Evaluating the coherence and time-domain profile of quantum cascade laser frequency combs

Phase shaping of dual-pumped Brillouin-Kerr frequency combs

We investigate the spectral phase characteristics of dual-pumped Kerr frequency combs generated in a bichromatic Brillouin fiber laser architecture with normal dispersion, producing square-like pulse profiles. Using a pulse shaper, we measure the relative phase between the pump Stokes and adjacent lines, revealing a symmetric phase relationship. Our results highlight good phase coherence of the comb. By manipulating spectral amplitudes and phases, we demonstrate the transformation into various optical waveforms. The stability of our low-noise frequency comb ensures reliable performance in practical settings.

Impact of higher-order dispersion on frequency-modulated combs

Frequency-modulated (FM) combs form spontaneously in free-running semiconductor lasers and possess a vast potential for spectroscopic applications. Despite recent progress in obtaining a conclusive theoretical description, experimental FM combs often exhibit non-ideal traits, which prevents their widespread use. Here we explain this by providing a clear theoretical and experimental study of the impact of the higher-order dispersion on FM combs. We reveal that spectrally dependent dispersion is detrimental for comb performance and leads to a decreased comb bandwidth and the appearance of spectral holes. These undesirable traits can be mended by applying a radio frequency modulation of the laser bias. We show that electrical injection-locking of the laser leads to a significant increase of the comb bandwidth, a uniform-like spectral amplitudes, and the rectification of the instantaneous frequency to recover a nearly linear frequency chirp of FM combs.

Nozaki-Bekki solitons in semiconductor lasers

Optical frequency-comb sources, which emit perfectly periodic and coherent waveforms of light1, have recently rapidly progressed towards chip-scale integrated solutions. Among them, two classes are particularly significant-semiconductor Fabry-Perót lasers2-6 and passive ring Kerr microresonators7-9. Here we merge the two technologies in a ring semiconductor laser10,11 and demonstrate a paradigm for the formation of free-running solitons, called Nozaki-Bekki solitons. These dissipative waveforms emerge in a family of travelling localized dark pulses, known within the complex Ginzburg-Landau equation12-14. We show that Nozaki-Bekki solitons are structurally stable in a ring laser and form spontaneously with tuning of the laser bias, eliminating the need for an external optical pump. By combining conclusive experimental findings and a complementary elaborate theoretical model, we reveal the salient characteristics of these solitons and provide guidelines for their generation. Beyond the fundamental soliton circulating inside the ring laser, we demonstrate multisoliton states as well, verifying their localized nature and offering an insight into formation of soliton crystals15. Our results consolidate a monolithic electrically driven platform for direct soliton generation and open the door for a research field at the junction of laser multimode dynamics and Kerr parametric processes.

Quantum walk comb in a fast gain laser

Synthetic lattices in photonics enable the exploration of light states in new dimensions, transcending phenomena common only to physical space. We propose and demonstrate a quantum walk comb in synthetic frequency space formed by externally modulating a ring-shaped semiconductor laser with ultrafast recovery times. The initially ballistic quantum walk does not dissipate into low supermode states of the synthetic lattice; instead, the state stabilizes in a broad frequency comb, unlocking the full potential of the synthetic frequency lattice. Our device produces a low-noise, nearly flat broadband comb (reaching 100 per centimeter bandwidth) and offers a promising platform to generate broadband, tunable, and stable frequency combs.

Time/frequency-domain characterization of a mid-IR DFG frequency comb via two-photon and heterodyne detection

Mid-infrared frequency combs are nowadays well-appreciated sources for spectroscopy and frequency metrology. Here, a comprehensive approach for characterizing a difference-frequency-generated mid-infrared frequency comb (DFG-comb) both in the time and in the frequency domain is presented. An autocorrelation scheme exploiting mid-infrared two-photon detection is used for characterizing the pulse width and to verify the optimal compression of the generated pulses reaching a pulse duration (FWHM) as low as 196 fs. A second scheme based on mid-infrared heterodyne detection employing two independent narrow-linewidth quantum cascade lasers (QCLs) is used for frequency-narrowing the modes of the DFG-comb down to 9.4 kHz on a 5-ms timescale.

Terahertz optical solitons from dispersion-compensated antenna-coupled planarized ring quantum cascade lasers

Quantum cascade lasers (QCLs) constitute an intriguing opportunity for the generation of on-chip optical dissipative Kerr solitons (DKSs). Originally demonstrated in passive microresonators, DKSs were recently observed in mid-infrared ring QCL paving the way for their achievement even at longer wavelengths. To this end, we realized defect-free terahertz ring QCLs featuring anomalous dispersion leveraging on a technological platform based on waveguide planarization. A concentric coupled waveguide approach is implemented for dispersion compensation, while a passive broadband bullseye antenna improves the device power extraction and far field. Comb spectra featuring sech² envelopes are presented for free-running operation. The presence of solitons is further supported by observing the highly hysteretic behavior, measuring the phase difference between the modes, and reconstructing the intensity time profile highlighting the presence of self-starting 12-picosecond-long pulses. These observations are in very good agreement with our numeric simulations based on a Complex Ginzburg-Landau Equation (CGLE).

Self-Induced Phase Locking of Terahertz Frequency Combs in a Phase-Sensitive Hyperspectral Near-Field Nanoscope

Chip-scale, electrically-pumped terahertz (THz) frequency-combs (FCs) rely on nonlinear four-wave-mixing processes, and have a nontrivial phase relationship between the evenly spaced set of emitted modes. Simultaneous monitoring and manipulation of the intermode phase coherence, without any external seeding or active modulation, is a very demanding task for which there has hitherto been no technological solution. Here, a self-mixing intermode-beatnote spectroscopy system is demonstrated, based on THz quantum cascade laser FCs, in which light is back-scattered from the tip of a scanning near-field optical-microscope (SNOM) and the intracavity reinjection monitored. This enables to exploit the sensitivity of FC phase-coherence to optical feedback and, for the first time, manipulate the amplitude, linewidth and frequency of the intermode THz FC beatnote using the feedback itself. Stable phase-locked regimes are used to construct a FC-based hyperspectral, THz s-SNOM nanoscope. This nanoscope provides 160 nm spatial resolution, coherent detection of multiple phase-locked modes, and mapping of the THz optical response of nanoscale materials up to 3.5 THz, with noise-equivalent-power (NEP) ≈400 pW √Hz^-1 . This technique can be applied to the entire infrared range, opening up a new approach to hyper-spectral near-field imaging with wide-scale applications in the study of plasmonics and quantum science, inter alia.

Analog FM free-space optical communication based on a mid-infrared quantum cascade laser frequency comb

Quantum cascade laser frequency combs are nowadays well-appreciated sources for infrared spectroscopy. Here their applicability for free-space optical communication is demonstrated. The spontaneously-generated intermodal beat note of the frequency comb is used as carrier for transferring the analog signal via frequency modulation. Exploiting the atmospheric transparency window at 4 µm, an optical communication with a signal-to-noise ratio up to 65 dB is realized, with a modulation bandwidth of 300 kHz. The system tolerates a maximum optical attenuation exceeding 35 dB. The possibility of parallel transmission of an independent digital signal via amplitude modulation at 5 Mbit/s is also demonstrated.

Real-time multimode dynamics of terahertz quantum cascade lasers via intracavity self-detection: observation of self mode-locked population pulsations

Mode-locking operation and multimode instabilities in Terahertz (THz) quantum cascade lasers (QCLs) have been intensively investigated during the last decade. These studies have unveiled a rich phenomenology, owing to the unique properties of these lasers, in particular their ultrafast gain medium. Thanks to this, in QCLs a modulation of the intracavity field intensity gives rise to a strong modulation of the population inversion, directly affecting the laser current. In this work we show that this property can be used to study in real-time the dynamics of multimode THz QCLs, using a self-detection technique combined with a 60GHz real-time oscilloscope. To demonstrate the potential of this technique we investigate a 4.2THz QCL operating in free-running, and observe a self-starting periodic modulation of the laser current, producing trains of regularly spaced, ∼100ps-long pulses. Depending on the drive current we find two distinct regimes of oscillation with dramatically different properties: a first regime at the fundamental cavity repetition rate, characterised by large amplitude and phase noise, with coherence times of a few tens of periods; a much more regular second-harmonic-comb regime, with typical coherence times of ∼10⁵ oscillation periods. We interpret these measurements using a set of effective semiconductor Maxwell-Bloch equations that qualitatively reproduce the fundamental features of the laser dynamics, indicating that the observed carrier-density and optical pulses are in antiphase, and appear as a rather shallow modulation on top of a continuous wave background. Thanks to its simple implementation and versatility, the demonstrated broadband self-detection technique is a powerful tool for the study of ultrafast dynamics in THz QCLs.

Femtosecond pulses from a mid-infrared quantum cascade laser

The quantum cascade laser has evolved to be a compact, powerful source of coherent mid-infrared light; however, its fast gain dynamics strongly restricts the formation of ultrashort pulses. As such, the shortest pulses reported so far were limited to a few picoseconds with some hundreds of milliwatts of peak power, strongly narrowing their applicability for time-resolved and nonlinear experiments. Here we demonstrate an approach capable of producing near-transform-limited subpicosecond pulses with several watts of peak power. Starting from a frequency-modulated phase-locked state, ultrashort high-peak-power pulses are generated via spectral filtering, gain modulation-induced spectral broadening and external pulse compression. We assess their temporal nature by means of a novel asynchronous sampling method, coherent beat note interferometry and interferometric autocorrelation. These results open new pathways for nonlinear physics in the mid-infrared.

Frequency comb ptychoscopy

Multiheterodyne techniques using frequency combs-radiation sources whose lines are perfectly evenly-spaced-have revolutionized science. By beating sources with the many lines of a comb, their spectra are recovered. Even so, these approaches are fundamentally limited to probing coherent sources, such as lasers. They are unable to measure most spectra that occur in nature. Here we present frequency comb ptychoscopy, a technique that allows for the spectrum of any complex broadband source to be retrieved using a comb. In this approach, the spectrum is reconstructed by unfolding the simultaneous beating of a source with each comb line. We demonstrate this both theoretically and experimentally, at microwave frequencies. This approach can reconstruct the spectrum of nearly any complex source to high resolution, and the speed, resolution, and generality of this technique will allow chip-scale frequency combs to have an impact in a wide swath of new applications, such as remote sensing and passive spectral imaging.

High-speed quantum cascade detector characterized with a mid-infrared femtosecond oscillator

Quantum cascade detectors (QCD) are photovoltaic mid-infrared detectors based on intersubband transitions. Owing to the sub-picosecond carrier transport between subbands and the absence of a bias voltage, QCDs are ideally suited for high-speed and room temperature operation. Here, we demonstrate the design, fabrication, and characterization of 4.3 µm wavelength QCDs optimized for large electrical bandwidth. The detector signal is extracted via a tapered coplanar waveguide (CPW), which was impedance-matched to 50 Ω. Using femtosecond pulses generated by a mid-infrared optical parametric oscillator (OPO), we show that the impulse response of the fully packaged QCDs has a full-width at half-maximum of only 13.4 ps corresponding to a 3-dB bandwidth of more than 20 GHz. Considerable detection capability beyond the 3-dB bandwidth is reported up to at least 50 GHz, which allows us to measure more than 600 harmonics of the OPO repetition frequency reaching 38 dB signal-to-noise ratio without the need of electronic amplification.

Direct Observation of Terahertz Frequency Comb Generation in Difference-Frequency Quantum Cascade Lasers

Terahertz quantum cascade laser sources based on intra-cavity difference frequency generation from mid-IR devices are an important asset for applications in rotational molecular spectroscopy and sensing, being the only electrically pumped device able to operate in the 0.6–6 THz range without the need of bulky and expensive liquid helium cooling. Here we present comb operation obtained by intra-cavity mixing of a distributed feedback laser at λ = 6.5 μm and a Fabry–Pérot device at around λ = 6.9 μm. The resulting ultra-broadband THz emission extends from 1.8 to 3.3 THz, with a total output power of 8 μW at 78 K. The THz emission has been characterized by multi-heterodyne detection with a primary frequency standard referenced THz comb, obtained by optical rectification of near infrared pulses. The down-converted beatnotes, simultaneously acquired, confirm an equally spaced THz emission down to 1 MHz accuracy. In the future, this setup can be used for Fourier transform based evaluation of the phase relation among the emitted THz modes, paving the way to room-temperature, compact, and field-deployable metrological grade THz frequency combs.

Terahertz Frequency Combs Exploiting an On-Chip, Solution-Processed, Graphene-Quantum Cascade Laser Coupled-Cavity

The ability to engineer quantum-cascade-lasers (QCLs) with ultrabroad gain spectra, and with a full compensation of the group velocity dispersion, at terahertz (THz) frequencies, is key for devising monolithic and miniaturized optical frequency-comb-synthesizers (FCSs) in the far-infrared. In THz QCLs four-wave mixing, driven by intrinsic third-order susceptibility of the intersubband gain medium, self-locks the optical modes in phase, allowing stable comb operation, albeit over a restricted dynamic range (∼20% of the laser operational range). Here, we engineer miniaturized THz FCSs, comprising a heterogeneous THz QCL, integrated with a tightly coupled, on-chip, solution-processed, graphene saturable-absorber reflector that preserves phase-coherence between lasing modes, even when four-wave mixing no longer provides dispersion compensation. This enables a high-power (8 mW) FCS with over 90 optical modes, through 55% of the laser operational range. We also achieve stable injection-locking, paving the way to a number of key applications, including high-precision tunable broadband-spectroscopy and quantum-metrology.

Mid-infrared quantum cascade laser frequency combs based on multi-section waveguides

We present quantum cascade laser (QCL) frequency comb devices with engineered waveguides for managing the dispersion. The QCL waveguide consists of multiple sections with different waveguide widths. The narrow and wide sections of the waveguide are designed in a way to compensate the group velocity dispersion (GVD) of each other and thereby produce a flat and slightly negative GVD for the QCL. The QCL exhibits continuous comb operation over a large part of the dynamic range of the laser. Strong and narrow-linewidth intermode beatnotes are achieved in a more than 300 mA wide operation current range. The comb device also features considerably high output power (>380mW) and wide optical bandwidth (>55cm^-1).

Mode-locked short pulses from an 8 μm wavelength semiconductor laser

Quantum cascade lasers (QCL) have revolutionized the generation of mid-infrared light. Yet, the ultrafast carrier transport in mid-infrared QCLs has so far constituted a seemingly insurmountable obstacle for the formation of ultrashort light pulses. Here, we demonstrate that careful quantum design of the gain medium and control over the intermode beat synchronization enable transform-limited picosecond pulses from QCL frequency combs. Both an interferometric radio-frequency technique and second-order autocorrelation shed light on the pulse dynamics and confirm that mode-locked operation is achieved from threshold to rollover current. Furthermore, we show that both anti-phase and in-phase synchronized states exist in QCLs. Being electrically pumped and compact, mode-locked QCLs pave the way towards monolithically integrated non-linear photonics in the molecular fingerprint region beyond 6 μm wavelength.

Producing pulses in the mid-IR often requires bulky sources and has been inaccessible with compact and versatile quantum cascade lasers (QCLs). Here, the authors demonstrate actively mode-locked, mid-IR QCL operation at room temperature.

Coherent multi-mode dynamics in a quantum cascade laser: amplitude- and frequency-modulated optical frequency combs

We cast a theoretical model based on effective semiconductor Maxwell-Bloch equations and study the dynamics of a multi-mode mid-infrared quantum cascade laser in a Fabry-Perot configuration with the aim to investigate the spontaneous generation of optical frequency combs. This model encompasses the key features of a semiconductor active medium, such as asymmetric, frequency-dependent gain and refractive index as well as the phase-amplitude coupling of the field dynamics provided by the linewidth enhancement factor, and some specific resonator features, such as spatial hole burning. Our numerical simulations are in excellent agreement with recent experimental results, showing broad ranges of comb formation in locked regimes, separated by chaotic dynamics when the field modes unlock. In the former case, we identify self-confined structures travelling along the cavity, while the instantaneous frequency is characterized by a linear chirp behaviour. In such regimes, we show that OFCs are characterized by concomitant and relevant amplitude and frequency modulation.

High performance quantum cascade laser frequency combs at λ ∼ 6 μm based on plasmon-enhanced dispersion compensation

We demonstrate quantum cascade laser (QCL) optical frequency combs emitting at λ ∼ 6 μm. A 5.5 μm-wide, 4.5 mm-long laser exhibits comb operation from -20 °C up to 50 °C. A maximum output power of 300 mW is achieved at 50 °C showing a robustness of the system. The laser output spectrum is ∼80 cm^-1 wide at the maximum current, with a mode spacing of 0.334 cm^-1, resulting in a total of 240 modes with an average power of 0.8 mW per mode. To achieve frequency comb operation, a plasmonic-waveguide approach is utilized. A thin, highly-doped indium phosphide (InP) layer is inserted in the top cladding design to compensate the positive dispersion of the system (material and waveguide). This approach can be further exploited to design QCL combs at even shorter wavelengths, down to 4 μm. Different ridge widths between 2.8 and 5.5 μm have been fabricated and characterized. All of the devices exhibit frequency comb operation. These observations demonstrate that the plasmonic-waveguide is a robust and reliable method for dispersion compensation of a semiconductor laser systems to achieve frequency comb operation.

QCL-Based Dual-Comb Spectrometer for Multi-Species Measurements at High Temperatures and High Pressures

Rapid multi-species sensing is an overarching goal in time-resolved studies of chemical kinetics. Most current laser sources cannot achieve this goal due to their narrow spectral coverage and/or slow wavelength scanning. In this work, a novel mid-IR dual-comb spectrometer is utilized for chemical kinetic investigations. The spectrometer is based on two quantum cascade laser frequency combs and provides rapid (4 µs) measurements over a wide spectral range (~1175-1235 cm-1). Here, the spectrometer was applied to make time-resolved absorption measurements of methane, acetone, propene, and propyne at high temperatures (>1000 K) and high pressures (>5 bar) in a shock tube. Such a spectrometer will be of high value in chemical kinetic studies of future fuels.

Ultrafast response of harmonic modelocked THz lasers

The use of fundamental modelocking to generate short terahertz (THz) pulses and THz frequency combs from semiconductor lasers has become a routine affair, using quantum cascade lasers (QCLs) as a gain medium. However, unlike classic laser diodes, no demonstrations of harmonic modelocking, active or passive, have been shown in THz QCLs, where multiple pulses per round trip are generated when the laser is modulated at the harmonics of the cavity's fundamental round-trip frequency. Here, using time-resolved THz techniques, we show for the first time harmonic injection and mode-locking in which THz QCLs are modulated at the harmonics of the round-trip frequency. We demonstrate the generation of the harmonic electrical beatnote within a QCL, its injection locking to an active modulation and its direct translation to harmonic pulse generation using the unique ultrafast nature of our approach. Finally, we show indications of self-starting harmonic emission, i.e., without external modulation, where the QCL operates exclusively on a harmonic (up to its 15th harmonic) of the round-trip frequency. This behaviour is supported by time-resolved simulations of induced gain and loss in the system and shows the importance of the electronic, as well as photonic, nature of QCLs. These results open up the prospect of passive harmonic modelocking and THz pulse generation, as well as the generation of low-noise microwave generation in the hundreds of GHz region.

Sensitivity of SWIFT spectroscopy

SWIFT spectroscopy (Shifted Wave Interference Fourier Transform Spectroscopy) is a coherent beatnote technique that can be used to measure the temporal profiles of periodic optical signals. While it has been essential in understanding the physics of various mid-infrared and terahertz frequency combs, its ultimate limits have not been discussed. We show that the envelope of a SWIFTS interferogram is physically meaningful and is directly related to autocorrelation. We derive analytical expressions for the SWIFTS signals of two prototypical cases-chirped pulses from a mode-locked laser and a frequency-modulated comb-and derive scaling laws for the noise of these measurements, showing how it can be mitigated. Finally, we confirm this analysis by performing the first SWIFTS measurements of near-infrared pulses from femtosecond lasers, establishing the validity of the technique for highly-dispersed sub-picojoule pulses.

In-Phase and Anti-Phase Synchronization in a Laser Frequency Comb

Coupled clocks are a classic example of a synchronization system leading to periodic collective oscillations. Already in 1665, Christiaan Huygens described this phenomenon as a kind of "sympathy" among oscillators. In this work, we describe the formation of two types of laser frequency combs as a system of oscillators coupled through the beating of the lasing modes. We experimentally show two completely different types of synchronization in a quantum dot laser-in-phase and splay-phase states. Both states can be generated in the same device, just by varying the damping losses of the system. This modifies the coupling among the oscillators. The temporal laser output is characterized using both linear and quadratic autocorrelation techniques. Our results show that both pulses and frequency-modulated states can be generated on demand within the same device. These findings allow us to connect laser frequency combs produced by amplitude-modulated and frequency-modulated lasers and link these to pattern formation in coupled systems such as Josephson-junction arrays.

Fully phase-stabilized quantum cascade laser frequency comb

Miniaturized frequency comb sources across hard-to-access spectral regions, i.e. mid- and far-infrared, have long been sought. Four-wave-mixing based Quantum Cascade Laser combs (QCL-combs) are ideal candidates, in this respect, due to the unique possibility to tailor their spectral emission by proper nanoscale design of the quantum wells. We demonstrate full-phase-stabilization of a QCL-comb against the primary frequency standard, proving independent and simultaneous control of the two comb degrees of freedom (modes spacing and frequency offset) at a metrological level. Each emitted mode exhibits a sub-Hz relative frequency stability, while a correlation analysis on the modal phases confirms the high degree of coherence in the device emission, over different power-cycles and over different days. The achievement of fully controlled, phase-stabilized QCL-comb emitters proves that this technology is mature for metrological-grade uses, as well as for an increasing number of scientific and technological applications.

Frequency-Modulated Combs Obey a Variational Principle

Laser dynamics encompasses universal phenomena that can be encountered in many areas of physics, such as bifurcation and chaos, mode competition, resonant nonlinearities, and synchronization-or locking-of oscillators. When a locking process occurs in a multimode laser, an optical frequency comb is produced, which is an optical spectrum consisting of equidistant modes with a fixed phase relationship. Describing the formation of self-starting frequency combs in terms of fundamental laser equations governing the field inside the cavity does not allow one, in general, to grasp how the laser synchronizes its modes. Our finding is that, in a particular class of lasers where the output is frequency modulated with small or negligible intensity modulation, a greatly simplified description of self-locking exists. We show that in quantum cascade lasers-solid-state representatives of these lasers characterized by an ultrashort carrier relaxation time-the frequency comb formation obeys a simple variational principle, which was postulated over 50 years ago and relies on the maximization of the laser output power. The conditions for the breakdown of this principle are also experimentally identified, shedding light on the behavior of many different types of lasers, such as dye, diode, and other cascade lasers. This discovery reveals that the formation of frequency-modulated combs is an elegant example of an optimization problem solved by a physical system.

Temporal characteristics of quantum cascade laser frequency modulated combs in long wave infrared and THz regions

We consider here a time domain model representing the dynamics of quantum cascade lasers (QCLs) generating frequency combs (FCs) in both THz and long wave infrared (LWIR λ = 8-12µm) spectral ranges. Using common specifications for these QCLs we confirm that the free running laser enters a regime of operation yielding a pseudo-randomly frequency modulated (FM) radiation in the time domain corresponding to FCs with stable phase relations in the frequency domain. We provide an explanation for this unusual behavior as a consequence of competition for the most efficient regime of operation. Expanding the model previously developed in [Opt. Eng. 57(1), 011009 (2017)] we analyze the performance of realistic THz and LWIR QCLs and show, despite the vastly different scale of many parameters, that both types of lasers offer very similar characteristics, namely FM operation with an FM period commensurate with the gain recovery time and an FM amplitude comparable with the gain bandwidth. We also identify the true culprit behind pseudo-random dynamics of the FM comb to be spatial hole burning, rather than the more pervasive spectral hole burning.

Achieving comb formation over the entire lasing range of quantum cascade lasers

Frequency combs based on quantum cascade lasers (QCLs) are finding promising applications in high-speed broadband spectroscopy in the terahertz regime, where many molecules have their "fingerprints." To form stable combs in QCLs, an effective control of group velocity dispersion plays a critical role. The dispersion of the QCL cavity has two main parts: a static part from the material and a dynamic part from the intersubband transitions. Unlike the gain, which is clamped to a fixed value above the lasing threshold, dispersion associated with the intersubband transitions changes with bias, even above the threshold, and this reduces the dynamic range of comb formation. Here, by incorporating tunability into the dispersion compensator, we demonstrate a QCL device exhibiting comb operation from I_th to I_max, which greatly expands the operation range of the frequency combs.

Molecular dispersion spectroscopy based on Fabry-Perot quantum cascade lasers

Two Fabry-Perot quantum cascade lasers are used in a differential dual comb configuration to perform rapidly swept dispersion spectroscopy of low-pressure nitrous oxide with <1  ms acquisition time. Active feedback control of the laser injection current enables simultaneous wavelength modulation of both lasers at kilohertz rates. The system demonstrates similar performance in both absorption and dispersion spectroscopy modes and achieves a noise-equivalent absorption figure of merit in the low 10^-4/Hz range.

Computational multiheterodyne spectroscopy

Dual-comb spectroscopy allows for high-resolution spectra to be measured over broad bandwidths, but an essential requirement for coherent integration is the availability of a phase reference. Usually, this means that the combs' phase and timing errors must be measured and either minimized by stabilization or removed by correction, limiting the technique's applicability. We demonstrate that it is possible to extract the phase and timing signals of a multiheterodyne spectrum completely computationally, without any extra measurements or optical elements. These techniques are viable even when the relative linewidth exceeds the repetition rate difference and can tremendously simplify any dual-comb system. By reconceptualizing frequency combs in terms of the temporal structure of their phase noise, not their frequency stability, we can greatly expand the scope of multiheterodyne techniques.

Time domain modeling of terahertz quantum cascade lasers for frequency comb generation

The generation of frequency combs in the mid-infrared and terahertz regimes from compact and potentially cheap sources could have a strong impact on spectroscopy, as many molecules have their rotovibrational bands in this spectral range. Thus, quantum cascade lasers (QCLs) are the perfect candidates for comb generation in these portions of the electromagnetic spectrum. Here we present a theoretical model based on a full numerical solution of Maxwell-Bloch equations suitable for the simulation of such devices. We show that our approach captures the intricate interplay between four wave mixing, spatial hole burning, coherent tunneling and chromatic dispersion which are present in free running QCLs. We investigate the premises for the generation of QCL based terahertz combs. The simulated comb spectrum is in good agreement with experiment, and also the observed temporal pulse switching between high and low frequency components is reproduced. Furthermore, non-comb operation resulting in a complex multimode dynamics is investigated.

Dynamics of ultra-broadband terahertz quantum cascade lasers for comb operation

We present an experimental investigation of the multimode dynamics and the coherence of terahertz quantum cascade lasers emitting over a spectral bandwidth of ~1THz. The devices are studied in free-running and under direct RF modulation. Depending on the pump current we observe different regimes of operation, where RF spectra displaying single and multiple narrow beat-note signals alternate with spectra showing a single beat-note characterized by an intense phase-noise, extending over a bandwidth up to a few GHz. We investigate the relation between this phase-noise and the dynamics of the THz modes through the electro-optic sampling of the laser emission. We find that when the phase-noise is large, the laser operates in an unstable regime where the lasing modes are incoherent. Under RF modulation of the laser current such instability can be suppressed and the modes coherence recovered, while, simultaneously, generating a strong broadening of the THz emission spectrum.