Third-order Harmonic Generation Research Articles

Ultraviolet supercontinuum generation using a differentially-pumped integrated glass chip

We investigate the generation of ultrabroadband femtosecond ultraviolet (UV) radiation via third-order harmonic generation in highly confined gas media. A dual-stage differential-pumping scheme integrated into a glass microfluidic chip provides an exceptional gas confinement up to several bar and allows the apparatus to be operated under high-vacuum environment. UV pulses are generated both in argon and neon with up to ∼0.8 μJ energy and 0.2% conversion efficiency for spectra that cover the UVB and UVC regions between 200 and 325 nm. Numerical simulations based on the unidirectional pulse propagation equation reveal that ionization plays a critical role for extending the spectral bandwidth of the generated third-harmonic pulse beyond the tripled 800 nm driving laser pulse bandwidth. By delivering UV supercontinua supporting Fourier transform limits below 2 fs, as well as comparable pulse energies with respect to capillary-based techniques that typically provide high spectral tunability but produce narrower bandwidths, our compact device makes a step forward towards the production and application of sub-fs UV pulses for the investigation of electron dynamics in neutral molecules.

Systematic investigations on frequency mixing response of ultrasonic shear horizontal and Rayleigh Lamb waves

The study of self- and cross-interactions of shear horizontal (SH) waves has garnered significant attention in the field of nonlinear ultrasonic practice. This interest stems from the potential high sensitivity of SH waves to microdamage and their low out-of-plane attenuation characteristics. However, due to the dispersive nature and intricate mechanisms governing guided wave propagations and interactions, the nonlinear responses of SH waves, particularly the third-order harmonic generation and wave mixing with Rayleigh Lamb (RL) waves, remain largely unexplored. This study presents a comprehensive investigation into the ultrasonic harmonic wave generation of SH guided waves. The research approach combines theoretical considerations and finite element modeling to investigate and discuss guided wave mixing involving SH and RL waves. Six cases of phase-matched wave mode pairs are developed based on deduced synchronism and symmetry conditions. A nonlinear material constitutive model, encompassing both the third- and fourth-order elastic constants, is incorporated into the simulation. The results of the numerical analysis reveal the existence of newly generated higher and combined harmonic waves in an intuitive manner. Specifically, the interactions between ultrasonic SH and RL guided waves are observed to generate second- and third-order combined harmonic waves at the mixing frequencies under internal resonant conditions. The nonlinear waves have a cumulative effect during the mixing period, with their amplitude remaining constant after passing through the mixing zone. This study provides the first observation of mode conversion and third-order combined harmonic generation of SH waves. The insights gained from the numerical perspective offer understandings of the frequency mixing response of SH waves.

Topological edge states and harmonic generation from one-dimensional photonic crystal

In this paper, in order to achieve certain one-dimensional (1D) topological edge states, we provide a method to construct an edge configuration from the two-periodic structures. Those two-periodic structures have different Zak phases that lead to some topological edge states found in the transmission spectrum. A field distribution shows the intense field localization effect around the interface. When the structure includes nonlinear material, the intense field localization field at the interface will result in nonlinear effect. The simulation based on a finite-difference time-domain (FDTD) method demonstrates that the topological edge states can result in the third-order harmonic (TH) generation.

Phase dependence of third-order harmonic generation in gases induced by two-color laser field

We experimentally demonstrate third-harmonic generation (THG) in gases ionized by a femtosecond laser pulse superimposed on its second-harmonic (SH). The mechanism of THG has been investigated, and it demonstrates that a third-order nonlinear process dominates at low pump intensity. Asymmetric third-harmonic (TH) spectra are observed at different time delays in two color fields, which are attributed to the process of the four-wave mixing (FWM) of the broad spectrum of pump pulses. A joint measurement on the terahertz (THz) and the TH is performed. It reveals that the optimized phase for the THG jumps from 0 to 0.5π as the pump intensity increases, which is different from the THz being a constant, and indicates that the THG arises from the nonlinearity of the third-order bound electrons to the tunnel-ionization current.

Onset of Bloch oscillations in the almost-strong-field regime

In the field of high-order harmonic generation from solids, the electron motion typically exceeds the edge of the first Brillouin zone. In conventional nonlinear optics, on the other hand, the excursion of band electrons is negligible. Here, we investigate the transition from conventional nonlinear optics to the regime where the crystal electrons begin to explore the first Brillouin zone. It is found that the nonlinear optical response changes abruptly already before intraband currents due to ionization become dominant. This is observed by an interference structure in the third-order harmonic generation of few-cycle pulses in a non-collinear geometry. Although approaching Keldysh parameter γ = 1, this is not a strong-field effect in the original sense, because the iterative series still converges and reproduces the interference structure. The change of the nonlinear interband response is attributed to Bloch motion of the reversible (or transient or virtual) population, similar to the Bloch motion of the irreversible (or real) population which affects the intraband currents that have been observed in high-order harmonic generation.

Linear and Nonlinear Optical Absorption of CdSe/CdS Core/Shell Quantum Dots in the Presence of Donor Impurity

Linear and nonlinear optical properties in colloidal CdSe/CdS core/shell quantum dots with different sizes have been theoretically investigated in the framework of effective mass approximation. The electron states in colloidal CdSe/CdS core/shell quantum dots have been calculated using the finite element method. The intraband linear and nonlinear absorption spectra have been calculated for colloidal CdSe/CdS core/shell quantum dots with different sizes. In addition, the dependences of the linear and nonlinear refractive index change on the incident light energy have been calculated. In the last section of the paper the second- and third-order harmonic generation spectra have been presented.

Detection and Location of Surface Damage Using Third-Order Combined Harmonic Waves Generated by Non-Collinear Ultrasonic Waves Mixing.

Metals which are widely used in many types of industries are usually subjected to fatigue and surface corrosion. There is a demand to detect the surface damage caused by fatigue and corrosion at an early stage to ensure the structural integrity. In this paper, a novel nonlinear ultrasonic technique based on the measure of third-order combined harmonic generation, is proposed to detect and locate the surface damage in 6061 aluminum alloy. Third-order combined harmonic generation caused by non-collinear mixing of one longitudinal wave and one transverse wave at different frequencies, is firstly analyzed and experimentally observed. An experimental procedure of nonlinear scanning is proposed for the damage detection and location by checking the variation of frequency nonlinear response. The correlations of nonlinear frequency mixing responses and surface damage in the specimens are obtained. Results show that the nonlinear response caused by fatigue damage and surface corrosion can be identified and located by this method. In addition, this approach can exclude the nonlinearity induced by the instruments and simplify the signal processing.

Phonon-assisted laser-induced third-order optical susceptibility for interband transition in a group II–VI asymmetric quantum well

Exciton–LO phonon interaction of the Fröhlich type is studied in the CdS/CdSe/CdS asymmetric double quantum well under an applied laser field. The intensity of laser effect on the exciton binding energy, oscillator strength, optical transition energies, and third-order harmonic generation are investigated by changing the right well sizes and barrier sizes. The laser-associated confined energies and their corresponding binding energies are brought out with the variation of well sizes. The position-dependent potential is altered by the laser-associated parameter. The laser-field-dependent third-order optical susceptibilities due to interband transitions in the asymmetric well are investigated. The effective Coulomb potential, using the Aldrich and Bajaj polaronic effect, is included in the Hamiltonian. The results show that the laser field considerably affects the confining potential of the quantum well and causes a drastic deformation of the confining potential profile. The obtained optical nonlinearities suffer a redshift in the asymmetric quantum well; also, their peak values are determined by the dipole matrix elements.

Third-order harmonic generation in a bi-chromatic elliptical laser field.

The low-order harmonic generation induced by a strong laser field produces a bright, ultrashort, supercontinuum radiation ranging from the terahertz to ultraviolet band. By controlling the phase-delay and ellipticity of the bi-chromatic laser fields, the third harmonic generation is experimentally and theoretically investigated for elucidating the mechanism of the low-order harmonics. The third harmonic generation is found to be strongly suppressed in the counter-rotating bi-chromatic laser field due to the selection rule for harmonic emissions. The continuum-continuum transition in the strong field approximation is extended to explain the third harmonic generation as a function of the phase delay and ellipticity of the bi-chromatic laser fields. Compared with the semi-classical photocurrent model, the continuum-continuum transition on the basis of quantum-mechanical treatment achieves better agreement with the experimental observations. Our work indicates that the overlapping in continuum states via different quantum paths of a single electron plays a role in low-order harmonics generation under elliptical bi-chromatic laser fields.

Interband optical Raman gain in a strained oxide quantum dot with Hylleraas co-ordinates

Exciton Raman scattering of a three-level system is observed in a CdO/ZnO quantum dot using the size dependent Smorodinsky–Winternitz potential. Resonance Raman excitation for the fundamental optical transition is concentrated in the present work. The differential cross section of Raman optical intensity associated with the exciton is computed with the incident photon energy and the geometrical confinement effect. Raman differential cross section is found by the third-order harmonic generation. The built-in internal fields are incorporated in the heterostructure. They arise between the interior and outer core/shell materials in the heterostructure which contains the spontaneous polarization and piezoelectric polarization. The Hamiltonian of the exciton is included with the dielectric mismatch effect and the variational approach with Hylleraas co-ordinates are employed to obtain the energy eigen values numerically. The energy dependent effective mass of electron and the size related strain-induced potentials for the conduction and valence bands are incorporated in the Hamiltonian. The nonlinear optical properties are obtained with the density matrix approach. The results show that the Raman intensities are more influenced in the strong confinement region. The resonance peak Raman intensity is observed as 6.84 (arb.units) for a 60 A spherical dot. The Raman gain is optimized by varying the dot size. And, the Raman optical gain as high as 240/cm is achieved for the dot radius, 22 A of CdO/ZnO spherical quantum dot. This can be employed for the potential applications in optical devices.

Nanocomposite for photonics — Nickel pyrophosphate nanocrystals synthesised in silica nanoreactors

Abstract Nanophotonics is one of the most important branches of electronics. The search for and design of novel and more efficient laser-operated materials seems to be fully justified. Therefore, here, we show how to fabricate materials that have an enhanced non-linear optical response using a procedure of synthesis in a silica nanoreactor. We obtained the initial material through the precise functionalisation of SBA-15 silica using nickel phosphonate units that were anchored inside the silica channels by propyl chains, which was then transformed into an optically active nanocomposite after thermal processing. Using thermogravimetry, transmission electron microscopy (TEM), Raman vibrational analysis, and N 2 sorption analysis, we analysed the thermal behaviour of the initial functional material. All research that is connected with second- and third-order optical harmonic generation enables the structural changes in these materials and their influence on their optical properties to be explored. Nonlinear optical measurements confirmed our assumption that material that is prepared using silica nanoreactors can have precisely tailored properties, in this case, nonlinear optical properties.

Fast and Efficient Approach for Computing the Nonlinearity in the Ring-Resonator-Based HTS Reaction-Type Filters

In this article, a fast and accurate method for computing the nonlinearities, such as third-order harmonic generation and third-order intermodulation distortion, in complex superconducting structures based on the ring resonators is proposed. First, a recap of the nonlinearity in the superconductors and its physical concept are mentioned. Then, the nonlinear circuit model of superconducting ring resonators (SRRs) is reviewed and developed to be applicable to complex structures, such as multipole SRR-based reaction-type Chebyshev filters. In the third section, it is shown that the combination of the harmonic balance method with the nonlinear circuit model computes the nonlinearity quickly and accurately. The method is applied to several SRR-based structures, and the computed nonlinearity is compared with the measurements in order to prove the claim.

Resonance-enhanced three-photon luminesce via lead halide perovskite metasurfaces for optical encoding

Lead halide perovskites have emerged as promising materials for photovoltaic and optoelectronic devices. However, their exceptional nonlinear properties have not been fully exploited in nanophotonics yet. Herein we fabricate methyl ammonium lead tri-bromide perovskite metasurfaces and explore their internal nonlinear processes. While both of third-order harmonic generation and three-photon luminescence are generated, the latter one is less affected by the material loss and has been significantly enhanced by a factor of 60. The corresponding simulation reveals that the improvement is caused by the resonant enhancement of incident laser. Interestingly, such kind of resonance-enhanced three-photon luminescence holds true for metasurfaces with a small period number of 4, enabling promising applications of perovskite metasurface in high-resolution nonlinear color nanoprinting and optical encoding. The encoded information ‘NANO’ is visible only when the incident laser is on-resonance. The off-resonance pumping and the single-photon excitation just produce a uniform dark or photoluminescence background.

Broadband Quasi-Phase-Matched Harmonic Generation in an On-Chip Monocrystalline Lithium Niobate Microdisk Resonator.

We reveal a unique broadband natural quasi-phase-matching (QPM) mechanism underlying an observation of highly efficient second- and third-order harmonic generation at multiple wavelengths in an x-cut lithium niobate (LN) microdisk resonator. For light waves in the transverse-electric mode propagating along the circumference of the microdisk, the effective nonlinear optical coefficients naturally oscillate periodically to change both the sign and magnitude, facilitating QPM without the necessity of domain engineering in the micrometer-scale LN disk. The second-harmonic and cascaded third-harmonic waves are simultaneously generated with normalized conversion efficiencies as high as 9.9%/mW and 1.05%/mW^{2}, respectively, thanks to the utilization of the highest nonlinear coefficient d_{33} of LN. The high efficiency achieved with the microdisk of a diameter of ∼30 μm is beneficial for realizing high-density integration of nonlinear photonic devices such as wavelength convertors and entangled photon sources.

Nonlinear electromagnetic response of few-layer graphene: A nonperturbative description

Nonperturbative approach based on exact solution of Boltzmann kinetic equation in the relaxation time approximation is developed for the study of nonlinear response of electron-doped few-layer graphene to a high-frequency electromagnetic field. It is shown that nonperturbative approach can be applied to a two-dimensional conductor with an arbitrary isotropic spectrum of carries. The cases of ABC stacked three-layer and ABC staked four-layer graphene are considered. The low-energy electron spectrum of such graphenes is characterized by the third and the fourth power in the momentum dependence, correspondingly. The transmission, reflection and absorption coefficients are calculated. It is shown that the transmission coefficient T of three- and four-layer graphene decreases under increase in the intensity of the incident wave I by the asymptotic law 1/2 T I  and 2/3 T I  , respectively. It is found that three-layer and four-layer graphenes demonstrate power-induced reflectance, in contrast to power-induced transparency in monolayer graphene. It is found that in the four-layer graphene irradiated by a monochromatic wave the induced electrical current contains only the first and the third harmonics. The analytical expression for the efficiency of the third-harmonic generation GTGH (the ratio of the intensity of third-harmonic radiation to the intensity of the incident wave) of the four-layer graphene is obtained. It is shown that only at rather small incident wave intensity the efficiency GTGH is proportional to the second power of I and at large incident wave intensity the efficiency GTGH approaches the constant quantity. Saturation of the efficiency of the third-order harmonic generation is caused by the increase of the reflection. In contrast, the efficiency of the third-order harmonic generation of monolayer graphene depends nonmonotonically on the intensity of the incident wave. The maximum is reached at rather small intensity I аnd the efficiency in the maximum is of order of 10-4 that is two orders of magnitude smaller than of four-layer graphene.

Third-harmonic generation from gold nanowires of rough surface considering classical nonlocal effect.

We demonstrate that the nonlocal dielectric response of metal, comparing with the traditional local model, will significantly boost the third-order harmonic generation (THG) from gold nanowires of rough surface by a factor of several orders of magnitude. The enhancement is probably due to the penetrated field into the fine nanostructures on the metal surface in nonlocal model. The anisotropy THG efficiency versus the angle of incidence is also demonstrated due to the inhomogeneous surface morphology. The possible ways to verify the nonlocal effect to the THG are demonstrated. The results have a general significance in explaining the experimental observations.

Electric field-induced nonlinear optical properties of a hydrogenic impurity in a GaAs/GaAlAs quantum dot: effects of spin–orbit interactions

Nonlinear optical properties, optical rectification coefficients and the second-order and third-order harmonic generation coefficients as a function of photon energy are dealt in a GaAs/Ga0.8Al0.2As quantum dot in the presence of electric field and the spin–orbit interactions. The Dresselhaus and the Rashba spin–orbit interactions are added in the Hamiltonian. The electric field-induced photoionization cross section with the normalized photon energy for an on-centre donor impurity in the quantum dot is studied. The effect of nonparabolicity is included in the Hamiltonian. The spin–orbit interaction as a function of photon energy is investigated. The computations are carried out within the framework of the single band effective mass approximation using variational technique and the compact density approach. It is found that the spin–orbit interaction coefficients show strong effects on the resonant position of harmonic generations. The results are compared with the recent investigations.

Mechanism for defect dependence of damage morphology in HfO2/SiO2 high reflectivity coating under nanosecond ultraviolet laser irradiation

High reflectivity coating is designed and fabricated with HfO2/SiO2 stacks. The laser-induced damage experiment is prepared by a third-order harmonic generation of Nd:YAG laser (355nm, 8ns). Typical damage micrographs are obtained using atomic force microscope (AFM) and scanning electron microscope (SEM). A theoretical model based on the thermal transfer is tried to describe the defect dependence of damage morphology. Three situations are considered in this model: single defect, couple defects and high absorption film. The calculated results show that the second situation agrees well with the experiment.

Generation of multicolor vacuum ultraviolet pulses through four-wave sum-frequency mixing in argon

We demonstrate efficient generation of multicolor vacuum ultraviolet pulses with excellent mode quality through ${\ensuremath{\chi}}^{(3)}$-based four-wave sum-frequency mixing and third-order harmonic generation of 400- and 267-nm femtosecond laser pulses in argon gas. The ${\ensuremath{\chi}}^{(3)}$-based nonlinear optical processes were optimized with appropriate control of gas pressure and group velocity delay between the driving pulses. Furthermore, the pulse breakup effects were observed for tightly focused ultraviolet pulses.

Plasmon‐Enhanced Second‐ and Third‐Order Harmonic Generation in Spherical Free‐Electron Nanoclusters with Diffuse Surface

AbstractThe nonlinear scattering of a laser pulse off spherical nanoclusters with free electrons and with a diffuse surface is examined in the collisionless hydrodynamics approximation in the framework of perturbation theory with respect to the laser pulse intensity, as well as of the steady‐state approximation. In a previous publication [S.V. Fomichev and W. Becker, Phys. Rev. A 81, 063201 (2010)] we reported the full nonlinear hydrodynamic model of forced collective electron motion confined to a cluster with diffuse surface and introduced two different perturbation theories corresponding to different laser intensity regimes. In the current paper, in the framework of this hydrodynamic model we focus on the properties of plasmon resonance‐enhanced third‐harmonic generation in a spherical cluster and its dependence on the shape of its diffuse surface whose role increases for nonlinear processes. At the same time, the quadrupole second‐harmonic generation in a spherical cluster is also inspected as a necessary intermediate step. Both cold metal clusters in vacuum or in a dielectric surrounding and hot laser‐heated and laser‐ionized clusters are considered within the same approach for a wide range of the fundamental laser frequency. Nonlinear laser excitation of the dipole plasmon Mie resonance in spherical clusters, as well as of other respective multipole plasmon resonances is investigated analytically and numerically in detail (position, width, and strength) versus the cluster‐surface diffuseness, the outer ionization degree in charged clusters, the electron‐density diffuseness, and their interplay. Under certain conditions, depending on the various cluster parameters, different secondary nonlinear resonances are found. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)