Third-harmonic Intensity Research Articles

Third-Harmonic Generation in Plasmonic Metasurfaces Fabricated by Direct Femtosecond Laser Printing

Direct ablation-free femtosecond laser printing has been used to fabricate a metasurface in the form of ordered arrays of hollow nanobumps on the surface of a thin gold film. Resonant dips in the reflection spectra of fabricated metasurfaces, as well as a resonant increase in the third-harmonic intensity by two orders of magnitude, at the spectral matching of the observed optical resonances of the structure and the pump wavelength of the fundamental harmonic indicate that such ordered nanostructures allows the existence of high-Q-factor collective plasmon resonances, which are associated with the excitation and destructive interference of plasmon-polariton waves.

Microwave third-harmonic generation due to mobile carriers in doped graphene: Effect of band-gap opening and carrier scattering

Abstract We develop a theory for microwave third-harmonic generation (THG) due to mobile carriers in doped graphene by employing the Boltzmann equation techniques. We put forward two distinct mechanisms to explain the microwave THG observed experimentally. These mechanisms are: (i) the Kane-model-like conduction band nonparabolicity, which arises in the presence of a finite gap of any origin between the conduction and the valence band, and (ii) the energy dependence of the electron-momentum relaxation time. We derive an explicit analytical expression for the third-harmonic component in the current density and employ it to evaluate the magnitude of the generated third harmonic as a function of the graphene’s doping level, which can be changed by electrostatic gating. The curve of third-harmonic intensity vs electron density exhibits a pronounced maximum, thus illustrating our principal conclusion that there is an optimal value of the electron density for which the microwave THG can be most efficient.

Grating-Assisted Surface Plasmon Resonance for Enhancement of Optical Harmonic Generation in Graphene

We investigate nonlinear optical second- and third-harmonic generation from graphene covered on dielectric gratings. The nonlinear optical response in graphene is dramatically enhanced when surface plasmon of graphene is excited. Compared with graphene on a flat dielectric, the enhancement factor of second- and third-harmonic generation is up to 106 and 108, respectively. We, in detail, studied the second- and third-harmonic generation intensity influenced by the angle of incidence, the Fermi level, and carrier mobility of graphene.

Topologically enhanced harmonic generation in a nonlinear transmission line metamaterial

Nonlinear transmission lines (NLTLs) are nonlinear electronic circuits used for parametric amplification and pulse generation, and it is known that left-handed NLTLs support enhanced harmonic generation while suppressing shock wave formation. We show experimentally that in a left-handed NLTL analogue of the Su-Schrieffer-Heeger (SSH) lattice, harmonic generation is greatly increased by the presence of a topological edge state. Previous studies of nonlinear SSH circuits focused on solitonic behaviours at the fundamental harmonic. Here, we show that a topological edge mode at the first harmonic can produce strong propagating higher-harmonic signals, acting as a nonlocal cross-phase nonlinearity. We find maximum third-harmonic signal intensities five times that of a comparable conventional left-handed NLTL, and a 250-fold intensity contrast between topologically nontrivial and trivial configurations. This work advances the fundamental understanding of nonlinear topological states, and may have applications for compact electronic frequency generators.

Characterization of the second- and third-harmonic optical susceptibilities of atomically thin tungsten diselenide

We report the first detailed characterization of the sheet third-harmonic optical susceptibility, χ(3)s, of tungsten diselenide (WSe2). With a home-built multiphoton microscope setup developed to study harmonics generation, we map the second and third-harmonic intensities as a function of position in the sample, pump power and polarization angle, for single- and few-layers flakes of WSe2. We register a value of |χ(3)s| ≈ 0.9 × 10−28 m3 V−2 at a fundamental excitation frequency of ℏω = 0.8 eV, which is comparable in magnitude to the third-harmonic susceptibility of other group-VI transition metal dichalcogenides. The simultaneously recorded sheet second-harmonic susceptibility is found to be |χ(2)s| ≈ 0.7 × 10−19 m2 V−1 in very good agreement on the order of magnitude with recent reports for WSe2, which asserts the robustness of our values for |χ(3)s|.

Line-current model for deriving the wavelength scaling of linear and nonlinear optical properties of thin elongated metallic rod antennas

Thin elongated rod antennas with a diameter smaller than the skin depth exhibit surface plasmon polariton modes that can propagate along the antenna while being reflected at the antenna ends. In the line-current model, a current is associated with these modes in order to approximate the optical properties of the antennas. We find that it is crucial to correctly derive the reflection of the surface plasmon polariton modes at the antenna ends for predicting the resonance position and shape accurately. Thus, the line-current model allows for deriving the wavelength scaling behavior of plasmonic near fields as well as the emitted third-harmonic intensity efficiently. Neglecting the frequency dependence of the nonlinear susceptibility, we find that the third-harmonic intensity of such metallic rod antennas scales as the fourth power of the frequency, whereas it decreases with the twelfth power within the limit of the generalized Miller’s rule.

Third harmonic from air breakdown plasma induced by nanosecond laser pulses

Harmonic generation is a nonlinear optical effect consisting in frequency up-conversion of intense laser radiation when phase-matching conditions are fulfilled. Here, we study the mechanisms involved in the third harmonic (TH) generation process, the conversion efficiency, and the properties of TH radiation generated in air by focusing infrared linearly polarized nanosecond laser pulses at intensities of the order of TW/cm2. By analyzing the emission from the air breakdown plasma, we demonstrate that filamentary breakdown plasma containing molecular nitrogen ions acts as an optical nonlinear medium enabling generation of TH radiation in the axial direction. The data reveal important properties of the TH radiation: maximum conversion efficiency of 0.04%, sinc2 dependence of the TH intensity on the square root of the pump intensity, and three times smaller divergence and pulse duration of TH as compared to the pump radiation.

Enhancing Third-Harmonic Generation with Spatial Nonlocality

As the geometrical feature of a nanostructure approaches the Thomas-Fermi screening length, the electron-level interaction induced nonlocality leads to the longitudinal resonance modes above bulk plasmon resonance frequency. In this work, we investigate the contribution of longitudinal modes to the enhancement of third-harmonic generation process. Specifically, we study a single Ag nanowire and a Ag nanowire dimer coated with third-order nonlinear dielectrics. By implementing hydrodynamic and nonlinear models together, we find that the spectral overlap of the longitudinal resonance modes with third order harmonics enables the improvement of the nonlinear conversion efficiency. The optimized results show that despite of reduced field enhancement for the fundamental resonance, the third-harmonic absorption intensities in nonlocal case can surpass the local calculation results by hundreds of times. Maximum third-harmonic scattering intensities can also be realized though appropriate design of both structures...

Enhanced photon lifetime in silicon nanowire arrays and increased efficiency of optical processes in them

Silicon nanowire (SiNW) arrays formed by metal-assisted chemical etching of boron low-doped crystalline silicon (c-Si) substrates were studied regarding enhanced efficiency of optical interactions in them. Along with high diffuse reflection of the structures under study, Raman and third-harmonic signals exhibited an order of magnitude growth compared to c-Si response in the near-infrared spectral region. Changes in the orientation dependencies of the third-harmonic intensity with SiNW length increase promoted the explanation of the optical peculiarities of SiNW arrays. Cross-correlation of the scattered radiation function evidenced that the effects could be explained by enhanced photon lifetime inside mesoscopic structure of SiNW arrays due to multiple scattering. Hence a correlation between the photon lifetime and the Raman and third-harmonic efficiency in SiNWs was revealed.

Giant enhancement of the third harmonic in graphene integrated in a layered structure

Graphene was shown to have strongly nonlinear electrodynamic properties. In particular, being irradiated by an electromagnetic wave with the frequency ω, it can efficiently generate higher frequency harmonics. Here, we predict that in a specially designed structure “graphene— dielectric—metal” the third-harmonic (3ω) intensity can be increased by more than two orders of magnitude as compared to an isolated graphene layer.

Nonlinear Interference and Tailorable Third-Harmonic Generation from Dielectric Oligomers

It is known that the nonlinear optical properties of photonic nanostructures can be modified substantially due to strong field confinement and optical resonances. In this contribution, we study third-harmonic generation from low-loss subwavelength silicon nanodisks arranged in the form of trimer oligomers with varying distance between the nanoparticles. Each of the nanodisks exhibits both electric and magnetic Mie-type resonances that are shown to affect significantly the nonlinear response. We observe the third-harmonic radiation intensity that is comparable to that of a bulk silicon slab and demonstrate a pronounced reshaping of the third-harmonic spectra due to interference of the nonlinearly generated waves augmented by an interplay between the electric and the magnetic dipolar resonances.

Third-harmonic pulse generation in one-dimensional photonic crystal structures

Enhanced third-harmonic generation in a one-dimensional photonic crystal doped with third-order nonlinear medium was numerically investigated using the multiple-scale method and the split-step Fourier transform. The optimal fundamental frequency for third-harmonic wave generation was determined from the transmission spectrum. The third-harmonic pulse intensities grow, depending on the structure thickness and the fundamental-frequency detuning parameter, which determines the band-edge phase matching condition. Furthermore, the total energy output of third-harmonic pulses, depending on the fundamental-frequency pulse width, may be more than 1000 times the energy produced by a phase-matched bulk medium. A narrow pulse with bandwidth less than the band-edge transmission peak enables high conversion efficiency. The maximum conversion efficiency of the forward component may be 12 to 13 orders of magnitude greater than that of the backward component.

Theory of third-harmonic generation using double half-Gaussian hollow beams and self-phase-matching

We first (to best of out knowledge) use the slowly varying envelope approximation (SVEA) to obtain the equation of third harmonic (TH) generated by focusing the double half-Gaussian hollow beams into an atomic medium. The two-dimension intensity distribution is achieved by simulating, and it is similar to that generated by the 0th order Bessel beams. In addition to the similarities between the experimental setups, we demonstrate the accuracy of the equation. Compared with that generated by the Bessel beams, the pattern of the TH intensity generated by the double half-Gaussian hollow beams has salient features.

Efficient bidirectional optical harmonics generation in three-dimensional photonic crystals

Noncollinear generation of second and third harmonics in three-dimensional photonic crystals of artificial opals is experimentally realized and interpreted in terms of nonlinear diffraction. A factor-of-two enhancement of second- and third-harmonic generation intensity in diffraction maxima directions is observed due to effective phase matching provided by photonic crystal periodicity. Bidirectional diffraction of third harmonics at crystallographic planes (111) and (1¯11) is observed. The broadening of nonspecular diffraction peaks is found to correspond to the polycrystalline structure of the opal samples.

Adaptive harmonic generation microscopy of mammalian embryos

Adaptive optics is implemented in a harmonic generation microscope using a wavefront sensorless correction scheme. Both the second- and third-harmonic intensity signals are used as the optimization metric. Aberration correction is performed to compensate both system- and specimen-induced aberrations by using an efficient optimization routine based upon Zernike polynomial modes. Images of live mouse embryos show an improved signal level and resolution.

Resonant frequency-domain interferometry via third-harmonic generation

A method for measuring resonances using a combination of third-harmonic generation and frequency-domain interferometry is described and demonstrated in an index-matched dielectric material. The phase of the third-harmonic spectrum of a pulse generated from a resonant NdAlO(3) thin film and a temporally displaced sapphire substrate pulse was measured by analyzing the spectral interference pattern. The appropriate combination of substrate and film signals was obtained by translating the sample through the laser focus while observing the third-harmonic intensity.

Self-stabilization of third-harmonic pulse during two-color filamentation in gases

Self-stabilization of the laser pulse parameters is demonstrated during the two-color filamentation of ultrashort and intense laser pulses in gases. Experimental data and results of numerical simulations show, in good qualitative agreement, that the root-mean-square values of the intensity fluctuations decrease below the initial value for the near-infrared pump pulse and the perturbative limit for the third-harmonic pulse in the filament. It is found that the stabilization of the third-harmonic intensity and energy are due to intensity clamping of the pump pulse and a constant ‘volume’ of the laser pulse during the nonlinear propagation inside the filament.

Third-harmonic generation in a one-dimensional photonic-crystal-based amorphous nanocavity

We report a large enhancement of third-harmonic generation in the one-dimensional dielectric photonic-crystal-based amorphous nanocavity. The enhancement took place at the frequency of defect mode and was a pure χ(3) nonlinear process. A great increase of third-harmonic intensity up to approximately five orders of magnitude was demonstrated, which was attributed to field localization in the range of nanocavity.

Symmetry and phase-matching properties of third-harmonic generation under the photoelastic effect in Ge-As-Se chalcogenide glasses

We discuss the study of three chalcogenide glasses of high third-order nonlinear electric susceptibility, AsSe4,GeSe4, and GeAsSe8. We measured the strain optical coefficients, and we determined dispersion equations of the refractive index from previously published measurements. From these data, we performed a theoretical study of a new scheme for third-harmonic generation in a glass where phase matching is created by a photoelastic effect. A complete symmetry analysis based on Curie principle allowed us to define the configuration of polarization of the interacting waves, leading to a nonzero cubic effective coefficient. The generated third-harmonic intensity is then calculated.

Third-Harmonic Generation from Single Gold Nanoparticles

We report the first observation of third-harmonic signals from individual gold colloids down to 40 nm diameter. Excited with 1-ps pulses at 1500 nm, the colloids generate 500-nm light, close to the plasmon resonance. The third-harmonic intensity varies as the square of the colloid surface area. Although weak, the third-harmonic signals of gold labels as small as 15 nm in diameter are expected to be accessible with 100-fs pulses. They could be used in microscopy for single-biomolecule tracking.