Second Harmonic Generation Coefficients Research Articles

Large bulk photovoltaic effect and second-harmonic generation in few-layer pentagonal semiconductors PdS2 and PdSe2

Recently, atomically thin PdSe2 semiconductors with rare pentagonal Se–Pd–Se monolayers were synthesized and were also found to possess superior properties such as ultrahigh air stability, tunable band gap and high carrier mobility, thus offering a new family of two-dimensional (2D) materials for exploration of 2D semiconductor physics and for applications in advanced opto-electronic and nonlinear photonic devices. In this work, we systematically study the nonlinear optical (NLO) responses [namely, bulk photovoltaic effect (BPVE), second-harmonic generation (SHG) and linear electric-optic (LEO) effect] of noncentrosymmetric bilayer (BL) and four-layer PdS2 and PdSe2 by applying the first-principles density functional theory with the generalized gradient approximation plus scissors-correction. First of all, we find that these few-layer PdX 2 (X = S and Se) exhibit prominent BPVE. In particular, the calculated shift current conductivity is in the order of 130 μA V−2, being very high compared to known BPVE materials. Similarly, their injection current susceptibilities are in the order of 100 × 108 A V−2 s−1, again being large. Secondly, the calculated SHG coefficients (χ (2)) of these materials are also large, being one order higher than that of the best-known few-layer group 6B transition metal dichalcogenides. For example, the maximum magnitude of χ (2) can reach 1.4 × 103 pm V−1 for BL PdSe2 at 1.9 eV and 1.2 × 103 pm V−1 at 3.1 eV for BL PdS2. Thirdly we find significant LEO coefficients for these structures in the low photon energy. All these indicate that 2D PdX 2 semiconductors will find promising NLO applications in light signal modulators, frequency converters, electro-optical switches and photovoltaic solar cells. Fourthly, we find that the large BPVE and SHG of the few-layer PdX 2 structures are due to strong intralayer directional covalent bonding and also 2D quantum confinement. Finally, we also discuss the prominent features of these NLO spectra of these materials in terms of their electronic structure and optical dielectric functions.

Synthesis, structure, linear and nonlinear optical properties of noncentrosymmetric quaternary diamond-like semiconductors, Cu2ZnGeSe4 (CZGSe) and the novel Cu4ZnGe2Se7

In this study, two quaternary diamond-like semiconductors (DLSs) in the Cu-Zn-Ge-Se system, the known Cu2ZnGeSe4 (also referred to as CZGSe) and the new Cu4ZnGe2Se7, are compared in terms of their crystal structures, electronic structures and physicochemical properties. Both compounds were prepared by high-temperature, solid-state synthesis at 800 °C. Single crystal X-ray diffraction was used to determine the structure of Cu4ZnGe2Se7. The structures of both Cu2ZnGeSe4 and Cu4ZnGe2Se7 can be considered as derivatives of cubic diamond. Cu4ZnGe2Se7, with a reduced symmetry due to the cation ordering pattern, adopts the Cu4NiSi2S7 structure type, with space group C2. The corner-sharing tetrahedra in Cu4ZnGe2Se7 are slightly distorted because the charge for some of the S2- anions is not compensated by the first-nearest-neighbor cations. Rietveld refinements using synchrotron X-ray powder diffraction data were used to assess the phase purity of the samples and confirm the bulk structural behavior. Diffuse reflectance UV/Vis/NIR spectroscopy shows that Cu2ZnGeSe4 and Cu4ZnGe2Se7 have direct optical bandgaps of 1.38 and 0.91 eV, respectively. Electronic structure calculations implementing density functional theory confirm the direct bandgap for Cu4ZnGe2Se7, with a calculated value of 0.62 eV. Both compounds are air stable, thermally stable up to relatively high temperatures, undergo phase transitions and have wide windows of optical clarity. The Kurtz-Perry powder technique was used to determine the second harmonic generation (SHG) responses using a commercial AgGaSe2 standard. While Cu4ZnGe2Se7 displays a weak SHG response, Cu2ZnGeSe4 exhibits a response that is greater than several benchmark materials, with a large SHG coefficient, χ(2), of 43 ± 6 pm/V at λ = 2900 nm.

Exciton-driven linear and nonlinear optical responses in metal monoxide monolayersMO(M=Mg,Ca,Cd) from first-principles calculations

We study the linear and nonlinear [second-harmonic generation (SHG)] spectra of metal monoxide $\mathrm{MO}$ ($M$=Mg,Ca,Cd) monolayers by using a first-principles approach based on many-body theory. Our results indicate that the strongly bound excitons in $\mathrm{MO}$ with planar structure characterize the optical properties, including both linear and SHG spectra. The optical bandgap ${E}_{\text{opt}}$ is 4.63, 3.71, and 1.27 eV, while the exciton binding energy is as large as 2.49, 2.37, and 1.13 eV, for MgO, CaO, and CdO, respectively. Moreover, the largest SHG coefficient of 586 pm/V is found in CdO monolayer with the smallest bandgap among the three $\mathrm{MO}$ materials. Most importantly, we find a linear relationship between the SHG coefficient and $\mathrm{Qd}/{E}_{\text{opt}}$ ($Q$ is the transferred Bader charge and $d$ is the bond length) which can be used as a descriptor to search for new two-dimensional nonlinear materials.

Mg2In3Si2P7: A Quaternary Diamond-like Phosphide Infrared Nonlinear Optical Material Derived from ZnGeP2.

Balancing the second-harmonic generation (SHG) coefficient, band gap, and birefringence is a vital but addressable challenge for designing infrared nonlinear optical materials. By applying a "rigidity-flexibility coupling" strategy, a quaternary diamond-like phosphide, Mg2In3Si2P7, with wurtzite-type superstructure was successfully designed and synthesized. Remarkably, it achieved the rare coexistence of giant second-harmonic generation (2 × ZnGeP2 and 7.1 × AgGaS2), suitable band gap (2.21 eV), moderate birefringence (0.107), and wide IR transparent range (0.56-16.4 μm). First-principles calculations revealed that the giant SHG response and large birefringence can be attributed to the synergy of arrangement-aligned [InP4] and [SiP4] tetrahedra. This work not only opens a new avenue for designing advanced infrared nonlinear optical materials but also may spur more explorations on quaternary diamond-like pnictides.

Strong bulk photovoltaic effect and second-harmonic generation in two-dimensional selenium and tellurium

Few-layer selenium and tellurium films have been recently prepared, and they provide a new platform to explore novel properties of two-dimensional (2D) elemental materials. In this work, we have performed a systematic first-principles study on the electronic, linear, and nonlinear optical (NLO) properties of atomically thin selenium and tellurium films within the density-functional theory with the generalized gradient approximation plus scissors correction using the band gaps from the relativistic hybrid Heyd-Scuseria-Ernzerhof functional calculations. Interestingly, we find that few-layer Se and Te possess large second-harmonic generation (SHG), linear electro-optic effect, and bulk photovoltaic effect. In particular, trilayer (TL) Te possesses large SHG coefficient, being more than 65 times larger than that of GaN, a widely used NLO material. Bilayer (BL) Te has huge static SHG coefficient, being more than 100 times larger than that of GaN. Furthermore, monolayer (ML) Se possesses large SHG coefficient. Moreover, we predict that TL Te exhibits strong bulk photovoltaic effect (BPVE), being greater than that of GeS, a polar system with the largest BPVE found so far. Although the shift current conductivities of bulk and 2D Se are comparable, the shift current conductivities of TL Te are five times larger than those of bulk Te. Finally, an analysis of the calculated electronic band structures indicates that the strong NLO responses of 2D Se and Te materials are primarily derived from their low-dimensional structures with high anisotropy, directional covalent bonding, lone-pair electrons, and relatively small band gaps. These findings provide a practical strategy to search for excellent NLO and BPVE materials.

The influence of second-harmonic generation under the external electric field and magnetic field of parabolic quantum dots

The second-harmonic generation (SHG) of parabolic quantum dots (QDs) with different confining potentials energies in the ρ and z directions under external electric and magnetic fields are studied theoretically. We have applied the compact-density-matrix approach and iterative method to obtain the SHG coefficients. The results indicate that the electric field and the size of QDs affect the peaks of SHG coefficient. In addition, the magnetic field and the radius of QDs not only strongly affect the value of the SHG peaks, but also cause the energy positions of the SHG coefficients to shift.

High-Performance Second-Harmonic-Generation (SHG) Materials: New Developments and New Strategies.

ConspectusSecond-harmonic-generation (SHG) causes the frequency doubling of light, which is very useful for generating high-energy lasers with specific wavelengths. Noncentrosymmetry (NCS) is the first requirement for an SHG process because the SHG coefficient is zero (χ2 = 0) in all centrosymmetric structures. At this stage, developing novel NCS crystals is a crucial scientific topic. Assembling polar units in an addictive fashion can facilely form NCS crystals with outstanding SHG performance. In this way, our group has obtained many different NCS crystals with extremely large SHG intensities (>5 × KDP or 1 × KTP). In this Account, we first provide a brief review of the development of SHG materials and concisely highlight the features of the excellent SHG materials. Then, we present four facile and rational molecular design strategies: (1) Traditional BO33--based crystals feature short absorption edges but usually suffer from relatively weak SHG performance (<5 × KDP). The combination of two types of pure π-conjugated anions (BO33- and NO3-) in a parallel fashion in the same compound has afforded a metal borate nitrate with a strong SHG effect. (2) To overcome the problems of the weak SHG effect and small birefringence in the less anisotropic QO4-based compounds, highly polarizable cations such as Hg2+ and Bi3+ are introduced into these systems, which greatly enhances both SHG effects and birefringence. (3) Iodate anions can be condensed into polynuclear iodate anions with a higher density of I5+ per unit cell, hence polyiodate anions can serve as excellent SHG-active groups. We developed a novel synthesis method for hydrothermal reactions under a phosphoric acid medium and obtained a series of metal polyiodates with strong SHG effects. In addition, as the number of iodate groups increases, the structural configuration of the polyiodate anion changes from linear to bent. (4) We introduce the concept of aliovalent substitution which features site-to-site atomic displacement at the structural level. Such aliovalent substitution led to new materials that have the same chemical stoichiometries or structural features as their parent compounds. Thus, aliovalent substitution can provide more experimental opportunities and afford new high-performance SHG materials. The introduction of a fluoride anion and the replacement of metal cations in the MO6 octahedron can result in new metal iodates with balanced properties including a large SHG effect, a wide band gap, and a high laser-induced damage threshold (LIDT) value. Finally, we briefly discuss several problems associated with the studies of SHG materials and give some prospects for SHG materials in the future.

Designing a Family of Aluminum-Containing Fluoroborate Crystals with Enhanced Birefringence and Second-Harmonic Generation Coefficients Based on the First-Principles Methods

Rb3Al3B3O10F (or RbAlBO3.33F0.33) is an F-deficient crystal grown at high temperature and reported to be a potential ultraviolet or deep ultraviolet (DUV) nonlinear optical crystal. However, the sy...

To improve the key properties of nonlinear optical crystals assembled with tetrahedral functional building units.

Nonlinear optical (NLO) crystals assembled with conventional non-π-conjugated tetrahedral functional building units (FBUs), generally referring to [PO4] and [BO4], usually exhibit weak nonlinearity and poor birefringence. It is currently proposed that partially substituting oxygen atoms with fluoride atoms in these FBUs could enhance these crucial properties. Hence, we investigated for the first time the NLO-related properties of NH4BAsO4F (ABAF), which was constructed from tetrahedral [BO3F] and [AsO4] FBUs, and enhancements of these properties were observed in this material, that is large second-harmonic generation (SHG) response (2 × KDP) and improved birefringence (0.03 at 1064 nm). Notably, both SHG coefficient and birefringence of ABAF exceeded those of a great majority of phosphates, sulfates, or boron phosphates and achieved a preferable balance. It is interesting that ABAF shows vast structural similarities to the typical NLO crystals Sr2Be2B2O7 (SBBO) and KBe2BO3F2 (KBBF), which might be the partial reason why it showed improvement in these vital properties. This work may afford some inspiration for enhancing the key performances of NLO crystals assembled with non-π-conjugated tetrahedra.

Significant second-harmonic generation and bulk photovoltaic effect in trigonal selenium and tellurium chains.

One-dimensional (1D) selenium and tellurium crystalize in helical chainlike structures and thus exhibit fascinating properties. By performing first-principles calculations, we have researched the linear and nonlinear optical (NLO) properties of 1D Se and Te, and find that both systems exhibit pronounced NLO responses. In particular, 1D Se is found to possess a large second-harmonic generation coefficient with the χ value being up to 7 times larger than that of GaN, and is even several times larger than that of the bulk counterpart. On the other hand, 1D Te also produces significant NLO susceptibility χ which exceeds that of bulk GaN by 5 times. Furthermore, 1D Te is shown to possess a prominent linear electro-optic coefficient rxxx(0). In particular, the Te chain exhibits a large shift current response and the maximum is twice as large as the maximal photovoltaic responses obtained from BaTiO3. Therefore, 1D Se and Te may find potential applications in solar energy conversion, electro-optical switches, and so on. Finally, the much stronger NLO effects of 1D Se and Te are attributed to their one-dimensional structures with high anisotropy, strong covalent bonding and lone-pair electrons. These findings will contribute further to experimental studies and the search for excellent materials with large NLO effects.

Role of external fields on the nonlinear optical properties of a n-type asymmetric $$\delta$$-doped double quantum well

The effects of in-growth applied electric fields and in-plane (x-oriented) magnetic fields on the nonlinear optical rectification (NOR), second harmonic generation (SHG) and third harmonic generation (THG) of n-type asymmetric double $$\delta$$ -doped GaAs quantum well are theoretically investigated. One-dimensional Schrodinger equation is solved by considering effective mass and parabolic band approximations to obtain subband energy levels and their related wave functions. The variations in the NOR, SHG and THG coefficients are determined by using the iterative solutions of the compact density matrix approach. Obtained results indicate that the applied electric field leads to optical red-shift on NOR, SHG and THG coefficients while the magnetic field causes optical blue-shift on that coefficients. Hence we can conclude that applied electromagnetic fields can be used to tune optical properties of devices working within the region of infrared electromagnetic spectrum.

Antiferromagnetism-induced second-order nonlinear optical responses of centrosymmetric bilayer CrI3

Antiferromagnetism (AF) in AB′-stacked centrosymmetric bilayer (BL) CrI3 breaks both spatial inversion (P) and time-reversal (T) symmetries but maintains the combined PTsymmetry, thus inducing novel second-order nonlinear optical (NLO) responses such as second-harmonic generation (SHG), linear electric-optic effect (LEO) and bulk photovoltaic effect (BPVE). In this work, we calculate AF-induced NLO responses of the BL CrI3 based on the density functional theory with the generalized gradient approximation (GGA) plus onsite Coulomb correlation (U), i.e., the GGA+U method. Interestingly, we find that the magnetic SHG, LEO and photocurrent in the AF BL CrI3 are huge, being comparable or even larger than that of the well-known nonmagnetic noncentrosymmetric semiconductors. For example, the calculated SHG coefficients are in the same order of magnitude as that of MoS2 monolayer (ML), the most promising 2D material for NLO devices. The calculated LEO coefficients are almost three times larger than that of MoS2 ML. The calculated NLO photocurrent in the CrI3BL is among the largest values predicted so far for the BPVE materials. On the other hand, unlike nonmagnetic semiconductors, the NLO responses in the AF BL CrI3 are nonreciprocal and also switchable by rotating magnetization direction. Therefore, our interesting findings indicate that the AF BL CrI3 will not only provide a valuable platform for exploring new physics of low-dimensional magnetism but also have promising applications in magnetic NLO and LEO devices such as frequency conversion, electro-optical switches, and light signal modulators as well as high energy conversion efficiency photovoltaic solar cells.

Comment on “Tunneling effect on second-harmonic generation in quantum dot molecule, Superlattices and Microstructures 91 (2016) 358–364”

Abstract A comment about the paper “Tunneling effect on second-harmonic generation in quantum dot molecule, Superlattices and Microstructures 91 (2016) 358–364” is provided. It is shown that the formula used by the authors for the study of the second-harmonic generation coefficient cannot apply in the system under study. Therefore, the results of the paper are incorrect.

Different mechanism of response of asymmetric lone pair electrons around ns2 cations to birefringence and second harmonic generation

The 6s2 lone-pair electrons (Pb2+, Bi3+) and 5s2 lone-pair electrons (Sn2+, Sb3+) show different responses to birefringence than they do to second harmonic generation (SHG). In the current work, different mechanisms of birefringence and SHG responses induced by Pb2+/Sn2+ cations were investigated using the first-principles method on AB2O3F2 (A = Ba, Sn, Pb). The obtained birefringence and SHG coefficients were in good agreement with the experimental values. The anisotropic lone-pair electron distribution was found at the states near the Fermi level containing cation sp-oxygen p states. Our analyses showed the birefringences of the AB2O3F2 (A = Ba, Sn, Pb) compounds to be directly affected by the anisotropic lone-pair electron distribution, however, the SHG responses of these three compounds have a more complicated relationship with the hybrid cation-oxygen states. The expanded hybrid cation-oxygen states including the lone-pair states were concluded to endow the PbB2O3F2 compound with a stronger SHG response than those displayed by the other compounds.

Finding Optimal Mid-Infrared Nonlinear Optical Materials in Germanates by First-Principles High-Throughput Screening and Experimental Verification.

Owing to wide infrared (IR) transparency ranges, high laser damage thresholds, and being easy to grow in open air, germanates are emerging as promising mid-infrared (mid-IR) nonlinear optical (NLO) materials. However, the germanates as NLO materials have not been investigated comprehensively and the crystals with large second harmonic generation (SHG) response have not been identified. Herein, we used the first-principles high-throughput screening pipeline for NLO materials to search for excellent NLO crystals from germanates collected in the inorganic crystal structure database. After two steps of screening, three crystals are picked out from 128 structures based on their predicted energy gaps, birefringences, and SHG coefficients. Subsequently, the three germanates are synthesized and measured. The results show that Pb3Ga2Ge4O14 and Ba2TiGe2O8 exhibit a wide energy gap (>3.1 eV) and a strong phase-matchable SHG intensity that are comparable to the benchmark AgGaS2 (0.8 and 1.2 × AgGaS2, respectively). In addition, the statistical analyses of different categories classified according to their cations show that the d0-transition metal and lone pair cations are more conducive to achieving a larger SHG response and birefringence compared to other cations in germanates. It gives a guideline for exploring new mid-IR NLO materials.

The laser field controlling on the nonlinear optical specifications of the electric field-triggered Rosen-Morse quantum well

We consider, for the first time, optical specifications such as the nonlinear optical rectification (NOR), the second harmonic generation (SHG) and the third harmonic generation (THG) of quantum well (QW) that has the Rosen-Morse potential confinement and is generated by GaAs/GaAlAs heterostructure. To do this, QW structure is firstly asymmetrized by applying an external electric field, as 10 kV/cm. Therefore, the electric field-triggered (F=10 kV/cm) Rosen-Morse QW (eftRMQW) is taken into consideration throughout the study. In this study, it is elucidated that how to control NOR, SHG and THG optical responses through monochromatic linearly polarized intense laser field (ILF). In order to be able to investigate the ILF effects, the time-dependent of ILF is removed to potential energy term of the wave equation by using Kramers-Henneberger (KH) and the dipole approximations, building the laser-dressed potential. Then, the bound state energies and the wave functions of eftRMQW are obtained using the diagonalization method within the effective mass approach and the parabolic approximation. The influences of the ILF and structural parameters of eftRMQW on NOR, SHG and THG coefficients are discussed in detail. The optimum of structure is ferreted out for devices design and applications that will consider eftRMQW, and for this optimum the alternative parameter analysis is carried out.

Modeling of the second harmonic generation in a lens-shaped InAs/GaAs quantum core/shell dot under temperature, pressure and applied electric field effects

In this paper, we explore the second harmonic generation (SHG) in a lens-shaped InAs/GaAs quantum core/shell (LSQCS). The three-dimensional Schrödinger equation is given under the framework of the effective mass approximation and it is solved by using the Finite Difference Method (FDM). In this work, we have studied the effects of the structure dimensions, the applied transverse electric field, the hydrostatic pressure and the temperature on the SHG. Obtained results show that the SHG coefficient experiences an obvious red shift and an increase in magnitude with increasing the core radius. Therefore, we note that the SHG experiences a blue shift (red shift) with increasing temperature (pressure). Moreover, both resonant peaks values of the SHG are not a monotonic function of the applied electric field. Thus, SHG reaches its optimized magnitude at a low electric field intensity which is directed along one side of the cross section of the structure under investigation. Finally, at a low electric field intensity, a comparative analysis has shown that the SHG magnitude in LSQCS was 22% higher than that of the uncapped single quantum dot (SQD and a red shift has occurred.

Enhancement of the second harmonic generation in a coupled lens-shaped quantum dots under wetting layer, temperature, pressure, and electric field effects

In this paper, a theoretical study of the second harmonic generation (SHG) in a coupled lens shaped InAs/GaAs quantum dots is presented within the framework of the compact density-matrix approach and the finite difference method. In literature, many theoretical studies have neglected the wetting layer (WL) effect. As well, other effects such as the pressure, the external electric field, the temperature and the structural dimensions are not introduced together. Furthermore, in many researches only a single quantum dot (SQD) with and without wetting layer is investigated. What is done in this work, a detailed and comprehensive study of a vertically coupled lens-shaped InAs/GaAs coupled to a WL is presented under the external proofs effects mentioned above. Also, the structural dimensions, the electric field, the relaxation rate, the hydrostatic pressure, and the temperature effects are explored in details and the SHG is optimized. We have found out that the wetting layer has been shown to be so influential on the SHG magnitude and on the corresponding resonant energy. So, calculated results show that a strong SHG coefficient can be obtained by choosing a group of the optimized structural dimensions and the external proofs previously mentioned above. With a good choice of these parameters, it’s found that the SHG coefficient reaches the order of magnitude of 10−7 m/V, which is larger than the corresponding values obtained with a SQD. Besides, obtained results revealed that a red or a blue-shifted energy can be obtained. This behavior in the SHG gives a new degree of freedom in regions of interest for optoelectronic device applications.

Rb3Na(H2C3N3O3)4·3H2O with Large Birefringence.

A mixed alkali-metal nonlinear optical (NLO) dihydro-cyanurate crystal Rb3Na(H2C3N3O3)4·3H2O has been synthesized via the hydrothermal method. Its calculated birefringence is about 0.368, which is very large, its ultraviolet (UV) cutoff edge is down to 230 nm, and the powder second harmonic generation (SHG) intensity is about 0.2 × KDP. In addition, a first-principles investigation of the electronic properties on Rb3Na(H2C3N3O3)4·3H2O was carried out. The calculated band gap and SHG coefficient values agree well with the experimental ones. These results suggest that it could be applied as a UV birefringent material.

The effect of intense laser field on the nonlinear optical features in asymmetric multiple step and inverse V-shaped multiple step quantum wells

For asymmetric multiple step quantum wells (AMS QWs) and asymmetric inverse V-shaped multiple step quantum wells (AIVSMS QWs), the nonlinear optical features, such as the nonlinear optical rectification (NOR), the second harmonic generation (SHG) and the third harmonic generation (THG) coefficients are analyzed as according on the intense laser field (ILF). The found consequences indicate that the ILF parameter confirms a vital influence on the shape and height of the confined potential profile of both AMS QWs and AIVSMS QWs, and the 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 AIVSMS QWs compared to AMS QWs were affected differently from ILF intensity. These results indicate that NOR, SHG, and THG coefficient of AMS QWs and AIVSMS QWs may be regulated in a preferred energy range and the magnitude of the resonance peak (RP) by tuning the ILF parameter. By varying the ILF parameter, it is feasible to classify blue or red shifts in RP locations of NOR, SHG and THG coefficients. Our results can be valuable in investigating new ways of manipulating the opto-electronic properties of semiconductor QW devices.Highlights•The electro-optical properties of AMS QWs and AIVSMS QWs vary by increasing ILF.•The change of AIVSMS QWs compared to AMS QWs is more affected by ILF.•NOR, SHG, and THG coefficients change with rising ILF.•RP spectrums show blue or red shifts as according to ILF.