Second-order Harmonic Generation Research Articles

Quadripartite entanglement from two-port resonator with second-order harmonic generation

Quantum entanglement is a crucial resource for performing quantum computing and constructing quantum communication networks. The preparation and manipulation of entangled light field are the basic elements of quantum communication. With the development of science and technology, multicolor multipartite entanglement is becoming a kind of special resource for quantum information, quantum networks, and quantum memory. In this paper, we propose a scheme of generating quadripartite entanglement among four output beams from a two-port frequency doubling resonator, in which a type-II phase matching nonlinear crystal is placed. We make two fundamental-frequency pump beams with the same frequency and vertical polarization pass through the nonlinear crystal to produce two frequency-doubling beams. There is a quadripartite entanglement between the frequency-doubling beams, which are output at two ports of the optical resonator, and the incident fundamental beams. Based on the transmission matrix from the coupled wave equation, the self-consistent equations of the intracavity modes and the corresponding noise properties of the output modes can be obtained. Then, the quadripartite entanglement produced from two second harmonic beams and two reflected fundamental-frequency pump beams, is verified by using the positive partial transposition criterion, in a wide range of pumping power and analysis frequency. The setup proposed in this work is compact and experimentally feasible. It is also convenient to separate the four entangled beams spatially, with different wavelengths and polarizations. When the beam wavelengths are matched with 1560 nm (low loss window of fiber) and 780 nm (atomic absorption line of Rb), this scheme can be more useful in both quantum communication and quantum memory.

Growth, Structural, Spectroscopic and Thermal Analyses of Novel Organic Brucinum-3, 5 –Dihydroxybenzoate Dihydrate Single Crystals for NLO Applications

Along the line of available efficient nonlinear optical (NLO) organic single crystals in the literature, it is worthwhile to bring in a novel organic single crystal of Brucinium-3,5-dihydroxybenzoate dihydrate (B35D) which was successfully grown utilizing the technique of slow evaporation of solution at ambient conditions. As the solubility of B35D was found to be the highest in water-ethanol 1:1 mixed solvent among the conventional solvents, crystallization of B35D was accomplished by making use of the solvent. The required confirmation of the crystal structure of the crystal and its lattice parameter could be achieved by the single-crystal X-ray diffraction analysis such that B35D was found to be crystallized in the monoclinic system with the non-centrosymmetric space group C2. The recording of UV-Vis-NIR transmittance spectrum of the crystal was undertaken between the range of 300 and 900 nm whereby the lower optical cutoff wavelength was identified to be 321 nm. The spectral study of photoluminescence was carried out in the range of 300-600 nm by which the band gap energy was calculated to be about 3.8 eV (at 373 nm) indicating that B35D has a violet fluorescence spectrum. The thermal stability and melting point of the title crystal have been investigated through Thermo gravimetric and differential thermal analysis (TG-DTA) such that the thermal stability of the crystal was found to be 95.6 °C. The Nd: YAG Q-switched laser was employed so as to obtain the laser-induced surface damage threshold of the specimen which was estimated to be 3.1 GW/cm2. The Vickers microhardness test was implemented in order to arrive at the mechanical strength of the crystal. The performed non-linear optical study could reveal that the second-order harmonic generation (SHG) efficiency of B35D crystal is 2.16 times higher than KDP. So that B35D crystals are among the class of NLO materials.

Na2Ba[Na2Sn2S7]: Structural Tolerance Factor-guided NLO Performance Improvement.

The strong mutual coupling of and even the opposite change in the key parameters, such as the band gap (Eg) and second-order harmonic generation (SHG), leads to the extreme scarcity in high-performance IR nonlinear optical (NLO) chalcogenides. Herein, we report 8 new sulfides, Na2Ba[(AgxNa1-x)2Sn2S7] (1, x = 0; 1 series, x = 0.1-0.6; Na2Ba[(Li0.58Na0.42)2Sn2S7], 1-0.6Li); Na2Sr[Cu2Sn2S7] (2); and Na2Ba[Cu2Sn2S7] (3). We use the structural tolerance factor ( [[EQUATION]] ) to connect the chemical composition, crystal structure, and NLO properties. Guided by these correlations, a better balance between Eg and SHG is realized in 1, which exhibits a large Eg of 3.42 eV and excellent NLO properties (SHG: 1.5 × AGS; laser-induced damage threshold: 12 × AGS), representing the best performance among the known Hg- or As-free sulfides to date.

Na2Ba[Na2Sn2S7]: Structural Tolerance Factor‐Guided NLO Performance Improvement

AbstractThe strong mutual coupling of and even the opposite change in the key parameters, such as the band gap (Eg) and second‐order harmonic generation (SHG), leads to the extreme scarcity in high‐performance IR nonlinear optical (NLO) chalcogenides. Herein, we report 8 new sulfides, Na2Ba[(AgxNa1−x)2Sn2S7] (1, x=0; 1 series, x=0.1–0.6; Na2Ba[(Li0.58Na0.42)2Sn2S7], 1‐0.6Li); Na2Sr[Cu2Sn2S7] (2); and Na2Ba[Cu2Sn2S7] (3). We use the structural tolerance factor ( ) to connect the chemical composition, crystal structure, and NLO properties. Guided by these correlations, a better balance between Eg and SHG is realized in 1, which exhibits a large Eg of 3.42 eV and excellent NLO properties (SHG: 1.5×AGS; laser‐induced damage threshold: 12×AGS), representing the best performance among the known Hg‐ or As‐free sulfides to date.

K3C6N7O3·2H2O: A Multifunctional Nonlinear Optical Cyamelurate Crystal with Colossal π-Conjugated Orbitals.

The delocalized π-conjugated units are considered as an advantageous gene for improving the optical nonlinearity of acentric crystals. For the first time, we synthesized a new acentric SHG-active metal cyamelurate crystal K3C6N7O3·2H2O (I) by a facile solution method, containing a colossal planar π-conjugated (C6N7O3)3- unit. It displays a strong second-order harmonic generation (SHG) of 4 × KDP and a giant anisotropic birefringence of 0.446 at 1064 nm. The theoretical calculations reveal that such substantial improvement is contributed from the strong molecular susceptibility of (C6N7O3)3- units and their near-perfect coplanar arrangement. Moreover, I exhibits a broadband ultraviolet photoluminescence at 366 nm, suggesting its multifunctional capacity and great potential for compact highly integrated optoelectronic devices.

Fingerprint of the Interbond Electron Hopping in Second-Order Harmonic Generation.

We experimentally explore the fingerprint of the microscopic electron dynamics in second-order harmonic generation (SHG). It is shown that the interbond electron hopping induces a novel source of nonlinear polarization and plays an important role even when the driving laser intensity is 2 orders of magnitude lower than the characteristic atomic field. Our model predicts anomalous anisotropic structures of the SHG yield contributed by the interbond electron hopping, which is identified in our experiments with ZnO crystals. Moreover, a generalized second-order susceptibility with an explicit form is proposed, which provides a unified description in both the weak and strong field regimes. Our work reveals the nonlinear responses of materials at the electron scale and extends the nonlinear optics to a previously unexplored regime, where the nonlinearity related to the interbond electron hopping becomes dominant. It paves the way for realizing controllable nonlinearity on an ultrafast time scale.

Optimizing the Nonlinear Optical Performance of an A-N-M-Q (A: Alkali Metal; N: d10 Metal; M: Main Group Metal; Q: Chalcogen) System.

Exploring new infrared nonlinear optical (IR NLO) materials with superior overall properties is scientifically and technically important. However, large second-order harmonic generation (SHG) efficiencies and high laser-induced damage thresholds (LIDT) are incompatible, which makes realizing this goal a challenge. The IR NLO performance of an A-NIIB-MIIIA-Q (Q: chalcogen) system was optimized by simultaneously modulating A/(M + N) and M/N ratios (A: alkali metal; N, M: tetra-coordinated metals), and SHG-LIDT balance was achieved. Three new sulfides, KCd3Ga5S11 (1), RbCd4Ga3S9 (2), and Cs2Cd2Ga8S15 (3), containing the same CdS4 and GaS4 but with different A/(Ga + Cd) and Ga/Cd ratios were obtained. Among these compounds, compound 3 exhibits both the largest SHG efficiency (0.5 × AgGaS2) and LIDT (35 × AgGaS2), which can be ascribed to the Ga/Cd modulation for enhancing the NLO functional motif distortions and SHG efficiency as well as the A/(Ga + Cd) modulation for enlarging the band gap and LIDT. Remarkably, compound 3 is the first phase-matchable IR NLO material in the A-NIIB-MIIIA-Q family. This article proposes a novel avenue to explore infrared nonlinear materials with superior comprehensive properties by modulating the A/(M + N) and M/N ratios.

Temperature-driven order-disorder structural transition in the oxygen sub-lattice and the complex superstructure of the high-temperature polymorph of CaSrZn2Ga2O7.

Structural order-disorder plays a decisive role in the physical properties of materials, such as magnetism, second-order harmonic generation, and ionic conductivity, and it is thus widely utilized to manipulate the crystal structure and understand structure-property correlations. Herein, we report the structural polymorphism, complex crystal structure and temperature-driven irreversible order-disorder phase transition of the polar oxides (Sr1-xCax)SrZn2Ga2O7. The low-temperature (LT) structure crystallizes in Pna21 with partial Zn/Ga ordering. Upon heating, (Sr1-xCax)SrZn2Ga2O7 undergoes an irreversible phase transition from orthorhombic Pna21 to hexagonal P63. Interestingly, the high-temperature (HT) P63 structure possesses an unexpected 3/2-fold superstructure rather than a substructure of the low-temperature (LT) Pna21 structure, which is a rare structural phenomenon in solid-state chemistry. This new HT superstructure is the most complex one in this series of oxides with 21 crystallographically independent sites determined accurately by a combination of the maximum entropy method and Rietveld refinement against high-resolution neutron powder diffraction data. In terms of the mechanism, this is a temperature-driven order-to-disorder transition in the oxygen sublattice. A careful structural analysis revealed that the oxygen disordering mainly occurs in the [SrO3] layers of the HT structure and it can be understood as respective clockwise and anticlockwise rotations of distinct GaO4-tetrahedra along the c-axis. Alternating current electrochemical impedance spectroscopic analysis revealed that the oxygen disordering in the HT structure is incapable of giving rise to oxide ionic conductivity but does lead to increased electronic conduction compared to the LT structure. The optical properties of the CaSrZn2Ga2O7 and Sr2Zn2Ga2O7 representatives are also investigated in-depth via diffuse reflectance spectroscopy and theoretic calculations.

Investigation on the Effects of MnCl2 Doping on Structural and Optical Properties of DAST Single Crystals as Materials for Second Order Nonlinear Optics

AbstractThe intent is to explore the optoelectronic properties of metal ions doped stilbazolium derivative, 4‐N,N′‐dimethylamino‐N‐methyl‐4‐stilbazolium tosylate (MnCl2‐DAST) nonlinear optical crystal materials for the existing technological necessities. The Mn‐DAST single crystals are crystallized by adopting the slow evaporation solution technique (SEST). The structural and crystallographic dimensions of grown crystals are affirmed using single‐crystal X‐ray diffraction and powder crystal X‐ray diffraction. Fourier transform infrared spectra are performed to explicate the functional groups and energy dispersive X‐ray analysis (EDAX) spectra confirm the presence of the chemical elements of grown crystals. The UV–vis absorption spectra of DAST and Mn‐DAST crystals exhibit all possible n–π* and π–π* electronic transitions. The blue shift is observed in the doped materials due to the exchange of lone pair electrons between the metal ions and organic molecule. Tremendously, the second order harmonic generation (SHG) efficiency of Mn (0.01 mol%) doped DAST crystals has 1.68 times larger than that of DAST crystal. From the metal‐organic crystals (Mn‐DAST), all the results brought out are the promising materials in the design of nonlinear optical applications.

A plastically bendable and polar organic crystal

An organic crystal of the polar space groupPcthat is capable of plastic bending is reported, and its high dielectric constant and strong second-order harmonic generation (SHG) effect have been demonstrated.

Generation of highly nonlinear irregular waves in a wave flume experiment: Spurious harmonics and their effect on the wave spectrum

Spurious harmonics generation can occur in wave basins when strongly nonlinear waves are generated with linear wave maker theory. For regular long crested waves, the phenomena is known to cause a beating pattern for the amplitude of the higher harmonics, while for irregular waves the effect is often thought to average out. We here report on recent experimental results for spurious harmonic generation for highly nonlinear irregular waves. Long crested waves at two depths are considered. We find a systematic distortion of the spectral shape which is non-uniform in space. The effect occurs in the linear and super harmonic region of the spectrum and is strongest at the smaller depth. We analyze the phenomenon through re-computations in a fully nonlinear wave model and the further application of a four-phase harmonic separation. We next extend the analysis to allow separation of the third- and first-order content of the first-harmonic wave field, by computation at two different amplitudes. The numerical results resembles the measured spectrum closely and the harmonic separation shows that the spectral distortion in the super-harmonic region is to large extent a property of the second-harmonic wave field. Further, the match between the first-harmonic spectrum and the original target spectrum is shown to improve strongly by the removal of the extracted third-order contribution. The observed spectral distortion in the linear frequency region can thus be explained by this third-order field.Returning to the second-order wave field, we demonstrate that the extracted second-order wave field with associated spectral distortion can be reproduced by application of the Sharma and Dean theory with inclusion of the reconstructed spurious wave field from the linear wave generation. Finally, the effect of the spurious second-order harmonic generation on the measured forces is discussed and quantified. We find that the force peak exceedance probability is less influenced by the spurious waves than the spectral shape. We link this to the smaller phase speed of the spurious waves, that makes them arrive later than the main wave packet and thus leads to a limited enhancement of the local peaks.

Generation of Intense Sub-10 fs Pulses at 385nm* *Supported by the National Key Research and Development Program of China (Grant No. 2019YFA0307703), the Major Research Plan of NSF of China (Grant No. 91850201), and the National Natural Science Foundation of China (Grant Nos. 11974426, 11974425, U1830206 and 11604386).

We demonstrated the generation and characterization of 9.7 fs, 180 μJ pulses centered at 385 nm via the frequency doubling of few-cycle near-infrared pulses. Both moderate conversion efficiency (9.5%) and broad phase matching bandwidth (20 nm) were achieved by shaping the spectra of the fundamental pulses. The strong intensity dependence of second-order harmonic generation and well controlled material dispersion ensured the inexistence of satellite pulses, which was confirmed by the self-diffraction frequency resolved optical gating measurement.

Wavelength and Polarization Dependence of Second-Harmonic Responses from Gold Nanocrescent Arrays

In the developing field of nonlinear plasmonics, it is important to understand the fundamental relationship between properties of the localized surface plasmon resonance (LSPR) of metallic nanostructures and their nonlinear optical responses. A detailed understanding of nonlinear responses from nanostructures with well-characterized LSPRs is an essential prerequisite for the future design of sophisticated plasmonic systems with advanced functions to control light. In this article, we investigate the second-order harmonic (SH) responses from gold nanocrescent (Au NC) antennas which have wavelength and polarization sensitive LSPRs in the visible and near-infrared wavelength ranges. The wavelength dependence of the SH intensity exhibits spectral profiles different from dipole LSPR bands in absorbance spectra. The incident polarization angle dependence was found to vary significantly when the excitation wavelength was tuned over the dipole band. Finite-difference time-domain calculations coupled with a nonlinear hydrodynamic model were carried out for Au NC arrays to investigate the local field enhancement of the incoming fundamental and emitting SH light. The experimental and theoretical results indicate that the effects of higher-order LSPRs, such as quadrupole and multipole resonances, occurring at SH wavelengths are important in governing the SH generation process. Also, it is shown that the incident polarization angle dependence of SH signals is very strongly sensitive to nanoscale variations in the NC’s shape.

Giant photogalvanic effect and second-harmonic generation in magnetic axion insulators

The second-order nonlinear optical (NLO) processes, such as photogalvanic effect and second-order harmonic generation (SHG), play crucial roles in probing and controlling light-matter interactions for energy and device applications. Combining quantum perturbation theory and first-principles simulations, we predict a giant injection-current photogalvanic effect and SHG in a family of emerging axion insulators, the even septuple layers of $\mathrm{MnB}{\mathrm{i}}_{2}\mathrm{T}{\mathrm{e}}_{4}$ (MBT) materials. Their amplitudes of photocurrent and SHG are about 1--2 orders of magnitude larger than those of proper ferroelectrics and antiferromagnetic $\mathrm{Cr}{\mathrm{I}}_{3}$. Moreover, unlike the widely studied injection current observed under circularly polarized light, the injection photocurrent of MBT only emerges under linearly polarized light, making it suitable for device applications. These unique characters are from a combination effect of parity-time symmetry and significant spin-orbit coupling. Our predicted enhanced NLOs are valuable for characterizing subtle magnetic orders and shed light on infrared photodetecting and photovoltaic applications based on magnetic topological materials.

Numerical and experimental investigations on second-order combined harmonic generation of Lamb wave mixing

The generation of second- and third-order combined harmonics induced by the interaction of two primary Lamb waves with different frequencies has been analyzed theoretically and observed experimentally in our previous research [W. Li et al., J. Appl. Phys. 124, 044901 (2018)]. However, only third-order combined harmonics were observed experimentally because in the experimental investigations, the conditions for both synchronism and the symmetric feature were not satisfied simultaneously for the generation of the second-order combined harmonics. In this paper, first, the numerical perspective of the second-order combined harmonic generation by the collinear interaction of two primary Lamb waves with different frequencies in an isotropic and homogeneous plate is investigated. The results indicate that the synchronism and symmetric feature of two primary Lamb waves selected significantly affect the generation of second-order combined harmonics at the mixing frequencies. Next, an experimental scheme is proposed to measure the second-order combined harmonics predicted theoretically and numerically, through which it is found that the experimental results agree well with that of the theoretical and numerical predictions. The numerical and experimental results in this paper provide a clear physical insight, not previously available, into the second-order combined harmonic generation induced by the collinear interaction of two primary ultrasonic Lamb waves.

LiGa0.54In0.46S2: A new infrared nonlinear optical material with large laser damage threshold designed by gallium substitution in LiInS2

Larger second-order harmonic generation (SHG) efficiency and high laser damage threshold (LDT) are two crucial requirements for the practical applications of IR nonlinear optical (NLO) materials. Li-(Ga, In)-Q2 (Q = S, Se) is a well-known IR NLO materials system, in which InQ bonds are more covalent than GaQ bonds and benefit larger SHG efficiency. However, the incompatibility between LDT and SHG leads to a smaller LDT of LiInS2 than that of LiGaS2. A new IR NLO compound LiGa0.54In0.46S2 was successfully synthesized by the introduction of gallium in LiInS2, where mixing Ga3+ in In3+ sites result in a wider band-gap of 3.86 eV and a smaller thermal expansion anisotropy value (0.26) compared with LiInS2, leading to the large LDT of 12 times that of commercial AgGaS2 under 1064 nm at room temperature. Meanwhile, the title compound had a relatively strong SHG efficiency of about 0.6 times that of AgGaS2 under a 1910 nm laser radiation. This work highlights the strategy of pursuing IR NLO materials with high LDTs by atom doping in classic material systems.

How To Maximize Birefringence and Nonlinearity of π-Conjugated Cyanurates.

Materials with large birefringence (Δn) are highly needed by fiber-optic isolators, whereas crystals showing strong second-order harmonic generation (SHG) are the key component for all-solid-state laser devices. Cyanurate constructed by the planar π-conjugated ring (C3N3O3, CY) is a class of fascinating materials exhibiting not only very large Δn (larger than that of calcite) but also strong SHG (2 times that of β-BaB2O4, BBO). Here, we report five new cyanurates (I-V) and their single-crystal structures; among them, II realizes a Δn = 0.4, the maximum in the cyanurate family, and IV realizes a d33 = 6.69 pm/V, one of the highest values in the cyanurate family. We discover a dependence between Δn and the coplanarity of the CY rings that is explicitly described by a Boltzmann function, in which the coplanarity is defined by the dihedral angle (γ) between the CY plane and the principal optical axes XY plane. II realizes the maximum Δn due to its zero γ that indicates perfect coplanarity. Such a Δn-γ dependence also allows the Δn prediction of cyanurates. Furthermore, we uncover that the SHG intensity of cyanurates increases monotonically as the angle (θ) between the maximum hyperpolarizability (βmax) vector and the crystal 21 polar axis decreases. We predict the dij to extend well beyond such a value and to maximize at θ = 0°. Our results have significant implications for the future rational design and discovery of high-performance materials of π-conjugated and other related systems.

BaCuSiTe3: A Noncentrosymmetric Semiconductor with CuTe4 Tetrahedra and Ethane-like Si2Te6 Units.

BaCuSiTe3 was prepared from the elements in a solid-state reaction at 973 K, followed by slow cooling to room temperature. This telluride adopts a new, hitherto unknown structure type, crystallizing in the noncentrosymmetric space group Pc with a = 7.5824(1) Å, b = 8.8440(1) Å, c = 13.1289(2) Å, β = 122.022(1)°, and V = 746.45(2) Å3 (Z = 4). The structure consists of a complex network of two-dimensionally connected CuTe4 tetrahedra and ethane-like Si2Te6 units with a Si-Si bond. This semiconducting material has an optical band gap of 1.65 eV and a low thermal conductivity of 0.50 W m-1 K-1 at 300 K. Calculations of its optical properties revealed a moderate birefringence of 0.23 and a second-order harmonic generation response of deff = 3.4 pm V-1 in the static limit.

Second-order harmonic generation of Lamb wave in prestressed plates

This paper investigates the second-order harmonics generation associated with propagation of Lamb wave in pre-stressed plates. The second-order harmonic phenomena appear in a weakly non-linear medium due to material and geometry nonlinearities. This study proposes finite element (FE) models to incorporate stress constitutive equations formulated by Murgnahan's strain energy function. The model is used to take into account the stress effect on second-order harmonic generation of Lamb wave propagation in weakly nonlinear media. The developed FE model is first validated against two-dimensional (2D) analytical solutions. A three-dimensional (3D) FE model is then developed and utilised to study more realistic problems, such as the rate of accumulation of the non-linear parameter β' at different wave propagation angles when the plate is subjected to a bi-axial stress and the effect of the applied stresses on second-order harmonic generation in a plate with a fatigue crack. The results demonstrate that the applied stresses can notably change the value of β' in different directions. The finding of this study can gain physical insight into the physical phenomenon of stress effect on second-order harmonic generation of Lamb wave. Thus, the current study opens an opportunity for the development of a new non-destructive stress evaluation technique for plate- and shell-like structural components. Moreover, the new technique can be easily incorporated with existing guided wave based-SHM systems and provide information regarding the change of the stress conditions. Such additional information can significantly improve the structural life prognosis and reduce risk of failures.

Experimental study on nonlinear−optical property of Ag4P2Se6

Mid−infrared (MIR) nonlinear optical (NLO) material is critical to laser frequency−conversion technology. Although the main commercial MIR NLO crystals (AgGaS2 AgGaSe2 and ZnGeP2) are practically used, they still have some intrinsic drawbacks, so that it is of great scientific significance to discover new materials with good MIR NLO performances. Among the main systems of chalcogenides to explore MIR NLO crystals, metal thiophosphates and selenophosphates are competitive for their structural diversities and strong covalent P−Q bonds. Here, Ag4P2Se6 (P212121) was selected to evaluate the second−order harmonic generation (SHG) property. As a result, the SHG response with phase−matching ability is about 0.5 times that of AgGaS2 at 2.05 μm in the particle range of 210–270 μm, and the laser damage threshold (LDT) is larger than that of AgGaS2. Remarkably, this compound is of low melt temperature of 642 °C with a congruent melting character, also possesses excellent chemical stability, facilitating its further crystal growth and fabrication.