Harmonic Generation Effect Research Articles

Excellent Static and dynamic hyperpolarizabilities of TM@C6O6Li6 (TM = Sc, Ti, V, Cr and Mn) complexes to prove their NLO applications

Static and dynamic hyperpolarizabilities of transition metals doped C6O6Li6 (TM@C6O6Li6, TM = Sc, Ti, V, Cr and Mn) organometallic complexes are explored for their nonlinear optical response. Interaction energies (Eint) of all TM@C6O6Li6 reveal that these complexes are thermodynamically stable. The highest interaction energy value is noticed for Sc@C6O6Li6 complex (−67.65 kcal mol−1). After doping of transition metals on C6O6Li6, HOMO-LUMO energy gap of respective complexes is significantly reduced and lies in the range of 1.50–2.08 eV, which notified the conducting behavior of complexes. The natural bond orbital charge (NBO) and molecular orbitals densities analyses are used to estimate the charge transfer in complexes and electronic densities of orbitals, respectively. UV-Vis analysis reflects that these complexes can be used in deep ultra-violet laser devices due to their transparency below 200 nm. NLO response is studied at both static and selected dynamic frequencies (532 nm and 1064 nm). The highest static first order hyperpolarizability value (βo = 2.05 ×104 au), third order hyperpolarizability (γtot = 1.99 ×107 au) with higher refractive index (n2 = 1.86 ×10−6 au) are observed for Cr@C6O6Li6 complex. The nonlinear optical properties including dc-Kerr effect and second harmonic generation effects are further enhanced at dynamic frequencies and their values are increased up to 1.26 × 1012 au. These results illustrate the use of these organometallics in optical technologies for achieving better dc-Kerr effect and second harmonic generation effects.

Highly Anisotropic Second-Order Nonlinear Optical Effects in the Chiral Lead-Free Perovskite Spiral Microplates

Chiral metal halide perovskites with intrinsic asymmetric structures have drawn increased research interest for the application of second-order nonlinear optics (NLO). However, designing chiral perovskites with the features of a large NLO coefficient, high laser-induced damage thresholds (LDT), and environmental friendliness remains a major challenge. Herein, we have synthesized two chiral hybrid bismuth halides: (R/S-MBA)4Bi2Br10 spiral structure microplates, templated by chiral (R/S)-methylbenzylamine (R/S-MBA). The as-grown chiral lead-free perovskite spiral microplates exhibit a recorded second harmonic generation (SHG) effect with a large effective second-order NLO coefficient (deff) of 11.9 pm V-1 and a high LDT of up to 59.2 mJ cm-2. More importantly, the twisted screw structures show competitive circular polarization sensitivity at 1200 nm with an anisotropy factor (gSHG-CD) of 0.58, which is about 3 times higher than that of reported Pb-based chiral perovskites. These findings provide a new platform to design multifunctional lead-free chiral perovskites for nonlinear photonic applications.

Two metal-free perovskite molecules with different 3D frameworks show reversible phase transition, dielectric anomaly and SHG effect.

Three-dimensional (3D) hybrid organic-inorganic perovskites (HOIPs) have attracted tremendous research interest due to their unique structure and promising applications. However, research on the design, synthesis and properties of this kind of metal-free crystalline material is still in the exploratory stage. Herein, two 3D perovskite molecules [1,4-3.2.2-dabcn]NH4Br3 (1) and [1,4-3.2.2-dabcn]NH4I3·0.5H2O (2) were obtained by reacting 1,4-diazabicyclo[3.2.2]nonane (1,4-3.2.2-dabcn) with NH4X (X = Br and I) in the corresponding concentrated halogen acids. The single X-ray diffraction results demonstrated that the inorganic framework structures in compounds 1 and 2 constructed with NH4Br and NH4I are completely different, caused by the radius of the bromide ion being smaller than that of the iodide ion. The 3D framework of compound 1 is constructed with a coplanar dimer [(NH4)2Br6]2- as the basic building unit, leading to the expanded 3D perovskite framework structure with a larger cavity to accommodate the 1,4-3.2.2-dabcn molecule. Nevertheless, compound 2 adopts a familiar 3D crystal framework structure with corner-sharing [(NH4)I6] octahedra, where the [1,4-3.2.2-dabcn] cations and water solvent molecule are confined in the cavities enclosed by the octahedra. Notably, both compounds exhibit reversible phase transition, dielectric anomaly and the second harmonic generation (SHG) effect. From the perspective of molecular design, this work is of great significance to guide the construction of new 3D metal-free perovskite molecular materials with reversible properties.

Cubic Nonlinearity of Tellurite and Chalcogenide Glasses: Terahertz-Field-Induced Second Harmonic Generation vs. Optical Kerr Effect

Third-order nonlinear susceptibilities χ3−2ω;ω,ω,0 and χ3−ω;ω,−ω,ω responsible for electric-field-induced second harmonic generation and the optical Kerr effect were measured and directly compared for tellurite and chalcogenide glasses. The nonlinear coefficients were found by measuring the second harmonic radiation from samples under the action of an external field of terahertz pulses and by the classical z-scan technique, respectively. The influence of ambient air and helium gas on second harmonic generation was analyzed. It was demonstrated that both susceptibilities χ3−2ω;ω,ω,0 and χ3−ω;ω,−ω,ω have close absolute values, which shows the dominant role of nonresonant electronic nonlinearity in the studied glasses.

Achieving Large Second Harmonic Generation Effects via Optimal Planar Alignment of Triangular Units

AbstractTrigonal planar units with large polarizability anisotropy and high physicochemical stability are ideal structural units for exploring nonlinear optical (NLO) materials. Integrating the merits of two types of triangular‐like moieties, a family of second‐order NLO‐active hybrid halides, MATX (X = Cl (1), Br (2), and I (3)), are achieved. MATX crystallizes in a nonpolar space group of 2c but exhibits the optimal spatial arrangement and superior NLO performance. The low coordination planar trigonal AgX3 units enable segregation in layers of the three‐winged propeller‐like Me3TPA units. All of the layers are packed in a perfect parallel fashion, making the functional materials exhibit superior NLO performances, including the phase matchable behavior with strong SHG responses (6.2/1, 6.5/2, and 7.6/3 times that of potassium dihydrogen phosphate), large birefringence (0.232/1, 0.252/2 and 0.260/3 at 1064 nm), high laser damage threshold, wide transparent window, and easiness of crystal growth. The first‐principles calculations reveal that the coexistence of strong linear and nonlinear optical properties are ascribed to the synergistic effect of the trigonal moieties. This study points out a useful path for the rational design of excellent NLO materials.

Decentering the Symmetry via Docking B and F in the KBe2BO3F2-Family Structure.

Deep-ultraviolet (DUV; <200 nm) nonlinear optical crystals arouse a great research interest in modern optical material science as they are key parts of solid-state lasers. Since KBe2BO3F2 (KBBF) still is the only crystal which can generate DUV coherent light practically, exploring other available structures in the DUV region by revising KBBF-family structure templates is necessary. In this paper, two KBBF-family structures are designed by adjusting the directions of BO3 groups or docking B and F atoms in known β-Be2BO3F (BBF). The first BBF structure with a P6322 space group is designed by strictly aligning the BO3 groups of even layers and odd layers in β-BBF. It is very interesting that docking B and F atoms forms novel B-F bonds, which destroy the inversion symmetry of the structure, making the centrosymmetric β-BBF structure with the R3̅c space group convert to a noncentrosymmetric BBF structure having the R3c space group. This noncentrosymmetric BBF structure exhibits a DUV cutoff edge shorter than 150 nm and a second harmonic generation effect comparable to that of KH2PO4 (KDP; d36 = 0.39 pm/V), indicating its feasibility as a frequency-doubling crystal in the DUV region. Our conversion design provides an effective way for uncovering noncentrosymmetric structures in KBBF-family structures.

Three polar indium phosphites exhibiting diverse structural networks and SHG-activity

Phosphites have attracted extensive attention for their abundant open-frameworks and special performances. Here, three inorganic indium phosphites, namely In2(HPO3)3(H2O) (1), In2(HPO3)3(H2O)3·(H2O) (2) and NH4[In(HPO3)2] (3), have been obtained via facile hydrothermal reactions. 1 and 2 crystallize in the same polar space group P21, and 3 crystalizes in the polar space group of P63mc. Isolated HPO3 tetrahedra connect to twisted InO6 octahedra via corner-sharing forming neutral 3D {In2(HPO3)3(H2O)}∞ and {In2(HPO3)3(H2O)3}∞ as well as 2D [In(HPO3)2]-∞ frameworks for 1–3, respectively. Second harmonic generation (SHG) effect measurements have shown that their phase-matched SHG signals are 0.17, 0.20 and 0.28 times of KDP. Thermal stability analyses, optical property measurements and theoretical studies of them were also performed.

Reversible Phase Transition and Second-Harmonic Response Based on a Zero-Dimensional Organic–Inorganic Hybrid Compound

The organic–inorganic hybrid materials (OIHMs) with stimuli-responsive features show the important scientific attraction in a multifunctional material application field, such as optoelectronic memory and sensors. Especially, designing a functional material with both dielectric switching and second-harmonic generation (SHG) remains attractive. Herein, we report a new OIHM [C7H15NCl] SbCl4 as a phase matching nonlinear optical material and dielectric switch functional materials. It undergoes a reversible phase transition at 297 K and exhibit a harmonic generation (SHG) effect of about 0.53 times that of KH2PO4 (KDP). Meanwhile, it also possesses potential semiconducting properties. This work might provide a strategy for designing novel multifunctional materials in the field of crystals and dielectrics.

Organic–Inorganic Hybrid Compound [H2-1,5-Diazabicyclo[3.3.0]octane]ZnBr4 with Reverse Symmetry Breaking Shows a Switchable Dielectric Anomaly and Robust Second Harmonic Generation Effect

An organic-inorganic hybrid molecule [3.3.0-H2dabco]ZnBr4 (1) with switchable phase transition, dielectric anomaly, and second harmonic generation (SHG) effect was synthesized by reaction of 1,5-diazabicyclo[3.3.0]octane (3.3.0-dabco) with ZnBr2 in concentrated hydrobromic acid aqueous solution. Differential scanning calorimetry (DSC) and dielectric measurements revealed that 1 exhibits a reversible high-temperature phase transition, accompanied by a distinct step-like dielectric anomaly at 373 K. Exceptionally, the single crystal structure analysis at different temperatures revealed that 1 undergoes reverse symmetry breaking during the phase transition, in which the high-symmetry space group Cc in the low temperature phase (LTP) is transformed to the low-symmetry space group P1̅ in the high temperature phase (HTP). In addition, with the conversion from the non-centrosymmetric (NCS) to the centrosymmetric (CS) space group, the SHG of 1 can switch from SHG-ON to SHG-OFF for at least four cycles without obvious decay.

AgGaGeSe4: An Infrared Nonlinear Quaternary Selenide with Good Performance

The symmetry of crystals is an extremely important property of crystals. Crystals can be divided into centrosymmetric and non-centrosymmetric crystals. In this paper, an infrared (IR) nonlinear optical (NLO) material AgGaGeSe4 was synthesized. The related performance analysis, nonlinear optical properties, and first-principle calculation of AgGaGeSe4 were also introduced in detail. In the AgGaGeSe4 structure, Ge4+ was replaced with Ga3+ and produced the same number of vacancies at the Ag+ position. The low content of Ge doping kept the original chalcopyrite structure and improved its optical properties such as the band gap. The UV-Vis diffuse reflection spectrum shows that the experimental energy band gap of AgGaGeSe4 is 2.27 eV, which is 0.48 eV larger than that of AgGaSe2 (1.79 eV). From the perspective of charge-transfer engineering strategy, the introduction of Group IV Ge elements into the crystal structure of AgGaSe2 effectively improves its band gap. The second harmonic generation (SHG) effect of AgGaGeSe4 is similar to that of AgGaSe2, and at 1064 nm wavelength, the birefringence of AgGaGeSe4 is 0.03, which is greater than that of AgGaSe2 (∆n = 0.02). The results show that AgGaGeSe4 possessed better optical properties than AgGaSe2, and can been broadly applied as a good infrared NLO material.

Influence of Halogens on the Growth Aspects of Allylthiourea Cadmium Complex Nonlinear Optical Single Crystals

Allylthiourea complex crystals is an organometallic complex, a new nonlinear optical materials with high second harmonic generation effect. Tri-allylthiourea cadmium chloride and Tri-allylthiourea cadmium bromide are the promising nonlinear optical crystals belonging to this family. Both the crystals have been grown from an aqueous solution by slow cooling technique. The solubility and growth optimization of the grown crystals in terms of pH were analyzed and the influence of the different halogen atoms on the properties of as grown single crystals was studied by conducting various characterization techniques. Powder X-ray diffraction studies revealed that both the crystals are trigonal crystal structure with R3C space group. The spectroscopic properties were investigated by recording the Fourier Transform Infra Red and UV-Visible-NIR spectroscopy. Spectrocopic study confirmed the coordination of metal and red shift of the grown crystal. Nonlinear behavior of the as grown crystals was identified by Kurtz powder technique. Thermal and electrical properties of the as grown crystals were also analyzed by thermogravimetric and dielectric studies. Influence of the halogens on the growth as well as the properties were studied.

A crystalline photochromic metalloviologen compound with a chiral ligand: Synthetic strategy and SHG-photoswitching property

Photochromic nonlinear optical (NLO) crystals may realize photoswitching of second harmonic generation (SHG) effect without the assistance of external stimuli or special supported media that other materials usually need. However, they were generally synthesized through chirality spontaneous separation or adopting a chiral species as a media, and thus the synthesis was not easy to control. In this article, we report the first NLO-photoswitchable crystalline material with a chiral ligand, which is also the first photochromic metalloviologen compound with NLO-photoswitchable properties. Our finding indicates that the direct use of a chiral unit as a ligand is a controllable approach to synthesize NLO-photoswitchable crystalline materials.

Correlation effects in high-order harmonic generation from finite systems

Using the Hubbard model we study how the process of high-order harmonic generation (HHG) is modified by beyond mean-field electron-electron correlation for both finite and bulk systems. A finite-size enhancement of the HHG signal is found and attributed to electrons backscattering off the lattice edges. Additionally, with increasing strength of the electron-electron correlation an enhancement of the high-frequency regime of the HHG spectrum is found. This is attributed to the on-site Coulomb repulsion between electrons giving rise to a localized quiver motion of the electrons. The finite-lattice enhancement dominates the HHG spectra from a few harmonic orders until a threshold from which the correlational enhancement dominates. This threshold is determined by the degree of correlation and decreases into the low-frequency regime for increasing electron-electron correlation. This infers that as the Mott insulator limit of high electron-electron correlation is approached, the finite-size effect on the electron dynamics becomes negligible.

Shedding light on the second order nonlinear optical responses of commercially available acidic azo dyes for laser applications

Nonlinear optics is a field of immense scientific interest and research owing to its extensive applications in photonics and optoelectronics. NLO materials are crucial components of optical fibers, optical computing, data processing devices, optical sensors, optical modulators, high density optical storage devices, and ultra-fast optical switches. Herein, five commercially available azo dyes, Acid Orange 5, Acid Orange 61, Direct Red 111, Food Yellow 6 and Metanil Yellow are theoretically investigated for their electronic and nonlinear optical properties using density functional theory (DFT) methods. Each azo dye exhibits one alkaline and two acidic forms therefore, all three forms of these azo dyes are considered for calculations. FMO analysis shows reduced HOMO-LUMO energy gaps (Eg) for acidic forms as compared to alkaline forms. The lowest HOMO-LUMO energy gap of 2.54 eV is observed for AO61 AC I acidic form. Furthermore, the effect of protonation of the dyes on nonlinear optical (NLO) responses are thoroughly investigated. The results at CAM-B3LYP/6-311+G(d) show that the protonation brings significant increase in nonlinear optical response. The highest first hyperpolarizability is observed for DR111 AC II (βo = 2.6 × 104au). The lowest hyperpolarizability calculated for Acid Orange 61 is even greater than that of the prototype, p-nitroaniline (1.2 × 103au). TD-DFT calculations are also carried out to find first hyperpolarizabilities βo by using two-level-model. The variations in dipole moments and excitation energies are the decisive factors for the increased first hyperpolarizabilities. In order to find the practical applications of the dyes in the field of nonlinear optics, dynamic hyperpolarizabilities for hyper-Rayleigh scattering (HRS), second harmonic generation (SHG) and electro-optical Pockel's effect (EOPE) are computed at a varying range of incident wavelengths. The results are found to be quite supportive for application of the studied azo dyes in second harmonic generation phenomenon.

Macroscopic effects in high-order harmonic generation - a focal-averaging method based on the integral solution of the wave equation.

A macroscopic theory of high-order harmonic generation (HHG) is presented, which applies a focal-averaging method based on the integral solution of the wave equation. The macroscopic high-harmonic yield is the coherent superposition of the single-atom contributions of all atoms of the generating medium, which are positioned at different spatial points of the laser focus and exposed to the space-time-dependent laser pulse. The HHG spectrum obtained in our macroscopic simulations is qualitatively different from the one obtained using the microscopic or single-atom theory of HHG. Coherent intensity focal averaging, the simpler and more approximate of two methods we introduced, gives the spectrum which forms a declining plateau with the same cutoff position as that of the microscopic spectrum. The second, more precise method, which we call coherent spatio-temporal focal averaging, shows that it is possible, changing the macroscopic conditions, to obtain an observable peak in the harmonic spectrum at an energy much lower than the microscopic cutoff energy. Generally, the high-harmonic yield appears to be dominated by the contributions of laser-pulse spatio-temporal regions with lower intensities as well as by interference, so that the high-energy plateau and its sharp cutoff are quenched in the theoretical simulation and, presumably, in the experiment. The height and position of this peak strongly depend on the macroscopic conditions. We confirmed these findings by applying our macroscopic theory to simulate two recent experiments with mid-infrared laser fields, one with a linearly polarized field and the other one with a bicircular field.

Cd4InO(BO3)3: A New Nonlinear Optical Crystal Exhibiting Strong Second Harmonic Generation Effect and Moderate Birefringence

A new noncentrosymmetric cadmium indium borate, Cd4InO(BO3)3 (CIBO) has been successfully developed via a standard solid-state reaction. Its crystal structure was confirmed by the single crystal X-ray diffraction, which shows that CIBO belongs to the non-centrosymmetric and polar space group Cm. Its structure contains the distorted InO6 and CdOn (n = 6, 8) polyhedra, which link together by sharing an edge or corner to build a three dimensions framework with BO3 triangles accommodated in tunnels. Benefiting from the approximately parallel configuration of BO3 triangles, CIBO exhibited a strong second harmonic generation (SHG) effect (3 × KDP), and moderate birefringence of 0.077@1064 nm. Further optical and thermal characterizations suggest that CIBO possesses a wide transparent window and good thermal stability. Theoretical calculation reveals that the macroscopic SHG coefficients of CIBO results from the synergistic effect of the parallel arrangement of BO3 groups and d10 Cd2+ cation.

Imprints of multielectron polarization effects in odd-even harmonic generation from CO molecules

Dynamic core-electron polarization (DCeP) is a correction to the single-active electron (SAE) approximation by considering a response of the core electrons to the time-dependent laser field. Despite being initially construed as a perturbative correction, in some cases especially atoms and molecules with large polarizabilities, DCeP can qualitatively alter predictions produced by the bare SAE theory. In this study, we unambiguously demonstrate the nonperturbative role of DCeP in the resolved odd-even high-order harmonic generation (HHG) of the CO molecule. In particular, we find that the even-to-odd ratio, i.e., the ratio between the harmonic intensities of even order and average of the two adjacent odd orders, changes by as much as one order of magnitude when DCeP is included, making the theoretically predicted values remarkably consistent with the experimental ones. This strong manifestation allows us to verify the DCeP role in HHG by experimental data. Furthermore, our analysis of the harmonic time profile shows that this agreement is not an artifact of the numerical method but reflects relevant physics, establishing that DCeP must be incorporated into the standard framework for strong-field physics.

Propagation time and nondipole contributions to intraband high-order harmonic generation

Applying the semiclassical model, we identify two connected effects in intraband high-order harmonic generation (HHG): (1) propagation time from the point of emission at the source to the point of detection, and (2) beyond-electric-dipole corrections to the light-matter interaction. These effects inherit information regarding the dispersion and cause specific features in the spectra including even-ordered harmonics in systems with space- and time-inversion symmetry. They can for certain experimental geometries be measured free of the dipole background.

Superalkali (Li2F, Li3F) doped Al12N12 electrides with enhanced static, dynamic nonlinear optical responses and refractive indices

In the present work, superalkalis (Li2F and Li3F) doped Al12N12 nanocages have been designed and investigated theoretically to elucidate the correlations between geometric, electronic and nonlinear optical properties. All complexes (A-E) are stable inorganic electrides as indicated by their interaction energies (−52.97 to −87.58 kcal/mol). The decrease in HOMO-LUMO energy gaps (5.44–5.87 eV) has caused a remarkable increase in the nonlinear optical response of A-E complexes. The maximum values of first hyperpolarizability (1.20 × 104 a.u.) and second hyperpolarizability (1.65 × 107 a.u.) have been achieved for complex A. The highest dynamic hyperpolarizability coefficients including second harmonic generation (9.08 × 105 a.u.) and electro-optic Pockel's effect (9.56 × 105 a.u.) are obtained for complex A at 532 nm. The electric field-induced second harmonic generation (up to 3.52 × 108 a.u.) and dc-Kerr effect (up to 8.13 ×108 a.u.) along with a large quadratic nonlinear refractive index (up to 5.41 × 10−11 a.u.) of the designed electrides reflected their large NLO response.

Two non-centrosymmetric scandium borate nonlinear optical crystals containing the B5O10 anion group

The spontaneous crystallization approach was used to synthesize two non-centrosymmetric scandium borate crystal materials, K3ScB6O12 (1) and K6NaSrSc2B15O30 (2), possessing the [B5O10]5− group. Both compounds exhibit wide band gaps of 5.75 and 5.92 eV, respectively. The second harmonic generation (SHG) effects of 1 and 2 are 1.3 and 0.7 times that of the commercial material KH2PO4 (KDP), respectively. According to the Kurtz-Perry approach, 2 demonstrates type-I phase-matchable. First-principles calculations on 2 are done to better understand the link between structure and performance. The calculated results reveal that the discrete arrangement of [B5O10]5− groups and the distorted ScO6 polyhedra in the structure are mainly responsible for the SHG response of 2. Furthermore, since 1 and 2 possess short ultraviolet (UV) cut-off edges, they may be applicable as nonlinear optical (NLO) materials in the UV region.