Harmonic frequency combs, in which the lasing modes are separated by a period of tens of free spectral ranges from each other, have been recently discovered in quantum cascade lasers (QCLs). There is an ongoing debate how the harmonic combs can be formed and stable under continuous pumping. Here we reproduce the harmonic state of lasing in QCLs by space-time-domain numerical simulations and show that the corresponding optical wave has a frequency-modulated (FM) nature, with the fundamental beat note in the electron population being suppressed. To understand the physics behind the formation and stability of the harmonic state, we develop a frequency-domain linearized analytic theory which analyzes the stability of single mode lasing with respect to the harmonic state formation and the instabilities of the resulting harmonic state. Our analysis shows how the instability of a single lasing mode can result in the growth of harmonic side modes. The coupling between the two side modes leads to opposite gains for FM and amplitude-modulated (AM) waves, and the FM gain is enhanced as compared to the AM gain. The dependence of the sideband gain spectrum on group velocity dispersion is also studied. While the instability gain of a single lasing mode does not prove that the harmonic state can be self-starting, we analyze the sideband instability gain in the presence of three strong harmonic modes and demonstrate that the harmonic state can be stable and self-supported.
We report experimental demonstration of continuous-wave cascaded-harmonic generation and Raman lasing in a millimeter-scale lithium niobate whispering-gallery resonator pumped at a telecommunication-compatible infrared wavelength. Intensity enhancement through multiple recirculations in the whispering-gallery resonator and quasi phase-matching through a nonuniform crystal poling enable simultaneous cascaded-harmonic generation up to the fourth-harmonic accompanied by stimulated Raman, two-photon, three-photon, and four-photon Raman scattering corresponding the molecular vibrational wavenumbers…
Harmonic comb state has proven to be emerging in quantum cascade lasers and promoted by an interplay between parametric gain and spatial hole burning. We report here on robust, pure, self-starting harmonic mode locking in Copper-based double-metal THz quantum cascade lasers. Different harmonic orders can be excited in the same laser cavity depending on the pumping condition and stable harmonic combs spanning more than 600 GHz bandwidth at 80 K are reported. Such devices can be RF injected and the free running coherence is assessed by means of self-mixing technique performed at 50 GHz. A theore…
For the growing demand of frequency combs in mid-infrared (mid-IR), known as the "molecular fingerprint" region of the spectrum [1], down conversion of near-IR frequency combs through half- harmonic generation offers numerous benefits including high conversion efficiency and intrinsic phase and frequency locking to the near-IR pump [2]. Hence cascaded half-harmonic generation promises a simple path towards extending the wavelength coverage of stable frequency combs. Here, we report a two-octave down-conversion of a frequency comb around 1 μm through cascaded half-harmonic generation with ~64% …
Optical frequency combs establish a rigid phase-coherent link between microwave and optical domains and are emerging as high-precision tools in an increasing number of applications. Frequency combs with large intermodal spacing are employed in the field of microwave photonics for radiofrequency arbitrary waveform synthesis and for generation of THz tones of high spectral purity in the future wireless communication networks. We demonstrate for the first time self-starting harmonic frequency comb generation with a THz repetition rate in a quantum cascade laser. The large intermodal spacing cause…
Silicon nitride (Si$_3$N$_4$) is an ever-maturing integrated platform for nonlinear optics. Yet, due to the absence of second-order ($χ^{(2)}$) nonlinearity, Si$_3$N$_4$ is mostly considered for third-order ($χ^{(3)}$) nonlinear interactions. Recently, this limitation was overcome by optical poling in both Si$_3$N$_4$ waveguides and microresonators via the photogalvanic effect, resulting in the inscription of quasi-phase-matched $χ^{(2)}$ gratings. Here, we report cascaded nonlinear effects in a normal dispersion Si$_3$N$_4$ microresonator with combined $χ^{(2)}$ and $χ^{(3)}$ nonlinearities. …
We demonstrate a coherent imaging system based on a terahertz (THz) frequency quantum cascade laser (QCL) phase-locked to a near-infrared fs-laser comb. The phase locking enables coherent electro-optic sampling of the continuous-wave radiation emitted by the QCL through the generation of a heterodyne beat-note signal. We use this beat-note signal to demonstrate raster scan coherent imaging using a QCL emitting at 2.5 THz. At this frequency the detection noise floor of our system is of 3 pW/Hz and the long-term phase stability is <3 degrees/h, limited by the mechanical stability of the apparatu…
A novel study on harmonic frequency combs emitted by Quantum Cascade Lasers (QCLs) is here presented, demonstrating the presence of intensity correlations between twin modes characterising the emission spectra. These originate from a Four-Wave Mixing (FWM) process driven by the active medium's third-order non-linearity. The study of such correlations is essential for the engineering of a new generation of semiconductor devices with the potential of becoming integrated emitters of light with quantum properties, such as squeezing and entanglement. Starting from experimental results, the limits o…
The realization of ultrahigh quality (Q) resonators regardless of the underpinning material platforms has been a ceaseless pursuit, because the high Q resonators provide an extreme environment of storage of light to enable observations of many unconventional nonlinear optical phenomenon with high efficiencies. Here, we demonstrate an ultra-high Q factor (7.1*10^6) microresonator on the 4H-silicon-carbide-on-insulator (4H-SiCOI) platform in which both \c{hi}^(2) and \c{hi}^(3) nonlinear processes of high efficiencies have been generated. Broadband frequency conversions, including second-, third…
High-harmonic generation (HHG) provides short-wavelength light that is useful for precision spectroscopy and probing ultrafast dynamics. We report efficient, phase-coherent harmonic generation up to 9th-order (333 nm) in chirped periodically poled lithium niobate waveguides driven by phase-stable $\leq$12-nJ, 100 fs pulses at 3 $μ$m with 100 MHz repetition rate. A mid-infrared to ultraviolet-visible conversion efficiency as high as 10% is observed, amongst an overall 23% conversion of the fundamental to all harmonics. We verify the coherence of the harmonic frequency combs despite the complex …
Reconfigurable all-optical inference via tunable second-harmonic generation and spin-orbit coupling cascade
Guangdong-HongKong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology, School of Physics and Optoelectronic Engineering, Foshan University（佛山大学物理与光电工程学院）；Key Laboratory of Optoelectronic Information and Sensing Technologies of Guangdong Higher Education Institutes, Department of Optoelectronic Engineering, Jinan University（暨南大学光电工程系）
Efficient and compact frequency converters are essential for frequency stabilization of terahertz sources. In this paper, we present a 3.5-THz, x6-harmonic, integrated Schottky diode mixer operating at room temperature. The designed frequency converter is based on a single-ended, planar Schottky diode with a sub-micron anode contact area defined on a suspended 2-$μ$m ultra-thin GaAs substrate. The dc-grounded anode pad was combined with the radio frequency E-plane probe, which resulted in an electrically compact circuit. At 200 MHz intermediate frequency, a mixer conversion loss of about 59 dB…
Nonlinear wave interaction of low amplitude gravitational waves in flat space-time is considered. Analogy with optics is established. It is shown that the flat metric space-time is equivalent to a centro-symmetric optical medium, with no second order susceptibility. The lowest order nonlinear effects are those due to the third order nonlinearity and include self-phase modulation and high harmonic generation. These processes lead to an efficient energy dilution of the gravitational wave energy over an increasingly large spectral range.
We present an extended study concerning the dynamics of dense and harmonic coherent regimes in quantum cascade lasers (QCLs) in a Fabry--Perot (FP) configuration emitting in the terahertz (THz) spectral region. Firstly, we study the device in free running operation, reproducing the main features of the self-generated of optical frequency combs (OFCs) and harmonic frequency combs (HFCs) in this spectral range, commenting on the points of difference from the mid-infrared region, and finding excellent agreement with the most recent experimental evidences. Then, we analyze the THz-QCL dynamics und…
The recent demonstration of a terahertz (THz) molecular gas laser pumped by a mid-infrared quantum cascade laser (QCL) has opened up new perspectives for this family of sources, traditionally relying on CO2-laser pumping. A so far open question concerning QCL-pumped THz molecular lasers (MLs) is related to their spectral purity. Indeed, assessing their frequency/phase noise is crucial for a number of applications potentially exploiting these sources as local oscillators. Here this question is addressed by reporting the measurement of the frequency noise power spectral density (PSD) of a THz ML…
We investigate the threshold of $χ^{(2)}$ frequency comb generation in lithium niobate whispering gallery microresonators theoretically and experimentally. When generating a frequency comb via second-harmonic generation, the threshold for the onset of cascaded second-order processes leading to a comb is found to be approximately 85 $μ$W. The second-harmonic generation efficiency up to this value is in excellent agreement with a previously known theoretical framework. This framework is extended here, showing that the onset of cascaded $χ^{(2)}$ processes and the maximum of the second-harmonic g…
The frequency noise power spectral density of a free-running quantum cascade laser frequency comb is investigated. A plateau is observed at high frequencies, attributed to the quantum noise limit set by the Schawlow-Townes formula for the total laser power on all comb lines. In our experiment, a linewidth of 292 Hz is measured for a total power of 25 mW. This result proves that the four-wave mixing process, responsible for the comb operation, effectively correlates the quantum noise of the individual comb lines.
One salient characteristic of Quantum Cascade Laser (QCL) is its very shor gain recovery time that so far thwarted the attempts to achieve self-mode locking of the device into a train of single pulses. We show theoretically that four wave mixing, combined with the short gain recovery time causes QCL to operate in the self-frequency-modulated regime characterized by a constant power in time domain and stable coherent comb in the frequency domain.Coherent frequency comb may enable many potential applications of QCL in sensing and measurement.
We present an experimental study of optical frequency comb generation based on cascaded quadratic nonlinearities inside a continuous-wave-pumped optical parametric oscillator. We demonstrate comb states which produce narrow-linewidth intermode beat note signals, and we verify the mode spacing uniformity of the comb at the Hz level. We also show that spectral quality of the comb can be improved by modulating the parametric gain at a frequency that corresponds to the comb mode spacing. We have reached a high average output power of over 4 W in the near-infrared region, at ~2 μm.
A recent publication on arXiv:1905.00668 suggests that the phase relationship within a frequency comb can be reconstructed from a heterodyne measurement using a reference comb. In principle, following this approach, such retrieval of optical phases appears possible, but should give rise to a temporally constant signal. Instead, arXiv:1905.00668 provides experimental evidence for a pronounced relative drift of the phases, which indicates that the modes of the comb are not coherently phase-locked. This temporal drift can be explained if the comb under test is not equidistant. This further means …
Optical frequency comb generation by continuous-wave-pumped cascaded quadratic nonlinearities (CQN) appears a promising alternative to well-established modelocked lasers, especially if access to the mid-infrared spectral region is needed. We report an experimental investigation of spectral properties of a CQN frequency comb, which is based on second-harmonic generation (SHG) and is pumped internally by a continuous-wave optical parametric oscillator. Our study focuses on SHG phase mismatch, which has drawn little attention in the previously reported CQN frequency comb research. The main observ…
We present a monolithic solution to extract efficiently light from terahertz quantum cascade lasers with metal-metal waveguides suitable for broadband frequency comb applications. The design is optimized for a bandwidth of 500 GHz around a center frequency of 2.6 THz. A five-fold increase in total output power is observed compared to standard metal-metal waveguides. The extractor features a single-lobed far-field pattern and increases the frequency comb dynamical range to cover more than 50 % of the laser dynamic range. Frequency comb operation up to a spectral bandwidth of 670 GHz is achieved…
Dual-comb spectroscopy is emerging as one of the most appealing applications of mid-infrared frequency combs for high-resolution molecular spectroscopy, as it leverages on the unique coherence properties of frequency combs combined with the high sensitivities achievable by mid-infrared molecular spectroscopy. Here we present an on-chip dual-comb source based on mid-infrared quantum cascade laser frequency combs, where two frequency combs are integrated on a single chip. Control of the combs repetition and offset frequencies is obtained by integrating micro-heaters next to each laser. We show t…
The cascade of resonant topological structures with $\mathcal{PT}$-symmetry breaking is shown to emit laser light with a frequency-comb spectrum. We consider optically active topological Aubry-André-Harper lattices supporting edge-modes at regularly spaced frequencies. When the amplified resonances in the $\mathcal{PT}$-broken regime match the edge modes of the topological gratings, we predict the emission of discrete laser lines. A proper design enables to engineer the spectral features for specific applications. The robustness of the topological protection makes the system very well suited f…
Quantum cascade lasers are compact sources capable of generating frequency combs. Yet key characteristics - such as optical bandwidth and power-per-mode distribution - have to be improved for better addressing spectroscopy applications. Group delay dispersion plays an important role in the comb formation. In this work, we demonstrate that a dispersion compensation scheme based on a Gires-Tournois Interferometer integrated into the QCL-comb dramatically improves the comb operation regime, preventing the formation of high-phase noise regimes previously observed. The continuous-wave output power …
A ~545 mW single-frequency tunable 520 nm green laser has been demonstrated using a periodically-poled potassium titanyl phosphate (PPKTP) bulk crystal based on single-pass third-harmonic generation (THG) of a 1560 nm laser via single-pass second-harmonic generation (SHG) followed by single-pass sum-frequency generation (SFG). In single-pass SHG, two cascaded periodically-poled magnesium-oxide-doped lithium niobate (PPMgO:LN) crystals were used, and ~3.5 W 780.25 nm doubled laser output is produced, corresponding to maximum doubling efficiency of 26.8%. The system can provide a pump source (52…
Frequency comb assisted diode laser spectroscopy, employing both the accuracy of an optical frequency comb and the broad wavelength tuning range of a tunable diode laser, has been widely used in many applications. In this letter we present a novel method using cascaded frequency agile diode lasers, which allows extending the measurement bandwidth to 37.4 THz (1355 to 1630 nm) at MHz resolution with scanning speeds above 1 THz/s. It is demonstrated as a useful tool to characterize a broadband spectrum for molecular spectroscopy and in particular it enables to characterize the dispersion of inte…
We introduce a new cascaded four-wave mixing technique which scales up the bandwidth of frequency combs generated by phase modulation of a continuous wave laser while simultaneously enhancing the spectral flatness. As a result we demonstrate a 10 GHz frequency comb with over 100 lines in a 10-dB bandwidth in which a record 75 lines are within a flatness of 1-dB. The cascaded four-wave mixing process increases the bandwidth of the initial comb generated by modulation of a CW laser by a factor of five. The broadband comb has approximately quadratic spectral phase, which is compensated upon propa…
We report on a heterogeneous active region design for terahertz quantum cascade laser based frequency combs. Dynamic range, spectral bandwidth as well as output power have been significantly improved with respect to previous designs. When operating individually the lasers act as a frequency comb up to a spectral bandwidth of 1.1 THz, while in a dispersed regime a bandwidth up to 1.94 THz at a center frequency of 3 THz can be reached. A self-detected dual-comb setup has been used to verify the frequency comb nature of the lasers.
We demonstrate a robust and simple method for measurement, stabilization and tuning of the frequency of cw mid-infrared (MIR) lasers, in particular of quantum cascade lasers. The proof of principle is performed with a quantum cascade laser at 5.4 μm, which is upconverted to 1.2 μm by sum-frequency generation in orientation-patterned GaAs with the output of a standard high-power cw 1.5 μm fiber laser. Both the 1.2 μm and the 1.5 μm waves are measured by a standard Er:fiber frequency comb. Frequency measurement at the 100 kHz-level, stabilization to sub-10 kHz level, controlled frequency tuning …
Quantum cascade lasers are proving to be instrumental in the development of compact frequency comb sources at mid-infrared and terahertz frequencies. Here we demonstrate a heterogeneous terahertz quantum cascade laser with two active regions spaced exactly by one octave. Both active regions are based on a four-quantum well laser design and they emit a combined 3~mW peak power at 15~K in pulsed mode. The two central frequencies are 2.3~THz (bandwidth 300~GHz) and 4.6~THz (bandwidth 270~GHz). The structure is engineered in a way that allows simultaneous operation of the two active regions in the…
We measure the inter-modal phase relation of a quantum cascade laser frequency comb operating at 8 um using a coherent beatnote spectroscopy. We find these phases to be reproducible after cycling the power of the device, and to be smoothly varying with driving current. Moreover, these phases describe a comb state exhibiting a simple, linear chirp, which in fact corresponds to the lowest state of chirp to minimise the amplitude modulation, as required for combs driven by four wave mixing in a gain medium with a short gain recovery lifetime.
The major development recently undergone by quantum cascade lasers has effectively extended frequency comb emission to longer-wavelength spectral regions, i.e. the mid and far infrared. Unlike classical pulsed frequency combs, their mode-locking mechanism relies on four-wave mixing nonlinear processes, with a temporal intensity profile different from conventional short-pulses trains. Measuring the absolute phase pattern of the modes in these combs enables a thorough characterization of the onset of mode-locking in absence of short-pulses emission, as well as of the coherence properties. Here, …
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 Fabry Perot 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. Our numerical simulations are in excellent agreement with recent experimental results, showing br…
Quantum cascade laser (QCL) frequency combs are a promising candidate for chemical sensing and biomedical diagnostics, requiring only milliseconds of acquisition time to record absorption spectra without any moving parts. They are electrically pumped and have a small footprint, making them an ideal platform for on-chip integration. Until now, optical feedback is fatal for frequency comb generation in QCLs and destroys intermodal coherence. This property imposes strict limits on the possible degree of integration. Here, we demonstrate coherent injection locking of the repetition frequency to a …
We demonstrate a scheme, based on a cascade of lithium niobate intensity and phase modulators driven by specially tailored radio frequency waveforms to generate an optical frequency comb with very high spectral flatness. In this work we demonstrate a 10 GHz comb with ~40 lines with spectral power variation below 1-dB and ~60 lines in total. The number of lines that can be generated is limited by the power handling capability of the phase modulator, and this can be scaled without compromising the spectral flatness. Furthermore, the spectral phase of the generated combs in our scheme is almost p…
We experimentally demonstrate a simple configuration for mid-infrared (MIR) frequency comb generation in quasi-phase-matched lithium niobate waveguides using the cascaded-$χ^{(2)}$ nonlinearity. With nanojoule-scale pulses from an Er:fiber laser, we observe octave-spanning supercontinuum in the near-infrared with dispersive-wave generation in the 2.5--3 $\textμ$m region and intra-pulse difference-frequency generation in the 4--5 $\textμ$m region. By engineering the quasi-phase-matched grating profiles, tunable, narrow-band MIR and broadband MIR spectra are both observed in this geometry. Final…
Optical frequency combs are revolutionising modern time and frequency metrology. In the past years, their range of applications has increased substantially, driven by their miniaturisation through microresonator-based solutions. The combs in such devices are typically generated using the third-order $χ^{(3)}$-nonlinearity of the resonator material. An alternative approach is making use of second-order $χ^{(2)}$-nonlinearities. While the idea of generating combs this way has been around for almost two decades, so far only few demonstrations are known, based either on bulky bow-tie cavities or o…
In the terahertz frequency range, the quantum cascade laser (QCL) is a suitable platform for the frequency comb and dual-comb operation. Improved comb performances have been always much in demand. In this work, by employing a symmetric thermal dissipation scheme, we report an improved frequency comb and dual-comb operation of terahertz QCLs. Two configurations of cold fingers, i.e., type A and B with asymmetric and symmetric thermal dissipation schemes, respectively, are investigated here. A finite-element thermal analysis is carried out to study the parametric effects on the thermal managemen…
It was recently demonstrated that broadband quantum cascade lasers can operate as frequency combs. As such, they operate under direct electrical pumping at both mid-infrared and THz frequencies, making them very attractive for dual-comb spectroscopy. Performance levels are continuously improving, with average powers over 100 mW and frequency coverage of 100 cm$^{-1}$ in the mid-infrared. In the THz range, 10 mW of average power and 600 GHz of frequency coverage are reported. As a result of the very short upper state lifetime of the gain medium, the mode proliferation in these sources arises fr…
We study the parametric wave interaction in qua- dratic nonlinear media with randomized distribution of the ferroelectric domains. In particular, we discuss properties of second and cascaded third harmonic generation. We derive analytical formulas describing emission properties of the second and third harmonics in the presence of domain disorder and show that the latter process is governed by the characteristics of the constituent processes, i.e. second harmonic generation and sum frequency mixing. We demonstrate the role of randomness on various second and third harmonic generation regimes su…
Frequency combs based on terahertz quantum cascade lasers feature broadband coverage and high output powers in a compact package, making them an attractive option for broadband spectroscopy. Here, we demonstrate the first multi-heterodyne spectroscopy using two terahertz quantum cascade laser combs. With just 100 $μ$s of integration time, we achieve peak signal-to-noise ratios exceeding 60 dB and a spectral coverage greater than 250 GHz centered at 2.8 THz. Even with room-temperature detectors we are able to achieve peak signal-to-noise ratios of 50 dB, and as a proof-of-principle we use these…
Nanometer-precision surface metrology of millimeter-size stepped objects using full-cascade-linked synthetic-wavelength digital holography using a line-by-line full-mode-extracted optical frequency comb
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, beingthe only electrically pumped device able to operate in the 0.6-6 THz range without the need of bulky andexpensive liquid helium cooling. Here we present comb operation obtained by intra-cavity mixing of adistributed feedback laser at λ = 6.5 μm and a Fabry-Pérot device at around λ = 6.9 μm. The resultingultra-broadband THz emission extends from 1.8 to 3.3 THz, with a total output power of…
We present homogeneous quantum cascade lasers (QCLs) emitting around 3 THz which display bandwidths up to 950 GHz with a single stable beatnote. Devices are spontaneously operating in a harmonic comb state, and when in a dense mode regime they can be injection locked at the cavity roundtrip frequency with very small RF powers down to -55 dBm. When operated in the electrically unstable region of negative differential resistance, the device displays ultra-broadband operation exceeding 1.83 THz ($Δf/f=50\%$) with high phase noise, exhibiting self-sustained, periodic voltage oscillations. The low …
