Second-harmonic Response Research Articles

Efficient second-harmonic generation of quasi-bound states in the continuum in lithium niobate thin film enhanced by Bloch surface waves

Abstract Nonlinear optics has generated a wide range of applications in the fields of optical communications, biomedicine, and materials science, with nonlinear conversion efficiency serving as a vital metric for its progress. However, the weak nonlinear response of materials, high optical loss, and inhomogeneous distribution of the light field hamper the improvement of the conversion efficiency. We present a composite grating waveguide structure integrated into a Bragg reflector platform. This design achieves high Q in the spectral range by exploiting the unique properties exhibited by the bound states in the Bloch surface wave-enhanced continuum, and efficient second-harmonic generation by close-field amplification with the optical field tightly localized in a nonlinear material. By manipulating the symmetry of the grating, a precise tune over the near field within a designated wavelength range can be achieved. Specifically, we select a photonic crystal configuration supporting surface waves, employing TE polarization conditions and an asymmetry factor of −0.1 between the composite gratings. This configuration resonates at a fundamental wavelength of 783.5 nm, exhibiting an impressive Q-factor of 106. Notably, at an incident light intensity of 1.33 GW/cm2, we achieve a normalized electric field strength of up to 940 at the fundamental frequency and a second-harmonic conversion efficiency of up to 6 × 10−3, significantly amplifying the second-harmonic response. The proposed configuration in this investigation has the potential to be integrated into the field of nonlinear optics for sensing frequency conversion applications.

A Multi-Scale Approach to Simulate the Nonlinear Optical Response of Molecular Nanomaterials.

Nonlinear optics is essential for many recent photonic technologies. Here, a novel multi-scale approach is introduced to simulate the nonlinear optical response of molecular nanomaterials combining ab initio quantum-chemical and classical Maxwell-scattering computations. In this approach, the first hyperpolarizability tensor is computed with time-dependent density-functional theory and incorporated into a multi-scattering formalism that considers the optical interaction between neighboring molecules. Such incorporation is achieved by a novel object: the Hyper-Transition(T)-matrix. With this object at hand, the nonlinear optical response from single molecules and also from entire photonic devices can be computed, including the full tensorial and dispersive nature of the optical response of the molecules, as well as the optical interaction between different molecules as, for example, in the lattice of a molecular crystal. To demonstrate the applicability of the novel approach, the generation of a second-harmonic signal from a thin film of an Urea molecular crystal is computed and compared to more traditional simulations. Furthermore, an optical cavity is designed, which enhances the second-harmonic response of the molecular film up to more than two orders of magnitude. This approach is highly versatile and accurate and can be the working horse for the future exploration of nonlinear photonic molecular materials in structured photonicenvironments.

Linear and nonlinear spin current response of anisotropic spin-orbit coupled systems

We calculate the linear and the second harmonic (SH) spin current response of two anisotropic systems with spin–orbit (SO) interaction. General expressions of wide applicability for the these response functions are first derived for a generic two-band Hamiltonian. The first system is a two-dimensional (2D) electron gas in the presence of Rashba and k-linear Dresselhaus SO couplings. The calculations show how narrow or wide the response spectra can be, what is their overall shape and size, and frequency shiftings, depending on which crystal orientation is selected. The quantitative knowing of this makes possible a comparative study for several orientations, which would allow to select a spectrum with particular characteristic. We find that vanishing linear and second order response tensors are achievable under SU(2) symmetry conditions, characterized by a collinear SO vector field. Additional conditions under which specific tensor components vanish are possible, without having such collinearity. Thus, a proper choice of the growth direction and SO strengths allows to select the polarization of the linear and SH spin currents according to the direction of flowing. The second system is an anisotropic 2D free electron gas with anisotropic Rashba interaction, which has been employed to study the optical conductivity of 2D puckered structures with anisotropic energy bands. The presence of mass anisotropy and an energy gap open several distinct scenarios for the allowed optical interband transitions, which manifest in the linear and SH response contrastingly. The linear response displays only out-of-plane spin polarized currents, while the SH spin currents flow with spin orientation lying parallel to the plane of the system strictly. The models illustrate the possibility of the nonlinear spin Hall effect in systems with SO interaction, under the presence or absence of time-reversal symmetry. The results suggest different ways to manipulate the linear and nonlinear optical generation of spin currents which could find spintronic applications.

Anisotropic linear and nonlinear excitonic optical properties of buckled monolayer semiconductors

The optical properties of two-dimensional materials are exceptional in several respects. They are highly anisotropic and frequently dominated by excitonic effects. Dipole-allowed second-order nonlinear optical properties require broken inversion symmetry. Hence, several two-dimensional materials show strong in-plane (IP) nonlinearity but negligible out-of-plane (OOP) response due to vertical symmetry. By considering buckled hexagonal monolayers, we analyze the critical role of broken vertical symmetry on their excitonic optical response. Both linear as well as second-order shift current and second-harmonic response are studied. We demonstrate that substantial OOP nonlinear response can be obtained, in particular, through off-diagonal tensor elements coupling IP excitation to OOP response. Our findings are explained by excitonic selection rules for OOP response and the impact of dielectric screening on excitons is elucidated.

Gate-Dependent Nonlinear Hall Effect at Room Temperature in Topological Semimetal GeTe

We experimentally investigate nonlinear Hall effect as zero-frequency and second-harmonic transverse voltage responses to ac electric current for topological semimetal GeTe. A thick single-crystal GeTe flake is placed on the Si/SiO2 substrate, where the p-doped Si layer serves as a gate electrode. We confirm that electron concentration is not gate-sensitive in thick GeTe flakes due to the gate field screening by bulk carriers. In contrast, by transverse voltage measurements, we demonstrate that the nonlinear Hall effect shows pronounced dependence on the gate electric field at room temperature. Since the nonlinear Hall effect is a direct consequence of a Berry curvature dipole in topological media, our observations indicate that Berry curvature can be controlled by the gate electric field. This experimental observation can be understood as a result of the known dependence of giant Rashba splitting on the external electric field in GeTe. For possible applications, the zero-frequency gate-controlled nonlinear Hall effect can be used for the efficient broad-band rectification.

Degenerate parametric down-conversion facilitated by exciton-plasmon polariton states in a nonlinear plasmonic cavity

We study the effect of degenerate parametric down-conversion (DPDC) in an ensemble of two-level quantum emitters (QEs) coupled via near-field interactions to a single surface plasmon (SP) mode of a nonlinear plasmonic cavity. For this purpose, we develop a quantum driven-dissipative model capturing non-equilibrium dynamics of the system in which incoherently pumped QEs have transition frequency tuned near the second-harmonic response of the SPs. Considering the strong coupling regime, i.e. the SP-QE interaction rate exceeds system dissipation rates, we find a critical SP-QE coupling attributed to the phase transition between normal and lasing steady states. Examining fluctuations above the system’s steady states, we predict new elementary excitations, namely, the exciton-plasmon polaritons formed by the two-SP quanta and single-exciton states of QEs. The contribution of two-SP quanta results in the linear scaling of the SP-QE interaction rate with the number of QEs, , as opposed to the -scaling known for the Dicke and Tavis–Cummings models. We further examine how SP-QE interaction scaling affects the polariton dispersions and power spectra in the vicinity of the critical coupling. For this purpose, we compare the calculation results assuming a finite ensemble of QEs and the model thermodynamic limit. The calculated power spectra predict an interplay of coherent photon emission by QEs near the second-harmonic frequency and correlated photon-pair emission at the fundamental frequency by the SPs (i.e. the photonic DPDC effect).

Strongly coupled surface plasmon resonance modes at both FF and SH in clusters of symmetrically distributed metallic nanospheres

Plasmonic nanoclusters play an important role in the rapid development of application of nanophotonics. In this article both the fundamental-frequency (FF) and second-harmonic (SH) responses of the complex nanoclusters (tetramer, hexamer, and octamer), constructed by coupled spherical plasmonic nanoparticles, are theoretically investigated. By using the multiple scattering algorithm, we present the comprehensive numerical analysis of the physical mechanisms pertaining to the linear and nonlinear coupled-plasmon modes, including ‘hot spot’ modes (HSMs) and ‘whispering-gallery’ modes (WGMs). Different from the symmetric coupling of plasmonic eigenmodes excited by the nanodimer, our analysis reveals that such coupled modes from the nanomultimers are the result of the ‘hybridization’ of symmetric and asymmetric coupling between adjacent dipole or higher-order multipole moments. Also, the remarkable enhancement as large as 3–4 orders of magnitude is achieved for the SH intensity when employing the plasmonic HSMs or WGMs at the FF. Interestingly, the nonlinear plasmonic HSMs and WGMs (the maximum Q up to 4800) can also be obtained by elaborately designing the system geometry. In addition, the resonant wavelengths of such coupled-plasmon modes can be linearly modulated within a broad range. These numerical results have potential applications in surface optical microscopy, plasmonic sensor and nanolaser.

Reversible Phase Transition and Second-Harmonic Response Based on a Zero-Dimensional Organic–Inorganic Hybrid Compound

The organic–inorganic hybrid materials (OIHMs) with stimuli-responsive features show the important scientific attraction in a multifunctional material application field, such as optoelectronic memory and sensors. Especially, designing a functional material with both dielectric switching and second-harmonic generation (SHG) remains attractive. Herein, we report a new OIHM [C7H15NCl] SbCl4 as a phase matching nonlinear optical material and dielectric switch functional materials. It undergoes a reversible phase transition at 297 K and exhibit a harmonic generation (SHG) effect of about 0.53 times that of KH2PO4 (KDP). Meanwhile, it also possesses potential semiconducting properties. This work might provide a strategy for designing novel multifunctional materials in the field of crystals and dielectrics.

Second-Harmonic Response in Magnetic Nodal-Line Semimetal Fe3GeTe2

We experimentally investigate second-harmonic transverse voltage response to ac electrical current for a magnetic nodal-line semimetal Fe3GeTe2 (FGT). For zero magnetic field, the observed second-harmonic voltage behaves as a square of the longitudinal current, as it should be expected for nonlinear Hall effect. The magnetic field behavior is found to be sophisticated: while the first-harmonic response shows the known anomalous Hall hysteresis in FGT, the second-harmonic Hall voltage is characterized by the pronounced high-field hysteresis and flat (B-independent) region with curves touching at low fields. The high-field hysteresis strongly depends on the magnetic field sweep rate, so it reflects some slow relaxation process. For the lowest rates, it is also accomplished by multiple crossing points. Similar shape of the second-harmonic hysteresis is known for skyrmion spin textures in nonlinear optics. Since skyrmions have been demonstrated for FGT by direct visualization techniques, we can connect the observed high-field relaxation with deformation of the skyrmion lattice. Thus, the second-harmonic Hall voltage response can be regarded as a tool to detect spin textures in transport experiments.

Optical second-harmonic response of axially symmetric media under tightly focused excitation: linear versus radial polarization

We compared the optical second-harmonic (SH) response of axially symmetric media excited by tightly focused radially and linearly polarized beams. The simulation performed showed a significant redistribution of energy between the lobes/cones of the SH radiation pattern, depending on the focusing accuracy in the case of a purely surface/interface nonlinearity. This phenomenon is due to the change in the contributions of second-order susceptibility tensor components to SH generation as we demonstrated via a comparison of SH patterns related to different components of the tensor. Replacement of the interface with a nonlinear layer leads to noticeable broadening of SH radiation patterns, which can allow one to distinguish surface nonlinearity from bulk. The model developed is applicable for SH generation by interfaces, films, and poled glasses.

Heteroanionic Control of Exemplary Second-Harmonic Generation and Phase Matchability in 1D LiAsS2-xSex.

The isostructural heteroanionic compounds β-LiAsS2-xSex (x = 0, 0.25, 1, 1.75, 2) show a positive correlation between selenium content and second-harmonic response and greatly outperform the industry standard AgGaSe2. These materials crystallize in the noncentrosymmetric space group Cc as one-dimensional 1/∞ [AsQ2]- (Q = S, Se, S/Se) chains consisting of corner-sharing AsQ3 trigonal pyramids with charge-balancing Li+ atoms interspersed between the chains. LiAsS2-xSex melts congruently for 0 ≤ x ≤ 1.75, but when the Se content exceeds x = 1.75, crystallization is complicated by a phase transition. This behavior is attributed to the β- to α-phase transition present in LiAsSe2, which is observed in the Se-rich compositions. The band gap decreases with increasing Se content, starting at 1.63 eV (LiAsS2) and reaching 1.06 eV (β-LiAsSe2). Second-harmonic generation measurements as a function of wavelength on powder samples of β-LiAsS2-xSex show that these materials exhibit significantly higher nonlinearity than AgGaSe2 (d36 = 33 pm/V), reaching a maximum of 61.2 pm/V for LiAsS2. In comparison, single-crystal measurements for LiAsSSe yielded a deff = 410 pm/V. LiAsSSe, LiAsS0.25Se1.75, and β-LiAsSe2 show phase-matching behavior for incident wavelengths exceeding 3 μm. The laser-induced damage thresholds from two-photon absorption processes are on the same order of magnitude as AgGaSe2, with S-rich materials slightly outperforming AgGaSe2 and Se-rich materials slightly underperforming AgGaSe2.

Second-order magnetic responses in quantum magnets: Magnetization under ac magnetic fields

We investigate second-order magnetic responses of quantum magnets against ac magnetic fields. We focus on the case where the $z$ component of the spin is conserved in the unperturbed Hamiltonian and the driving field is applied in the $xy$ plane. We find that linearly polarized driving fields induce a second-harmonic response, while circularly polarized fields generate only a zero-frequency response, leading to a magnetization with a direction determined by the helicity. Employing an unbiased numerical method, we demonstrate the nonlinear magnetic effect driven by the circularly polarized field in the XXZ model and show that the magnitude of the magnetization can be predicted by the dynamical spin structure factor in the linear response regime.

Observation of Giant Surface Second-Harmonic Generation Coupled to Nematic Orders in the van der Waals Antiferromagnet FePS3.

Second-harmonic generation has been applied to study lattice, electronic, and magnetic proprieties in atomically thin materials. However, inversion symmetry breaking is usually required for the materials to generate a large signal. In this work, we report a giant second-harmonic generation that arises below the Néel temperature in few-layer centrosymmetric FePS3. A layer-dependent study indicates the detected signal is from the second-order nonlinearity of the surface. The magnetism-induced surface second-harmonic response is 2 orders of magnitude larger than those reported in other magnetic systems, with the surface nonlinear susceptibility reaching 0.08-0.13 nm2/V in 2-5 L samples. By combing linear dichroism and second-harmonic generation experiments, we further confirm the giant second-harmonic generation is coupled to nematic orders formed by the three possible Zigzag antiferromagnetic domains. Our study shows that the surface second-harmonic generation is also a sensitive tool to study antiferromagnetic states in centrosymmetric atomically thin materials.

One-Side Capping in Two-Dimensional WO3-Type Materials Leading to Strong Second-Harmonic Response

One-Side Capping in Two-Dimensional WO₃-Type Materials Leading to Strong Second-Harmonic Response

Modulating the temporal dynamics of nonlinear ultrafast plasmon resonances

Surface plasmon-induced nonlinear optical resonances have shown immense potential in advanced optical imaging and nonlinear photonic devices. However, the ultrashort lifetime of these intense nonlinear fields inhibits their effective use in the vast applications of quantum plasmonics. Here, we propose enhancement in the lifetime of fast decaying second harmonic (SH) plasmon mode through a weak and pure resonant interaction with a two-level quantum emitter (QE). We compute the time evolution of SH response under a two-coupled oscillator model, in which we examine the interaction of short-lived SH mode supported by Au nanoparticle (AuNP) with long-lived dark mode (DM) or QE systems. To analyze the effect of spectral and temporal properties of DM and QE on the SH field, we evaluate the lifetime enhancement factor as a function of coupling strength and tuned resonant frequencies. The results show that tiny object like QE with sharp spectral bandwidth, small decay rate, and large oscillating strength is more efficient to control and probe the temporal dynamics of the SH field, as compared to DM which have a wide spectral bandwidth. Also, we control the lifetime of the SH mode after the natural decay time of the fundamental mode (FM), which distinguishes SH mode irrespective of its spatial convolution with elementary modes. Our proposed AuNP-QE coupled plasmonic system supporting nonlinear signal with enhanced temporal character paves its way for designing efficient on-chip nonlinear optical devices and can be a powerful tool in ultrahigh resolution nonlinear optical imaging.

Observation of strong and anisotropic nonlinear optical effects through polarization-resolved optical spectroscopy in the type-II Weyl semimetal Td−WTe2

The unique bulk crossing points in the band structure of topological Weyl semimetals have been shown to enhance nonlinear optical and optoelectronic properties, even for light at optical wavelengths. Such pronounced nonlinear optical effects have been studied in type-I Weyl semimetals, yet few studies have quantified these effects in type-II Weyl semimetals. We here present an optical experimental study with polarization resolution of two nonlinear optical effects in the type-II Weyl semimetal ${T}_{\mathrm{d}}\text{\ensuremath{-}}\mathrm{W}{\mathrm{Te}}_{2}$. We begin by investigating the bulk optical second-harmonic response of this material using the rotational anisotropy of the second-harmonic generation. This technique allows us to simultaneously investigate the dependence of the second-harmonic response on the symmetry of the crystal and to quantify the size of that response, which we compare to other nonlinear crystals. We then use polarized time-resolved optical reflectivity spectroscopy to identify the nonlinear optical effect of impulsive stimulated Raman scattering as the origin of the coherent oscillations of the 0.25-THz shear mode. We find that the strength of this response in ${T}_{\mathrm{d}}\text{\ensuremath{-}}\mathrm{W}{\mathrm{Te}}_{2}$ is enhanced compared with the observation of other modes excited through the displacive excitation of coherent phonons. Notably, both the second-harmonic response and the coherent excitations of the phonons demonstrate strong anisotropy, displaying a clear dependence on the polarization of the light used in the experiments. We use point-symmetry analyses of the material to guide our understanding of these observations and perform fluence-dependent measurements to investigate the electron-phonon coupling.

A case-control study of visual, auditory and audio-visual sensory interactions in children with autism spectrum disorder.

To assess the relative integrity of early visual and auditory processes in autism spectrum disorder (ASD), we used frequency-tagged visual and auditory stimulation and high-density electroencephalogram recordings of unimodal and dual-modality responses in a case–control design. To test for the specificity of effects on ASD, we recorded from a smaller group of children with attention-deficit hyperactivity disorder (ADHD). Horizontal 3 cycle per degree (cpd) gratings were presented at 5 Hz, and a random stream of /ba/, /da/, /ga/ syllables was presented at 6 Hz. Grating contrast response functions were measured unimodally and in the presence of a 64-dB auditory input. Auditory response functions were measured unimodally and in the presence of a 40% contrast grating. Children with ASD (n = 34) and ADHD (n = 13) showed a common lack of audio–visual interaction compared to typically developing children (n = 40) when measured at the first harmonic of the visual stimulus frequency. Both patient groups also showed depressed first harmonic responses at low contrast, but the ADHD group had consistently higher first-harmonic responses at high contrast. Children with ASD had a preferential loss of second-harmonic (transient) responses. The alteredtransient responses in ASD are likely to arise very early in the visual pathway and could thus have downstream consequences for many other visual mechanisms and processes. The alteration in audio–visual interaction could be a signature of a comorbid phenotype shared by ASD and ADHD, possibly due to alterations in attentional selection systems.

Large Second-Harmonic Response and Giant Birefringence of CeF2(SO4) Induced by Highly Polarizable Polyhedra.

Second-harmonic generation (SHG) response and birefringence are two critically important properties of nonlinear optical (NLO) materials. However, the simultaneous optimization of these two key properties remains a major challenge because of their contrasting microstructure requirements. Herein, we report the first tetravalent rare-earth metal fluorinated sulfate, CeF2(SO4). Its structure features novel net-like layers constructed by highly distorted [CeO4F4] polyhedra, which are further interconnected by [SO4] tetrahedra to form a three-dimensional structure. CeF2(SO4) exhibits the strongest SHG effect (8 times that of KH2PO4) and the largest birefringence for sulfate-based NLO materials, the latter exceeding the birefringent limit for oxides. Theoretical calculations and crystal structure analysis reveal that the unusually large SHG response and giant birefringence can be attributed to the introduction of the highly polarizable fluorinated [CeO4F4] polyhedra as well as the favorable alignment of [CeO4F4] polyhedra and [SO4] tetrahedra. This research affords a new paradigm for the designed synthesis of high-performance NLO materials.

Strong second-harmonic response from semiconductor–dielectric interfaces

In this study, an analysis of the second-harmonic generation (SHG) response from surfaces containing dielectric-semiconductor interfaces with sub-wavelength features is presented. The investigated medium is a metamaterial where the SHG response is governed by the symmetry breaking between consecutive layers. The examined material is composed of a periodic structure based on 50 nm silicon nitride and 10 nm indium gallium zinc oxide (IGZO) fabricated on a quartz glass substrate. The elementary cell consists of a pair of materials in an exchangeable order. The preliminary results show a promising application of the amorphous IGZO as a nonlinear optical material, whose optical characteristics can be controlled by the fabrication process itself. Prepared structures give a remarkably high SHG response. For an effective thickness of the structure equal to 240 nm, a more than 250-fold increase in SHG compared to the reference substrate is observed.

Second Harmonic Generation in Arrays of Nanoholes in a Silver Film

Specific features of optical second harmonic (SH) generation in arrays of chiral helical nanoholes in a silver film are studied experimentally. An increase in the intensity of the second-order nonlinear optical response is observed in the region of anomalous resonant transmission. The significant role of the rotational symmetry of the array of nanoholes in the formation of the SH response is revealed, which determines the azimuthal dependence of both the intensity of the second-order optical signal and the SH circular dichroism.