Second Harmonic Generation Coefficients Research Articles

Depending on the intense laser field of the nonlinear optical rectification, second and third harmonic generation in asymmetric parabolic-step and inverse parabolic-step quantum wells

The nonlinear optical rectification (NOR), the second harmonic generation (SHG) and the third harmonic generation (THG) coefficients in asymmetric parabolic-step quantum wells (APSQW) and asymmetric inverse parabolic-step quantum wells (AIPSQW) are considered as depending on the intense laser field (ILF). The found consequences indicate that ILF parameter approves a dynamic influence on the shape, width and height of the confined potential profile of both APSQW and AIPSQW, and the alterations of the dipole moment matrix elements and the energy levels (ELs) are followed on the profile of the confined potential. The potential profile and height of the AIPSQW compared to APSQW were affected differently from ILF intensity. With and without the ILF, the ELs in the APSQW are smaller than in the AIPSQW. These results designate that NOR, SHG, and THG coefficient of APSQW and AIPSQW may be controlled in a chosen energy range and the magnitude of the resonance peak (RP) by increasing ILF value. By modifying the ILF parameter, it is possible to classify red or blue shifts at the RP positions of the NOR, SHG and THG coefficients. We hope that our results will offer significant development of optical devices in many potential device applications for the appropriate selection of ILF values.

Second-harmonic generation in single-layer monochalcogenides: A response from first-principles real-time simulations

Second Harmonic Generation (SHG) of single-layer monochalcogenides, such as GaSe and InSe, has been recently reported [2D Mater. 5 (2018) 025019; J. Am. Chem. Soc. 2015, 137, 79947997] to be extremely strong with respect to bulk and multilayer forms. To clarify the origin of this strong SHG signal, we perform first-principles real-time simulations of linear and non-linear optical properties of these two-dimensional semiconducting materials. The simulations, based on ab-initio many-body theory, accurately treat the electron-hole correlation and capture excitonic effects that are deemed important to correctly predict the optical properties of such systems. We find indeed that, as observed for other 2D systems, the SHG intensity is redistributed at excitonic resonances. The obtained theoretical SHG intensity is an order of magnitude smaller than that reported at the experimental level. This result is in substantial agreement with previously published simulations which neglected the electron-hole correlation, demonstrating that many-body interactions are not at the origin of the strong SHG measured. We then show that the experimental data can be reconciled with the theoretical prediction when a single layer model, rather than a bulk one, is used to extract the SHG coefficient from the experimental data.

Prediction of Fluorooxoborates with Colossal Second Harmonic Generation (SHG) Coefficients and Extremely Wide Band Gaps: Towards Modulating Properties by Tuning the BO3/BO3F Ratio in Layers

AbstractFluorooxoborates have inspired investigations of deep‐ultraviolet (DUV) nonlinear optical (NLO) materials that can meet the multiple criteria. Herein, five stable structures with the composition of BaB2O3F2 (I–V) are discovered using the ab initio evolutionary algorithm. Among them, BaB2O3F2‐I has been synthesized experimentally and confirms the reliability of the method. All of the predicted structures possess extremely wide band gaps (8.1–9.0 eV). Moreover, four new structures exhibit giant second harmonic generation (SHG) coefficients (>3×KDP, d36=0.39 pm V−1). A novel type of the [BOF] layer with BO3:BO3F ratio of [1:1] is found in BaB2O3F2‐II and BaB2O3F2‐III. While BaB2O3F2‐IV and BaB2O3F2‐V are solely composed of the BO3F group and have colossal SHG coefficients (ca. 4×KDP). It gives the direct evidence that the BO3F group could generate strong SHG effect. Most importantly, the influences of BO3:BO3F ratio and their number density on band gap, birefringence and SHG effects are investigated.

Prediction of Fluorooxoborates with Colossal Second Harmonic Generation (SHG) Coefficients and Extremely Wide Band Gaps: Towards Modulating Properties by Tuning the BO3 /BO3 F Ratio in Layers.

Fluorooxoborates have inspired investigations of deep-ultraviolet (DUV) nonlinear optical (NLO) materials that can meet the multiple criteria. Herein, five stable structures with the composition of BaB2 O3 F2 (I-V) are discovered using the ab initio evolutionary algorithm. Among them, BaB2 O3 F2 -I has been synthesized experimentally and confirms the reliability of the method. All of the predicted structures possess extremely wide band gaps (8.1-9.0 eV). Moreover, four new structures exhibit giant second harmonic generation (SHG) coefficients (>3×KDP, d36 =0.39 pm V-1 ). A novel type of the [BOF] layer with BO3 :BO3 F ratio of [1:1] is found in BaB2 O3 F2 -II and BaB2 O3 F2 -III. While BaB2 O3 F2 -IV and BaB2 O3 F2 -V are solely composed of the BO3 F group and have colossal SHG coefficients (ca. 4×KDP). It gives the direct evidence that the BO3 F group could generate strong SHG effect. Most importantly, the influences of BO3 :BO3 F ratio and their number density on band gap, birefringence and SHG effects are investigated.

Dependence of the Second-Harmonic Generation Response on the Cell Volume to Band-Gap Ratio.

The second-harmonic generation (SHG) coefficients of 12 nonlinear optical chalcopyrites, ABC2 (A = Zn, Cd; B = Si, Ge, Sn; C = P, As) were calculated by first-principles methods to find that given the primitive cell volume V and the band gap Eg of ABC2, the SHG coefficients dav of ABC2 increase almost linearly with increasing value of V/Eg. This suggests that a noncentrosymmetric crystal has a large SHG response when it consists of large atoms, leading to a small band gap.

Tailoring second-order nonlinear optical effects in coupled quantum dot-metallic nanosphere structures using the Purcell effect

We study the modification of second-order nonlinear optical processes, like nonlinear optical rectification and second-harmonic generation, of a quantum dot that is coupled to a metallic nanosphere. We show that the strong variation of the spontaneous decay rate of the quantum dot near the metallic nanosphere can lead to strong enhancement or suppression of the nonlinear optical rectification and second-harmonic generation coefficients depending on the distance of the quantum dot from the surface of the nanosphere and on the direction of the electric dipole moment of the quantum dot. The nonlinear optical coefficients are also strongly influenced by the pure dephasing rate of the quantum dot.

Nonlinear Optical Rectification, Second and Third Harmonic Generations in Square-Step and Graded-Step Quantum Wells under Intense Laser Field

For square-step quantum wells (SSQWs) and graded-step quantum wells (GSQWs), the nonlinear optical rectification (NOR), second harmonic generation (SHG) and third harmonic generation (THG) coefficients under an intense laser field (ILF) are analyzed. The found results indicate that ILF can ensure a vital influence on the shape and height of the confined potential profile of both SSQWs and GSQWs, and alterations of the dipole moment matrix elements and the energy levels are adhered on the profile of the confined potential. According to the results, the potential profile and height of the GSQWs are affected more significantly by ILF intensity compared to SSQWs. These results indicate that NOR, SHG and THG coefficients of SSQWs and GSQWs may be calibrated in a preferred energy range and the magnitude of the resonance peak (RP) by tuning the ILF parameter. It is feasible to classify blue or red shifts in RP locations of NOR, SHG and THG coefficients by varying the ILF parameter. Our results can be useful in investigating new ways of manipulating the opto-electronic properties of semiconductor QW devices.

Effect of applied external fields on the nonlinear optical properties of a Woods-Saxon potential quantum well

In this present work a detailed theoretical study on the influence of the static electric, magnetic, and non-resonant intense THz laser fields on the nonlinear optical properties such as nonlinear optical rectification (NOR) and second harmonic generation (SHG), of a quantum well that has the Woods-Saxon potential profile. The static electric and high-frequency intense THz laser fields are applied along the growth-direction of the structure whilst the static magnetic field is applied perpendicular to them. The outcome of the numerical calculation demonstrates that, both the peak potions of the NOR and SHG coefficients exhibit a blue-shift with the increment of the static electric and magnetic fields, but their peak amplitudes increases with the magnitude of the electric field whilst decreases with the magnitude of the magnetic field. However, the peak positions of the NOR and SHG coefficients exhibit firstly a blue-shift, and then a red-shift with the increment of the laser intensity, but their peak amplitudes increases. We hope that these theoretical results will be useful for designing new optoelectronic devices with a performance tailored by the adjustment of the applied fields.

Refractive Index Modulates Second-Harmonic Responses in RE8O(CO3)3(OH)15X (RE = Y, Lu; X = Cl, Br): Rare-Earth Halide Carbonates as Ultraviolet Nonlinear Optical Materials

The first series of rare-earth chloride/bromine carbonate nonlinear optical (NLO) crystals, RE8O(CO3)3(OH)15X (RE = Y, Lu; X = Cl, Br), have been synthesized with a facile hydrothermal method. All of the title compounds were isostructural with the noncentrosymmetric space group P63 (no. 173), and their structures can be described as the [REO4(CO3)3] units connect the adjacent infinite [RE7O25]∞ layers in the a–b plane to form an intricate three-dimensional framework, and the Br– or Cl– anions were located in the center of equilateral triangles formed by the RE(3)O7 polyhedra. The measured second-harmonic generation (SHG) effects of Y8O(CO3)3(OH)15Cl, Lu8O(CO3)3(OH)15Cl, Y8O(CO3)3(OH)15Br, and Lu8O(CO3)3(OH)15Br were 1.65, 2.22, 1.83, and 3.00 times that of KH2PO4, respectively. Our study revealed that the difference of SHG efficiency was mainly derived from the different refractive indices of crystals when the orientation of [CO3]2– groups that had a relationship with the SHG coefficient was almost identical. Furthermore, the birefringences of the four crystals were successively measured to be 0.045, 0.062, 0.073, and 0.088 (λ = 546.1 nm), which were very favorable for realizing phase-matching in the visible and UV region. In addition, with a wide transparent region from UV to near infrared, they can be excellent UV NLO materials.

Li<sub>2</sub>BaSiSe<sub>4</sub>: A new metal-mixed selenide with outstanding second-harmonic generation

Nonlinear optical (NLO) materials as important frequency-conversion devices in solid state lasers, have attracted unprecedented attentions in laser science and technology. In infrared (IR) region, NLO materials display more important roles in view of critical application prospect including laser guidance, resource exploration and long-distance laser communication etc. AgGaS2, AgGaSe2 and ZnGeP2 are selected as the commercial IR NLO materials, but they exihibit low laser damage thresholds (LDT) induced by their small bandgaps, which limit their further applications in high energy laser systems. Therefore, it is still a big challenge to obtain new IR NLO materials, which could balance the demand of large second-harmonic generation (SHG) and high laser damage threshold. As a NLO material, the non-centrosymmetrical structure is the prerequisite condition, and mix-metal chalcogenides have attracted much attention since their structures exhibit a variety of acentric units arising from the combination of different center metals, which show different sizes, coordination preferences, and packing characteristics. Previous investigations indicate that the introduction of alkali and alkali earth metals is good for obtaining large band gap because they may avoid the d-d and f-f electron transition like popular LiGaS2, BaGa4S7 etc. Moreover, compared with sulfides, selenides produce larger SHG responses. Therefore, in this work, in aim at the balanced optical properties, we selected electricity-positive alkali metal Li, alkali earth metal Ba, silicon in IVA group and selenium as the raw materials. Through high temperature flux method, we have obtained a metal-mixed selenide Li2BaSiSe4. The raw materials are weighted with the molar ratio of 2:1:1:4, and then loaded into the graphite crucible, finally sealed in a silicon tube under ethane-oxygen flame. The tube is put in a program-computed furnace with the temperature program as blow: (1) heat from room temperature to 190°C in 3 h and keep at this temperature for 300 min; (2) heat from 190 to 450°C in 10 h and keep at this temperature for 20 h; (3) heat from 450 to 850°C in 10 h and keep at this temperature for 30 h; (4) cool from 850 to 400°C in 100 h and turn down the furnace. Optical characterizations contain single crystal X-Ray diffraction (XRD), powder XRD, Raman spectrum, UV-vis-NIR diffuse reflection spectrum, and SHG responses measurement at 2.09 μm. Moreover, theoretical calculations have also made to further investigate the relationship between properties and structure, including band structure, density of states, birefringence and SHG coefficients. Single crystals with millimeter sizes used for single crystal XRD and Raman spectrum are picked from the synthesized polycrystal under a microscope. The powder samples used for powder XRD characterization and UV-vis-NIR diffuse reflection are obtained from the ground polycrystals. The powder SHG responses are measured with sieved crystals in six different size ranges: 38−55, 55−88, 88−105, 105−150, 150−200, 200−250 μm, with AgGaS2 in the same particle size ranges as the references. The band gap of Li2BaSiSe4 is obtained from UV-vis-NIR diffuse reflection data converted by Kubelka-Munk function, which is measured to be 2.47 eV, which is larger than AgGaSe2 (1.83 eV). The SHG response is measured with 2.09 μm laser, and the result shows that Li2BaSiSe4 is type-I phase matchable and is equal to that of commercially applied AgGaS2. In conclusion, the introduction of Li and Ba could enlarge the band gap compared with classical AgGaSe2, but the SHG response need more rational designation to maintain at a high level.

Pb4B6O13: A Polar Lead Oxyborate with Uncommon ∞(B6O12)6- Layers Exhibiting a Large Second Harmonic Generation Response.

A new lead oxyborate, Pb4B6O13, has been successfully synthesized by introducing stereochemically active Pb2+ cations and distorted OPb4 tetrahedra into asymmetric borates. Pb4B6O13 exhibits an unprecedented two-dimensional ∞(B6O12)6- layer structure with a large second harmonic generation (SHG) response that is 3 times that of KH2PO4. In addition, theoretical work, including dipole moment calculations, electronic structure, and SHG coefficients combined with SHG density analysis, is reported. The results suggest that the enhanced SHG of Pb4B6O13 is attributed to the synergy effect of three functional units.

Excellent Infrared Nonlinear Optical Crystals BaMO(IO₃)₅ (M = V, Ta) Predicted by First Principle Calculations.

Two nonlinear optical crystals, BaVO(IO3)5 and BaTaO(IO3)5, are designed by substituting Nb with V and Ta, respectively, in BaNbO(IO3)5, which is itself a recently synthesized infrared nonlinear optical (NLO) material. The designs of BaVO(IO3)5 and BaTaO(IO3)5 from BaNbO(IO3)5 are based on the following motivation: BaVO(IO3)5 should have a larger second-harmonic generation (SHG) coefficient than BaNbO(IO3)5, as V will result in a stronger second-order Jahn-Teller effect than Nb due to its smaller ion radius; at the same time, BaTaO(IO3)5 should have a larger laser-damage threshold, due to the fact that Ta has a smaller electronegativity leading to a greater band-gap. Established on reliable first-principle calculations, it is demonstrated that BaVO(IO3)5 has a much larger SHG coefficient than BaNbO(IO3)5 (23.42 × 10−9 vs. 18.66 × 10−9 esu); and BaTaO(IO3)5 has a significantly greater band-gap than BaNbO(IO3)5 (4.20 vs. 3.55 eV). Meanwhile, the absorption spectra and birefringences of both BaVO(IO3)5 and BaTaO(IO3)5 are acceptable for practice, suggesting that these two crystals can both be expected to be excellent infrared NLO materials.

Synthesis, Structure, and Properties of the Non-Centrosymmeteric Compound LiNaRbB5O8(OH)2

A new non-centrosymmetric hydroxyl alkali metal borate LiNaRbB5O8(OH)2 has been grown under mild hydrothermal conditions at 220 °C. LiNaRbB5O8(OH)2 belongs to the orthorhombic space group Aba2, with a = 11.3017(5) A, b = 10.9956(5) A, c = 9.2860(4) A, and Z = 2. The crystal structure of LiNaRbB5O8(OH)2 consists of Li/Na–O, Rb–O polyhedra, and [B5O8(OH)2]3– groups. The transmittance spectrum of the LiNaRbB5O8(OH)2 exhibits an absorption edge less than 200 nm in the UV region. The powder second-harmonic generation coefficient in LiNaRbB5O8(OH)2 is about one-third that of KH2PO4 (KDP) based on the Kurtz-Perry method. First principle calculations based on band structure, density of states, and optical properties are used to better understand the relationship between electronic structure and optical properties.

Synthesis, crystal structures and nonlinear optical properties of polymorphism: α- and β-RbHgI3·H2O

New noncentrosymmetric polymorphs, namely, α- and β-RbHgI3·H2O, have been synthesized by conventional solution reaction. The two titled compounds crystallize in the monoclinic space groups Cc (no. 9) and Pc (no. 7), respectively. In their crystal structures, [HgI4] tetrahedrons connect with each other via sharing corners into one-dimensional (1-D) [HgI3] chains, and then all the 1-D chains connect with [Rb(H2O)]+ complexes to form the three-dimensional (3-D) frameworks. The consistent packing style results in a strong macroscopic nonlinear optical effect due to the superimposition of the microscopic second-order susceptibilities of [HgI4] tetrahedra. Powder second-harmonic generation (SHG) measurements show that both α- and β-RbHgI3·H2O are phase-matchable (type I), and the measured SHG coefficients are about 15.0 and 14.0 times that of KH2PO4 (KDP). Both the compounds exhibit wide transparency from near UV to mid and far-infrared region, suggesting that α- and β-RbHgI3·H2O are potential infrared NLO crystals. Band structure and optical property were also calculated by DFT methods.

Growth and characterization of nonlinear optical crystal Gamma glycine by the additive of lithium bromide

Single crystal of γ-glycine, a polymorphic form of glycine, was grown by slow solvent evaporation technique by the additive of lithium bromide. It was grown from the aqueous solution of glycine and lithium bromide in 2:1 M ratio respectively at room temperature. Good quality of γ-glycine single crystals was harvested up to the dimension of 25 × 22 × 20 mm3. In order to reveal its properties, the grown single crystals were subjected to various characterizations. Powder X-ray diffraction of the grown crystal was recorded and indexed. The unit cell parameters of the crystals were estimated by single crystal x-ray diffraction and they were compared with the literature values. The identification of the functional groups and hence the compound present in the crystalline sample by FTIR analysis confirms the polymorphic form of glycine. Optical transmittance studies were carried out by UV–Vis-NIR transmission spectrum in the range of 200–1100 nm wavelength. The powdered sample of the crystal was subjected to Kurtz Perry powder technique to find the coefficient of Second harmonic generation. The second harmonic generation (SHG) conversion efficiency of γ-glycine crystal is more than twice when compared with KDP crystal. The grown γ-glycine crystal was further characterized by Thermo gravimetric analysis (TGA) and Differential thermal analysis, to find its thermal stability and decomposition temperature. Dielectric constant and Dielectric loss were determined at different frequencies with respect to various temperatures. The mechanical properties such as microhardness and yield strength were evaluated by Vicker’s microhardness tester.

Computer-Assisted Design of a Superior Be2BO3F Deep-Ultraviolet Nonlinear-Optical Material.

Deep-ultraviolet (DUV) nonlinear-optical (NLO) materials generating coherent DUV light by a direct second-harmonic-generation (SHG) process have long been pursued as industrially useful lasers. For several decades, KBe2BO3F2 (KBBF) has been regarded as the best DUV-NLO material; it is characterized by a short DUV phase-matching edge of 161 nm and a large SHG coefficient of 0.47 pm/V. However, it suffers a strong layering tendency, hindering the growth of large crystals for commercial use. Here, we use a computer-aided swarm structure searching technique to design an alternative DUV-NLO material with a new atmospheric-pressure phase Be2BO3F2 with a P6̅2 c space group (γ-BBF) that outperforms the DUV-NLO properties of KBBF. The predicted DUV phase-matching edge and SHG coefficient of γ-BBF are 152 nm and 0.70 pm/V, respectively. The structure of γ-BBF reduces the layering tendency compared with KBBF because of the absence of K atoms in the γ-BBF crystal. Our work paves the way for superior DUV-NLO materials that can be grown as large crystals for commercial applications.

Deep-ultraviolet nonlinear optical materials: Development trend and innovative exploration

With the rapid development of all-solid-state laser technology in the field of optical communication, optical processing and optical storage, deep-ultraviolet (deep-UV, wavelengths below 200 nm) nonlinear optical (NLO) materials have become a hot topic at home and abroad. Coherent radiation in the deep-UV is possible with excimer lasers, e.g., F2 excimer at 157 nm. However, solid-state lasers in these wavelength ranges are often preferred owing to handling ease, narrow bandwidth, tunability, high energy density, and high peak power density. An excellent manner to generate coherent deep-UV light is through solid-state lasers using cascaded frequency conversion with NLO materials. Deep-UV NLO crystals, which can double the frequency of incident light to the deep-UV region, are essential for all-solid-state laser. The prerequisites for deep-UV NLO crystals are crystallographically noncentrosymmetric (NCS), wide optical transparency window, large second harmonic generation (SHG) response, phase- matching capability, and easy growth of large (centimeter size) high quality single crystals. For years, there has been a “200 nm wall”, that is, no material is available for deep-UV SHG. Over the past decades, great efforts have been made on chemical design and synthesis of deep-UV NLO materials. Currently, only KBe2BO3F2 (KBBF) crystal is capable for generating deep-UV light through direct sixth harmonic generation of the Nd:YAG laser. The infinite ∞[Be2BO3F2]− single layers in KBBF provide a relatively large SHG coefficient ( d 11=0.47 pm/V) and a sufficient birefringence (Δ n =0.07@1064 nm). However, the KBBF crystals have insurmountable intrinsic defects, such as the high toxicity of the beryllium oxide, and the serious layer growth habit, which greatly restrict its commercialization and application process. Therefore, researchers are actively exploring the next generation of deep-UV NLO materials. In this review, we will first briefly discuss the history of deep-UV NLO crystals. The main factors that restrict the development of deep-UV NLO crystals were highlighted, emphasizing one of the greatest challenges after the material is synthesized is its large single-crystal growth. In the second section, we will focus on progress and trend of deep-UV NLO materials in recent ten years and divide them into different categories according to different material systems and structural features. Five groups of materials are given—beryllium borates, beryllium-free borates, carbonate-fluorides, phosphates and fluorooxoborates. The absorption edge, powder SHG efficiency and birefringence of these materials are summarized in detail. In this section, the development of fluorooxoborates is discussed and the important achievements are reviewed systematically. In addition, the major contradictions among bandgap, NLO coefficient and birefringence were discussed and the methods of theoretical structure prediction algorithms for solving these problems were proposed in order to provide reference for discovering new deep-UV NLO materials.

The Large Second‐Harmonic Generation of LiCs2PO4 is caused by the Metal‐Cation‐Centered Groups

AbstractWe evaluated the individual atom contributions to the second harmonic generation (SHG) coefficients of LiCs2PO4 (LCPO) by introducing the partial response functionals on the basis of first principles calculations. The SHG response of LCPO is dominated by the metal‐cation‐centered groups CsO6 and LiO4, not by the nonmetal‐cation‐centered groups PO4 expected from the existing models and theories. The SHG coefficients of LCPO are determined mainly by the occupied orbitals O 2p and Cs 5p as well as by the unoccupied orbitals Cs 5d and Li 2p. For the SHG response of a material, the polarizable atomic orbitals of the occupied and the unoccupied states are both important.

The Large Second-Harmonic Generation of LiCs2 PO4 is caused by the Metal-Cation-Centered Groups.

We evaluated the individual atom contributions to the second harmonic generation (SHG) coefficients of LiCs2 PO4 (LCPO) by introducing the partial response functionals on the basis of first principles calculations. The SHG response of LCPO is dominated by the metal-cation-centered groups CsO6 and LiO4 , not by the nonmetal-cation-centered groups PO4 expected from the existing models and theories. The SHG coefficients of LCPO are determined mainly by the occupied orbitals O 2p and Cs 5p as well as by the unoccupied orbitals Cs 5d and Li 2p. For the SHG response of a material, the polarizable atomic orbitals of the occupied and the unoccupied states are both important.

A Joint Strategy To Evaluate the Microscopic Origin of the Second-Harmonic-Generation Response in Nonpolar ABCO3F Compounds.

In this paper, a joint strategy was proposed to investigate the microscopic origin of the second-harmonic-generation (SHG) response in nonpolar ABCO3F compounds. The SHG coefficients of ABCO3F were evaluated using finite-field and sum-over-states methods. The tendency of the obtained SHG tensors is in good agreement with the powder SHG response. The atomic contribution was investigated using variation of the atomic charges and bandwidth of occupied atomic states. The results show that oxygen states play a key role in determining the SHG response, and the neighboring divalent cations exert a indirect influence via covalent interaction. The bidentate bonding pattern is beneficial to obtaining a largely enhanced SHG response.