Order Nonlinear Response Research Articles

Quantum geometry quadrupole-induced third-order nonlinear transport in antiferromagnetic topological insulator MnBi2Te4

The study of quantum geometry effects in materials has been one of the most important research directions in recent decades. The quantum geometry of a material is characterized by the quantum geometric tensor of the Bloch states. The imaginary part of the quantum geometry tensor gives rise to the Berry curvature while the real part gives rise to the quantum metric. While Berry curvature has been well studied in the past decades, the experimental investigation on the quantum metric effects is only at its infancy stage. In this work, we measure the nonlinear transport of bulk MnBi2Te4, which is a topological anti-ferromagnet. We found that the second order nonlinear responses are negligible as required by inversion symmetry, the third-order nonlinear responses are finite. The measured third-harmonic longitudinal (Vxx3ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${V}_{{xx}}^{3\\omega }$$\\end{document}) and transverse (Vxy3ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${V}_{{xy}}^{3\\omega }$$\\end{document}) voltages with frequency 3ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega$$\\end{document}, driven by an a.c. current with frequency ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega$$\\end{document}, show an intimate connection with magnetic transitions of MnBi2Te4 flakes. Their magnitudes change abruptly as MnBi2Te4 flakes go through magnetic transitions from an antiferromagnetic state to a canted antiferromagnetic state and to a ferromagnetic state. In addition, the measured Vxx3ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${V}_{{xx}}^{3\\omega }$$\\end{document} is an even function of the applied magnetic field B while Vxy3ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${V}_{{xy}}^{3\\omega }$$\\end{document} is odd in B. Amazingly, the field dependence of the third-order responses as a function of the magnetic field suggests that Vxx3ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${V}_{{xx}}^{3\\omega }$$\\end{document} is induced by the quantum metric quadrupole and Vxy3ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${V}_{{xy}}^{3\\omega }$$\\end{document} is induced by the Berry curvature quadrupole. Therefore, the quadrupoles of both the real and the imaginary part of the quantum geometry tensor of bulk MnBi2Te4 are revealed through the third order nonlinear transport measurements. This work greatly advanced our understanding on the connections between the higher order moments of quantum geometry and nonlinear transport.

QuDPy: A Python-based tool for computing ultrafast non-linear optical responses

Nonlinear Optical Spectroscopy is a well-developed field with theoretical and experimental advances that have benefited multiple disciplines, including chemistry, biology, and physics. However, for the accurate interpretation of the corresponding multi-dimensional spectra, there is a need for precise quantum dynamical simulations based on model Hamiltonians. In this article, we present the initial release of our code, QuDPy (Quantum Dynamics in Python), which provides a robust numerical platform for performing quantum dynamics simulations based on model systems, including open quantum systems. A distinguishing feature of our approach is the ability to specify various high-order optical response pathways in the form of double-sided Feynman diagrams through a straightforward input syntax. This syntax outlines the time-ordering of ket-sided or bra-sided optical interactions acting on the time-evolving density matrix of the system. We utilize the quantum dynamics capabilities of QuTip to simulate the spectral response of complex systems, allowing us to compute virtually any n-th order optical response of the model system. To illustrate the utility of our approach, we provide a series of example calculations. Program summaryProgram Title:QuDPyCPC Library link to program files:https://doi.org/10.17632/5xm9pm24cz.1Developer's repository link:https://github.com/sa-shah/QuDPyLicensing provisions: MIT LicenseProgramming language: Python (v3.7)Supplementary material: Available as Google Colab Files.Example 1: https://tinyurl.com/y3j5jmmrExample 2: https://tinyurl.com/37vwntn5External packages:•QuTip (v.4.7) and dependencies i.e. Numpy, Matplotlib (https://qutip.org/)•UFSS Automatic Diagram Generator (https://github.com/peterarose/ufss)Nature of problem: Accurate quantum simulations of complex systems are required in order to understand and interpret multi-dimensional ultrafast spectroscopic signals. This code provides an open-source/multi-platform method that facilitates the generation of higher-order non-linear optical responses for an arbitrary molecular or material system given a model input Hamiltonian and bath model.Solution method: We use the double-sided Feynman diagram method [1, 2] to generate (symbolically) a set of response functions corresponding to the nth order non-linear response of the system to a series of laser pulses using the UFSS package [3] We then perform a series of accurate quantum dynamics calculations using the QuTip package [4] to generate the numerical response and spectra which correspond to specific experimental conditions.

Gravitational response of topological quantum states of matter

Identifying novel topological properties of topological quantum states of matter, such as exemplified by the quantized Hall conductance, is a valuable step towards realizing materials with attractive topological attributes that guarantee their imperviousness to realistic imperfections, disorder and environmental disturbances. Is the gravitational coupling coefficient of topological quantum states of matter a promising candidate? Substantially building on well established results for quantum Hall states, using disclinations as tools for controlled creation of pristine spatial curvature free of undesirable artifacts such as would interfere with the electronic motion of interest, herein we report that a large class of lattice topological states of matter exhibit gravitational response, i.e., charge response to intrinsic spatial curvature. This phenomenon is characterized by a topologically quantized coupling constant. Remarkably, the charge-gravity relationship remains linear in the curvature, up to the maximum curvature achievable on the lattice, demonstrating absence of higher order nonlinear response. Our findings facilitate articulating the physical principles underlying the topological quantization of the gravitational coupling constant, in analogy with the insights offered by the Chern number description of the quantized Hall conductance.

Unravelling the nonlinear ideal density response of many-body systems

Nonlinear density response theory is revisited focusing on the harmonically perturbed finite temperature uniform electron gas. Within the non-interacting limit, brute force quantum kinetic theory calculations for the quadratic, cubic, quartic and quintic responses reveal a deep connection with the linear response. Careful analysis of the static long wavelength limit led us to conjecture a canonical non-interacting form that expresses arbitrary order nonlinear responses as the weighted sum of the linear responses evaluated at all multiple harmonics. This harmonic expansion is successfully validated against ab initio path integral Monte Carlo simulations.

Unifying semiclassics and quantum perturbation theory at nonlinear order

Nonlinear electrical response permits a unique window into effects of band structure geometry. It can be calculated either starting from a Boltzmann approach for small frequencies, or using Kubo’s formula for resonances at finite frequency. However, a precise connection between both approaches has not been established. Focusing on the second order nonlinear response, here we show how the semiclassical limit can be recovered from perturbation theory in the velocity gauge, provided that finite quasiparticle lifetimes are taken into account. We find that matrix elements related to the band geometry combine in this limit to produce the semiclassical nonlinear conductivity. We demonstrate the power of the new formalism by deriving a quantum contribution to the nonlinear conductivity which is of order \tau^{-1}τ−1 in the relaxation time \tauτ, which is principally inaccessible within the Boltzmann approach. We outline which steps can be generalized to higher orders in the applied perturbation, and comment about potential experimental signatures of our results.

Investigational studies of crystalline, optical, dielectric, thermal, mechanical, second besides third order nonlinear optical properties of urea itaconic acid solitary material

In this research work, we used low temperature growth technique (Slow cooling method) for the growth of nonlinear optical and antimicrobial activity of fully-fledged organic Urea Itaconic acid (UITA) crystal. The model was crystallised with a monoclinic crystal structure in the centrosymmetric space group P21/c. The single crystal X-ray diffraction (SXRD) method was used to determine the crystal characteristics of the compounds. To validate the presence of separate functional groups, a Fourier transform infra-red test is utilised. The crystallinity and phase purity of the entire crystal is confirmed by the X-ray diffraction pattern of the detected Bragg peaks. The optical transmission window and shorter UITA wavelength cut-off were established using UV-Vis-NIR studies. Defects were also analysed by the dielectric loss, dielectric constant and AC conductivity studies. The mechanical stability of growing crystal was required to identify using Vickers microhardness analysis and by the Hays-Kendall approach, the effect of hole size (ISE) and the proportional stability model (PSRM) was adequately explained. Using energy dispersion spectrometry, the presence of urea and itaconic acid was confirmed. The differential thermal analysis (DTA) and thermogravimetric (TG) technique were studied by thermal effects of crystal. Using Z scan method the good third order nonlinear response for different planes (1 0 0), (0 0 1) and (1 1 − 1) of the UITA crystal sample were determined. Potentially threatening microbe’s activity utilised to analysis antimicrobial chattels. UITA sample were taken into the solubility and width of the metastable region. The good crystal perfection is showed that the grown crystals using by HRXRD and etching studies. Using on classical nucleation theory, the final nucleation constraints such as phase to phase strain, Gibbs free energy transformation, critical radius, molecular count in the critical nucleus and nucleation rate were calculated for the UITA sample. Second Order NLO behaviour of the grown crystals were confirmed by Kurtz powder procedure.

A first principles study of nonlinear optical properties of a quinoline derivative

AbstractA quinoline derivative, 4‐(quinolin‐2‐ylmethylene)aminophenol was synthesized and structurally characterized by single crystal X‐ray diffraction. The crystal packing behavior and intermolecular interactions were examined by Hirshfeld surface analyses, 2D fingerprint plots and QTAIM analysis. The second order nonlinear response of 4‐(quinolin‐2‐ylmethylene)aminophenol molecule immersed in DMSO was investigated at PCM/DFT/CAM‐B3LYP/6–311++G(d,p) level. Theoretical calculations of the Hyper‐Rayleigh scattering (HRS) first hyperpolarizability were performed using two different procedures, the Sum‐over‐states scheme and the energy derivative method from Gaussian16. The HRS first hyperpolarizability results were compared with obtained for other organic compounds and shown that the 4‐(quinolin‐2‐ylmethylene)aminophenol presents a good nonlinear optical response.

Wafer-Scale Demonstration of Low-Loss (∼0.43 dB/cm), High-Bandwidth (>38 GHz), Silicon Photonics Platform Operating at the C-Band

The key advantage of silicon photonics comes from its potential for large scale integration, in a low-cost and scalable fashion. This has sustained the growth in the area despite disadvantages such as the lack of a monolithic light source, or the absence of a second order non-linear response (χ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(2)</sup> ). Thus far, the work in the field has focused on reporting individual devices from a single die, with excellent performances. Wafer-level results, an area which has not been addressed sufficiently, is a critical aspect of silicon photonics and will provide the community with information regarding scalability and variation, which will be the key differentiating advantage of silicon photonics over other photonic platforms. In this work, we report the development of a low-loss, high-bandwidth C-band silicon photonic platform on a 200 mm CMOS-compatible process line, demonstrating wafer-level performance in the process. Ultra-low waveguide propagation loss with median values as low as 0.43 dB/cm has been achieved. Silicon Mach-Zehnder and microring modulators with median bandwidth of 38.5 and 43 GHz respectively are presented. Finally, germanium waveguide-integrated photodetectors with median bandwidth of 43 GHz are reported. The results reported in this work are comparable to prior demonstrations concerning individual devices. The baseline designs on this platform presented in this work can be accessed commercially from CompoundTek.

Spectroscopic fingerprints of gapped quantum spin liquids, both conventional and fractonic

We explain how gapped quantum spin liquids, both conventional and 'fractonic', may be unambiguously diagnosed experimentally using the technique of multidimensional coherent spectroscopy. 'Conventional' gapped quantum spin liquids (e.g. $Z_2$ spin liquid) do not have clear signatures in linear response, but do have clear fingerprints in non-linear response, accessible through the already existing experimental technique of two dimensional coherent spectroscopy. Type I fracton phases (e.g. X-cube) are (surprisingly) even easier to distinguish, with strongly suggestive features even in linear response, and unambiguous signatures in non-linear response. Type II fracton systems, like Haah's code, are most subtle, and may require consideration of high order non-linear response for unambiguous diagnosis.

Giant Nonlinear Circular Dichroism from Intersubband Polaritonic Metasurfaces.

Nonlinear metasurfaces are advancing into a new paradigm of "flat nonlinear optics" owing to the ability to engineer local nonlinear responses in subwavelength-thin films. Recently, attempts have been made to expand the design space of nonlinear metasurfaces through nonlinear chiral responses. However, the development of metasurfaces that display both giant nonlinear circular dichroism and significantly large nonlinear optical response is still an unresolved challenge. Herein, we propose a method that induces giant nonlinear responses with near-unity circular dichroism using polaritonic metasurfaces with optical modes in chiral plasmonic nanocavities coupled with intersubband transitions in semiconductor heterostructures designed to have giant second and third order nonlinear responses. A stark contrast between effective nonlinear susceptibility elements for the two spin states of circularly polarized pump beams was seen in the hybrid structure. Experimentally, near-unity nonlinear circular dichroism and conversion efficiencies beyond 10-4% for second- and third-harmonic generation were achieved simultaneously in a single chip.

The effect of the sodium content on the structure and the optical properties of thermally poled sodium and niobium borophosphate glasses

Six niobium rich glasses presenting different sodium contents were synthetized. On the basis of complementary infrared and Raman analysis, the influence of the sodium content and its role on the structure of the glasses prior to and following poling was examined. Correlative second harmonic generation (SHG)/Raman microscopy on the poled glasses cross section has shown a co-localization of the SHG signal and the structural variations. It also evidenced similar structural rearrangements whether sodium is removed through poling (230–300 °C) or through the alkali content defined by the starting glass compositions (melted at 1300–1500 °C). The effect of the sodium content on the optical properties, prior to and after thermal poling, is also discussed. It was found that refractive index variations induced by poling (ranging between 10−3 and 3 × 10−2) are mainly the result of a density decrease in the poled region rather than compositional and structural changes. The electro-optic origin of the poling-induced second order nonlinear response is confirmed by the Maker Fringe SHG analysis, and the evolution of χ(2) (2–2.5 pm/V) with the sodium content is discussed based on a selection of parameters influencing either the third order susceptibility [χ(3)] or the internal electric field strength of the poled layer.

The pivotal role of the pyridine ring in enhancing second order nonlinearity in methoxy substituted chalcones

In the present article, the linear and nonlinear optical properties of an organic chalcone derivative, 3-(3,4-dimethoxyphenyl)-1-(pyridin-2-yl) prop-2-en-1-one (DMPP) are examined and relationship between the crystal structure and the material property has been analyzed and the results are presented. The crystal has the ability to transmit wider range of EM radiation. The optical band gap evaluated by plotting Tauc’s graph is 3.08 eV. Third order nonlinear response of the material is studied by the open aperture z scan experiment. The second harmonic generation efficiency obtained by Kurtz experiment is 7.4 times that of urea. The material's NLO response is analyzed with the help of the literature, and it can be concluded that the optimal arrangements of planar molecules in the crystal structure combined by the hydrogen bond interactions result in an increase in SHG efficiency. Further, the role of pyridine ring at the benzoyl arm on the NLO property of methoxy substituted chalcones is also discussed. Due to the wider transparency window and large SH conversion capability, DMPP can be used for various opto electronic applications.

Can second order nonlinear spectroscopies selectively probe optically "dark" surface states in small semiconductor nanocrystals?

Second order nonlinear responses such as sum frequency and second harmonic generation arise from the response of a material system to the second power of an incident electromagnetic field through the material's first hyperpolarizability or second-order optical susceptibility. These quantities are nonzero only for noncentrosymmetric systems, but different length scales of the noncentrosymmetry give rise to second harmonic or sum frequency radiation with different spatial and coherence characteristics. This perspective discusses the possible contributions to the second-order signal from films of small semiconductor quantum dots and addresses whether such experiments are expected to selectively enhance transitions to surface defects or trap states in such systems. It points out how "surface" and "bulk" contributions to the sum frequency or the second harmonic signal should be distinguishable through their angular dependence in a scattering geometry. It also explores possible mechanisms whereby second order spectroscopies might provide access to surface states that are very weak or absent in other forms of optical spectroscopy.

Comparison of Stimuli for Nonlinear System Response Classification

As part of the development of an automated virtual design classification approach for nonlinear structural dynamics, alternative excitation functions are evaluated with respect to their overall performance and efficiency in feature-based response analysis. Robust design of nonlinear structures requires analysis of extensive parameter variations. Both the character of the stimulus and feature metrics used are central to the performance of a response classification approach. The main purpose of this study is to compare stimulus candidates with respect to their efficiency in response classification. A deterministic multilevel, multifrequency stepped-sine periodic test function is used as a baseline. Order-wise differences between generalized and linearized system frequency response functions are evaluated by a selected feature metric to allow categorization into primary, sub and super harmonic responses, as well as odd and even order response distortions. An alternative excitation function type is the pseudorandom phase multi-sine. Its robust variant estimates the best linear approximation of the generalized frequency response function and related nonlinear and noise variances, which can be used for response classification. The fast variant of this method further detects and classifies occurring even and odd order nonlinear responses using a hypothesis test. This article describes the application of these three methods to a virtually running two-piece rotor shaft model. Time response signals from simulated test parameter variations are used to calculate selected nonlinear feature metric values. The total simulation and measurement time, as well as the predictive performance in a few typical nonlinear response cases are evaluated.

Crystal growth, structure and Z-scan studies of novel diisopropylammonium nicotinate crystal

A novel diisopropylammonium nicotinate crystal having third order nonlinear properties was synthesized and grown. In order to obtain insights into the crystalline structure and lattice parameters of the titled new compound, single crystal X-ray diffraction technique was employed. All the molecular interactions present inside the titled crystal were studied by 3D Hirshfeld surface analysis. The suitability of the material in optical applications was supported by UV–Vis and photoluminescence spectroscopy. The titled compound is transparent in the entire visible range having a band gap of 4.08 eV and optical cut-off at 294 nm. Thermal stability of the grown crystal was assessed by TGA/DTA analysis. The third order nonlinear response was estimated by Z-scan technique.

The effects of laser intensities on nonlinear properties for Ag nanoparticles colloid

A huge potential from researchers was presented for enhancing the nonlinear optical response for materials that interacts by light. In this work, we study the nonlinear optical response for chemically prepared nano- fluid of silver nanoparticles in de-ionized water with TSC (Tri-sodium citrate) protecting agent. By the means of self-defocusing technique and under CW 473 nm blue laser, the reflected diffraction pattern were observed and recorded by CCD camera. The results demonstrate that, the Ag nano-fluid shows a good third order nonlinear response and the magnitude of the nonlinear refractive index was in the order of 10−7 cm2/W. We determine the maximum change of the nonlinear refractive index and the related phase shift for the material at six input laser intensities.

I See Your Effort: Force-Related BOLD Effects in an Extended Action Execution-Observation Network Involving the Cerebellum.

Action observation (AO) is crucial for motor planning, imitation learning, and social interaction, but it is not clear whether and how an action execution–observation network (AEON) processes the effort of others engaged in performing actions. In this functional magnetic resonance imaging (fMRI) study, we used a “squeeze ball” task involving different grip forces to investigate whether AEON activation showed similar patterns when executing the task or observing others performing it. Both in action execution, AE (subjects performed the visuomotor task) and action observation, AO (subjects watched a video of the task being performed by someone else), the fMRI signal was detected in cerebral and cerebellar regions. These responses showed various relationships with force mapping onto specific areas of the sensorimotor and cognitive systems. Conjunction analysis of AE and AO was repeated for the “0th” order and linear and nonlinear responses, and revealed multiple AEON nodes remapping the detection of actions, and also effort, of another person onto the observer’s own cerebrocerebellar system. This result implies that the AEON exploits the cerebellum, which is known to process sensorimotor predictions and simulations, performing an internal assessment of forces and integrating information into high-level schemes, providing a crucial substrate for action imitation.

Self-assembled para-Nitroaniline polymeric thin films as highly efficient generators of second harmonic light

Intense well-polarized second harmonic light was generated by para-Nitroaniline self-assembled thin films in different polymeric host matrices. The large area films of the organic chromophore with micron thickness were produced using a modified version of capillary growth. Analysis of the generated second harmonic light indicates that the para-Nitroaniline molecules, which nominally crystalize in a centrosymmetric space group, were organized into structures with an appreciable second order susceptibility dominated by a single tensor element. Under the best conditions, the film's effective second order optical susceptibility is slightly greater than that of beta barium borate for incident light at 800 nm. Generalizing this approach to a broad range of organic molecules with strong individual molecular second order nonlinear responses, but which ordinarily form centrosymmetric organic crystals, could open a new pathway for the fabrication of efficient thin film second harmonic light generators.

Crystal growth, spectroscopic, DFT computational and third harmonic generation studies of nicotinic acid

An organic centrosymmetric nicotinic acid (NA) single crystal has been grown employing slow evaporation method in water. NA crystallizes in monoclinic system with centric space group P21/C. The experimental and theoretical investigation includes vibrational spectra based on Hartree – Fock (HF) and density functional theory (DFT) has been applied using different function at B3LYP level of theory using 6-311G++(d,p) basis set. The optical transparency of the title molecule was examined by TD- DFT analysis and for comparison basis experimental UV–Vis spectrum was recorded. The interaction of charge within the molecule was analyzed and the HOMO - LUMO energy gap was evaluated. The value of dipole moment, Mulliken charge and molecular electrostatic potential were estimated at the same level of theory. Also the first order hyper polarizability for NA was calculated. The dielectric behavior of the grown crystal was determined for few selected temperatures. The third order nonlinear response of NA has been examined using Z-scan technique and nonlinear susceptibility (χ3), nonlinear refraction (n2) and nonlinear absorption coefficient (β) has been calculated. The current results clearly indicate that the title compound is an excellent applicant in the domain of opto – electronic applications.

Efficient second harmonic generation by para-nitroaniline embedded in electro-spun polymeric nanofibres

Intense well polarized second harmonic light was generated by poly(methyl methacrylate) nanofibres with embedded para-nitroaniline nanocrystals. Subwavelength diameter fibres were electro-spun using a 1:2 weight ratio of chromophore to polymer. Analysis of the generated second harmonic light indicates that the para-nitroaniline molecules, which nominally crystalize in the centrosymmetric space group, were organized into noncentrosymmetric structures leading to a second order susceptibility dominated by a single tensor element. Under the best deposition conditions, the nanofibrers display an effective nonlinear optical susceptibility approximately two orders of magnitude greater than that of potassium dihydrogen phosphate. Generalizing this approach to a broad range of organic molecules with strong individual molecular second order nonlinear responses, but which nominally form centrosymmetric organic crystals, could open a new pathway for the fabrication of efficient sub-micron sized second harmonic light generators.