Second-order Nonlinear Optical Susceptibility Research Articles

Designing a 2D van der waals oxide with lone-pair electrons as chemical scissor

Abstract 2D van der Waals (vdW) materials are known for their intriguing physical properties, but their rational design and synthesis remain a great challenge for chemists. In this work, we successfully synthesized a new non-centrosymmetric oxide, i.e. InSbMoO6, with Sb3+ lone-pair electrons serving as chemical scissor to generate its 2D vdW crystal structure. Monolayer and few-layer InSbMoO6 flakes are readily obtained via facile mechanical exfoliation. They exhibit strong second-harmonic generation (SHG) response with an effective second-order nonlinear optical susceptibility $\chi _{{\rm{eff}}}^{{\rm{(2)}}}\ $of 32.4 pm·V−1. Meanwhile, the SHG response is in-plane anisotropic and directly proportional to the layer thickness, independent of layer parity. In addition, the InSbMoO6 flakes exhibit excellent thermal and atmospheric stability, along with pronounced anisotropy in Raman spectroscopy. This work implies that using lone-pair electrons as chemical scissor is an effective strategy for designing and synthesizing new 2D vdW materials for integrated photonic applications.

Generation of second harmonic at wide conversion band in GRIN multimode fibers

Optical poling of multimode graded-index fibers (GRIN) has emerged as a promising technique for creating periodic inscriptions of the second-order nonlinear optical susceptibility χ(2), enabling the generation of a second harmonic in silica fibers. In this work, we investigate the generation of multiple spectral peaks using a continuous broadband source in the infrared domain, generated in the same fiber by a femtosecond laser with a central wavelength different from the one used for the poling process. Building upon theoretical foundations, this work contributes at explaining how second and third-order nonlinear processes participate to the broad generation of the second harmonic in GRIN fibers.

Zinc metal complexes synthesized by a green method as a new approach to alter the structural and optical characteristics of PVA: new field for polymer composite fabrication with controlled optical band gap.

The current study employed a novel approach to design polymer composites with modified structural and declined optical band gaps. The results obtained in the present work for polymer composites can be considered an original method to make a new field for research based on green chemistry. Natural dyes extracted from green tea were mixed with hydrated zinc acetate (Zn(CH3COO)2·2H2O) to produce a metal complex. FTIR results comprehensively established the formation of the Zn-metal complex. The interaction among various components of PVA : Zn-metal complex composite was investigated using FTIR spectroscopy. The non-existence of anion bands of acetate in the Zn-metal complex spectrum confirms the formation of the Zn-metal complex. XRD analysis reveals that the Zn-metal complex improves the amorphous phase of the PVA-based composites. The absorption edge of the doped films shifted towards the lower photon energies. Optical dielectric properties were used to determine N/m*, ε ∞, τ, μ opt, ω p, and ρ opt; the W-D model was used to calculate E d, E o and n o parameters. The optical dielectric loss parameter was used to determine the optical band gap while the Tauc model was employed to identify various types of electron transitions. The optical energy band gap was 6.05 eV for clean PVA while it decreased to 1 eV for PVA inserted with the Zn-metal complex. The increase in Urbach energy from 0.26 eV to 0.45 eV is an evidence of the boost of amorphous phases in PVA : Zn-metal complex composites. The nonlinear refractive index and the first-order and second-order nonlinear optical susceptibilities were determined. The value of E o obtained from the W-D model closely matches the optical energy band gap obtained from the Tauc model, which indicates the precision of the analysis in the present study. The increase in SELF and VELF in the composite films establishes that new energy states assigned to the added Zn-metal complex amplify the probability of light-matter interaction.

Absolute local conformation of poly(methyl methacrylate) chains adsorbed on a quartz surface.

Polymer chains at a buried interface with an inorganic solid play a critical role in the performance of polymer nanocomposites and adhesives. Sum frequency generation (SFG) vibrational spectroscopy with a sub-nanometer depth resolution provides valuable information regarding the orientation angle of functional groups at interfaces. However, in the case of conventional SFG, since the signal intensity is proportional to the square of the second-order nonlinear optical susceptibility and thereby loses phase information, it cannot be unambiguously determined whether the functional groups face upward or downward. This problem can be solved by phase-sensitive SFG (ps-SFG). We here applied ps-SFG to poly(methyl methacrylate) (PMMA) chains in direct contact with a quartz surface, shedding light on the local conformation of chains adsorbed onto the solid surface. The measurements made it possible to determine the absolute orientation of the ester methyl groups of PMMA, which were oriented toward the quartz interface. Combining ps-SFG with all-atomistic molecular dynamics simulation, the distribution of the local conformation and the driving force are also discussed.

Interband second-order nonlinear optical susceptibility of asymmetric coupled quantum wells

Asymmetric molecular bonds possess a microscopic second-order nonlinear optical polarizability p(2). Crystals built from them possess a macroscopic second-order nonlinear optical susceptibility, χ(2), if their structure lacks centrosymmetry. χ(2) can be enhanced by introducing additional asymmetry at the meta-structural level. Here, we use a dipole matrix formalism to calculate χ(2) of asymmetric GaAs/AlGaAs coupled quantum well structures at telecommunication frequencies, for which interband (rather than previously considered intersubband) optical transitions govern optical nonlinearities. Using unit cell and envelope wavefunctions and considering all possible transitions between two bound electron and two bound hole states, we predict tenfold enhancement in χ(2) in previously underexplored ranges of quantum well asymmetry and coupling barrier thickness. This work paves the way toward enhanced, tailorable second-order optical nonlinearities for semiconductor digital alloy and superlattice structures.

Berry Curvature Dipole Induced Giant Mid-Infrared Second-Harmonic Generation in 2D Weyl Semiconductor.

Due to its inversion-broken triple helix structure and the nature of Weyl semiconductor, 2D Tellurene (2D Te) is promising to possess a strong nonlinear optical response in the infrared region, which is rarely reported in 2D materials. Here, a giant nonlinear infrared response induced by large Berry curvature dipole (BCD) is demonstrated in the Weyl semiconductor 2D Te. Ultrahigh second-harmonic generation response is acquired from 2D Te with a large second-order nonlinear optical susceptibility (χ(2) ), which is up to 23.3 times higher than that of monolayer MoS2 in the range of 700-1500nm. Notably, distinct from other 2D nonlinear semiconductors, χ(2) of 2D Te increases extraordinarily with increasing wavelength and reaches up to 5.58nmV-1 at ≈2300nm, which is the best infrared performance among the reported 2D nonlinear materials. Large χ(2) of 2D Te also enables the high-intensity sum-frequency generation with an ultralow continuous-wave (CW) pump power. Theoretical calculations reveal that the exceptional performance is attributed to the presence of large BCD located at the Weyl points of 2D Te. These results unravel a new linkage between Weyl semiconductor and strong optical nonlinear responses, rendering 2D Te a competitive candidate for highly efficient nonlinear 2D semiconductors in the infrared region.

Crystal structure, electronic structure, and optical properties of Cu4ZnGe2S7 and Cu4CdGe2S7: Polar diamond-like semiconductors exhibiting second harmonic generation

The novel I4-II-IV2-VI7 quaternary diamond-like semiconductors (DLSs), Cu4ZnGe2S7 and Cu4CdGe2S7, were prepared from the constituent elemental powders at elevated temperatures. Cu4ZnGe2S7 crystallizes in the polar, chiral space group C2 and adopts the Cu4NiSi2S7 structure-type, which can be considered a derivative of the cubic diamond structure. The cadmium analog takes on the Cu5Si2S7 structure-type, which is related to the hexagonal diamond structure, and displays polar, Cc space group symmetry. Both compounds contain [Ge2S7]6- anions created by corner-sharing GeS4 tetrahedra. The crystal structures were carefully evaluated using: 1) extended connectivity tables, 2) minimum bounding ellipsoid analysis, and 3) bond valence sum (BVS) and global instability index (G) calculations. Both compounds are thermally stable up to temperatures exceeding 950 °C and melt incongruently. As assessed using diffuse reflectance spectroscopy, Cu4ZnGe2S7 and Cu4CdGe2S7 possess optical bandgaps of 1.65 eV and 1.90 eV, respectively, which are narrower than the analogous I2-II-IV-VI4 DLSs. Electronic structure calculations show that both compounds are direct-bandgap semiconductors with significant contributions of Cu-d and S-p orbitals to the states at the top of the valence band. While Cu4CdGe2S7 displays a weak second harmonic generation (SHG) response, the second-order nonlinear optical susceptibility, χ(2), of Cu4ZnGe2S7 is 14.8 ± 1.5 pm V-1, assessed using the Kurtz-Perry powder method and an optical-grade AgGaSe2 (AGSe) reference. Both compounds exhibit laser-induced damage threshold values similar to AGSe, ∼0.1 GW cm-2, for λ = 1.064 µm using picosecond laser pulses. Most importantly, Cu4ZnGe2S7 exhibits a phase-matching behavior at λ = 3.1 µm. These results suggest that Cu4ZnGe2S7 holds potential for use in low-powered laser applications involving efficient wave mixing in the mid-IR region.

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

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

Generation of a coherent squeezed like state defined with the Lie--Trotter product formula using a nonlinear photonic crystal

Abstract In this paper, we investigate how to generate coherent squeezed like light using a nonlinear photonic crystal. Because the photonic crystal reduces the group velocity of the incident light, if it is composed of a material with a second-order nonlinear optical susceptibility $\chi^{(2)}$, the interaction between the nonlinear material and the light passing through it strengthens and the quantum state of the emitted light is largely squeezed. Thus, we can generate a coherent squeezed like light with a resonating cavity in which the nonlinear photonic crystal is placed. This coherent squeezed like state is defined with the Lie--Trotter product formula and its mathematical expression is different from those of conventional squeezed coherent states. We show that we can obtain this coherent squeezed like state with a squeezing level $15.9$ dB practically by adjusting physical parameters for our proposed method. Feeding the squeezed light whose average number of photons is given by one or two into a beam splitter and splitting the flow of the squeezed light into a pair of entangled light beams, we estimate their entanglement quantitatively.
This paper is a sequel to H.~Azuma, J. Phys. D: Appl. Phys. \textbf{55}, 315106 (2022).

Second order nonlinear optical properties of poled films containing azobenzenes tailored with azulen-1-yl-pyridine

Azo compounds, which are highly versatile molecules, have attracted a considerable attention both for their fundamental properties and for practical applications, especially in photonics. The conjugated azo-aromatic systems containing 4-(R-azulen-1-yl)-2,6-dimethyl-pyridine were investigated for their nonlinear optical properties. These molecules were embedded in polymethyl methacrylate (PMMA) matrix, and the obtained guest-host systems were processed into good optical quality thin film by spin coating technique. The dipolar moments of dissolved in PMMA molecules were oriented by applying a high DC electric field at a temperature close to the polymer glass transition temperature. The second - order nonlinear optical (NLO) properties of poled films were studied by the optical second harmonic generation technique (SHG). The poling kinetics, studied by in situ SHG as well as the measured second-order NLO susceptibilities of poled films are reported and discussed.

First-principles evaluation of the second harmonic generation response of reference organic and inorganic crystals.

Using the CRYSTAL17 package at the coupled-perturbed Kohn-Sham (CPKS) level, periodic boundary conditions first-principles calculations are enacted to predict the second harmonic generation second-order nonlinear optical (NLO) susceptibility, χ(2), values of six historical NLO crystals. This selection allowed the comparison between state-of-the-art calculations and experiment. Several computational aspects are tackled to define conditions where the results are converged with respect to the range of lattice summations, to the number of k-points in the first Brillouin zone, to the order of the multipole expansions for evaluating the long-range part of the electrostatic interactions, as well as to the atomic basis set size. A valence triple zeta basis set supplemented with polarization functions has been selected. Then, χ(2) calculations have been performed using a range of exchange-correlation functionals (XCFs). Results show the large impact of the amount of Hartree-Fock (HF) exchange on the amplitude but also on the signon the χ(2) tensor components. To a given extent, these amplitude effects are consistent with results on molecules, but the signreversal effects and the non-monotonic behavior of the χ(2) tensor components as a function of the amount of HF exchange are scarcely found for molecules. Then, using the recommended range-separated hybrid XCFs, the CPKS scheme leads to good agreement with experimental data for potassium dihydrogenophosphate, urea, and χZXX (2) of LiNbO3. The agreement is more questionable for χZZZ (2) of LiNbO3 whereas it remains poor for ammonium dihydrogenophosphate and 2-methyl-4-nitroaniline, with large underestimations by about a factor of 3, opening a path to further fine-tuning of the ranges of inclusion of HF exchange.

Experimental and Theoretical Heterodyne-Detected Sum Frequency Generation Spectroscopy of Isotopically Pure and Diluted Water Surfaces.

The χ(2) (second-order nonlinear optical susceptibility) spectrum of the water surface has been a matter of debate for a few decades. Here, we report that we experimentally measured the isotopic dilution dependence of the χ(2) spectrum and theoretically reproduced it by employing the quantum/classical mixed approach with a new idea to subtract an artifact. The present theoretical framework allows for clarifying the effects of the intramolecular, intermolecular, and Fermi resonance couplings on the OH-stretch vibrational spectra of water at the surface as well as in the bulk.

Generation of entangled photons with a second-order nonlinear photonic crystal and a beam splitter

We discuss the generation of entangled photons using a nonlinear photonic crystal and beam splitter. In our method, the photonic crystal is assumed to be composed of a material with a large second-order nonlinear optical susceptibility . Our proposal relies on two facts: (1) A nonlinear photonic crystal changes coherent incident light into squeezed light. (2) A beam splitter transforms the squeezed light into entangled light beams flying in two different directions. We estimate the yield efficiency of pairs of entangled photons per pulse of the very weak coherent light for our method at 0.0783 for a specific concrete example. Our method is more effective because the conversion efficiency (entangled biphotons per incident pump photons) in the spontaneous parametric downconversion is of the order of . The only drawback is that it requires very fine tuning of the frequency of signal photons fed into the photonic crystal; for example, an adjustment is given by Hz for the signal light of Hz. We investigate the application of entangled photons produced by our method to the BB84 quantum key distribution protocol, and we explore how to detect an eavesdropper. We suggest that our method is promising for decoy-state quantum key distribution using weak coherent light.

Efficient Second-Harmonic Generation in Si-GaP Asymmetric Coupled-Quantum-Well Waveguides

We present a theoretical investigation of efficient second harmonic generation in the cubic lattice-matched N-doped Si/GsP multiple quantum well system integrated in a strip waveguide in the silicon-on-insulator platform. A “giant” second-order nonlinear optical susceptibility is obtained in an asymmetric coupled quantum well (ACQW) stack by engineering the 1-2 and 1-3 inter-subband spacings for resonance at both a ∼4 μm pump wavelength and a ∼2μm harmonic wavelength. Generation has been simulated as a function of the quantum well physical parameters, the infrared absorption losses, and the detuning from the double resonance condition. For TM pumps at 3.75 μm and 4.24 μm, a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\boldsymbol{\chi }}_{{\bm{zzz}}}^{(2)}$</tex-math></inline-formula> value ranging from 7.73 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> pm/V to 1.13 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> pm/V has been calculated and a maximum conversion efficiency ranging between 1.23%/W and 1.68%/W has been obtained, where the waveguide coherence length was 5.57 μm and 6.16 μm.

Optimization of second-order nonlinear optical susceptibilities in 1D GaN photonic crystal

We report the modeling and optimization of 1D periodic structures for second-order nonlinear effects. We present the work done in modeling to determine the location of the electromagnetic field in periodic structures. This modeling, carried out in a simple one dimension, makes it possible to mastery the properties of these structures and to study the influence of the different physical parameters on these properties. It allowed us to optimize structures for second-order nonlinear effects by focusing on the two essential factors of nonlinear polarization intensity and phase matching. This study, carried out in 1D structures, was extended to 1D planar structures (called 1.5D) used in guided optics and applied to the design of a 1.5D photonic crystal structure made in a Gallium Nitride layer for the second harmonic generation.

Nonlinear optical properties of a new polar bismuth tellurium oxide fluoride, Bi3F(TeO3)(TeO2F2)3

A novel noncentrosymmetric polar bismuth tellurium oxide fluoride, Bi3F(TeO3)(TeO2F2)3, has been hydrothermally synthesized by using Bi2O3, TeO2, and HF solution at 230 °C. The structural backbone of Bi3F(TeO3)(TeO2F2)3 is composed of several polyhedra with lone pair cations, such as BiO6F3, TeO2F2, and TeO3. The asymmetric geometric features found from the polyhedra of Bi3+ and Te4+ should be attributed to the lone pairs on the cations. The overall framework of Bi3F(TeO3)(TeO2F2)3 can be considered as a three-dimensional hexagonal tungsten oxide-like topology. The UV–vis diffuse reflectance spectral data suggest that the title compound has a wide band gap of ca. 3.85 eV due to the distortions of the asymmetric units, as well as the electronegative fluoride anions. Second-harmonic generation (SHG) measurements using a 1064 nm radiation indicate that Bi3F(TeO3)(TeO2F2)3 reveals a nonphase-matching behavior and ca. 9 times larger SHG counts than that of α-SiO2. The near-static value of the second-order nonlinear optical susceptibility, χS(2), of the reported compound is calculated to be ca. 5.1 ± 0.6 pm/V. The wavelength-dependent SHG measurements indicate that the SHG counts of Bi3F(TeO3)(TeO2F2)3 decrease as the excitation wavelength increases from 1064 to 1600 nm.

Second‐Order Optical Response in Electrically Polarized Sodo‐Niobate Amorphous Thin Films: Particularity of Multilayer Systems

Herein, our attention is focused on the second‐order optical properties of thermally poled sodo‐niobate amorphous thin films through an original methodology that combines both macroscopic and microscopic second harmonic generation techniques. By probing the geometry and the magnitude of the second‐order nonlinear (SONL) optical response at different scales, a key aspect of thin film's poling mechanisms compared with bulk glasses is demonstrated that lies in the appearance of a charge accumulation at the film/substrate interface and that is described by the Maxwell–Wagner effect. A way to minimize this effect is then proven by promoting an induced built‐in static field in the plane of the film using a microstructured electrode. A SONL optical susceptibility as high as 29 pm V−1 is measured and its geometry and location are controlled at the micrometer scale; it constitutes an improvement of at least one order of magnitude compared with other poled amorphous inorganic materials and is comparable with that of lithium niobate single crystal.

Current-induced second harmonic generation of Dirac or Weyl semimetals in a strong magnetic field

We theoretically investigate the second harmonic generation (SHG) of Dirac or Weyl semimetals under parallel DC electric and strong magnetic fields using the Boltzmann equation approach. The DC current-induced SHG process originates from the optical intraband transitions of the Landau subbands. It is a remarkable fingerprint of three-dimensional Dirac or Weyl dispersions and absent in other materials. An analytical formula for the SHG tensor is derived, and it shows chirality independence. The second-order nonlinear optical susceptibility is proportional to the DC field, giving strong optical nonlinearity up to ${10}^{5}\phantom{\rule{0.28em}{0ex}}\mathrm{pm}/\mathrm{V}$ with THz light, which is several orders larger than that of the usual materials. More interesting, the second harmonic conductivity is found to exhibit periodicity in magnetic field $1/B$ oscillations, which are similar to the Shubnikov--de Haas oscillations. Thus our work proposes another approach for SHG and potential applications of Dirac or Weyl semimetals in nonlinear optics.

Characterization of pathological thyroid tissue using polarization-sensitive second harmonic generation microscopy

AbstractPolarization-sensitive second harmonic generation (SHG) microscopy is an established imaging technique able to provide information related to specific molecular structures including collagen. In this investigation, polarization-sensitive SHG microscopy was used to investigate changes in the collagen ultrastructure between histopathology slides of normal and diseased human thyroid tissues including follicular nodular disease, Grave's disease, follicular variant of papillary thyroid carcinoma, classical papillary thyroid carcinoma, insular or poorly differentiated carcinoma, and anaplastic or undifferentiated carcinoma ex vivo. The second-order nonlinear optical susceptibility tensor component ratios, χ(2)zzz′/χ(2)zxx′ and χ(2)xyz′/χ(2)zxx′, were obtained, where χ(2)zzz′/χ(2)zxx′ is a structural parameter and χ(2)xyz′/χ(2)zxx′ is a measure of the chirality of the collagen fibers. Furthermore, the degree of linear polarization (DOLP) of the SHG signal was measured. A statistically significant increase in χ(2)zzz′/χ(2)zxx′ values for all the diseased tissues except insular carcinoma and a statistically significant decrease in DOLP for all the diseased tissues were observed compared to normal thyroid. This finding indicates a higher ultrastructural disorder in diseased collagen and provides an innovative approach to discriminate between normal and diseased thyroid tissues that is complementary to standard histopathology.Polarization-second harmonic microscopy was utilized to investigate whether collagen ultrastructure in thyroid due to four carcinoma types and Graves' disease could be differentiated in human histopathology samples. Three parameters were extracted, revealing that the degree of linear polarization and χ(2)zzz/χ(2)zxx were effective in differentiating some diseases, while the parameter χ(2)xyz/χ(2)zxx was less effective.

Nonlinear optical process of second-order nonlinear optical susceptibility χ133(2) in an organic nonlinear optical crystal DAST.

A large unexamined second-order nonlinear optical (NLO) process is found in a 4-N,N-dimethylamino-4'-N'-methyl stilbazolium tosylate (DAST) crystal, which has a large figure of merit among NLO crystals. In second-order NLO processes using a DAST crystal, the χ111(2) process of light excitation is commonly used, involving a-axis polarized light excitation with light generation of a-axis polarized light. However, there have been few studies of other second-order NLO susceptibility processes to date. In this Letter, terahertz (THz) wave generation via second-order NLO processes based on the χ133(2) second-order NLO susceptibility of the DAST crystal was investigated. By adjusting the polarization direction of the excitation light using a prism-coupled Cerenkov phase-matching method, efficient generation of THz waves was achieved using a process involving χ133(2). The magnitude of the NLO constant χ133(2) estimated from the THz intensity ratio was 77.8 pm/V. These results indicate that prism-coupled Cherenkov phase matching can be used to identify undiscovered NLO processes for NLO crystals.