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.

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 relativity, dark-matter searches and gravitational-wave detection. The ability to connect optical clocks to a distant satellite could enable space-based very long baseline interferometry, advanced satellite navigation, clock-based geodesy and thousandfold improvements in intercontinental time dissemination.

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.

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 output. As a consequence, it is now used in numerous sensing applications that require a combination of high bandwidth and high precision. 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.

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.

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.

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.

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.

Comparing Optical Oscillators across the Air to Milliradians in Phase and 10^{-17} in Frequency.

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.

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.

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.

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.

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 at one second and below 10 at 1000 seconds.

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.

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.

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.

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.

Speckle phase noise in coherent laser ranging: fundamental precision limitations.

Frequency-modulated continuous-wave laser detection and ranging (FMCW LADAR) measures the range to a surface through coherent detection of the backscattered light from a frequency-swept laser source. The ultimate limit to the range precision of FMCW LADAR, or any coherent LADAR, to a diffusely scattering surface will be determined by the unavoidable speckle phase noise. Here, we demonstrate the two main manifestations of this limit.

Frequency-noise removal and on-line calibration for accurate frequency comb interference spectroscopy of acetylene.

We demonstrate that using appropriate signal-processing techniques allows us to greatly improve the signal-to-noise ratio and accuracy of frequency comb interference spectroscopy measurements. We show that the phase noise from the continuous wave laser used as local oscillator is common to all beat notes and can be removed, enabling longer coherent integration time. An on-line calibration of the spectrum normalizes the frequency response of the electronics.

Fully referenced single-comb interferometry using optical sampling by laser-cavity tuning.

The correction of setup and laser instabilities in a single-comb interferometric measurement using optical sampling by laser-cavity tuning is investigated. A two-reference solution that allows full correction of the interferogram is presented. The technique is compared to a slightly simpler one-reference correction.

Continuous real-time correction and averaging for frequency comb interferometry.

Interferograms from a dual-comb spectrometer are continuously corrected and averaged in real-time. The algorithm is implemented on a field-programmable gate array (FPGA) development board. The chosen approach and the algorithm are described.

Optical referencing technique with CW lasers as intermediate oscillators for continuous full delay range frequency comb interferometry.

This paper presents a significant advancement in the referencing technique applied to frequency comb spectrometry (cFTS) that we proposed and demonstrated recently. Based on intermediate laser oscillators, it becomes possible to access the full delay range set by the repetition rate of the frequency combs, overcoming the principal limitation observed in the method based on passive optical filters. With this new referencing technique, the maximum spectral resolution given by each comb tooth is achievable and continuous scanning will improve complex reflectometry measurements.