Second Harmonic Generation Wave Research Articles

Optical second harmonic generation in anisotropic multilayers with complete multireflection of linear and nonlinear waves using ♯SHAARP.ml package

Optical second harmonic generation (SHG) is a nonlinear optical effect widely used for nonlinear optical microscopy and laser frequency conversion. Closed-form analytical solution of the nonlinear optical responses is essential for evaluating materials whose optical properties are unknown a priori. A recent open-source code, ♯SHAARP.si, can provide such closed form solutions for crystals with arbitrary symmetries, orientations, and anisotropic properties at a single interface. However, optical components are often in the form of slabs, thin films on substrates, and multilayer heterostructures with multiple reflections of both the fundamental and up to ten different SHG waves at each interface, adding significant complexity. Many approximations have therefore been employed in the existing analytical approaches, such as slowly varying approximation, weak reflection of the nonlinear polarization, transparent medium, high crystallographic symmetry, Kleinman symmetry, easy crystal orientation along a high-symmetry direction, phase matching conditions and negligible interference among nonlinear waves, which may lead to large errors in the reported material properties. To avoid these approximations, we have developed an open-source package named Second Harmonic Analysis of Anisotropic Rotational Polarimetry in Multilayers (♯SHAARP.ml). The reliability and accuracy are established by experimentally benchmarking with both the SHG polarimetry and Maker fringes using standard and commonly used nonlinear optical materials as well as twisted 2-dimensional heterostructures.

Augmentation of surface plasmon-enhanced second harmonic generation from Au nanoprisms on SiO2/Si: interference contribution.

We present an augmentation of Surface Plasmon (SP)-enhanced second harmonic generation (SHG) due to interference field enhancement in Au nanoprisms (AuNPs) on SiO2-coated Si substrates. The SiO2 spacer contributed for the optical interference and increased the coupling efficiency of the pump light with the SP polarization as well as a decoupling efficiency of the SHG waves from nonlinear polarization. The intensity of the SP-enhanced SHG signals increased 4.5-fold with respect to the AuNPs on the bare SiO2 substrate by setting the SiO2 spacer layer to the appropriate thickness. The numerical analysis revealed that the optimal SHG conversion was determined by the balance between the degree of the optical interference at the fundamental and SHG wavelengths.

Phase-matched second-harmonic generation in hybrid polymer-LN waveguides

Here we propose a hybrid polymer-LN waveguide for achieving phase-matched second-harmonic generation (SHG). From the aspect of super-mode theory, the geometric parameters of the hybrid semi-nonlinear waveguide were optimized to utilize both symmetric (even) and antisymmetric (odd) modes of the pump and SHG waves so as to facilitate phase matching with large modal overlap. Phase matching between a fundamental even (TE00-like) mode at 1320 nm and a fundamental odd (TE01-like) mode at 660 nm was found with a calculated modal overlap integral of 0.299, while utilizing the largest nonlinear coefficient d 33, and achieving an efficient calculated normalized conversion efficiency of 148% W−1⋅cm−2. Considering the fabrication feasibility of such hybrid waveguide with features including etchless, large dimension, and low structural sensitivity, we believe our findings would provide a useful reference for future on-chip efficient nonlinear conversion devices.

The role of nonlocal response in second harmonic generation at metasurfaces with triangular metaatoms

Metasurface consisting of square array of obtuse isosceles triangle metaatoms is found to exhibit much more efficient second harmonic generation (SHG) compared to that of split ring resonators and its heptagonal modification, experimentally as well as numerically. All of them are designed to lack inversion symmetry in horizontal direction but to have vertical symmetry, and to meet the double resonance condition for vertically-polarized fundamental and horizontally-polarized SHG waves. SHG efficiencies were estimated numerically for each structure by evaluating an overlap integral of second order nonlinear polarization and field distribution at the SHG wavelength. The large overlap integral for the triangle metasurface is ascribed to the nonlocal response at the SHG wavelength. Current induced at the center of the triangle near the obtuse angle by horizontally polarized light at SHG wavelength flows toward two corners of acute angles. As a result, polarization charges oscillate in time at the surfaces of two acute corners, which results in strong field oscillation away from the center where the electric field is applied to majority of free electrons. Experimentally observed wavelength dependence of SHG efficiencies for the three metasurfaces are reasonably reproduced by a numerical estimation.

Full Complex‐Amplitude Modulation of Second Harmonic Generation with Nonlinear Metasurfaces

AbstractMetasurfaces have shown unprecedented capabilities and flexibilities for optical wave manipulation, which provide a powerful platform for the integration and minimization of multifunctional optical devices. However, the realization of the multidimensional manipulation of harmonic waves generated by nonlinear metasurfaces is still a challenge due to the lack of a theoretical guidance. Here, an efficient design strategy of nonlinear metasurfaces based on the hydrodynamic model of the free electron dynamics is demonstrated to realize the full complex‐amplitude modulation of the second harmonic generation (SHG). As a proof concept, three multifunctional nonlinear metasurfaces are designed, in which both the amplitude and the phase of the SHG waves are efficiently and independently manipulated. With numerical and experimental validations, the proposed nonlinear metasurfaces can realize the spin‐selective SHG optical vortices with independent topological charges. The design strategy of nonlinear metasurfaces shall boost the applications of nonlinear metasurfaces in optical information, optical multifunctional integration, and so on.

Study of fundamental wave depletion in intracavity second harmonic generation.

In this paper, a novel approach to modelling intracavity second harmonic generation (SHG) in periodically poled MgO-doped lithium niobate (PPLN) is presented and verified against experimental results. This approach involves combining the coupled nonlinear wave equations with a rate equation model for a diode-pumped solid-state Nd:YVO4 laser, taking into account both the depletion of the fundamental wave due to the energy conversion from the fundamental wave to the SHG wave and the reduction of the fundamental wave within a laser cavity due to the loss as a result of the SHG nonlinear process. It was shown that the theoretical simulation matched the experimental results well, while also providing physical insight into the importance of the fundamental wave depletion in the intracavity SHG nonlinear processes. The resulting model is computationally simple and has the potential to generalize to the other nonlinear processes such as three-wave mixing and optical parametric oscillation.

Second-harmonic generation spectroscopy in gold nanorod-based epsilon-near-zero metamaterials.

The interest in hyperbolic metamaterials is fueled by fascinating optical properties exhibited by this class of artificial media. Their optical features originate from hyperbolic dispersion emerging due to the shape anisotropy of the metal-dielectric composite. In this work, we study experimentally and numerically the second-harmonic generation (SHG) in ordered arrays of Au nanorods embedded in porous aluminum oxide. Strong increase of the SHG intensity in the vicinity of the epsilon-near-zero (ENZ) spectral point accompanied by dramatic phase modulation of the SHG wave is revealed. These effects are attributed to resonant enhancement of the electric field of the light wave and transition from the elliptical to hyperbolic dispersion law in hyperbolic metamaterials near the ENZ point.

Second harmonic conversions of surface-plasmon-polariton–enhanced optical fields in nonlinear optics polymer/Ag/glass structures

Optical fields enhanced by surface plasmon polaritons (SPPs) on metal-dielectric interfaces are useful for increasing several light-matter interactions, and application to nonlinear optics (NLO) is one of the most important uses of this type of structure. Most previous studies on this subject took advantage of the nonlinear susceptibilities of metal surfaces. However, the limited NLO light-matter interaction lengths prevented the transfer of the technologies to practical use. In the present paper, we tried to overcome this problem by growing NLO polymer thin films on metal surfaces. The NLO responses of the system were characterized by second-harmonic generation (SHG) spectroscopy. Our experimental results suggested that SPP-enhanced optical fields induced not only surface nonlinearities in Ag but also bulk nonlinearities in NLO polymer. There was an optimal polymer thickness for the SHG conversions, and a greater thickness did not always result in higher conversion. The maximum conversion efficiency was approximately 40 times higher than that of the nonpolymer-coated bare Ag surface. The growth and propagation of the SHG waves were addressed with a numerical approach combining the transfer matrix method and Green's function analysis. The SHG conversion efficiencies were determined by three factors, the SPP-field enhancement factor, the nonlinear light-matter interaction length, and the degree of interference between the forward- and backward-propagating SHG waves. The latter two factors predominantly determined the optimal SHG conversion efficiencies. The proposed strategy of hybridizing NLO polymers brings us closer to practical uses for nonlinear plasmonics.

Full vectorial feature of second-harmonic generation with full Poincaré beams

We demonstrate the full vectorial feature of second-harmonic generation (SHG), i.e., from infrared full Poincare beams to visible full Poincare beams, based on two cascading type I phase-matching beta barium borate crystals of orthogonal optical axes. We visualize the structured features of the vectorial SHG wave by using Stokes polarimetry and show the interesting doubling effect of the polarization topological index, i.e., a low-order full Poincare beam is converted to a high-order one. However, the polarization singularities of both C points and L lines are found to keep invariant during the SHG process. Our scheme could offer a deeper understanding on the interaction of vectorial light fields with media and can be generalized to other nonlinear optical effects.

Polarized second-harmonic-generation spectroscopy for Au nanorods arrayed on SiO2 substrates at localized surface plasmon resonances

Polarized second-harmonic-generation (SHG) spectroscopy was studied for Au nanorods arrayed on fused silica substrates at localized surface plasmon (LSP) resonances. The geometry of the nanorods is centrosymmetric and electric dipolar second-order nonlinearities are forbidden for such a geometry. However, second-order nonlinearities are permitted for rods with sizes comparable to light wavelengths by taking advantage of the field retardation effect across the rods. In the study, we demonstrated SHG by photoexciting nanorods at an oblique incidence in two optical configurations. Independent of the configuration, efficient SHG was obtained when the excitation light was polarized in the LSP direction. The SHG waves were p-polarized, irrespective of the configuration and the excitation light polarization. The polarization behaviors were well reproduced by using numerically simulated field distributions. This comprehensive study classified the roles of the field retardation in the second-order nonlinearities of Au nanorods.

Ultrathin Nonlinear Metasurface for Optical Image Encoding.

Security of optical information is of great importance in modern society. Many cryptography techniques based on classical and quantum optics have been widely explored in the linear optical regime. Nonlinear optical encryption in which encoding and decoding involve nonlinear frequency conversions represents a new strategy for securing optical information. Here, we demonstrate that an ultrathin nonlinear photonic metasurface, consisting of meta-atoms with 3-fold rotational symmetry, can be used to hide optical images under illumination with a fundamental wave. However, the hidden image can be read out from second harmonic generation (SHG) waves. This is achieved by controlling the destructive and constructive interferences of SHG waves from two neighboring meta-atoms. In addition, we apply this concept to obtain gray scale SHG imaging. Nonlinear metasurfaces based on space variant optical interference open new avenues for multilevel image encryption, anticounterfeiting, and background free image reconstruction.

Cascaded third-harmonic generation with one KDP crystal.

For KH₂PO₄ (KDP) crystal, the phase-matching directions of type-II second-harmonic generation (SHG) and type-II third-harmonic generation (THG) for 1μm lasers are almost identical, i.e., at (θ=60°, φ=0°) around. Utilizing this special property, we designed a THG converter based on one KDP crystal. A quarter-wave (λ/4) plate was used to adjust the polarization of the SHG wave, and a round-trip optical path was used to realize the SHG and THG procedures successively. When the fundamental light source was a 1064nm, 40ps pulse laser, the maximum THG output at 355nm was 1.13mJ, and the highest THG conversion efficiency was 30.7%. To the best of our knowledge, this is the first time that the cascaded frequency upconversion processes are realized in one bulk nonlinear optical crystal. This method possesses many advantages for future applications, including high efficiency, a wide-working waveband, low cost, and applicability to many other crystals such as DKDP, ADP, DADP, and Gd_xY_1-xCOB.

Phase matching of backward second harmonic generation assisted by lattice structure in collagen tissues.

Phase matching of backward second harmonic generation (SHG) in a periodic structure of collagen fibrils is investigated through theoretical modeling, simulation, and experiments. The lattice structure of collagen fibrils is considered to provide a virtual momentum for assisting the phase matching of backward SHG. Phase matching over a relatively wide excitation wavelength range is achieved by tilting the angle of the fundamental excitation and SHG wave vectors. The SHG intensity in the periodic structure is simulated to quantify the phase matching effect. The effect of the fundamental excitation and the SHG emission angles on the peak excitation wavelength of the SHG excitation spectrum is further validated in experiments, where the excitation and emission angles are controlled by spatial filtering. It is found that an optimized excitation wavelength exists for a certain collagen fibril structure, which shifts toward a shorter wavelength when the excitation and emission angles are increased. Our results show that the lattice structure of collagen fibrils can assist the phase matching, providing a mechanism for generating backward SHG in multiphoton microscopy.

Surface second-harmonic generation based on periodically poled LiNbO3 nonlinear optical crystal

We have generated a second-harmonic generation (SHG) of a Q-switched microchip Nd:YAG laser on the surface of a periodically poled LiNbO3 (PPLN) nonlinear crystal near the grazing incidence angle. Three individual SHG waves as transmitted homogeneous, inhomogeneous and reflected radiations have been generated and their intensities are measured and characterized within a desirable range of about 10 different incidence angles of the Nd:YAG laser as pump source on the PPLN surface. The basic of surface nonlinear radiation is also investigated and similar results are calculated and extracted from the theory. Comparison between calculated and measured data shows that they are in good agreement with each other.

High-Power, Highly Efficient Second-Harmonic Generation in a Periodically Poled ${\hbox {MgO}}{:}{\hbox {LiNbO}}_{3}$ Planar Waveguide

We designed a single-pass quasi-phase-matched second-harmonic generation (SHG) device with a planar waveguide; the device comprised a Y-cut 5 mol% MgO-doped LiNbO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> (MgO:LiNbO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> ) crystal core that was 3 mum thick and SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> cladding. The waveguide provided a high coupling efficiency of 95% between an incident Gaussian beam and the fundamental guided mode of a fundamental wave; it also provided high electric-field confinement in the case of both the fundamental and SHG waves in the core. Thus, a high overlap between nonlinear polarization and an SHG-guided mode was attained. The bonding of the device with the waveguide side positioned downward to a heat sink provided a large heat radiation area when pumping with a near-collimated Gaussian beam, which reduced the temperature rise and its gradient along the waveguide to minimize the phase mismatch. We demonstrated the green light generation of 1.6 W with 40% conversion efficiency using a 7-mm-long sample and 1.2-W SHG with 60% efficiency using an 18-mm-long sample.

Enhancement of second harmonic generation in helical Scliquid crystals

Abstract In a ferroelectric liquid crystal, a special type of phase-matching for optical second harmonic generation (SHG) is possible, where two counter-propagating fundamental waves create second harmonic waves at the edge of the selective reflection band. We compute the SHG intensity in such a situation and show that, at slight detuning from exact phase-matching, useful resonance enhancement can be obtained. A considerable amount of SHG also appears when the second harmonic frequency is in the reflection band, where the SHG wave is non-propagating.

In‐situ SHG Studies of Ionic and Molecular Adsorption on Surface Structure of Au(111)‐Electrodes

AbstractWe report on the application of Second Harmonic Generation (SHG) to in‐situ studies of the influence of bromide and pyridine adsorption on surface reconstruction of Au(111) electrodes (Au(111)‐(√3 x 23)), and on the potential induced reorientation of adsorbed pyridine molecules. In the latter case a phase transition in the adsorbate layer has been observed which is accompanied by a significant phase shift of the emitted SHG wave, indicating changes of surface electronic levels upon adsorption of pyridine.