Nonlinear Harmonic Generation Research Articles

Efficient second-harmonic generation in a lithium niobate metasurface governed by high-Q magnetic toroidal dipole resonances.

Lithium niobate (LN) is an excellent nonlinear optical material due to its large nonlinear coefficient, low loss, and broad optical transparency window. So, it is widely used in the generation of nonlinear harmonics. Magnetic toroidal dipole (MTD) resonance is a special optical resonance mode, which can effectively localize the light field inside the device, thus enhancing the nonlinear effects of the materials. In this work, we numerically study the second-harmonic generation (SHG) effect of the LN metasurface based on the MTD mode with a high quality factor (Q-factor). The designed LN nanorod dimer metasurface supports high Q-factor MTD guided mode resonances (GMRs), which are excited by varying the center spacing of the two nanorods, and the Q-factor can be controlled by the offset distance. The excited MTD can effectively confine the electric field within the device, which enables the LN metasurface SHG conversion efficiency to reach 1.15 × 10-2. In addition, by adjusting the structural parameters, it is possible to effectively modulate the wavelength and conversion efficiency of the SHG. Our results provide a new route for high-quality nonlinear light sources.

Effect of morphology on the optical limiting of BiVO4 films

Precise control over the morphology and crystal structure of semiconductor-based optical materials is essential for optimizing their nonlinear optical properties. Morphological factors significantly affect the material’s interaction with light, influencing nonlinear absorption, harmonic generation, and optical confinement. In this study, the nonlinear optical (NLO) properties and optical limiting (OL) performance of bismuth vanadate (BiVO4) films depending on precursor solution pH condition, powder morphology and weight percentage of the BiVO4 powders in PMMA (10–30 wt.%) were investigated. The BiVO4 powders were synthesized via the hydrothermal method and the effect of precursor solution pH (pH of 1, 7.5 and 12) was investigated on the size and morphology of the BiVO4 powders. BiVO4 films were prepared using the spin coating method utilizing the BiVO4 powders and PMMA. The bandgap values of films were found to change from 3.39 to 3.56 eV depending on the BiVO4 growth solution pH. The nonlinear absorption coefficients (βeff), saturation intensity thresholds (ISAT) and optical limiting (OL) threshold were obtained using the open aperture (OA) Z-scan experiment. It has been observed that the nonlinear absorption and optical limitation performance of the BiVO4 films can be altered by changing the powder morphology and BiVO4 weight concentration. BiVO4 thin films fabricated using a precursor solution pH 12 and weight concentration of 30 wt.% showed the best performance among all fabricated films with the highest nonlinear absorption coefficient (βeff), saturation density threshold (ISAT) and lowest OL threshold value.

Macroscopic Twisting of Chiral Metal Halide Single Crystals Driven by Thermo-Induced Topochemical Dehydration.

Dynamic twisting crystals, combining the features of dynamic crystals and twisting crystals, promise advanced applications in targeted drug delivery, biosensors, microrobots, and spiral optoelectronics. However, the determination of dynamic twisting crystals with specific directions remains a formidable challenge in practical applications. Herein, based on organic-inorganic hybrid metal halide (OIHMH) single crystals, we have realized the chirality-induced macroscopic twisting of single crystals driven by a thermo-induced topochemical dehydration reaction. These crystals exhibit molecular-chirality-induced twisting upon heating, along with reversals in their linear chiroptical circular dichroism and nonlinear chiroptical second harmonic generation circular dichroism. Such an induced twisting has been attributed to the alteration of the helical arrangement of chiral cation post-topochemical dehydration. The feasibility of tuning the macroscopic twisting of OIHMH single crystals and the switching in their linear and nonlinear chiroptical properties might open up new avenues for developing dynamic crystals for microactuating and optoelectronic applications.

Unseeded one-third harmonic generation in optical fibers

We propose a new concept to generate efficient one-third harmonic light from an unseeded third harmonic process in optical fibers. Our concept is based on the dynamic constant (Hamiltonian) of the nonlinear third harmonic generation in optical fibers and includes a periodic array of nonlinear fibers and phase compensation elements. We test our concept with a simulation of the nonlinear interaction between the fundamental and third harmonic modes of a realistic optical fiber, demonstrating high-efficiency one-third harmonic generation. Our work opens a new approach to achieving the so far elusive one-third harmonic generation in optical fibers.

Shape unrestricted topological corner state based on Kekulé modulation and enhanced nonlinear harmonic generation

Abstract Topological corner states have been extensively utilized as a nanocavity to increase nonlinear harmonic generation due to their high Q-factor and robustness. However, the previous topological corner states based nanocavities and nonlinear harmonic generation have to comply with particular spatial symmetries of underlying lattices, hindering their practical application. In this work, we design a photonic nanocavity based on shape unrestricted topological corner state by applying Kekulé modulation to a honeycomb photonic crystal. The boundaries of such shape unrestricted topological corner state are liberated from running along specific lattice directions, thus topological corner states with arbitrary shapes and high Q-factor are excited. We demonstrate enhancement of second (SHG) and third harmonic generation (THG) from the topological corner states, which are also not influenced by the geometry shape of corner. The liberation from the shape restriction of corner state and nonlinear harmonic generation are robust to lattice defects. We believe that the shape unrestricted topological corner state may also find a way to improve other nonlinear optical progress, providing great flexibility for the development of photonic integrated devices.

Tunable third harmonic generation based on high-Q polarization-controlled hybrid phase-change metasurface

Abstract Dielectric metasurfaces have made significant advancements in the past decade for enhancing light–matter interaction at the nanoscale. Particularly, bound states in the continuum (BICs) based on dielectric metasurfaces have been employed to enhance nonlinear harmonic generation. However, conventional nonlinear metasurfaces are typically fixed in their operating wavelength after fabrication. In this work, we numerically demonstrate tunable third harmonic generation (THG) by integrating a dielectric metasurface with the phase-change material Ge2Sb2Te5 (GST). The hybrid phase-change metasurface can support two BICs with different electromagnetic origins, which are transformed into two high-Q quasi-BICs through the introduction of structural asymmetry. The two quasi-BICs are selectively excited by controlling the polarization of incident light, and their wavelengths are tunable due to the phase transition of GST. Notably, the efficiency of THG is significantly enhanced at the fundamental wavelengths corresponding to the two quasi-BICs, and the operating wavelength for THG enhancement can be dynamically tuned through the GST phase transition. Furthermore, the wavelength of THG enhancement can be further tuned by manipulating the polarization of pump light. Additionally, a high-Q analog of electromagnetically induced transparency is numerically achieved through the interaction between a low-Q Mie resonance and a quasi-BIC mode, which also improves the THG efficiency. The high-Q polarization-controlled hybrid phase-change metasurface holds promise for applications in dynamically tunable nonlinear optical devices.

Realizing quasi-bound states in the continuum with stable resonant wavelength through compensation mechanism

All-dielectric metasurfaces underpinned by the physics of bound states in the continuum (BICs) have surged interest due to their spectral selectivity and strong light confinement. In this work, We propose a compensation mechanism for SP-BIC with stable resonance wavelength and controllable Q-factor. Here we take metasurfaces consisting of four nano-square disks as an example to break the symmetry of the unit cell by both x-compensation and y-compensation, respectively, and the resonance wavelengths are stable. The results show that the four nanodisks are excited in two modes with x-compensation and y-compensation when only C2 symmetry is preserved, and in one mode with x-compensation and y-compensation when only σx symmetry is preserved. Multiple decomposition results show that the loop dipole and magnetic dipole dominate the modes that retain only C2 symmetry excitation. In contrast, the magnetic dipole dominates the mode that retains only the σx symmetry excitation. Both modes excited by the compensation mechanism have stable resonances with high q-factors under the condition of preserving only C2 symmetry or only σx symmetry. Metasurfaces realized by the compensation mechanism may find promising applications in enhanced light-matter interactions such as lasers, sensing, strong coupling, and nonlinear harmonic generation.

Extrinsic Nonlinear Kerr Rotation in Topological Materials under a Magnetic Field.

Topological properties in quantum materials are often governed by symmetry and tuned by crystal structure and external fields, and hence, symmetry-sensitive nonlinear optical measurements in a magnetic field are a valuable probe. Here, we report nonlinear magneto-optical second harmonic generation (SHG) studies of nonmagnetic topological materials including bilayer WTe2, monolayer WSe2, and bulk TaAs. The polarization-resolved patterns of optical SHG under a magnetic field show nonlinear Kerr rotation in these time-reversal symmetric materials. For materials with 3-fold rotational symmetric lattice structure, the SHG polarization pattern rotates just slightly in a magnetic field, whereas in those with mirror or 2-fold rotational symmetry, the SHG polarization pattern rotates greatly and distorts. These different magneto-SHG characters can be understood by considering the superposition of the magnetic field-induced time-noninvariant nonlinear optical tensor and the crystal-structure-based time-invariant counterpart. The situation is further clarified by scrutinizing the Faraday rotation, whose subtle interplay with crystal symmetry accounts for the diverse behavior of the extrinsic nonlinear Kerr rotation in different materials. Our work illustrates the application of magneto-SHG techniques to directly probe nontrivial topological properties, and underlines the importance of minimizing extrinsic nonlinear Kerr rotation in polarization-resolved magneto-optical studies.

Effect of magnesium and zinc doping of lithium niobate crystals on nonlinear optical characteristics

The theoretical and experimental values of nonlinear optical susceptibilities for lithium niobate crystals double doped with cations (Zn2+:Mg2+) with similar concentrations obtained using the method of direct and homogeneous impurity introduction were analyzed. The length of Li-O bonds in double-doped crystals (LiNbO3:Zn2+:Mg2+) determined the value of the nonlinear optical second harmonic generation (SHG) coefficients. It was found that impurity and intrinsic defects make a positive contribution to the tensor coefficients of the second-order nonlinear optical susceptibility (dij). The results indicated that the LiNbO3:Zn2+:Mg2+ (3.83:0.97 mol%) crystal is the most suitable medium for SHG application among the crystals studied in the paper, as it showed the maximum calculated value of the nonlinear optical coefficient d33 which was equal to −55.26(2) × 10−9 cm/statV. The measured second harmonic conversion efficiency for this crystal was η = 36%.

Effects of Applied External Fields on the Nonlinear Optical Third Harmonic Generation in a GaAs/Ga0.7Al0.3As Quantum Dots

Effects of Applied External Fields on the Nonlinear Optical Third Harmonic Generation in a GaAs/Ga0.7Al0.3As Quantum Dots

Numerical Investigations of Nonlinearly Generated Disturbance Waves in High-Speed Boundary Layers

In several experimental investigations of hypersonic boundary-layer transition, higher harmonics of the linearly unstable second mode waves as well as low-frequency waves, which are not related to first mode waves, have been observed. It has been conjectured that the higher harmonics are nonlinearly generated by a self-interaction mechanism of the linearly amplified second mode waves. Several hypotheses regarding the origin of the low-frequency waves and their role in the transition process have been put forth. However, a clear understanding of the origin and role of these low-frequency disturbances in the transition process is difficult to attain from experiments and thus still not completely achieved. The nonlinear generation of higher harmonics and low-frequency disturbances is relevant because in high-speed boundary layers, second modes can reach very large amplitudes, which can lead to a considerable stretching of the transitional regime where these nonlinearly generated waves can then reach significant amplitudes and participate in the transition process. To shed light on this unresolved issue, numerical investigations were carried out for a flared cone at Mach 6. These calculations have shown that nonlinear interactions of sufficiently large-amplitude second mode waves can generate low-frequency disturbances. This was confirmed by a theoretical nonlinear interaction model.

Tunable mode conversion in a mechanical metamaterial via second harmonic generation

Mode conversion of elastic waves is ubiquitous in solids and has various applications in medical imaging, signal processing, vibration suppression, etc. Nonlinear harmonic generation in mechanical metamaterials is a way to achieve efficient, self-adaptive mode conversion, but is hindered by the required while difficult-to-meet phase matching condition. Moreover, enhanced mode conversion usually works in a narrow frequency band, and lacks of tunability. In this paper, we realize wide band, tunable enhanced mode conversion via second harmonic generation (SHG), with a pre-strained, translation-rotation coupled mechanical metamaterial. We demonstrate the realization experimentally and numerically, along with an analytical discrete model developed to reveal the origin of the tunability. It is shown that the pre-strain gives rise to hardening in stretch and softening in compression, broadening the effective frequency range of the enhanced mode conversion. Moreover, the pre-strain affects not only the geometrical configuration but also the on-site stiffness of the metamaterial, both of which are responsible for the tunability of the enhanced mode conversion. A transverse instability induced by compression is also revealed, showing unusual effect on the enhanced mode conversion during the initial period of time. Our work can inspire new device designs for vibration control, signal processing and non-destructive testing.

Higher-order hybrid topological bound states in a non-Hermitian system.

Higher-order topological states, such as the corner and pseudo-hinge states, have been discovered in both Hermitian and non-Hermitian systems. These states have inherent high-quality factors that make them useful in the application of photonic devices. In this work, we design a non-Hermiticity solely induced Su-Schrieffer-Heeger (SSH) lattice and demonstrate the existence of diverse higher-order topological bound states in the continuum (BICs). In particular, we first uncover some hybrid topological states that occur in the form of BICs in the non-Hermitian system. Furthermore, these hybrid states with an amplified and localized field have been demonstrated to excite nonlinear harmonic generation with high efficiency. The appearance of these topological bound states will advance the study of the interplay of topology, BICs, and non-Hermitian optics.

Effects of applied external fields on the nonlinear optical second harmonic generation in a GaAs/Ga0.7Al0.3As quantum dots

This work has studied some nonlinear optical properties of Al0.3Ga0.7As/GaAs quantum dot system with tangent-square potential (TSP), with special emphasis on the role of second harmonic generation (SHG) coefficient under hydrostatic pressure and temperature. Due to the strain of external application conditions, the changes of the energy level and wave function of the neutron band in the system structure provide valuable insights into the optical properties of the quantum dot structure. In this paper, we report the effects of structural parameters, temperature and hydrostatic pressure on the SHG coefficient. According to the results obtained in the work, it can be reported that the nonlinear optical properties of the quantum dot system can be improved by adjusting the hydrostatic pressure and temperature. At the same time, the interaction of various parameters has produced some interesting observations, which are relevant in relevant research fields.

Toroidal dipole bound states in the continuum based on hybridization of surface lattice resonances.

Obtaining a high quality factor (Q factor) in applications based on metasurfaces is crucial for improving device performance. Therefore, bound states in the continuum (BICs) with ultra-high Q factors are expected to have many exciting applications in photonics. Breaking the structure symmetry has been viewed as an effective way of exciting quasi-bound states in the continuum (QBICs) and generating high-Q resonances. Among these, one exciting strategy is based on the hybridization of surface lattice resonances (SLRs). In this study, we investigated for the first time the Toroidal dipole bound states in the continuum (TD-BICs) based on the hybridization of Mie surface lattice resonances (SLRs) in an array. The unit cell of metasurface is made of a silicon nanorods dimer. The Q factor of QBICs can be precisely adjusted by changing the position of two nanorods, while the resonance wavelength remains quite stable against the change of position. Simultaneously, the far-field radiation and near-field distribution of the resonance are discussed. The results indicate that the toroidal dipole dominates this type of QBIC. Our results indicate that this quasi-BIC can be tuned by adjusting the size of the nanorods or the lattice period. Meanwhile, through the study of the shape variation, we found that this quasi-BIC exhibits excellent robustness, whether in the case of two symmetric or asymmetric nanoscale structures. This will also provide large fabrication tolerance for the fabrication of devices. Our research results will improve the mode analysis of surface lattice resonance hybridization, and may find promising applications in enhancing light-matter interaction, such as lasing, sensing, strong-coupling, and nonlinear harmonic generation.

Dual-Modal Nanoplasmonic Light Upconversion through Anti-Stokes Photoluminescence and Second-Harmonic Generation from Broadband Multiresonant Metal Nanocavities.

Metal nanocavities can generate plasmon-enhanced light upconversion signals under ultrashort pulse excitations through anti-Stokes photoluminescence (ASPL) or nonlinear harmonic generation processes, offering various applications in bioimaging, sensing, interfacial science, nanothermometry, and integrated photonics. However, achieving broadband multiresonant enhancement of both ASPL and harmonic generation processes within the same metal nanocavities remains challenging, impeding applications based on dual-modal or wavelength-multiplexed operations. Here, we report a combined experimental and theoretical study on dual-modal plasmon-enhanced light upconversion through both ASPL and second-harmonic generation (SHG) from broadband multiresonant metal nanocavities in two-tier Ag/SiO2/Ag nanolaminate plasmonic crystals (NLPCs) that can support multiple hybridized plasmons with high spatial mode overlaps. Our measurements reveal the distinctions and correlations between the plasmon-enhanced ASPL and SHG processes under different modal and ultrashort pulsed laser excitation conditions, including incident fluence, wavelength, and polarization. To analyze the observed effects of the excitation and modal conditions on the ASPL and SHG emissions, we developed a time-domain modeling framework that simultaneously captures the mode coupling-enhancement characteristics, quantum excitation-emission transitions, and hot carrier population statistical mechanics. Notably, ASPL and SHG from the same metal nanocavities exhibit distinct plasmon-enhanced emission behaviors due to the intrinsic differences between the incoherent hot carrier-mediated ASPL sources with temporally evolving energy and spatial distributions and instantaneous SHG emitters. Mechanistic understanding of ASPL and SHG emissions from broadband multiresonant plasmonic nanocavities marks a milestone toward creating multimodal or wavelength-multiplexed upconversion nanoplasmonic devices for bioimaging, sensing, interfacial monitoring, and integrated photonics applications.

Time‐dependent coupled‐cluster theory

AbstractRecent years have witnessed an increasing interest in time‐dependent coupled‐cluster (TDCC) theory for simulating laser‐driven electronic dynamics in atoms and molecules, and for simulating molecular vibrational dynamics. Starting from the time‐dependent bivariational principle, we review different flavors of single‐reference TDCC theory with either orthonormal static, orthonormal time‐dependent, or biorthonormal time‐dependent spin orbitals. The time‐dependent extension of equation‐of‐motion coupled‐cluster theory is also discussed, along with the applications of TDCC methods to the calculation of linear absorption spectra, linear and low‐order nonlinear response functions, highly nonlinear high harmonic generation spectra and ionization dynamics. In addition, the role of TDCC theory in finite‐temperature many‐body quantum mechanics is briefly described along with a few other application areas.This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Theoretical and Physical Chemistry > Spectroscopy Software > Simulation Methods

Quasi-symmetry-protected BICs in a double-notched silicon nanodisk metasurface.

Bound states in the continuum (BICs) hold great promise in enhancing light-matter interaction as they have an infinite Q-factor. To date, the symmetry-protected BIC (SP-BIC) is one of the most intensively studied BICs because it is easily found in a dielectric metasurface satisfying certain group symmetry. To convert SP-BICs into quasi-BICs (QBICs), structural symmetry shall be broken so that external excitation can access them. Usually, the unit cell's asymmetry is created by removing or adding parts of dielectric nanostructures. The QBICs are usually excited only by s-polarized or p-polarized light because of the symmetry-breaking of the structure. In this work, we investigate the excited QBIC properties by introducing double notches on the edges of highly symmetrical silicon nanodisks. The QBIC shares the same optical response under the s-polarized and p-polarized light. The effect of polarization on coupling efficiency between the QBIC mode and incident light is studied, and the highest coupling efficiency occurs at a polarization angle of 135 ∘, which corresponds to the radiative channel. Moreover, the near-field distribution and multipole decomposition confirm that the QBIC is dominated by the magnetic dipole along the z direction. It is noted that the QBIC covers a wide spectrum region. Finally, we present an experimental confirmation; the measured spectrum shows a sharp Fano resonance with a Q-factor of 260. Our results suggest promising applications in enhancing light-matter interaction, such as lasing, sensing, and nonlinear harmonic generation.

Doubly-resonant enhanced second-harmonic generation and its wide-band tunability

The second-harmonic generation (SHG) from the doubly-resonant metasurfaces composed of the U-shaped and the rectangular apertures on an optically opaque gold film is investigated theoretically. By engineering the fundamental plasmonic resonances of the composite metasurfaces to match the excitation and the second-harmonic wavelengths, respectively, the doubly-resonant enhanced SHG intensity of almost an order of magnitude is obtained, compared with the singly-resonant U-apertures. In addition, the satisfaction of doubly-resonant condition can be extended to a wide wavelength range by changing the refractive index of the surrounding medium, which benefits from the two fundamental plasmonic resonances oscillating at frequencies of a two-fold relationship. Our work provides a new way to enhance the efficiency of nonlinear harmonic generation.

Theoretical analysis of high-order harmonic generation in liquids by a semiclassical method

The study of high-order harmonic generation in liquid-state materials is still in its infancy. Quantitative models are highly required to understand the mechanisms. Here we develop a semiclassical method to investigate the ultrafast electron dynamics in liquids under monochromatic and two-color laser fields in momentum space. By assuming that different $k$ values are decoupled, we construct a quasienergy band for the liquid model and give the group velocity of the ionized electrons under the driving field. It successfully predicts the caustic enhancement of the liquid harmonic spectrum. We also find that the cutoff of the liquid harmonic spectrum is determined by the $k$-dependent band gap. Our results provide a different perspective for analyzing the nonlinear and nonperturbative liquid-state harmonic generation.