transfer in weak turbulence across short links. These results confirm that the two-way reciprocity of the free-space time-of-flight is maintained both under strong turbulence and with the use of adaptive optics. The demonstrated robustness of optical two-way time transfer against strong turbulence and its compatibility with adaptive optics is encouraging for future femtosecond clock synchronization over very long distance ground-to-air free-space paths.

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.

Chirped pulse heterodyne for optimal beat note detection between a frequency comb and a continuous wave laser.

Chirped pulse heterodyne is proposed to maximize the signal-to-noise ratio (SNR) when measuring the beat note between an optical frequency comb and a continuous wave (CW) laser. The noise model reveals that all the comb power within the largest possible detection bandwidth can be used to increase the SNR. The chirped comb/CW interference experiment is shown to be equivalent to CW/CW interference, using the comb's spectrally available power. The approach can also greatly alleviate dynamic range issues when detected pulsed heterodyne signals. A beat note SNR of 68.3 dB in a 100 kHz bandwidth is achieved.

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.

Broadband noise limit in the photodetection of ultralow jitter optical pulses.

Applications with optical atomic clocks and precision timing often require the transfer of optical frequency references to the electrical domain with extremely high fidelity. Here we examine the impact of photocarrier scattering and distributed absorption on the photocurrent noise of high-speed photodiodes when detecting ultralow jitter optical pulses. Despite its small contribution to the total photocurrent, this excess noise can determine the phase noise and timing jitter of microwave signals generated by detecting ultrashort optical pulses. A Monte Carlo simulation of the photodetection process is used to quantitatively estimate the excess noise. Simulated phase noise on the 10 GHz harmonic of a photodetected pulse train shows good agreement with previous experimental data, leading to the conclusion that the lowest phase noise photonically generated microwave signals are limited by photocarrier scattering well above the quantum limit of the optical pulse train.