Terahertz Third-harmonic Generation Research Articles

Tracing the dynamics of superconducting order via transient terahertz third-harmonic generation.

Ultrafast optical control of quantum systems is an emerging field of physics. In particular, the possibility of light-driven superconductivity has attracted much of attention. To identify nonequilibrium superconductivity, it is necessary to measure fingerprints of superconductivity on ultrafast timescales. Recently, nonlinear THz third-harmonic generation (THG) was shown to directly probe the collective degrees of freedoms of the superconducting condensate, including the Higgs mode. Here, we extend this idea to light-driven nonequilibrium states in superconducting La2-xSrxCuO4, establishing an optical pump-THz-THG drive protocol to access the transient superconducting order-parameter quench and recovering on few-picosecond timescales. We show in particular the ability of two-dimensional TH spectroscopy to disentangle the effects of optically excited quasiparticles from the pure order-parameter dynamics, which are unavoidably mixed in the pump-driven linear THz response. Benchmarking the gap dynamics to existing experiments shows the ability of driven THG spectroscopy to overcome these limitations in ordinary pump-probe protocols.

Dynamical interplay between superconductivity and pseudogap in cuprates as revealed by terahertz third-harmonic generation spectroscopy

We report on nonlinear terahertz third-harmonic generation (THG) measurements on YBa 2 Cu 3 O 6+ x thin films. Different from conventional superconductors, the THG signal starts to appear in the normal state, which is consistent with the crossover temperature T * of pseudogap over broad doping levels. Upon lowering the temperature, the THG signal shows an anomaly just below T c in the optimally doped sample. Notably, we observe a beat pattern directly in the measured real-time waveform of the THG signal. We elaborate that the Higgs mode, which develops below T c , couples to the mode already developed below T * , resulting in an energy level splitting. However, this coupling effect is not evident in underdoped samples. We explore different potential explanations for the observed phenomena. Our research offers valuable insight into the interplay between superconductivity and pseudogap.

Enhanced terahertz third-harmonic generation based on the graphene-assisted meta-grating structure

The nonlinear response of optical materials provides a valuable approach for optical switching and nonlinear frequency conversion. However, the nonlinear responses of bulk crystals are often very weak, requiring higher pump energy for pumping. In this work, we investigate the significant enhancement of third harmonic generation (THG) at terahertz frequencies using an ultra-thin nonlinear meta-grating metasurface assisted by graphene strips. In this structure, the incident pump light experiences strong confinement and enhancement along the graphene surface caused by the generation of strongly localized surface plasmon resonances. Utilizing the significant third-order nonlinear conductivity of graphene, it becomes possible to achieve high THG conversion efficiency even at low pump intensities. The research results indicate that, at low incident intensity of 10 kW/cm2, the third harmonic wave conversion efficiency can reach approximately 2.8 %. We also thoroughly investigate the impact of meta-grating structural parameters, graphene Fermi level, incident angle, and pump light intensity on THG operation characteristics. Our study findings provide an effective approach for greatly boosting the THG conversion efficiency in the terahertz frequency bands, opening new avenues in the development of novel compact frequency converters and modulators that are emerging in terahertz chip integration and nonlinear devices.

Terahertz Third-Harmonic Generation in Topological Insulators Based on Bismuth and Antimony Chalcogenides

Terahertz third-harmonic generation in topological insulators based on bismuth and antimony chalcogenides has been experimentally investigated. It has been found that the third-harmonic conversion efficiency is inversely proportional to the electron Fermi energy; among the materials under study, antimony telluride has the highest conversion efficiency.

Enhanced terahertz third-harmonic generation by bound states in the continuum in graphene grating-like metamaterial

Non-linear metamaterials hold great promise for enhanced terahertz harmonic generation. Here, we numerically investigate enhanced terahertz third-harmonic generation (THG) by exploiting the symmetry-protected bound states in the continuum (BICs) in graphene grating-like metamaterial. By symmetry breaking of metamaterials, BICs transform into quasi-BICs. The high Q-factor and strong localized field enhancement is achieved at quasi-BICs, leading to a boosted THG process with low incident intensity of fundamental frequency. The THG conversion efficiency reaches 3.1% at an incident intensity of 100 kW/cm2. The remarkably enhanced non-linear optical process in the proposed non-linear metamaterial constitutes an outstanding platform for on-chip terahertz non-linear conversion applications.

Enhanced terahertz third-harmonic generation in graphene–metal metasurface with bound states in the continuum

We propose a graphene–metal metasurface with bound states in the continuum (BICs) for the enhancement of terahertz (THz) third-harmonic generation (THG). With the adjustment of graphene Fermi level, the parameter-tuned BICs produced by the graphene–metal metasurface can make the transition to distinct quasi-BICs. It enables strong confinement of the localized field in monolayer graphene. By exploiting the large third-order nonlinearity of graphene, the efficient THG process at the quasi-BICs can be boosted under low pump threshold. With the 50 kW/cm2 of fundamental THz incidence, a THG conversion efficiency as high as ∼3% is achievable at the quasi-BICs regime. This renders the BIC metasurfaces very attractive for THz nonlinear photonics.

Enhanced terahertz third harmonic generation with high-order guided-mode resonance of graphene plasmonic gratings

We present a unique scheme to efficiently enhance terahertz third harmonic generation (THG). By exploiting the high-order guided-mode resonance of graphene plasmonic grating, the off-plane transverse localized field can be suppressed, which enables the electromagnetic energy to be tightly concentrated and significantly enhanced in the monolayer graphene. Meanwhile, high density of in-plane hot spots can be excited to form a quasi-continuous enhanced-field profile called as hot surface. This can bring about the giant nonlinearity enhancement of terahertz field-graphene interaction, greatly pushing forward the enhanced THG in monolayer graphene to breakout the limitation of various patterned metamaterials. It is anticipated that the graphene plasmonic grating has promising application for nonlinear terahertz spectroscopy, imaging and communication.

Grating-Graphene Metamaterial as a Platform for Terahertz Nonlinear Photonics.

Nonlinear optics is an increasingly important field for scientific and technological applications, owing to its relevance and potential for optical and optoelectronic technologies. Currently, there is an active search for suitable nonlinear material systems with efficient conversion and a small material footprint. Ideally, the material system should allow for chip integration and room-temperature operation. Two-dimensional materials are highly interesting in this regard. Particularly promising is graphene, which has demonstrated an exceptionally large nonlinearity in the terahertz regime. Yet, the light–matter interaction length in two-dimensional materials is inherently minimal, thus limiting the overall nonlinear optical conversion efficiency. Here, we overcome this challenge using a metamaterial platform that combines graphene with a photonic grating structure providing field enhancement. We measure terahertz third-harmonic generation in this metamaterial and obtain an effective third-order nonlinear susceptibility with a magnitude as large as 3 × 10–8 m2/V2, or 21 esu, for a fundamental frequency of 0.7 THz. This nonlinearity is 50 times larger than what we obtain for graphene without grating. Such an enhancement corresponds to a third-harmonic signal with an intensity that is 3 orders of magnitude larger due to the grating. Moreover, we demonstrate a field conversion efficiency for the third harmonic of up to ∼1% using a moderate field strength of ∼30 kV/cm. Finally, we show that harmonics beyond the third are enhanced even more strongly, allowing us to observe signatures of up to the ninth harmonic. Grating-graphene metamaterials thus constitute an outstanding platform for commercially viable, CMOS-compatible, room-temperature, chip-integrated, THz nonlinear conversion applications.

Phase-resolved Higgs response in superconducting cuprates

In high-energy physics, the Higgs field couples to gauge bosons and fermions and gives mass to their elementary excitations. Experimentally, such couplings can be inferred from the decay product of the Higgs boson, i.e., the scalar (amplitude) excitation of the Higgs field. In superconductors, Cooper pairs bear a close analogy to the Higgs field. Interaction between the Cooper pairs and other degrees of freedom provides dissipation channels for the amplitude mode, which may reveal important information about the microscopic pairing mechanism. To this end, we investigate the Higgs (amplitude) mode of several cuprate thin films using phase-resolved terahertz third harmonic generation (THG). In addition to the heavily damped Higgs mode itself, we observe a universal jump in the phase of the driven Higgs oscillation as well as a non-vanishing THG above Tc. These findings indicate coupling of the Higgs mode to other collective modes and potentially a nonzero pairing amplitude above Tc.

Polarization-resolved terahertz third-harmonic generation in a single-crystal superconductor NbN: Dominance of the Higgs mode beyond the BCS approximation

Recent advances in time-domain terahertz (THz) spectroscopy have unveiled that resonantly-enhanced strong THz third-harmonic generation (THG) mediated by the collective Higgs amplitude mode occurs in s-wave superconductors, where charge-density fluctuations (CDF) have also been shown to contribute to the nonlinear third-order susceptibility. It has been theoretically proposed that the nonlinear responses of Higgs and CDF exhibit essentially different polarization dependences. Here we experimentally discriminate the two contributions by polarization-resolved intense THz transmission spectroscopy for a single-crystal NbN film. The result shows that the resonant THG in the transmitted light always appears in the polarization parallel to that of the incident light with no appreciable crystal axis dependence. When we compare this with the theoretical calculation here with the BCS approximation and the dynamical mean-field theory for a model of NbN constructed from first principles, the experimental result strongly indicates that the Higgs mode rather than the CDF dominates the THG resonance in NbN. A possible mechanism for this is discussed such as the retardation effect in the phonon-mediated pairing interaction beyond BCS.

Terahertz nonlinear optics with strained p-type quantum wells

Valence-subband nonparabolicity is shown theoretically to lead to nonlinearities associated with terahertz third-harmonic generation in strained p -type quantum wells. For strained InAs quantum wells it is found that the corresponding value of chi((3)) can be as large as ~10(-12)(m/V)(2). The predicted values of chi((3)) are in the range of those associated with intersubband transitions in the mid-infrared region of the spectrum.