Recent developments have enabled the practical realization of optical elements in which the polarization of light may vary spatially. We present an extension of Fourier optics—matrix Fourier optics—for understanding these devices and apply it to the design and realization of metasurface gratings implementing arbitrary, parallel polarization analysis. We show how these gratings enable a compact, full-Stokes polarization camera without standard polarization optics. Our single-shot polarization camera requires no moving parts, specially patterned pixels, or conventional polarization optics and may enable the widespread adoption of polarization imaging in machine vision, remote sensing, and other areas.

We report the observation of a clear single-mode instability threshold in continuous-wave Fabry-Perot quantum cascade lasers (QCLs). The instability is characterized by the appearance of sidebands separated by tens of free spectral ranges (FSR) from the first lasing mode, at a pump current not much higher than the lasing threshold. As the current is increased, higher-order sidebands appear that preserve the initial spacing, and the spectra are suggestive of harmonically phase-locked waveforms. We present a theory of the instability that applies to all homogeneously broadened standing-wave lasers. The low instability threshold and the large sideband spacing can be explained by the combination of an unclamped, incoherent Lorentzian gain due to the population grating, and a coherent parametric gain caused by temporal population pulsations that changes the spectral gain line shape. The parametric term suppresses the gain of sidebands whose separation is much smaller than the reciprocal gain recovery time, while enhancing the gain of more distant sidebands. The large gain recovery frequency of the QCL compared to the FSR is essential to observe this parametric effect, which is responsible for the multiple-FSR sideband separation. We predict that by tuning the strength of the incoherent gain contribution, for example by engineering the modal overlap factors and the carrier diffusion, both amplitude-modulated (AM) or frequency-modulated emission can be achieved from QCLs. We provide initial evidence of an AM waveform emitted by a QCL with highly asymmetric facet reflectivities, thereby opening a promising route to ultrashort pulse generation in the mid-infrared. Together, the experiments and theory clarify a deep connection between parametric oscillation in optically pumped microresonators and the single-mode instability of lasers, tying together literature from the last 60 years.

Optical frequency combs1,2 establish a rigid phase-coherent link between microwave and optical domains and are emerging as high-precision tools in an increasing number of applications 3 . Frequency combs with large intermodal spacing are employed in the field of microwave photonics for radiofrequency arbitrary waveform synthesis 4,5 and for generation of THz tones of high spectral purity in the future wireless communication networks 6,7 . 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 caused by the suppression of tens of adjacent cavity modes originates from a parametric contribution to the gain due to temporal modulations of the population inversion in the laser 8,9 . The mode spacing of the harmonic comb is shown to be uniform to within 5 × 10 −12 parts of the central frequency using multiheterodyne self-detection. This new harmonic comb state extends the range of applications of quantum cascade laser frequency combs 10-13 . Several techniques to generate optical frequency combs (OFCs) have been demonstratedin the last decades based on different nonlinear mechanisms that fulfill the modelocking condition. Originally, passively modelocked lasers based on saturable absorption and Kerr lensing were used to create short light pulses, and were subsequently shown to also constitute frequency combs. This type of modelocking is an example of amplitude-modulated modelocking, so-named for the temporal behavior of the electric field of the emitted light. However, these techniques usually result in elaborate optical systems. More recently, new routes promising chip-scale comb generators have been investigated based on optically-pumped ultra-high-quality-factor crystalline microresonators 14-16 and on broadband quantum cascade lasers (QCLs) with specially designed multistage active regions 10,17 . In both cases the essential underlying mechanism responsible for the generation of OFCs is cascaded four-wave mixing (FWM) enabled by a third-order χ (3) Kerr nonlinearity. The temporal behavior of these OFCs is not restricted to ultrashort pulses but can represent rather sophisticated waveforms due to a non-trivial relationship among the spectral phases of the comb teeth. In fact, the output of a QCL-based frequency comb resembles that of a frequency-modulated laser with nearly constant output intensity 10,18 .A novel mechanism of OFC generation in QCLs was suggested by the recent discovery of a new laser state 19 , which comprises many modes separated by higher harmonics of the 2 cavity free spectral range (FSR) (Figure 1a). This spectrum radically differs from that of fundamentally modelocked QCL combs where adjacent cavity modes are populated ( Figure 1b THz repetition rates in other semiconductor lasers 20 . Rather, the modes are locked passively due to the behavior of the QCL gain medium itself.In this work we employed two Fabry-Perot (FP) QCLs fabricated from the same growth process with 6 mm-long cavit...

The terahertz region of the electromagnetic spectrum has been the least utilized owing to inadequacies of available sources. We introduce a compact, widely frequency-tunable, extremely bright source of terahertz radiation: a gas-phase molecular laser based on rotational population inversions optically pumped by a quantum cascade laser. By identifying the essential parameters that determine the suitability of a molecule for a terahertz laser, almost any rotational transition of almost any molecular gas can be made to lase. Nitrous oxide is used to illustrate the broad tunability over 37 lines spanning 0.251 to 0.955 terahertz, each with kilohertz linewidths. Our analysis shows that laser lines spanning more than 1 terahertz with powers greater than 1 milliwatt are possible from many molecular gases pumped by quantum cascade lasers.

Bifunctional active regions, capable of light generation and detection at the same wavelength, allow a straightforward realization of the integrated mid-infrared photonics for sensing applications. Here, we present a high performance bifunctional device for 8 μm capable of 1 W single facet continuous wave emission at 15 °C. Apart from the general performance benefits, this enables sensing techniques which rely on continuous wave operation, for example, heterodyne detection, to be realized within a monolithic platform and demonstrates that bifunctional operation can be realized at longer wavelength, where wavelength matching becomes increasingly difficult and that the price to be paid in terms of performance is negligible. In laser operation, the device has the same or higher efficiency compared to the best lattice-matched QCLs without same wavelength detection capability, which is only 30% below the record achieved with strained material at this wavelength.

No abstract

The recently discovered ability of the quantum cascade laser to produce a harmonic frequency comb has attracted new interest in these devices for both applications and fundamental laser physics. In this review we present an extensive experimental phenomenology of the harmonic state, including its appearance in mid-infrared and terahertz quantum cascade lasers, studies of its destabilization induced by delayed optical feedback, and the assessment of its frequency comb nature. A theoretical model explaining its origin as due to the mutual interaction of population gratings and population pulsations inside the laser cavity will be described. We explore different approaches to control the spacing of the harmonic state, such as optical injection seeding and variation of the device temperature. Prospective applications of the harmonic state include microwave and terahertz generation, picosecond pulse generation in the mid-infrared, and broadband spectroscopy.

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 lockingof 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.