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.

Nonlinear Nano-Imaging of Interlayer Coupling in 2D Graphene-Semiconductor Heterostructures.

The emergent electronic, spin, and other quantum properties of 2D heterostructures of graphene and transition metal dichalcogenides are controlled by the underlying interlayer coupling and associated charge and energy transfer dynamics. However, these processes are sensitive to interlayer distance and crystallographic orientation, which are in turn affected by defects, grain boundaries, or other nanoscale heterogeneities. This obfuscates the distinction between interlayer charge and energy transfer. Here, nanoscale imaging in coherent four-wave mixing (FWM) and incoherent two-photon photoluminescence (2PPL) is combined with a tip distance-dependent coupled rate equation model to resolve the underlying intra- and inter-layer dynamics while avoiding the influence of structural heterogeneities in mono- to multi-layer graphene/WSe2 heterostructures. With selective insertion of hBN spacer layers, it is shown that energy, as opposed to charge transfer, dominates the interlayer-coupled optical response. From the distinct nano-FWM and -2PPL tip-sample distance-dependent modification of interlayer and intralayer relaxation by tip-induced enhancement and quenching, an interlayer energy transfer time of τ ET ≈ ( 0 . 35 - 0.15 + 0.65 ) $\tau _{\rm ET} \approx (0.35^{+0.65}_{-0.15})$  ps consistent with recent reports is derived. As a local probe technique, this approach highlights the ability to determine intrinsic sample properties even in the presence of large sample heterogeneity.

Ultrafast Nanoimaging of Electronic Coherence of Monolayer WSe2.

Transition-metal dichalcogenides (TMDs) have demonstrated a wide range of novel photonic, optoelectronic, and correlated electron phenomena for more than a decade. However, the coherent dynamics of their excitons, including possibly long dephasing times and their sensitivity to spatial heterogeneities, are still poorly understood. Here we implement adiabatic plasmonic nanofocused four-wave mixing (FWM) to image the coherent electron dynamics in monolayer WSe2. We observe nanoscale heterogeneities at room temperature with dephasing ranging from T2 ≲ 5 to T2 ≳ 60 fs on length scales of 50-100 nm. We further observe a counterintuitive anticorrelation between FWM intensity and T2, with the weakest FWM emission at locations of longest coherence. We interpret this behavior as a nonlocal nano-optical interplay between spatial coherence of the nonlinear polarization and disorder-induced scattering. The results highlight the challenges associated with heterogeneities in TMDs limiting their photophysical properties, yet also the potential of their novel nonlinear optical phenomena.

Creating a near-perfect circularly polarized terahertz beam through the nonreciprocity of a magnetoplasma.

Compared to other parts of the electromagnetic spectrum, the terahertz frequency range lacks efficient polarization manipulation techniques, which is impeding the proliferation of terahertz technology. In this work, we demonstrate a tunable and broadband linear-to-circular polarization converter based on an InSb plate containing a free-carrier magnetoplasma. In a wide spectral region (∼ 0.45 THz), the magnetoplasma selectively absorbs one circularly polarized mode due to electron cyclotron resonance and also reflects it at the edges of the absorption band. Both effects are nonreciprocal and contribute to form a near-zero transmission band with a high isolation of -36 dB, resulting in the output of a near-perfect circularly polarized terahertz wave for an incident linearly polarized beam. The near-zero transmission band is tunable with magnetic field to cover a wide frequency range from 0.3 to 4.8 THz.

Hyperbolic Polaritons in Topological Nodal Ring Semimetals.

In mirror-symmetric systems, there is a possibility of the realization of extended gapless electronic states characterized as nodal lines or rings. Strain induced modifications to these states lead to the emergence of different classes of nodal rings with qualitatively different physical properties. Here we study optical response and the electromagnetic wave propagation in type I nodal ring semimetals, in which the low-energy quasiparticle dispersion is parabolic in momentum k_{x} and k_{y} and is linear in k_{z}. This leads to a highly anisotropic dielectric permittivity tensor in which the optical response is plasmonic in one spatial direction and dielectric in the other two directions. The resulting normal modes (polaritons) in the bulk material become hyperbolic over a broad frequency range, which is furthermore tunable by the doping level. The propagation, reflection, and polarization properties of the hyperbolic polaritons not only provide valuable information about the electronic structure of these fascinating materials in the most interesting region near the nodal rings but also pave the way to tunable hyperbolic materials with applications ranging from anomalous refraction and waveguiding to perfect absorption in ultrathin subwavelength films.

Maximally Efficient Biphoton Generation by Single Photon Decay in Nonlinear Quantum Photonic Circuits.

We develop a general nonperturbative formalism and propose a specific scheme for maximally efficient generation of biphoton states by parametric decay of single photons. We show that the well-known critical coupling concept of integrated optics can be generalized to the nonlinear coupling of quantized photon modes to describe the nonperturbative optimal regime of a single-photon nonlinearity and establish a fundamental upper limit on the nonlinear generation efficiency of quantum-correlated photons, which approaches unity for low enough absorption losses.

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.

Nanocavity Clock Spectroscopy: Resolving Competing Exciton Dynamics in WSe2/MoSe2 Heterobilayers.

Transition-metal dichalcogenide heterostructures are an emergent platform for novel many-body states from exciton condensates to nanolasers. However, their exciton dynamics are difficult to disentangle due to multiple competing processes with time scales varying over many orders of magnitude. Using a configurable nano-optical cavity based on a plasmonic scanning probe tip, the radiative (rad) and nonradiative (nrad) relaxation of intra- and interlayer excitons is controlled. Tuning their relative rates in a WSe2/MoSe2 heterobilayer over 6 orders of magnitude in tip-enhanced photoluminescence spectroscopy reveals a cavity-induced crossover from nonradiative quenching to Purcell-enhanced radiation. Rate equation modeling with the interlayer charge transfer time as a reference clock allows for a comprehensive determination from the long interlayer exciton (IX) radiative lifetime τIXrad = (94 ± 27) ns to the 5 orders of magnitude faster competing nonradiative lifetime τIXnrad = (0.6 ± 0.2) ps. This approach of nanocavity clock spectroscopy is generally applicable to a wide range of excitonic systems with competing decay pathways.

Tunable ultrasharp terahertz plasma edge in a lightly doped narrow-gap semiconductor.

Plasma edges in metals typically occur in the visible range, producing characteristic colors of metals. In a lightly doped semiconductor, the plasma edge can occur in the terahertz (THz) frequency range. Due to low scattering rates and variable electron densities in semiconductors, such THz plasma edges can be extremely sharp and greatly tunable. Here, we show that an ultrasharp THz plasma edge exists in a lightly n-doped InSb crystal with a record-high transmittance slope of 80 dB/THz. The frequency at which this sharp edge happens can be readily tuned by changing the temperature, electron density, scattering rate, and sample thickness. The edge frequency exhibited a surprising increase with decreasing temperature below 15 K, which we explain as a result of a weak-to-strong transition in the scattering rate, going from ωτ  ≫ 1 to ωτ âˆ¼ 1. These results indicate that doped narrow-gap semiconductors provide a versatile platform for manipulating THz waves in a controllable manner, especially as a high-pass filter with an unprecedented on/off ratio.

High-power narrow spectrum GaSb-based DBR lasers emitting near 2.1 µm.

Stable high-power narrow-linewidth operation of the 2.05-2.1 µm GaSb-based diode lasers was achieved by utilizing the sixth-order surface-etched distributed Bragg reflector (DBR) mirrors. The DBR multimode devices with 100 µm wide ridge waveguides generated ∼850mW in the continuous wave (CW) regime at 20°C. The device CW output power was limited by thermal rollover. The laser emission spectrum was defined by Bragg reflector reflectivity at all operating currents in a wide temperature range. The devices operated at DBR line with detuning from gain peak exceeding 10 meV.

Anisotropic Flow Control and Gate Modulation of Hybrid Phonon-Polaritons.

Light-matter interaction in two-dimensional photonic or phononic materials allows for the confinement and manipulation of free-space radiation at sub-wavelength scales. Most notably, the van der Waals heterostructure composed of graphene (G) and hexagonal boron nitride (hBN) provides for gate-tunable hybrid hyperbolic plasmon phonon-polaritons (HP3). Here, we present the anisotropic flow control and gate-voltage modulation of HP3 modes in G-hBN on an air-Au microstructured substrate. Using broadband infrared synchrotron radiation coupled to a scattering-type near-field optical microscope, we launch HP3 waves in both hBN Reststrahlen bands and observe directional propagation across in-plane heterointerfaces created at the air-Au junction. The HP3 hybridization is modulated by varying the gate voltage between graphene and Au. This modifies the coupling of continuum graphene plasmons with the discrete hBN hyperbolic phonon polaritons, which is described by an extended Fano model. This work represents the first demonstration of the control of polariton propagation, introducing a theoretical approach to describe the breaking of the reflection and transmission symmetry for HP3 modes. Our findings augment the degree of control of polaritons in G-hBN and related hyperbolic metamaterial nanostructures, bringing new opportunities for on-chip nano-optics communication and computing.

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.

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.

Magnetopolaritons in Weyl Semimetals in a Strong Magnetic Field.

Exotic topological and transport properties of Weyl semimetals have generated a lot of excitement in the condensed matter community. Here we show that Weyl semimetals in a strong magnetic field are highly unusual optical materials. The propagation of electromagnetic waves is affected by an interplay between the plasmonic response of chiral Weyl fermions and extreme anisotropy induced by a magnetic field. The resulting magnetopolaritons possess a number of peculiar properties, such as hyperbolic dispersion, photonic stop bands, coupling-induced transparency, and broadband polarization conversion. These effects can be used for optical spectroscopy of these materials including detection of the chiral anomaly or for broadband terahertz or infrared applications.

Enhanced Third-Order Optical Nonlinearity Driven by Surface-Plasmon Field Gradients.

Efficient nonlinear optical frequency mixing in small volumes is key for future on-chip photonic devices. However, the generally low conversion efficiency severely limits miniaturization to nanoscale dimensions. Here we demonstrate that gradient-field effects can provide for an efficient, conventionally dipole-forbidden nonlinear response. We show that a longitudinal nonlinear source current can dominate the third-order optical nonlinearity of the free electron response in gold in the technologically important near-IR frequency range where the nonlinearities due to other mechanisms are particularly small. Using adiabatic nanofocusing to spatially confine the excitation fields, from measurements of the 2ω_{1}-ω_{2} four-wave mixing response as a function of detuning ω_{1}-ω_{2}, we find up to 10^{-5} conversion efficiency with a gradient-field contribution to χ_{Au}^{(3)} of up to 10^{-19} m^{2}/V^{2}. The results are in good agreement with the theory based on plasma hydrodynamics and underlying electron dynamics. The associated increase in the nonlinear conversion efficiency with a decreasing sample size, which can even overcompensate the volume decrease, offers a new approach for enhanced nonlinear nano-optics. This will enable more efficient nonlinear optical devices and the extension of coherent multidimensional spectroscopies to the nanoscale.

Four-Wave Mixing in Landau-Quantized Graphene.

For Landau-quantized graphene, featuring an energy spectrum consisting of nonequidistant Landau levels, theory predicts a giant resonantly enhanced optical nonlinearity. We verify the nonlinearity in a time-integrated degenerate four-wave mixing (FWM) experiment in the mid-infrared spectral range, involving the Landau levels LL-1, LL0 and LL1. A rapid dephasing of the optically induced microscopic polarization on a time scale shorter than the pulse duration (∼4 ps) is observed, while a complementary pump-probe experiment under the same experimental conditions reveals a much longer lifetime of the induced population. The FWM signal shows the expected field dependence with respect to lowest order perturbation theory for low fields. Saturation sets in for fields above ∼6 kV/cm. Furthermore, the resonant behavior and the order of magnitude of the third-order susceptibility are in agreement with our theoretical calculations.

Stability of High-Density Two-Dimensional Excitons against a Mott Transition in High Magnetic Fields Probed by Coherent Terahertz Spectroscopy.

We have performed time-resolved terahertz absorption measurements on photoexcited electron-hole pairs in undoped GaAs quantum wells in magnetic fields. We probed both unbound- and bound-carrier responses via cyclotron resonance and intraexciton resonance, respectively. The stability of excitons, monitored as the pair density was systematically increased, was found to dramatically increase with increasing magnetic field. Specifically, the 1s-2p_{-} intraexciton transition at 9 T persisted up to the highest density, whereas the 1s-2p feature at 0 T was quickly replaced by a free-carrier Drude response. Interestingly, at 9 T, the 1s-2p_{-} peak was replaced by free-hole cyclotron resonance at high temperatures, indicating that 2D magnetoexcitons do dissociate under thermal excitation, even though they are stable against a density-driven Mott transition.

Active mode-locking of mid-infrared quantum cascade lasers with short gain recovery time.

We investigate the dynamics of actively modulated mid-infrared quantum cascade lasers (QCLs) using space- and time-domain simulations of coupled density matrix and Maxwell equations with resonant tunneling current taken into account. We show that it is possible to achieve active mode locking and stable generation of picosecond pulses in high performance QCLs with a vertical laser transition and a short gain recovery time by bias modulation of a short section of a monolithic Fabry-Perot cavity. In fact, active mode locking in QCLs with a short gain recovery time turns out to be more robust to the variation of parameters as compared to previously studied lasers with a long gain recovery time. We investigate the effects of spatial hole burning and phase locking on the laser output.

Strong magneto-optical effects due to surface states in three-dimensional topological insulators.

We show that a thin film of a three-dimensional topological insulator such as Bi(2)Se(3)or Bi(2)Te(3) can exhibit strong linear and nonlinear magneto-optical effects in a transverse magnetic field. In particular, one can achieve an almost complete circular polarization of an incident terahertz or mid-infrared radiation and an efficient four-wave mixing.

Efficient nonlinear generation of THz plasmons in graphene and topological insulators.

Surface plasmons in graphene may provide an attractive alternative to noble-metal plasmons due to their tighter confinement, peculiar dispersion, and longer propagation distance. We present theoretical studies of the nonlinear difference frequency generation (DFG) of terahertz surface plasmon modes supported by two-dimensional layers of massless Dirac electrons, which includes graphene and surface states in topological insulators. Our results demonstrate strong enhancement of the DFG efficiency near the plasmon resonance and the feasibility of phase-matched nonlinear generation of plasmons over a broad range of frequencies.