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.

Active mid-infrared ring resonators.

High-quality optical ring resonators can confine light in a small volume and store it for millions of roundtrips. They have enabled the dramatic size reduction from laboratory scale to chip level of optical filters, modulators, frequency converters, and frequency comb generators in the visible and the near-infrared. The mid-infrared spectral region (3-12 µm), as important as it is for molecular gas sensing and spectroscopy, lags behind in development of integrated photonic components. Here we demonstrate the integration of mid-infrared ring resonators and directional couplers, incorporating a quantum cascade active region in the waveguide core. It enables electrical control of the resonant frequency, its quality factor, the coupling regime and the coupling coefficient. We show that one device, depending on its operating point, can act as a tunable filter, a nonlinear frequency converter, or a frequency comb generator. These concepts extend to the integration of multiple active resonators and waveguides in arbitrary configurations, thus allowing the implementation of purpose-specific mid-infrared active photonic integrated circuits for spectroscopy, communication, and microwave generation.

Radially and Azimuthally Pure Vortex Beams from Phase-Amplitude Metasurfaces.

To exploit the full potential of the transverse spatial structure of light using the Laguerre-Gaussian basis, it is necessary to control the azimuthal and radial components of the photons. Vortex phase elements are commonly used to generate these modes of light, offering precise control over the azimuthal index but neglecting the radially dependent amplitude term, which defines their associated corresponding transverse profile. Here, we experimentally demonstrate the generation of high-purity Laguerre-Gaussian beams with a single-step on-axis transformation implemented with a dielectric phase-amplitude metasurface. By vectorially structuring the input beam and projecting it onto an orthogonal polarization basis, we can sculpt any vortex beam in phase and amplitude. We characterize the azimuthal and radial purities of the generated vortex beams, reaching a purity of 98% for a vortex beam with l =50 and p = 0. Furthermore, we comparatively show that the purity of the generated vortex beams outperforms those generated with other well-established phase-only metasurface approaches. In addition, we highlight the formation of "ghost" orbital angular momentum orders from azimuthal gratings (analogous to ghost orders in ruled gratings), which have not been widely studied to date. Our work brings higher-order vortex beams and their unlimited potential within reach of wide adoption.

Resonators with tailored optical path by cascaded-mode conversions.

Optical resonators enable the generation, manipulation, and storage of electromagnetic waves. The physics underlying their operation is determined by the interference of electromagnetic waves, giving rise to the resonance spectrum. This mechanism causes the limitations and trade-offs of resonator design, such as the fixed relationship between free spectral range, modal linewidth, and the resonator's refractive index and size. Here, we introduce a new class of optical resonators, generating resonances by designing the optical path through transverse mode coupling in a cascaded process created by mode-converting mirrors. The generalized round-trip phase condition leads to resonator characteristics that are markedly different from Fabry-Perot resonators and can be tailored over a wide range. We confirm the existence of these modes experimentally in an integrated waveguide cavity with mode converters coupling transverse modes into one supermode. We also demonstrate a transverse mode-independent transmission and show that its engineered spectral properties agree with theoretical predictions.

Accurately Measuring Molecular Rotational Spectra in Excited Vibrational Modes.

Although gas phase rotational spectroscopy is a mature field for which millions of rotational spectral lines have been measured in hundreds of molecules with sub-MHz accuracy, it remains a challenge to measure these rotational spectra in excited vibrational modes with the same accuracy. Recently, it was demonstrated that virtually any rotational transition in excited vibrational modes of most molecules may be made to lase when pumped by a continuously tunable quantum cascade laser (QCL). Here, we demonstrate how an infrared QCL may be used to enhance absorption strength or induce lasing of terahertz rotational transitions in highly excited vibrational modes in order to measure their frequencies more accurately. To illustrate the concepts, we used a tunable QCL to excite v3 R-branch transitions in N2O and either enhanced absorption or induced lasing on 20 v3 rotational transitions, whose frequencies between 299 and 772 GHz were then measured using either heterodyne or modulation spectroscopy. The spectra were fitted to obtain the rotational constants B3 and D3, which reproduce the measured spectra to within the experimental uncertainty of ± 5 kHz. We then show how this technique may be generalized by estimating the threshold power to make any rotational transition lase in any N2O vibrational mode.

Multifunctional wide-angle optics and lasing based on supercell metasurfaces.

Metasurfaces are arrays of subwavelength spaced nanostructures that can manipulate the amplitude, phase, and polarization of light to achieve a variety of optical functions beyond the capabilities of 3D bulk optics. However, they suffer from limited performance and efficiency when multiple functions with large deflection angles are required because the non-local interactions due to optical coupling between nanostructures are not fully considered. Here we introduce a method based on supercell metasurfaces to demonstrate multiple independent optical functions at arbitrary large deflection angles with high efficiency. In one implementation the incident laser is simultaneously diffracted into Gaussian, helical and Bessel beams over a large angular range. We then demonstrate a compact wavelength-tunable external cavity laser with arbitrary beam control capabilities - including beam shaping operations and the generation of freeform holograms. Our approach paves the way to novel methods to engineer the emission of optical sources.

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.

Remote structuring of near-field landscapes.

The electromagnetic near field enables subwavelength applications such as near-field microscopy and nanoparticle manipulation. Present methods to structure the near field rely on optical antenna theory, involving nanostructures that locally convert propagating waves into confined near-field patterns. We developed a theory of remote rather than local near-field shaping, based on cascaded mode conversion and interference of counterpropagating guided waves with different propagation constants. We demonstrate how to structure at will the longitudinal and transverse variation of the near field, allowing for distributions beyond the conventional monotonic decay of the evanescent field. We provide an experimental realization that confirms our theory. Our method applies to fields with arbitrary polarization states and mode profiles, providing a path toward three-dimensional control of the near field.

Frequency combs induced by phase turbulence.

Wave instability-the process that gives rise to turbulence in hydrodynamics1-represents the mechanism by which a small disturbance in a wave grows in amplitude owing to nonlinear interactions. In photonics, wave instabilities result in modulated light waveforms that can become periodic in the presence of coherent locking mechanisms. These periodic optical waveforms are known as optical frequency combs2-4. In ring microresonator combs5,6, an injected monochromatic wave becomes destabilized by the interplay between the resonator dispersion and the Kerr nonlinearity of the constituent crystal. By contrast, in ring lasers instabilities are considered to occur only under extreme pumping conditions7,8. Here we show that, despite this notion, semiconductor ring lasers with ultrafast gain recovery9,10 can enter frequency comb regimes at low pumping levels owing to phase turbulence11-an instability known to occur in hydrodynamics, superconductors and Bose-Einstein condensates. This instability arises from the phase-amplitude coupling of the laser field provided by linewidth enhancement12, which produces the needed interplay of dispersive and nonlinear effects. We formulate the instability condition in the framework of the Ginzburg-Landau formalism11. The localized structures that we observe share several properties with dissipative Kerr solitons, providing a first step towards connecting semiconductor ring lasers and microresonator frequency combs13.

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.

Widely tunable compact terahertz gas lasers.

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.

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.

Radio frequency transmitter based on a laser frequency comb.

Since the days of Hertz, radio transmitters have evolved from rudimentary circuits emitting around 50 MHz to modern ubiquitous Wi-Fi devices operating at gigahertz radio bands. As wireless data traffic continues to increase, there is a need for new communication technologies capable of high-frequency operation for high-speed data transfer. Here, we give a proof of concept of a compact radio frequency transmitter based on a semiconductor laser frequency comb. In this laser, the beating among the coherent modes oscillating inside the cavity generates a radio frequency current, which couples to the electrodes of the device. We show that redesigning the top contact of the laser allows one to exploit the internal oscillatory current to drive a dipole antenna, which radiates into free space. In addition, direct modulation of the laser current permits encoding a signal in the radiated radio frequency carrier. Working in the opposite direction, the antenna can receive an external radio frequency signal, couple it to the active region, and injection lock the laser. These results pave the way for applications and functionality in optical frequency combs, such as wireless radio communication and wireless synchronization to a reference source.

The harmonic state of quantum cascade lasers: origin, control, and prospective applications [Invited].

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.

Contact compliance effects in the frictional response of bioinspired fibrillar adhesives.

The shear failure and friction mechanisms of bioinspired adhesives consisting of elastomer arrays of microfibres terminated by mushroom-shaped tips are investigated in contact with a rigid lens. In order to reveal the interplay between the vertical and lateral loading directions, experiments are carried out using a custom friction set-up in which normal stiffness can be made either high or low when compared with the stiffness of the contact between the fibrillar adhesive and the lens. Using in situ contact imaging, the shear failure of the adhesive is found to involve two successive mechanisms: (i) cavitation and peeling at the contact interface between the mushroom-shaped fibre tip endings and the lens; and (ii) side re-adhesion of the fibre's stem to the lens. The extent of these mechanisms and their implications regarding static friction forces is found to depend on the crosstalk between the normal and lateral loading directions that can result in contact instabilities associated with fibre buckling. In addition, the effects of the viscoelastic behaviour of the polyurethane material on the rate dependence of the shear response of the adhesive are accounted for.