Second Harmonic Generation Coefficients Research Articles

K2 PbX][Ga7 S12 ] (X=Cl, Br, I): The First Lead-Containing Cationic Moieties with Ultrahigh Second-Harmonic Generation and Band Gaps Exceeding the Criterion of 2.33eV.

In contrast to anionic group theoryofnonlinearoptical(NLO)materials that second-harmonic generation (SHG) responses mainly originate from anionic groups, structural regulation on the cationic groups of salt-inclusionchalcogenides(SICs)is performed to make them also contribute to the NLOeffects. Herein, the stereochemically active lone-electron-pair Pb2+ cation is first introduced to the cationic groups of NLO SICs, and the resultant [K2 PbX][Ga7 S12 ] (X=Cl, Br, I) are isolated via solid-state method. The features of their three-dimensional structures comprise highly oriented [Ga7 S12 ]3- and [K2 PbX]3+ frameworks derived from AgGaS2 , which display the largest phase-matching SHG intensities (2.5-2.7×AgGaS2 @1800nm) among all SICs. Concurrently, three compounds manifest band gap values of 2.54, 2.49, and 2.41eV(exceedingthe criterion of 2.33eV),whichcan avoid two-photon absorption under the fundamental laser of 1064nm, along with the relatively low anisotropy of thermal expansion coefficients, leading to improved laser-induceddamagethresholds(LIDTs) values of 2.3, 3.8, and 4.0 times that of AgGaS2 . In addition, the density of states and SHG coefficient calculations demonstrate that the Pb2+ cations narrow the band gaps and benefit SHG responses.

Nonlinear optical properties of superalkali@teetotum boron clusters with potential applications on the electro-optic modulator

The development of nonlinear optics has revolutionized the photonic and optoelectronic fields in recent years.In this paper, we have designed a new class of donor–acceptor frameworks with enhanced nonlinear optical (NLO)properties using a series of superalkalis including Li3O, Li2NaO, LiNa2O, Li2KO, LiK2O as donors and three sizes of teetotum boron clusters (B14, B18, and B22) as acceptors. A systematic first-principles study has been performed on the electronic, linear, and NLO properties of superalkali@Bnassemblies. Besides the static non-linearity, the frequency-dependent electro-optic Pockel's effect (EOPE), second harmonic generation (SHG), and nonlinear refractive index have also been evaluated. In the case of dynamic NLO, the SHG process has a stronger NLO response than EOPE. At the typical experimental frequency of the Nd:YAG laser (ω = 0.04282) a.u., the SHG coefficients are about 2–3 times larger than the corresponding EOPE at this wavelength. Also, the nonlinear refractive index shows a remarkable response atω = 0.04 a.u. for LiK2O@B14.

Stabilization of the Polar Structure and Giant Second‐Order Nonlinear Response of Single Crystal γ‐NaAs0.95Sb0.05Se2

AbstractThe dearth of suitable materials significantly restricts the practical development of infrared (IR) laser systems with highly efficient and broadband tuning. Recently, γ‐NaAsSe2 is reported, and it exhibits a large nonlinear second‐harmonic generation (SHG) coefficient of 590 pm V−1 at 2 µm. However, the crystal growth of γ‐NaAsSe2 is challenging because it undergoes a phase transition to centrosymmetric δ‐NaAsSe2. Herein, the stabilization of non‐centrosymmetric γ‐NaAsSe2 by doping the As site with Sb, which results in γ‐NaAs0.95Sb0.05Se2 is reported. The congruent melting behavior is confirmed by differential thermal analysis with a melting temperature of 450 °C and crystallization temperature of 415 °C. Single crystals with dimensions of 3 mm × 2 mm are successfully obtained via zone refining and the Bridgman method. The purification of the material plays a significant role in crystal growth and results in a bandgap of 1.78 eV and thermal conductivity of 0.79 Wm−1 K−1. The single‐crystal SHG coefficient of γ‐NaAs0.95Sb0.05Se2 exhibits an enormous value of |d11| = 648 ± 74 pm V−1, which is comparable to that of γ‐NaAsSe2 and ≈20× larger than that of AgGaSe2. The bandgap of γ‐NaAs0.95Sb0.05Se2 (1.78 eV) is similar to that of AgGaSe2, thus rendering it highly attractive as a high‐performing nonlinear optical material.

Study of SHG and LE-O Susceptibilities of InAs Crystal: Linear Absorption Taken into Account

We applied a model involving two coupled anharmonic oscillators (electronic and ionic) to estimate the Second Harmonic Generation (SHG) and Linear Electro-Optic (LE-O) susceptibilities of InAs crystal. The crystal of InAs belongs to III-V group compounds owing cubic zinc-blende-type structure. Linear absorption is considered for the selected spectral region 1250 nm – 390 nm. So, the contribution of the imaginary part of the involved complex linear ionic susceptibility to the resultant SHG and LE-O susceptibilities is taken into account and hence the absolute value of complex-linear ionic susceptibility is used in place of the complex-linear ionic susceptibility in the computation of SHG and LE-O coefficients. All of the four constants (nonlinear strength factors), appearing in the model, are determined with the help of experimental data of SHG susceptibility measured in the selected region of 1076 nm-535 nm. Application of such calculated nonlinear strength factors in the concerned modelled expressions, SHG and LE-O susceptibility coefficients are computed as a function of frequency to illustrate the dispersion in the region of 1250 nm –390 nm.

Role of large Rashba spin-orbit coupling in second-order nonlinear optical effects of polar BiB3O6

The $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{BiB}}_{3}{\mathrm{O}}_{6}$ (BIBO) is a widely used nonlinear optical (NLO) crystal in ultraviolet (UV) energy region. Although the spin-orbit coupling (SOC) effect on the band structure of BIBO has been investigated, the role of SOC effect on the second-order NLO properties is still unclear. In this article, using the first-principles calculations, we discover the unusual polar lone-pair electron can induce large Rashba SOC effect in the electronic structure of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{BiB}}_{3}{\mathrm{O}}_{6}$ (BIBO), which can fundamentally change its NLO responses around the band edge. For the second harmonic generation (SHG), it is found that the inclusion of SOC effect can significantly improve the accuracy of SHG coefficients calculations in BIBO, closer to the experimentally measured values. Importantly, we also find the large Rashba SOC effect can strongly modulate the photodriven high-order charge/spin currents in BIBO, giving rise to large bulk photovoltaic effect, large circular photogalvanic effect, and an unusual spin photocurrent effect. Interestingly, the roles of SOC in tuning the charge and spin currents are quite different. Accordingly, we propose the spin current switching around the band edge induced by the large Rashba SOC in a BIBO crystal. Our study not only provides a deep and complete understanding on the unique roles of Rashba SOC effect in the second-order NLO properties of BIBO, but also suggests the BIBO crystal may be used for UV-range spintronics and optoelectronics.

La2B3O4(OH)3(SO4)2: A new rare-earth borate-sulfate with second-harmonic generation response

The first example of lanthanide borate-sulfate compound, namely, La2B3O4(OH)3(SO4)2 has been obtained through hydrothermal synthesis, which belongs to polar space group Pna2(1) (No. 33). Its structure possesses double lanthanum sulfate layers in the ab plane in which the lanthanide ions are bridged by SO4 tetrahedra. These layers are further cross-linked by borate chains into the final 3D framework. It is noteworthy that this compound is the first lanthanide borate-sulfate which crystalizes in polar space group and it displays second-harmonic generation (SHG) signal of about 0.1 times that of KH2PO4. The SHG coefficient of the compound is ascribed to the synergistic effect of SO4 units and borate units. Meanwhile, distorted LaOx polyhedra also play an important role in the contribution to SHG response.

Phosphites: A Nonlinear Optical Materials System with a Wide Band Gap and Moderate Second-Harmonic Generation Effect

Ultraviolet (UV) nonlinear optical (NLO) materials have crucial practical applications in modern laser science and technology. Phosphates are promising candidates for searching UV NLO materials. However, small optical anisotropy of high-symmetrized (PO4)3- tetrahedron hinders phase matching (PM) in the UV wavelength range. Herein, a low-symmetrized phosphite anionic group (HPO3)2- is proposed as a new NLO-active group that exhibits a larger optical anisotropy and second-harmonic generation (SHG) coefficients than (PO4)3-. Accordingly, two phosphites, (C(NH2)3)2Zn(HPO3)2 and [Al2(HPO3)3(H2O)3]·H2O, that contain (HPO3)2- groups are screened out and synthesized. The UV absorption edges of the two compounds are 6.18 and 6.23 eV, respectively. (C(NH2)3)2Zn(HPO3)2 exhibited an SHG intensity of 1 times that of KDP at 1064 nm. This work proposes a new NLO-active fundamental building unit (FBU) and a new materials system for searching NLO materials.

LiAlS2: A promising infrared frequency-conversion material with ultrawide band gap and high laser-induced damage threshold

The development of infrared (IR) nonlinear optical (NLO) crystals could foster their wide applications in civil and military fields. Thus, IR NLO materials with a wide band gap, high laser-induced damage threshold, and lack of two-photon absorption are urgently needed. This work reports the comprehensive optical properties of LiAlS2 through systematic experimental characterizations and the first principle study. The results confirmed the congruently melting feature of LiAlS2, type-I phase matching (PM) performance, and its second-harmonic generation (SHG) response (0.2 × AgGaS2 at 2.09 µm). Notably, LiAlS2 shows the widest band gap of 5.13 eV among the selected IR NLO materials and an ultrahigh laser-induced damage threshold about 28 times that of AgGaS2. The structure-property relationship analysis indicates that the [AlS4] tetrahedra determine the optical band gap and primarily contribute to the SHG response. Moreover, the calculated effective SHG coefficient deff, the refractive index dispersion relation, and the shortest PM wavelength are reported. The results of this study indicate that LiAlS2 can be a promising IR NLO material in high-energy laser systems.

Effects of external fields on the nonlinear optical rectification and second harmonic generation of GaAs/GaAlAs zigzag quantum well

For the first time, the impact of externally applied static electric and magnetic field on the nonlinear optical rectification (NOR) and second harmonic generation (SHG) coefficients of GaAs/GaAlAs zigzag quantum well is theoretically investigated in this study. Additionally, we examined the effect of physical parameters such as width and depth of the structure on these coefficients. We have numerically solved the time-independent Schrödinger equation by using the diagonalization method under the effective mass approximation for obtaining subband energy levels and wave functions of the structure, and then we have used the compact density matrix method to obtain the analytical expressions of NOR and SHG coefficients. The obtained numerical results showed that when the magnitude of the externally applied electric and magnetic fields is increased, the peak position of NOR and SHG shifts to blue, and by increasing the width and potential depth of the quantum well, it shifts to red.

From Phosphate Fluoride to Fluorophosphate: Design of Novel Ultraviolet/Deep-Ultraviolet Nonlinear Optical Materials for BePO3F with Optical Property Enhancement.

Fluorine-containing compounds have stimulated the exploration of ultraviolet/deep-ultraviolet nonlinear optical (NLO) materials. Alkali/alkaline-earth metal phosphates are one of the important potential systems as NLO materials, while the common small birefringence limits the phase-matching (PM) ability in the ultraviolet/deep-ultraviolet region. Herein, by applying a "fluorination synergy-induced enhancement of optical property" strategy, novel structures of phosphate fluoride/fluorophosphate in BePO3F with good thermodynamic/dynamic stability and promising NLO-related properties are discovered via performing crystal structure prediction combined with first-principles calculations. BePO3F-I-VI exhibit relatively large birefringence of 0.025, 0.048, 0.049, 0.049, 0.059, and 0.063 at 1064 nm, respectively. Simultaneously, BePO3F-I (Pc) is a new thermodynamically stable phosphate fluoride which possesses a wide band gap (Eg = 8.03 eV), large second-harmonic generation (SHG) coefficient (d11 = 0.67 pm/V, 1.7 × KDP), and the shortest PM wavelength of 292 nm. Other five thermodynamically metastable noncentrosymmetric (NCS) BePO3F structures (II-VI) belong to fluorophosphates and exhibit deep-ultraviolet PM wavelengths of 187, 183, 186, 188, and 196 nm. It reveals that the aligned nonbonding O 2p orbitals of [BeO2F2] and [PO4] units lead to a large SHG coefficient in the phosphate fluoride BePO3F-I. For fluorophosphates (BePO3F-II-VI), the synergy of [BeO3] planar units and [PO3F] units induces relatively large birefringence. Our research results provide an idea for exploring novel high-performance NLO materials.

Second-Harmonic-Generation Effect and Giant Optical Birefringence in the Weyl Material CaAgAs.

Nonlinear-optical (NLO) materials suitable for the "8-14 μm" atmospheric transparent window are in urgent need. Arsenide is one of the most promising material systems for such an application. However, the second-harmonic-generation (SHG) effect of arsenide is difficult to characterize using the conventional powder SHG technique with a 2 μm fundamental laser. To overcome this problem, we focused on a novel arsenide Weyl material, CaAgAs, with a zero band gap and proposed a modified powder SHG measurement method for narrow-band-gap materials. We successfully observed the SHG signal of CaAgAs, which was approximately 0.7 times that of CdGeAs2. Moreover, on the basis of first-principles calculations, the largest SHG coefficient for CaAgAs is equal to 236 pm/V, and the ionic bonds in the [Ca3As13] motif play an indispensable role for the SHG effect because of the distorted Kagome lattice pattern. CaAgAs is predicted to have strong optical anisotropy with a giant optical birefringence of 0.52.

The second harmonic generation in GaAs/GaAlAs spherical quantum dots under Woods-Saxon plus attractive inversely quadratic potential

We examine the profile of second harmonic generation (SHG) for GaAs/GaAlAs spherical quantum dots (QDs) of Woods-Saxon (WS) plus attractive inversely quadratic (AIQ) potential under the joint influence of additional factors (pressure and temperature) and structural parameters (strengths and radius). The energies and wave functions in GaAs/GaAlAs spherical QDs under WS-AIQ limiting potential are calculated using the parametric Nikiforov-Uvarov (NU) method. Depending on the calculated energies and corresponding wave functions, the SHG coefficient is examined by the iterative procedure in the density matrix method for this system. Finally, the calculated results display that a strong SHG coefficient response, and red shift or blue shift energy can be acquired by adjusting parameters.

Optical Second Harmonic Generation in GaAs/Ga1−xAlxAs Quantum Dots with Screened Kratzer Potential

Herein, the second harmonic generation (SHG) associated with intersubband transitions in semiconductor quantum dots (QDs) is studied theoretically, with emphasis on the effects of the screened Kratzer (SK) potential parameters and regulating factors, such as temperature and the depth of potential. The Nikiforov–Uvarov Functional Analysis (NUFA) method is applied for solving the radial Schrödinger equation. Then, the formulae for the SHG coefficient are derived using the compact‐density‐matrix method. The results display that the SK potential parameters and the regulating factors play a key role in both the peak and position changes of the SHG in semiconductor QDs system.

Nonlinear optical properties of lithium niobate crystals doped with alkaline earth and rare earth elements

Nonlinear optical properties of lithium niobate crystals doped with alkaline-earth (Zn2+) and rare-earth (Er3+) elements were quantitatively studied from the chemical bond viewpoint of crystal. The different influences of Zn and Er dopants on the dielectric response of LiNbO3 were compared. The value of nonlinear optical second-harmonic generation coefficients was determined mainly by the Li–O bonds both in LiNbO3:Zn and LiNbO3:Er crystals. We observed sharp changes in the second order nonlinear optical response of Zn-doped LiNbO3 single crystals at 1064 nm with increasing Zn concentration in the crystal. The calculated values of the nonlinear optical coefficients for the LiNbO3:Zn crystals exceed those for the LiNbO3:Er crystals. The LiNbO3:Zn crystal with dopant concentration 5.48 mol.% is the most suitable crystal for the second-harmonic conversion.

Tetracyanobutadienyl-Based Nonlinear Optical Dendronized Hyperbranched Polymer Synthesized via [2+2]Cycloaddition Polymer Postfunctionalization.

Dendronized hyperbranched polymers (DHPs) can provide advantages for both hyperbranched polymers and dendrimers, making them a promising structure platform for high-performance second-order nonlinear optical (NLO) materials. Herein, a new A3 +B2 -type DHP (HP2) is reported through facile and efficient [2+2]cycloaddition polymer postfunctionalization, in which tetracyanobutadienyl-based moieties are introduced as the main chromophores while isophorone-bridged moieties serve as the isolation chromophores. Benefiting from this unique hyperbranched structure design, the measured second-harmonic generation coefficient of HP2 can reach up to 96.6pmV-1 with high thermal stability, making it a good material candidate for second-order NLO applications.

The second and third-harmonic generation of spherical quantum dots under modified Kratzer plus screened Coulomb potential

We report the second harmonic generation (SHG) and third harmonic generation (THG) of GaAs/GaAlAs spherical quantum dots (QDs) with the modified Kratzer (MK) plus screened Coulomb (SC) potential in the presence of hydrostatic pressure and temperature. The eigen energies and wave functions can be deduced under the frame work of Nikiforov–Uvarov (NU) method. Then we calculate the SHG and THG coefficients within the framework of the density matrix method. Numerical calculations revealed that the SHG coefficient has two formants and THG coefficient has three formants depend on the energies and parameters of our system. The results indicate that these parameters bring about significant changes on the SHG and THG coefficients.

SrZnSnSe4: A quaternary selenide with large second harmonic generation and birefringence

Infrared nonlinear optical (NLO) materials with great laser conversion efficient play a key role in military and civil fields. SrZnSnSe4 was synthesized via replacing S elements with Se in SrZnSnS4 compound. SrZnSnSe4 crystallizes a two-dimensional layered structure with nearly parallel alignment of anionic groups [ZnSe4] and [SnSe4]. The experimental results show that the second harmonic generation (SHG) is about 5 times of AgGaS2, and the band gap of SrZnSnSe4 is 1.82 eV by direct measured method. In combination with theoretical calculation, the SHG coefficients of SrZnSnSe4 is d33 = 30.03 pm/V, and the birefringence is 0.290 at incident laser of 1240 nm, which can contribute to phase matching. These evidences show that SrZnSnSe4 can balance well among band gap, frequency doubling effect and birefringence, therefore, it is an excellent candidate for infrared NLO materials.

Effects of hydrostatic pressure, temperature and Al-concentration on the second-harmonic generation of tuned quantum dot/ring under a perpendicular magnetic field

The simultaneous effects of hydrostatic pressure, temperature and Al-concentration on the second-harmonic generation (SHG) coefficient for GaAs/Ga1−xAlxAs tuned quantum dot/quantum ring (QD/QR) under parabolic-inverse squared potential plus the modified Gaussian potential in a perpendicular magnetic field are studied in detail. The analytical expression of the SHG coefficient can be obtained using the density matrix theory and iterative method. The numerical results of GaAs/Ga1−xAlxAs tuned QD/QR are given. The result of calculation illuminates that the applied magnetic field, Al-concentration, hydrostatic pressure, temperature and the harmonic confinement frequency can make an impact on energy level interval, the product of matrix elements, transition frequency and other factors so that the peak value of SHG coefficient and resonance peak changing under the action of these factors. Furthermore, the depth and the radius of the QD have a bearing on the SHG coefficient.

Intra-Molecular Electrical Field Regulated Nonlinear Catalyst Charge Transfer in the Organic Conjugated Molecular System

The application of organic conjugated molecular systems to photocatalysis is based on the charge transition with different electronegative substituents and the electron–hole separation behavior of charge transfer under light excitation. In this work, the relationship between the intra-molecular electrical field and molecular second-order nonlinear optical properties is investigated theoretically by the sum-of-states (SOS) method. We use substituents with different electron affinity energy to construct internal electric fields with different properties in similar conjugated systems. The studies of these systems reveal the intra-molecular electric field strength and mode regulation of nonlinear optical coefficients and explain its physical mechanism. The intra-molecular charge recombination caused by the electrostatic potential multipole field of different substituents changes the transition behavior of one-photon, resulting in the enhancement of nonlinear optical properties (second-harmonic generation and sum-frequency coefficient) greater than 104.

Second and third harmonic generation in linear, concave and convex conical GaAs quantum dots

Second harmonic generation (SHG) and third harmonic generation (THG) in quantum dots with cylindrical geometry are studied by solving the Schrödinger equation within the effective mass approximation. The cylindrical nanostructures are a linear cone, convex cone and a concave cone compared with the solid cylindrical quantum dot. Results show that for the different cylindrical quantum dots of the same base radius, peaks of both the SHG and THG coefficients occur at different photon energies, and in order of increasing photon energy: solid cylinders, convex cones, linear cones and the concave cones. Additionally, peaks of both SHG and THG coefficients in conical quantum dots are more separated in energy than those associated with a purely solid cylindrical quantum dot. Potential applications and other features are discussed.