Second Harmonic Generation Spectra Research Articles

Harnessing physics-guided neural networks for tailoring the orbital angular momentum spectrum in second harmonic generation

The management of orbital angular momentum (OAM) in frequency conversion processes is essential for numerous applications such as quantum and classical optical communications. This paper presents a wavefront modulation approach for the fundamental beam in second harmonic generation (SHG) to efficiently control the OAM spectrum. We employ an inverse design method to derive the necessary wavefront shape of the fundamental beam for achieving a desired SHG OAM spectrum. Specifically, we introduce an efficient inverse design technique based on physics-guided neural networks (PGNNs) that incorporates the coupled equations governing SHG, aimed at tailoring the OAM spectrum of SHG. Utilizing the proposed PGNN, we design the phase pattern for a spatial light modulator (SLM) to shape the wavefront of the fundamental beam. Furthermore, we present a novel loss function, to our knowledge, that effectively links the OAM of the SHG spectrum and efficiency to the SLM phase pattern and crystal temperature, independent of empirical weight coefficients. The proposed PGNN facilitates the purification of the SHG OAM spectrum, even when the fundamental beam comprises mixed Laguerre–Gaussian (LG) modes. Additionally, we demonstrate the generation of desired SHG spectra using the proposed PGNN framework. This study introduces what we believe to be a groundbreaking inverse design method for developing photonic devices with customized functionalities, addressing challenges associated with traditional data-driven deep learning techniques.

Harnessing complexity: Nonlinear optical phenomena in L-shapes, nanocrescents, and split-ring resonators.

We conduct systematic studies of the optical characteristics of plasmonic nanoparticles that exhibit C2v symmetry. In particular, we analyze three distinct geometric configurations: an L-type shape, a crescent, and a split-ring resonator shaped like the Greek letter π. Optical properties are examined using the finite-difference time-domain method. It is demonstrated that all three shapes exhibit two prominent plasmon modes associated with the two axes of symmetry. This is in addition to a wide range of resonances observed at high frequencies corresponding to quadrupole modes and peaks due to sharp corners. Next, to facilitate nonlinear analysis, we employ a semiclassical hydrodynamic model, where the electron pressure term is explicitly accounted for. This model goes beyond the standard Drude description and enables capturing nonlocal and nonlinear effects. Employing this model enables us to rigorously examine the second-order angular resolved nonlinear optical response of these nanoparticles in each of the three configurations. Two pumping regimes are considered, namely, continuous wave (CW) and pulsed excitations. For CW pumping, we explore the properties of the second harmonic generation (SHG). Polarization and angle-resolved SHG spectra are obtained, revealing strong dependence on the nanoparticle geometry and incident wave polarization. The C2v symmetry is shown to play a key role in determining the polarization states and selection rules of the SHG signal. For pulsed excitations, we discuss the phenomenon of broadband terahertz (THz) generation induced by the difference-frequency generation . It is shown that the THz emission spectra exhibit unique features attributed to the plasmonic resonances and symmetry of the nanoparticles. The polarization of the generated THz waves is also examined, revealing interesting patterns tied to the nanoparticle geometry. To gain deeper insight, we propose an analytical theory that agrees very well with the numerical experiments. The theory shows that the physical origin of the THz radiation is the mixing of various frequency components of the fundamental pulse by the second-order nonlinear susceptibility. An expression for the far-field THz intensity is derived in terms of the incident pulse parameters and the nonlinear response tensor of the nanoparticle. The results presented in this work offer new insights into the linear and nonlinear optical properties of nanoparticles with C2v symmetry. The demonstrated strong SHG response and efficient broadband THz generation hold great promise for applications in nonlinear spectroscopy, nanophotonics, and optoelectronics. The proposed theoretical framework also provides a valuable tool for understanding and predicting the nonlinear behavior of other related nanostructures.

Second Harmonic Generation from exciton-polaritons: Strong coupling between monolayer WS[formula omitted] and multilayer WSe[formula omitted] metasurfaces Quasibound states in the continuum

The second harmonic generation (SHG) from exciton-polaritons, produced by the strong coupling between quantum emitters and cavity photons, can provide a unique insight for controlling nonlinear responses on the nanoscale. Achieving SHG generally depends on phase matching, limited by nonlinear materials and nanostructure fabrication. Here, we demonstrate a novel way to obtain tunable SHG from van der Waals metasurfaces composed of nanostructured multilayer WSe2 strong coupling with monolayer WS2. By breaking symmetry via varying the metasurface unit tilted angle and period, quasibound state in the continuum (q-BIC) mode resonances energy is tuned across the monolayer WS2 exciton resonance energy, enabling anticrossing behavior of strong coupling in both reflection spectrum and SHG spectrum, which means that SHG was successfully observed by strong coupling. Furthermore, the SHG spectrum can be tuned by changing the armchair direction of the monolayer WS2 and pump polarization direction. Moreover, the mechanism of exciton-polaritonic SHG is investigated by a coupled nonlinear oscillator model, which reveals the SHG origin from exciton-polaritons, providing a new rule for fine-tuning the SHG. Our work provides a new strategy and additional freedom in the nonlinear light-matter interaction and coherent control of the SHG in integrated photonic devices.

Exciton-Driven and Layer-Independent Linear and Nonlinear Optical Properties in NbOCl2.

We investigate the electronic structure and linear and nonlinear [second-harmonic generation (SHG)] spectra of the NbOCl2 monolayer, bilayer, and bulk by using a real-time first-principles approach based on many-body theory. First, the interlayer couplings between NbOCl2 layers are very weak, due to the relatively large interlayer distance, saturation of the p orbital of Cl atoms, and high degree of localization of charge density around the Nb atom for both the lowest conduction band and the highest valence band. Second, the quasiparticle gaps and exciton binding energy for the three systems show layer-dependent features and decrease with an increase in layer thickness. Most importantly, the linear and SHG spectra of the NbOCl2 monolayer, bilayer, and bulk are dominated by strong excitonic resonances and exhibit layer-independent features due to the weak interlayer couplings. Our findings demonstrate that excitonic effects should be included in studying the optical properties of not only two-dimensional materials but also layered bulk materials with weak interlayer couplings.

Inversion Symmetry-Broken Tetralayer Graphene Probed by Second-Harmonic Generation.

Stacking orders provide a unique way to tune the properties of two-dimensional materials. Recently, ABCB-stacked tetralayer graphene has been predicted to possess atypical elemental ferroelectricity arising from its symmetry breaking but has been experimentally explored very little. Here, we observe pronounced nonlinear optical second-harmonic generation (SHG) in ABCB-stacked tetralayer graphene while absent in both ABAB- and ABCA-stacked allotropes. Our results provide direct evidence of symmetry breaking in ABCB-stacked tetralayer graphene. The remarkable contrast in the SHG spectra of tetralayer graphene allows straightforward identification of ABCB domains from the other two kinds of stacking order and facilitates the characterization of their crystalline orientation. The employed SHG technique serves as a convenient tool for exploring the intriguing physics and novel nonlinear optics in ABCB-stacked graphene, where spontaneous polarization and intrinsically gapped flat bands coexist. Our results establish ABCB-stacked graphene as a unique platform for studying the rare ferroelectricity in noncentrosymmetric elemental structures.

Time‐Resolved Optical Response of the Dicke's Model via the Nonequilibrium Green's Function Approach

Due to their conceptual appeal and computational convenience, two‐level systems (TLSs) and generalizations are used to investigate nonlinear behavior in quantum optics and assess the applicability of theoretical methods. Herein, the focus is on second‐harmonic generation (SHG) and, as system of interest, on the Dicke model, which consists of several TLSs inside an optical cavity. The main aspect addressed is the scope of nonequilibrium Green's function (NEGF) to describe the effect of inhomogeneities and electron–electron (e–e) interactions on the SHG signal. For benchmarking purposes, exact diagonalization (ED) results are also presented and discussed. SHG spectra obtained with NEGF and ED are found to be in very good mutual agreement in most situations. Furthermore, inhomogeneity in the TLS and e–e interactions reduce the SHG signal, and the reduction is stronger with inhomogeneity than with interactions. This trend is consistently noted across different (small to large) system sizes. Finally, a modified NEGF approach is proposed to account for cavity leakage, where the quantum photon fields are coupled to a bath of classical oscillators. As expected, within this mixed quantum‐classical scheme, a decrease in the intensity of the fluorescent spectra takes place depending on the entity of leakage.

Nonlinear Optical Responses of Janus MoSSe/MoS2 Heterobilayers Optimized by Stacking Order and Strain.

Nonlinear optical responses in second harmonic generation (SHG) of van der Waals heterobilayers, Janus MoSSe/MoS2, are theoretically optimized as a function of strain and stacking order by adopting an exchange-correlation hybrid functional and a real-time approach in first-principles calculation. We find that the calculated nonlinear susceptibility, χ(2), in AA stacking (550 pm/V) becomes three times as large as AB stacking (170 pm/V) due to the broken inversion symmetry in the AA stacking. The present theoretical prediction is compared with the observed SHG spectra of Janus MoSSe/MoS2 heterobilayers, in which the peak SHG intensity of AA stacking becomes four times as large as AB stacking. Furthermore, a relatively large, two-dimensional strain (4%) that breaks the C3v point group symmetry of the MoSSe/MoS2, enhances calculated χ(2) values for both AA (900 pm/V) and AB (300 pm/V) stackings 1.6 times as large as that without strain.

Angle Measurement Based on Second Harmonic Generation Using Artificial Neural Network

This article proposed an angle measurement method based on second harmonic generation (SHG) using an artificial neural network (ANN). The method comprises three sequential parts: SHG spectrum collection, data preprocessing, and neural network training. First, the referenced angles and SHG spectrums are collected by the autocollimator and SHG-based angle sensor, respectively, for training. The mapping is learned by the trained ANN after completing the training process, which solves the inverse problem of obtaining the angle from the SHG spectrum. Then, the feasibility of the proposed method is verified in multiple-peak Maker fringe and single-peak phase-matching areas, with an overall angle measurement range exceeding 20,000 arcseconds. The predicted angles by ANN are compared with the autocollimator to evaluate the measurement performance in all the angular ranges. Particularly, a sub-arcsecond level of accuracy and resolution is achieved in the phase-matching area.

Anisotropy-enhanced second-harmonic generation from graphene-wrapped nanoparticles

Due to the various applications of second-harmonic generation (SHG), achieving high SHG conversion efficiency is highly appreciated. In this paper, we achieve high SHG conversion efficiency from graphene-wrapped radial anisotropic nanoparticles by combining the strong second-order nonlinear effects of graphene and the field-enhancing effects of anisotropic materials. We find that the nonlinear conversion efficiency of radial anisotropic nanoparticles can be several orders of magnitude higher than that of isotropic counterpart. This is because the radial anisotropic provides the additional enhancement of field intensity near the boundary, and the graphene that provides SHG nonlinear effect is located at the particle boundary where the fundamental frequency field is significantly enhanced. Meanwhile, the highly tunable characteristic of graphene offers additional flexibility for manipulating the SHG spectrum in actual applications. Our results provide a promising method for improving the nonlinear conversion efficiency of photonic devices and the sensitivity of the nonlinear sensor.

Competition between oxygen and water molecules on SiO2/P-doped Si surface: The electrical dipole evolution on water/oxygen-adsorbed oxide surface

The performance of gas sensors is greatly influenced under humidity environment due to the dynamic correlation between water and oxygen molecules. In this work, we utilize the charge trapping characteristic to study surface gas adsorption and demonstrate the competitive adsorption behaviors between oxygen and water vapor from the perspective of electrical dipole by observing the evolution of second harmonic generation (SHG). By analyzing the trapping time constant of time-dependent SHG spectrum, we propose a dynamic model of the way water molecules weaken oxygen adsorption and develop water adsorption layer. Results show that the electric field created by charge trapping would further align the water molecules and enhance the SHG intensity. Here, a viewpoint of analyzing the net surface dipole change due to the adsorption–desorption on SiO2 surface to realize the energy preferable state is presented and provides a pathway for solving the water–sensor interaction problems in gas sensor.

The interfacial structure of super-concentration LiNO3 aqueous electrolyte studied by second harmonic generation.

The interfacial structure of a super-concentration LiNO3 aqueous electrolyte was studied using non-resonant second harmonic generation (SHG) and heterodyne-detected SHG spectra. First, we investigated the electric double layer structure at the air/LiNO3 interface. As the concentration of LiNO3 increased, the SHG intensity first increased and then remained unchanged, while the SHG phase changed by about 5°. These results reveal that there was only a small amount of NO3 - at the interface. The increase of the SHG intensity resulted from the thickening of the interfacial water molecular layer. In addition, we studied the broadening mechanism of the electrochemical stability window (ESW) for the super-concentrated LiNO3 aqueous electrolyte. During cyclic voltammetry scanning, the potential-dependent SHG curves of the Pt/LiNO3 interface verify that at the cathodic end of the ESW, as the concentration of LiNO3 increased, the orientation angle θ of Pt-H changed less and the number density Ns of Pt-H gradually decreased, which indicates the decrease of the number of adsorbed H atoms on the Pt electrode surface. Therefore, the decrease of the number of free water molecules on the Pt electrode surface resulted in an expanded ESW.

High-resolution nanosecond spectroscopy of even-parity Rydberg excitons in Cu2O

We present a study of even parity Rydberg exciton states in cuprous oxide using time-resolved second harmonic generation (SHG). Excitonic states with principal quantum number n = 5 - 12 were excited by nanosecond pulses around 1143 nm. Using time-resolved single-photon counting, the coherently generated second harmonic was isolated both temporally and spectroscopically from inelastic emission due to lower-lying free and bound excitonic states, which included narrow resonances at 1.99 eV associated with an exceptional lifetime of 641 $\pm$ 7 $\mu$s. The near transform-limited excitation bandwidth enabled detailed measurements of the exciton lineshape and position, from which we obtained values for the quantum defects of the S and D excitonic states associated with the appropriate crystal symmetries. Odd parity P and F excitonic states were also observed, in accordance with predicted quadrupole-allowed two-photon excitation processes. We compared our measurements to conventional one-photon spectroscopy in the same sample, and find that the SHG spectrum is cut off at a lower principal quantum number (n = 12 vs n = 15). We attribute this effect to a combination of spatial inhomogeneities and local heating, and discuss the prospects for observing higher principal quantum number even parity states in future experiments.

Role of interlayer coupling in second harmonic generation in bilayer transition metal dichalcogenides

Little is known about the role of weak interlayer coupling in the second harmonic generation (SHG) effects of two-dimensional van der Waals (vdW) systems. In this article, taking homo-bilayer $MoS_2/MoS_2$ and hetero-bilayer $MoS_2/MoSe_2$ as typical examples, we have systemically investigated their SHG susceptibilities as a function of interlayer hopping strength using first-principles calculations. For the SHG at zero frequency limit of both $MoS_2/MoS_2$ and $MoS_2/MoSe_2$, although the increase of tint can increase the intensities of interlayer optical transitions (IOT), the increased band repulsion around G point can eventually decrease their SHG values; the larger the tint, the smaller the SHG response. For the SHG spectra of $MoS_2/MoSe_2$ in the low photon-energy region, opposite to the $MoS_2/MoS_2$, their peak values are very sensitive to the variable tint, due to the strong $t_{int}$-dependent IOT dominating in the band edge; the larger the tint, the larger the SHG. For the SHG of $MoS_2/MoS_2$ in the high photon-energy region, comparing to the $MoS_2/MoSe_2$, their peak values will decrease in a much more noticeable way as the $t_{int}$ increases, due to the larger reduction of band nesting effect. Our study not only can successfully explain the puzzling experimental observations for the different SHG responses in different bilayer transition-metal dichalcogenides under variable tint, but also may provide a general understanding for designing controllable the SHG effects in the vdW systems.

Unveiling the Molecular Dynamics in a Living Cell to the Subcellular Organelle Level Using Second-Harmonic Generation Spectroscopy and Microscopy.

Second-harmonic generation (SHG) microscopy has been proved to be a powerful method for investigating the structures of biomaterials. SHG spectra were also generally used to probe the adsorption and cross-membrane transport of molecules on lipid bilayers in situ and in real time. In this work, we applied SHG and two-photon fluorescence (TPF) spectra to investigate the dynamics of an amphiphilic ion with an SHG and TPF chromophore, D289 (4-(4-diethylaminostyry)-1-methyl-pyridinium iodide), on the surface of human chronic myelogenous leukemia (K562) cells and the subcellular structures inside the cells. The adsorption and cross-membrane transport of D289 into the cells and then into the organelles such as mitochondria were revealed. SHG images were also recorded and used to demonstrate their capability of probing molecular dynamics in organelles in K562 cells. This work demonstrated the first SHG investigation of the cross-membrane transport dynamics on the surface of subcellular organelles. It may also shed light on the differentiation of different types of subcellular structures in cells.

Exciton-driven linear and nonlinear optical responses in metal monoxide monolayersMO(M=Mg,Ca,Cd) from first-principles calculations

We study the linear and nonlinear [second-harmonic generation (SHG)] spectra of metal monoxide $\mathrm{MO}$ ($M$=Mg,Ca,Cd) monolayers by using a first-principles approach based on many-body theory. Our results indicate that the strongly bound excitons in $\mathrm{MO}$ with planar structure characterize the optical properties, including both linear and SHG spectra. The optical bandgap ${E}_{\text{opt}}$ is 4.63, 3.71, and 1.27 eV, while the exciton binding energy is as large as 2.49, 2.37, and 1.13 eV, for MgO, CaO, and CdO, respectively. Moreover, the largest SHG coefficient of 586 pm/V is found in CdO monolayer with the smallest bandgap among the three $\mathrm{MO}$ materials. Most importantly, we find a linear relationship between the SHG coefficient and $\mathrm{Qd}/{E}_{\text{opt}}$ ($Q$ is the transferred Bader charge and $d$ is the bond length) which can be used as a descriptor to search for new two-dimensional nonlinear materials.

Ultimate conversion efficiency of second harmonic generation in all-dielectric resonators of quasi-BICs in consideration of nonlinear refraction of dielectrics

We investigate second harmonic generation (SHG) in all-dielectric resonance nanostructures of high-Q factors assisted by quasi-bound states in the continuum (quasi-BICs). The typical resonators, e.g., guided-mode resonance gratings and asymmetric metasurfaces, fabricated by AlGaAs were numerically studied with the consideration of nonlinear refraction of AlGaAs. The resonance peak and line-shape of linear transmission and SHG spectra in the resonators can be dramatically changed under intense pump intensities. The SHG conversion efficiency in the nanostructures working at quasi-BICs is much lower than the traditionally expected values without considering the nonlinear refraction of dielectrics. The ultimate SHG conversion efficiency is finally obtained. The investigation has the significance for the design and understanding of efficient nonlinear metasurfaces of high-Q factors.

Second Harmonic Generation from Phase-Engineered Metasurfaces of Nanoprisms.

Metasurfaces of gold (Au) nanoparticles on a SiO-Si substrate were fabricated for the enhancement of second harmonic generation (SHG) using electron beam lithography and lift-off. Triangular Au nanoprisms which are non-centro-symmetric and support second-order nonlinearity were examined for SHG. The thickness of the SiO spacer is shown to be an effective parameter to tune for maximising SHG. Electrical field enhancement at the fundamental wavelength was shown to define the SHG intensity. Numerical modeling of light enhancement was verified by experimental measurements of SHG and reflectivity spectra at the normal incidence. At the plasmonic resonance, SHG is enhanced up to ∼3.5 × 10 times for the optimised conditions.

CW demonstration of SHG spectral narrowing in a PPLN waveguide generating 2.5 W at 780 nm.

Periodically poled lithium niobate (PPLN) waveguides are a proven and popular means for efficient wavelength conversion. However, conventional PPLN waveguides typically have small mode field diameters (MFD) (≲6 µm) or significant insertion and/or propagation losses, limiting their ability to operate at multi-watt power levels. In this work we utilise zinc indiffused PPLN ridge waveguides that have a larger MFD, favourable pump/SHG modal overlap, and low insertion losses. Here for the first time, we have demonstrated continuous wave (CW) spectral narrowing from a PPLN waveguide, both with high efficiency and multi-watt second harmonic generation (SHG). 2.5 W of 780 nm has been produced by SHG of an amplified 1560 nm telecom laser with a device efficiency of 58% in a 4.0-cm long ridge waveguide. We have modelled conversion efficiency and applied experimentally measured waveguide parameters to show excellent agreement to the SHG spectra. Spectral narrowing of the full width half maximum (FWHM) of 35.7% has been measured as the nonlinear drive is increased. This work demonstrates that single-pass, multi-watt, CW SHG at 780 nm is feasible from our PPLN waveguide in the large conversion regime.

Buried Liquid Interfaces as a Form of Chemistry in Confinement: The Case of 4-Dimethylaminobenzonitrile at the Silica-Aqueous Interface.

Time-resolved fluorescence emission and resonance-enhanced second harmonic generation (SHG) spectra were collected from 4-dimethylaminobenzonitrile (DMABN) adsorbed to the aqueous-silica interface in order to identify how strongly associating solvent-substrate interactions change DMABN's photoisomerization properties. In bulk polar solution, DMABN forms an excited twisted intramolecular charge-transfer (TICT) state that emits with a distinctive, solvatochromic fluorescent signature. At the silica-aqueous interface, the TICT fluorescence disappears, similar to DMABN's behavior in nonpolar environments. SHG spectra confirm that the interface is, in fact, polar, and DMABN's unusual fluorescence emission acquired from the interface is attributed to strong hydrogen bonding associations between the water molecules and the silica surface that prevent adsorbate isomerization. Additionally, SHG spectra show a strong resonance at long wavelengths that is unexpected based on bulk absorbance spectra and selection rules for nonlinear hyperpolarizabilities. Using both Zerner's INDO semiempirical and TD-DFT calculations, this spectroscopic behavior is attributed to a combination of strong electric fields present at the aqueous-silica interface and surface-induced changes to DMABN's ground-state molecular structure.

Pump Power Effects on Second Harmonic Stimulated Electromagnetic Emissions During Ionosphere Heating

AbstractDue to the potential for new diagnostic capabilities, there has been renewed interest in the generation of ionospheric stimulated electromagnetic emissions (SEEs) near the second harmonic of the pump frequency (ω0), a process known as second harmonic generation (SHG). Observations of SHG during experiments at the High Frequency Active Auroral Research Program facility in which ω0 was stepped near the third harmonic of the electron gyrofrequency, 3ωce, and the transmit power linearly increased over the heating cycle at each ω0, were reported recently. A key observation was the linkage between SEEs within ±30 Hz of ω0, due to stimulated Brillouin scatter, and within ±30 Hz of 2ω0. This current work reports further High Frequency Active Auroral Research Program observations that compare the time evolution of SEEs including SHG under the following two transmit power conditions (I) linear power ramp (II) maximum available power (2.8 MW). During these experiments, ω0 was stepped near 3ωce and also 2ωce. The results show that SEEs within ±100 Hz of ω0 and 2ω0 are both suppressed within a few seconds when the ionosphere is irradiated with the maximum available power. These SEEs appear to be suppressed before the onset of field‐aligned irregularities at the upper hybrid layer which is not in line with previous reports. Thus, other mechanisms, which are discussed, could possibly be responsible for the observed suppression of stimulated Brillouin scatter and SHG. Some preliminary diagnostics are derived from the SHG spectra temporal evolution by leveraging concepts from the field of laser plasma interactions.