Second Harmonic Generation Efficiency Research Articles

Enhanced Photon-Pair Generation Based on Thin-Film Lithium Niobate Doubly Resonant Photonic Crystal Cavity

In this work, a doubly resonant photonic crystal (PhC) cavity is proposed to enhance second harmonic generation (SHG) efficiency and photon pair generation rate (PGR). Through the exploration of geometry parameters, a band-edge mode within the light cone is identified as the first harmonic (FH) mode, and a band-edge mode outside the light cone is designated as the second harmonic (SH). Subsequently, by increasing the layers of the core region, a heterostructure PhC cavity is designed. The results showcase a doubly resonant PhC cavity achieving a 133/W SHG efficiency and a photon pair generation rate of 3.7 × 108/s. The exceptional conversion efficiency is attributed to the high quality factors Q observed in the FH and SH modes with values of approximately 280,000 and 2100, respectively. The remarkably high Q factors compensate for nonlinear efficiency degradation caused by detuning, simultaneously making the manufacturing process easier and more feasible. This work is anticipated to provide valuable insights into efficient nonlinear conversion and photon pair generation rates.

Observation of Anisotropic Second Harmonic Generation in Two-Dimensional Niobium Diselenide.

The intrinsic anisotropy of NbSe2 provides a favorable prerequisite of second harmonic generation (SHG) and rich possibilities for tailoring its nonlinear optical (NLO) properties. Here we report the highly efficient SHG of mechanically exfoliated NbSe2 flakes. The nonlinear optical response changes with excitation wavelengths, layer thicknesses, and polarizations of the excitation laser. The anisotropic SHG response further exhibits the intrinsic non-centrosymmetric crystal structure and could effectively assign the crystalline orientation of NbSe2 flakes. Interestingly, although NbSe2 flakes with tens of nanometers thickness experience attenuations in SHG performance, more efficient SHG anisotropy ratios were obtained, which are around 4 times higher than that of the 5-layer counterpart. The determined second-order nonlinearities of NbSe2 flakes (monolayer: ∼1.0 × 103 pm/V; 3-layer: ∼73 pm/V) are comparable to those of the commonly reported two-dimensional materials (e.g., MoS2, WSe2, graphene) with the same number of layers and much higher than those of commercial nonlinear optical crystals.

Interfacial Second-Harmonic Generation via Superposition of Symmetries in a Double-Resonance-Enhanced Plasmonic Nanocavity.

Second-harmonic generation (SHG) has rapidly advanced with the miniaturization of on-chip devices and has found many applications, including optical frequency conversion, nonlinear imaging, and quantum technology. However, owing to the obvious phase-matching constraints involved in nonlinear optical interactions in bulk crystals and the decrease in the length and strength of nonlinear interactions in nanophotonic and surface/interface systems, improving the SHG efficiency and manipulating its optical properties at the nanoscale are challenging tasks. Herein, a monocrystalline silver microplate and nanocube-coupled nanocavity with double-resonance plasmonic modes and an ultrasmall gap were constructed, resulting in efficiently enhanced SHG. In particular, the SHG from the silver microplate (111) is polarization-dependent, and the anisotropy of the SHG in the plasmonic nanocavity can be further controlled via the superposition of symmetries at the interface and plasmonic waveguide-cavity modes. The interfacial SHG provides technology for developing lattice surface atomic arrangement and nanostructure rapid characterization, nonlinear light sources, and on-chip nonlinear nanophotonic devices.

CUDA-based focused Gaussian beams second-harmonic generation efficiency calculator

We present an object-oriented programming (OOP) CUDA-based package for fast and accurate simulation of second-harmonic generation (SHG) efficiency using focused Gaussian beams. The model includes linear as well as two-photon absorption that can ultimately lead to thermal lensing due to self-heating effects. Our approach speeds up calculations by nearly 40x (11x) without (with) temperature profiles with respect to an equivalent implementation using CPU. The package offers a valuable tool for experimental design and study of 3D field propagation in nonlinear three-wave interactions. It is useful for optimization of SHG-based experiments and mitigates undesired thermal effects, enabling improved oven designs and advanced device architectures, leading to stable, efficient high-power SHG. Program summaryProgram Title:cuSHGCPC Library link to program files:https://doi.org/10.17632/hn76s7x848.1Developer's repository link:https://github.com/alfredos84/cuSHGLicensing provisions: MITProgramming language:▪, CUDANature of problem: The problem that is solved in this work is that of second-harmonic generation (SHG) performance degradation in a nonlinear crystal with focused Gaussian beams due to thermal effects. By placing the nonlinear crystal in an oven that controls temperature, the package computes the involved electric fields along the medium. The implemented model includes the linear and nonlinear absorption which occasionally lead to self-heating effect, degrading the performance of the SHG.Solution method:: The coupled differential equations for three-wave interactions, which describe the field evolution along the crystal are solved using the well-known Split-Step Fourier method. The temperature profiles are estimated using the finite-elements method. The field evolution and thermal effects are embedded in a self-consistent algorithm that sequentially and separately solves the electromagnetic and thermal problems until the system reaches the steady state. Due to the eventual computational demand that some problems may have, we chose to implement the coupled equations in the ▪/CUDA programming language. This allows us to significantly speed up simulations, thanks to the computing power provided by a graphics processing unit (GPU) card. The output files obtained are the interacting electric fields and the temperature profile, which have to be analyzed during post-processing.

Magnetic modes for enhancing second harmonic generation at ultraviolet frequencies

Enhancing nonlinear frequency conversions at ultraviolet (UV) frequencies holds immense significance in contemporary physics and nanophotonics. In this work, we have theoretically demonstrated a highly efficient UV second-harmonic generation (SHG) in the Al nanorod−LiNbO3 (LN)−Al film nanostructure by two orders of magnitude higher compared to the conventional LiNbO3 nanostructure in this range. This result is acquired by designing a simple Al nanoparticle-Al film plasmonic system that generates magnetic resonances at near-UV frequencies to confine light to the LN, which can highly enhance the electromagnetic field and lead to strong interactions with the large nonlinear susceptibility. Our research provides profound insights into the pivotal role of plasmon-induced magnetic resonance (PIMR) modes in UV-SHG processes, thereby opening up new avenues for the development of nanoscale UV nanosources and nonlinear metasurface applications at subwavelength scale.

An integrated 3C-silicon carbide-on-insulator photonic platform for nonlinear and quantum light sources

Silicon carbide (SiC) polytypes are emerging for integrated nonlinear and quantum photonics due to their wide-bandgap energies, second-order optic nonlinearity and process compatibility with complementary metal-oxide-semiconductor technologies. Among polytypes, 3C-SiC is the only one epitaxially grown on wafer-scale silicon substrates. However, on-chip nonlinear and quantum light sources leveraging the second-order nonlinearity of 3C-SiC have not been reported to our knowledge. Here, we design and fabricate an elliptical microring on 3C-SiC. We demonstrate a nonlinear light source with a second-harmonic generation efficiency of 17.4±0.2%W−1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$17.4\\pm 0.2 \\% {W}^{-1}$$\\end{document} and difference-frequency generation with a signal-idler bandwidth of 97 nm. We demonstrate a spontaneous parametric down-conversion source with a photon-pair generation rate of 4.8 MHz and a coincidence-to-accidental ratio of 3361±84\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3361\\pm 84$$\\end{document}. We measure a low heralded single-photon second-order coherence gH2=0.0007\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${g}_{H}^{\\left(2\\right)}=0.0007$$\\end{document}. We observe time-bin entanglement with a visibility of 86.0±2.4%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$86.0\\pm 2.4 \\%$$\\end{document} using this source. Our work paves a way toward SiC-based on-chip nonlinear and quantum photonic circuits.

Giant enhancement of second harmonic generation via merging bound states in the continuum for vacuum ultraviolet radiation

Vacuum ultraviolet (VUV) light plays a crucial role in various scientific and technological fields, such as nanolithography and biomedical treatments. However, the inherent nonlinear optical coefficient of nonlinear optical crystals is typically very low, and increasing the action length is often necessary to improve the nonlinear conversion efficiency. This makes it challenging for these materials to achieve high-density optoelectronic integration at the micro-/nano-scale. In this study, we propose a design for generating coherent VUV radiation close to 175 nm using second harmonic generation (SHG) with an absolute efficiency exceeding 1.2‰ mW−1. This is achieved by merging multiple bound state in the continuum modes in a free-standing photonic crystal slab. Even with fabrication imperfections at a level lower than 10% disorder, the SHG efficiency of the samples remains robust, maintaining an efficiency of at least 2‰. This research provides a beneficial platform for generating efficient VUV light in the nanoscale.

Efficient second harmonic generation in a high-Q Fabry-Perot microresonator on x-cut thin film lithium niobate.

Microresonators facilitate enhanced light-matter interactions within a limited space, showing great promise for nonlinear optics. Here, we demonstrate a high-quality (Q) factor Fabry-Perot microresonator (FPR) for second harmonic generation (SHG) on an x-cut thin film lithium niobate (TFLN) platform. The FPR exhibits Q factors of Qpump = 1.09 × 105 and QSH = 1.15 × 104 at the 1560 nm pump wavelength and 780 nm second harmonic wavelength, respectively. Under low pump power, a normalized SHG efficiency of 158.5 ± 18.5%/W is attained. We experimentally verify that increased temperatures mitigate photorefractive effects that degrade SHG performance. This work highlights the immense capabilities of one-dimensional planar optical waveguide resonators for efficient on-chip nonlinear wavelength conversion.

Modulating Polarization in Second Harmonic Generation through Symmetry Evolution in Plasmonic Lattices.

We report a strategy for preparing cost-effective plasmonic square lattices with tunable unit structures of circles, crosses, and circle-cross pairs on a centimeter scale. The asymmetrical electromagnetic (EM) field distribution of the lattice enhances second harmonic generation (SHG) under oblique incidence. The SHG signals are progressively strengthened as the unit symmetry decreases from C∞v (circle) to C4v (cross) to C2v (circle-cross pair). The peak SHG signal is observed from the plasmonic lattice with a circle-cross pair, showcasing a conversion efficiency of 1.0 × 10-2, which is a 7.3-fold enhancement relative to the dielectric lattice comprised of circle units. This notably high conversion efficiency of SHG is on par with that of phase-matched bulk nanostructures under normal incidence, benefiting from the Bloch-surface plasmon polariton (Bloch-SPP) modes associated with the distribution of the photonic local density of states (LDOS). Furthermore, the SHG emission exhibits distinctive directional and polarization characteristics as the unit symmetry is reduced. This work offers valuable insights into a structural symmetry-dependent SHG in plasmonic lattices and the way forward for the design of functional nonlinear plasmonic devices.

Double-pass second-harmonic generation of picosecond pulses with custom-poled KTP crystal

We present the double-pass second-harmonic generation (SHG) of picosecond pulses with a custom-poled potassium titanyl phosphate (KTP) nonlinear crystal. The average output power of 466 mW at central wavelength of 515.7 nm is obtained with the input of 1.2 W fundamental laser pulses. Compared to the highest conversion efficiency of 29.1% in the single-pass SHG, the conversion efficiency in the double-pass SHG is increased to 38.8%. Moreover, the average RMS stability of 0.67% in 2 hours and high beam quality (M2 < 1.10) of the second-harmonic pulses is observed. The presented results provide an efficient method to enhance the conversion efficiency of SHG for picosecond pulses.

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

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

Growth, mechanical, thermal, electrical, linear, and nonlinear optical studies of urea resorcinol single crystals for NLO applications

Urea Resorcinol (UR) was synthesized and grown using the slow cooling technique to form a possible organic nonlinear optical crystal. Single crystal X-ray diffraction analysis was used to determine the shape and lattice characteristics of the generated UR crystals. The crystallinity was verified using a high-resolution X-ray diffraction examination. The emission and transparency of the formed crystal were revealed by optical studies including photoluminescence and UV–visible-NIR spectrum analyses. Through the use of an optical microscope and the Vickers microhardness tester, its mechanical behavior was investigated and the density of its etch pits was estimated. The investigations were also conducted on the UR crystal's microphysical properties, including its dielectric tensor, dielectric loss, and thermal analysis. An Nd:YAG laser was used to quantify the laser-induced surface damage and the results were connected to the grown crystal's specific heat capacity. By using the Kurtz and Perry technique, the efficiency of second harmonic generation was determined for different UR crystal particle sizes that have good phase matchability, and its SHG output was compared to urea.

Single crystal of barium bis para-nitrophenolate para-nitrophenol tetrahydrate for NLO applications: crystal growth and DFT analysis

Abstract Single crystals of barium bis para-Nitrophenolate para-Nitrophenol tetrahydrate (BBPNT) were grown via the slow evaporation technique. The crystal dimensions were measured to be 15 mm × 10 mm × 6 mm. The BBPNT crystal was analyzed using X-ray diffraction, FTIR spectrum, UV–vis spectrum, dielectric studies, thermo-gravimetric (TG) differential thermal analyses (DTA), Vickers microhardness test, second-harmonic generation efficiency, Z-scan technique, PL spectra, and laser damage threshold studies. These findings were previously published in our paper. In the current situation, the theoretical methods include analyzing several aspects, such as the molecular structure determined using X-ray experimentation at its lowest energy state. This analysis is then contrasted by means of density functional theory (DFT) with a suitable set of basic functions. The first-order hyperpolarizability may also be determined via the use of Density Functional Theory (DFT) methods. The molecule’s stability, resulting from hyper conjugative interactions, was examined using the natural bond orbital approach to analyses its nonlinear optical activity and charge delocalization. The magnitude of the HOMO–LUMO energy gap indicates the potential for charge transfer inside the molecule. The investigation of donor-acceptor interactions was conducted using NBO analysis based on optimized ground state geometries.

Record Second-Harmonic Generation and Birefringence in an Ultraviolet Antimonate by Bond Engineering.

Oxides have attracted considerable attention owing to their potential for nonlinear optical (NLO) applications. Although significant progress has been achieved in optimizing the structural characteristics of primitives (corresponding to the simplest constituent groups, namely, cations/anions/neutral molecules) comprising the crystalline oxides, the role of the primitives' interaction in determining the resultant functional structure and optical properties has long been underappreciated and remains unclear. In this study, we employ a π-conjugated organic primitive confinement strategy to manipulate the interactions between primitives in antimonates and thereby significantly enhance the optical nonlinearity. Chemical bonds and relatively weak H-bonding interactions promote the formation of cis- and trans-Sb(III)-based dimer configurations in (C5H5NO)(Sb2OF4) (4-HPYSOF) and (C5H7N2)(Sb2F7) (4-APSF), respectively, resulting in very different second-harmonic generation (SHG) efficiencies and birefringences. In particular, 4-HPYSOF displays an exceptionally strong SHG response (12 × KH2PO4 at 1064 nm) and a large birefringence (0.513 at 546 nm) for a Sb(III)-based NLO oxide as well as a UV cutoff edge. Structural analyses and theoretical studies indicate that polarized ionic bond interactions facilitate the favorable arrangement of both the inorganic and organic primitives, thereby significantly enhancing the optical nonlinearity in 4-HPYSOF. Our findings shed new light on the intricate correlations between the interactions of primitives, inorganic primitive configuration, and SHG properties, and, more broadly, our approach provides a new perspective in the development of advanced NLO materials through the interatomic bond engineering of oxides.

Coherent control of enhanced second-harmonic generation in a plasmonic nanocircuit using a transition metal dichalcogenide monolayer

Nonlinear nanophotonic circuits, renowned for their compact form and integration capabilities, hold potential for advancing high-capacity optical signal processing. However, limited practicality arises from low nonlinear conversion efficiency. Transition metal dichalcogenides (TMDs) could present a promising avenue to address this challenge, given their superior optical nonlinear characteristics and compatibility with diverse device platforms. Nevertheless, this potential remains largely unexplored, with current endeavors predominantly focusing on the demonstration of TMDs’ coherent nonlinear signals via free-space excitation and collection. In this work, we perform direct integration of TMDs onto a plasmonic nanocircuitry. By controlling the polarization angle of the input laser, we show selective routing of second-harmonic generation (SHG) signals from a MoSe2 monolayer within the plasmonic circuit. Routing extinction ratios of 14.86 dB are achieved, demonstrating good coherence preservation in this hybrid nanocircuit. Additionally, our characterization indicates that the integration of TMDs leads to a 13.8-fold SHG enhancement, compared with the pristine nonlinear plasmonic nanocircuitry. These distinct features—efficient SHG generation, coupling, and controllable routing—suggest that our hybrid TMD-plasmonic nanocircuitry could find immediate applications including on-chip optical frequency conversion, selective routing, switching, logic operations, as well as quantum operations.

Guanidinium Vanadate [C(NH2)3]3VO4·2H2O Revealing Enhanced Second-Harmonic Generation and Wide Band Gaps.

A new guanidinium-templated vanadate, [C(NH2)3]3VO4·2H2O, has been synthesized in a phase-pure form. It crystallizes in a noncentrosymmetric polar space group, Cc, and the crystal structure is built upon a framework of guanidinium, vanadate tetrahedra, and water molecules linked by hydrogen bonds. Notably, optical measurements reveal that the material exhibits an approximately 9.6-fold enhancement in second-harmonic generation efficiency compared to its phosphate analogue. The enhancement can be attributed to the increased geometrical distortion of the VO4 tetrahedra. Furthermore, we found that the coordination number of the central vanadium atom significantly affects the optical band gaps. Among various coordination numbers, the 4-coordinate VO4 tetrahedra are found to be more favorable for widening the optical band gap of materials compared to the 5- and 6-coordinate vanadium polyhedra, as demonstrated by this work.

AIE‐Active Ferrocene Appended Linear (D‐π‐A) Aromatic Ester Chromophores: Structural, Theoretical and Effect on Phenyl Ring on Luminescence and Nonlinear Optical Properties

AbstractIn the present research, a new ferrocene‐appended linear donor‐π‐acceptor (D‐π‐A) ester chromophore Fc‐(C6H4)2‐COOC2H5 (2) was synthesized and characterized using various spectroscopic techniques. The molecular structure of chromophore 2 was determined using single‐crystal X‐ray diffraction analysis, revealing its crystallization in the monoclinic crystal system with the P21/n space group. The chromophore Fc‐C6H4‐COOC2H4 (1) was utilized to compare its photophysical and nonlinear optical characteristics with those of 2. Cyclic voltammetry revealed a single‐electron transfer mechanism from Fe2+↔Fe3+. The emission solvatochromism studies show a polarized excited state in response to increasing solvent polarity, indicating charge transfer processes. Interestingly, in mixed aqueous media (THF/H2O), the chromophores exhibit intensified fluorescence due to restricted intra‐molecular rotation (RIR), despite weak emission in THF solvent. Chromophore 2 demonstrated 1.5 times higher second harmonic generation (SHG) efficiency than 1, attributed to its extended π‐conjugation from an additional phenyl ring and reduced antiparallel alignments. Despite its centrosymmetric crystal packing, chromophore 2 exhibited SHG efficiency due to non‐covalent interactions (C−H⋅⋅⋅π) in the crystal lattice. Density Functional Theory (DFT) calculations, employing various functionals, provided insights into dipole moment and first hyperpolarizability, with B3LYP‐hybrid functional underestimating hyperpolarizability values owing to long‐range charge transfer interactions within the D‐π‐A systems, aligning closely with experimental findings.

Resonant second-harmonic generation of self-focused oblique incident laser beam in plasma

The present manuscript aims to realize the effect of self-focusing on second-harmonic generation (SHG) by oblique incident laser beams in plasma. When an intense laser beam is obliquely incident on the plasma, it is resolved into reflected and refracted components, and resonant SHG is produced in the reflected component on account of the self-focusing of the incident laser. With the help of paraxial approximation, we have obtained a mathematical expression for the beam width parameter and for the normalized amplitude of the second harmonic. It has been observed that the amplitude of the second-harmonic pulse is significantly influenced by the intensity of the incident laser beam, the wiggler magnetic field, and the normalized plasma frequency. The analysis was performed for different values of the angle of incidence and laser parameters. The results show stronger self-focusing and, hence, efficient SHG when the angle of incidence is the critical angle.

In Situ Chiral Template Approach to Synthesize Homochiral Lead Iodides for Second‐Harmonic Generation

AbstractHomochiral halide perovskites have gained increasing attention because of their fascinating optoelectronic properties and prospective applications in laser technologies. However, the limited choice of chiral organic templates severely restricts their structural diversity and second‐harmonic generation (SHG) effects. Here, we present an in situ chiral template approach for the synthesis of one‐dimensional (1D) homochiral lead iodides. A chiral imine (L‐ipp) template was generated in situ by reacting L‐proline (L‐pro) and acetone under ambient conditions. Notably, L‐ipp can cooperate with L‐pro to direct the formation of a homochiral lead iodide with dual chiral templates, which is unprecedented in crystalline metal halides. The homochiral lead iodide containing both L‐ipp and L‐pro shows a strong SHG response of 8.0 times that of KH2PO4 (8.0×KDP). The SHG efficiency is one of the largest values reported to date for any homochiral lead halides under 1064 nm laser irradiation. A comparative study shows that homochiral 1D lead iodides containing either L‐ipp or L‐pro exhibit relatively weak SHG responses (≤1.0×KDP). This work demonstrates the advantage of using two different chiral templates over a single chiral template in enhancing the SHG responses of halide materials.

In Situ Chiral Template Approach to Synthesize Homochiral Lead Iodides for Second-Harmonic Generation.

Homochiral halide perovskites have gained increasing attention because of their fascinating optoelectronic properties and prospective applications in laser technologies. However, the limited choice of chiral organic templates severely restricts their structural diversity and second-harmonic generation (SHG) effects. Here, we present an in situ chiral template approach for the synthesis of one-dimensional (1D) homochiral lead iodides. A chiral imine (L-ipp) template was generated in situ by reacting L-proline (L-pro) and acetone under ambient conditions. Notably, L-ipp can cooperate with L-pro to direct the formation of a homochiral lead iodide with dual chiral templates, which is unprecedented in crystalline metal halides. The homochiral lead iodide containing both L-ipp and L-pro shows a strong SHG response of 8.0 times that of KH2 PO4 (8.0×KDP). The SHG efficiency is one of the largest values reported to date for any homochiral lead halides under 1064 nm laser irradiation. A comparative study shows that homochiral 1D lead iodides containing either L-ipp or L-pro exhibit relatively weak SHG responses (≤1.0×KDP). This work demonstrates the advantage of using two different chiral templates over a single chiral template in enhancing the SHG responses of halide materials.