Second Harmonic Generation Coefficients Research Articles

Nonlinear Optical Second Harmonic Generation Characteristics in Cylindrical GaAs/Ga1–ηAlηAs Quantum Dots

This article theoretically examines the effect of various variables on the second harmonic generation (SHG) coefficients of cylindrical GaAs/Ga1–ηAlηAs quantum dots. The iterative approach and the compact‐density matrix method have been utilized to determine the expression of the SHG coefficient. The outcomes demonstrate that the variation of the SHG coefficient is closely related to structural parameters, external conditions, and incident photon energy.

The electronic structures and optical properties induced by spin-orbit-coupling in LiPbPO4 compound

Phosphate materials are excellent candidates for nonlinear optical materials, thus necessitating a comprehensive and in-depth study of them. Here, inspired by the interesting phenomenon induced by the spin-orbit coupling (SOC) effect, we extend it to LiPbPO4 compounds using a first-principles approach to probe the influence of SOC on the electronic structure and optical properties of post-transition metal compounds. The results show that only the bottom of the conduction band shows an energy level splitting with the inclusion of SOC, which is analyzed to come from the SOC in the Pb 6p state since the SOC in the O 2p state is very weak. The splitting of the conduction band triggers the decrease of the band gap and the change of the optical properties. The performance analysis shows that both the refractive index and the second harmonic generation (SHG) coefficient are enhanced with the inclusion of SOC, however, the change in the birefringence is insignificant, and it is further found that the enhanced SHG coefficient values are closer to the experimental values. In conclusion, our study reveals the impact of SOC effect on the electronic structure and optical properties of LiPbPO4 compounds, contributing to a deeper understanding of the nonlinear optical in post-transition metal compounds.

Second harmonic generation in Harmonic-Gaussian asymmetric double quantum well: effect of magnetic and intense laser fields

We have theoretically analyzed the effects of externally applied fields (magnetic and intense laser) as well as various structural parameters such as well width, barrier width, barrier height, and structural asymmetry on the second harmonic generation (SHG) coefficients of GaAs/Al0.3Ga0.7As Harmonic-Gaussian asymmetric double quantum wells (QW). The time-independent Schrödinger equation was solved using the diagonalization method and effective mass approximation to obtain the energy eigenvalues and eigenfunctions of the structure. An expression derived within the compact density matrix approach has been used to evaluate the second harmonic generation (SHG) coefficient. Our numerical results indicate that increasing the magnitude of the magnetic (intense laser) field causes the peak positions of SHG to shift towards higher energy regions/blue (lower energy regions/red). On the other hand, as the structural parameters A1 and A2 ( k and z0 ) increase, the peak positions of the SHG coefficients exhibit a shift towards higher energy regions/blue (lower energy regions/red). We expect that the results of our study will contribute to the development of new optoelectronic devices based on the Harmonic-Gaussian asymmetric double quantum well structure.

The first Hg-based oxychalcogenide Sr2HgGe2OS6: Achieving balanced IR nonlinear optical properties through synergistic cation and anion substitution

Recently, newly emerging Hg-based chalcogenides with fascinating non-centrosymmetric (NCS) structures and superior optical properties have received wide attention as candidates for infrared nonlinear optics (IR-NLO). However, simultaneously optimizing three key performance indicators in these materials, namely the second-harmonic generation coefficient (deff), optical energy gap (Eg), and birefringence (Δn), remains a major challenge due to their often-competing structural requirements. Herein, the first Hg-based oxychalcogenide, Sr2HgGe2OS6, was rationally obtained using a synergistic strategy of cation and anion design based on the well-known melilite-type oxide Sr2ZnGe2O7. By substituting Hg2+ for Zn2+ cations and S2− for O2− anions, Sr2HgGe2OS6 features new 2D Cairo pentagonal tiling layers of [HgGe2OS6]4–, separated by charge-balanced Sr2+ cations. Notably, it exhibits well-balanced IR-NLO properties with a substantial deff (1.2 × AgGaS2@2050 nm), wide Eg (3.25 eV) resulting in a favorable laser-induced damage threshold (15.6 × AgGaS2@1064 nm), broad transparent window (up to 14.3 μm), and sufficient calculated Δn (0.147@2050 nm) for phase-matching ability across a wide range. Moreover, detailed theoretical analyses suggest that the simultaneous presence of excellent linear and NLO properties in Sr2HgGe2OS6 can be attributed to the cooperative effect of heteroligand [Ge2OS6] and tetrahedral [HgS4] asymmetric functional motifs. This study offers valuable insights into the development of NCS materials through logical chemical substitution strategies, and the intriguing optical properties of this new oxychalcogenide holds promise for applications in the IR-NLO field.

Electro-optic effects of lithium borate crystals studied by first-principles method

In respect to the electro-optic (EO) effect, LiB3O5 (LBO) and Li2B4O7 (LB4) contain the same elements but represent two extremes in the family of nonlinear optical (NLO) borate crystals: one with large second harmonic generation (SHG) coefficients but very small reported EO coefficients, the latter has extremely small SHG coefficients yet EO coefficients were found even larger than the practical EO modulator crystal β-BaB2O4 (BBO). The puzzle was unraveled through first-principles studies of the two crystals and it is found that the vibrational and electronic contributions to the EO effect were canceled in LBO and the major contributions are from piezoelectric induced effect for LB4 with electronic contributions negligible. In addition to the EO and NLO coefficients, dielectric, elastic, piezoelectric and elasto-optic constants are all obtained simultaneously. More importantly, fully determining the elastic, elasto-optic constants, all 4th rank tensors, can be adopted to calibrate the experimental uncertainties and help to design practical surface acoustic wave (SAW) or acoustic optic modulator (AOM) devices.

Nonlinear Optical Mechanism of β‐BaB2O4 Revealed by Experimental Electron Density

AbstractNonlinear optical (NLO) materials are of immense scientific and technological importance. However, debate has long prevailed theoretically regarding the structural origin of the second harmonic generation (SHG) effect. In this work, the experimental electron density (ED) of controversial β‐BaB2O4 (BBO) is studied by high‐resolution X‐ray diffraction, indicating that the [B3O6]3− motif dominates two large non‐zero SHG tensors (d222 and d311) while Ba atoms contribute mostly to the smallest one (d333), and the atomic SHG contributions of terminal O atoms in [B3O6]3− motifs are much larger than those of B and bridged O atoms, clarifying the disputes on its NLO response mechanism. Besides, the contraction of inner electron shells (5s25p6) of the Ba atom and partial covalent behavior of the Ba─O interaction are first observed experimentally. Furthermore, the SHG coefficients of BBO derived from experimental ED are in excellent agreement with those from bulk crystals, providing a high‐efficient and low‐cost method of screening high‐performance NLO materials with just an easy‐to‐obtain tiny crystal.

High harmonic generations in GaAs/AlGaAs superlattice: Effect of electric and magnetic field

In this study, we have examined the nonlinear optical rectification (NOR), the second harmonic generation (SHG), and the third harmonic generation (THG) coefficients of the AlxGa1-xAs/GaAs superlattice with a periodically increased barrier width under magnetic field (B) and electric field (F). All calculations are completed using the finite element method under the effective mass approximation. The electric field's polarity (±) changes the probability density of wavefunctions. For B = 0, F = −5 kV/cm (particularly for the difference between energy levels (Efi)) is a critical value. Whereas the Efi value decreases between −40 <F < −5 kV/cm, then it increases in the range of −5<F < 40 kV/cm. This change causes a red or blue shift in the optical spectrum. We also see that F = 40 kV/cm causes a change in the transition energies of the structure more than F = −40 kV/cm. The confinement of electrons under applied magnetic fields occurs in the center of the superlattice. The NOR, SHG, and THG coefficients can be adjusted over a wide energy range and size of the resonance peak with changes in the F and B values. It is believed that with the combined effect of the electric and magnetic fields, the electro-optical properties of the superlattices can be tuned for the desirable property of semiconductor optical device applications.

MgSiP2: An Infrared Nonlinear Optical Crystal with a Large Non‐Resonant Phase‐Matchable Second Harmonic Coefficient and High Laser Damage Threshold

AbstractSuperior infrared nonlinear optical (NLO) crystals are in urgent demand in the development of lasers and optical technologies for communications and computing. The critical challenge is to find a crystal with large non‐resonant phase‐matchable NLO coefficients and high laser damage threshold (LDTs) simultaneously, which however scale inversely. This work reports such a material, MgSiP2, that exhibits a large second harmonic generation (SHG) coefficient of d14≈d36 = 89 ± 5 pm V−1 at 1550 nm fundamental wavelength, surpassing the commercial NLO crystals AgGaS2, AgGaSe2, and ZnGeP2. First principles theory reveals the polarizability and geometric arrangement of the [SiP4] tetrahedral units as the origin of this large nonlinear response. Remarkably, it also exhibits a high LDT value of 684 GW cm−2, which is six times larger than ZnGeP2 and three times larger than CdSiP2. It has a wide transparency window of 0.53–10.35 µm, allowing broadband tunability. Further, it is Type I and Type II phase‐matchable with large effective SHG coefficients of deff,I ≈80.2 pm V−1 and deff,II ≈73.4 pm V−1. The outstanding properties of MgSiP2 make it a highly attractive candidate for optical frequency conversion in the infrared.

Effects of applied external fields on the nonlinear optical second harmonic generation in a GaAs/Ga0.7Al0.3As quantum dots

This work has studied some nonlinear optical properties of Al0.3Ga0.7As/GaAs quantum dot system with tangent-square potential (TSP), with special emphasis on the role of second harmonic generation (SHG) coefficient under hydrostatic pressure and temperature. Due to the strain of external application conditions, the changes of the energy level and wave function of the neutron band in the system structure provide valuable insights into the optical properties of the quantum dot structure. In this paper, we report the effects of structural parameters, temperature and hydrostatic pressure on the SHG coefficient. According to the results obtained in the work, it can be reported that the nonlinear optical properties of the quantum dot system can be improved by adjusting the hydrostatic pressure and temperature. At the same time, the interaction of various parameters has produced some interesting observations, which are relevant in relevant research fields.

The second, third harmonic generations and nonlinear optical rectification of the Mathieu quantum dot with the external electric, magnetic and laser field

In this study, the nonlinear optical properties of the InxGa1−xAs/GaAs Mathieu quantum dot (MQD) are investigated for the first time, focusing on the nonlinear optical rectification (NOR), second harmonic generation (SHG), and third harmonic generation (THG). The effects of external fields such as the electric field, magnetic field, and laser radiation field on the nonlinear optical properties of MQD are examined, along with structural parameters such as quantum dot depth and width determined by the indium concentration. The motivation of the study is to explain the NOR, SHG, and THG characteristics of MQD in response to changes in external fields and structural factors. To investigate the effects of the laser field, the time-dependent part of the laser field is transferred to the potential energy term of the wave equation using the Kramers–Henneberger (KH) and dipole approximations, creating a laser-dressed potential. Then, the effective potential wave equation is solved using the tridiagonal matrix method. The effects of external fields and structural parameters of MQD on the NOR, SHG, and THG coefficients are discussed in detail. The optimality of the structure for device design and applications considering MQD is revealed, and alternative parameter analysis is conducted for this optimality.

Recent advances in IR nonlinear optical chalcogenides with well-balanced comprehensive performance

Infrared nonlinear optical (IR-NLO) crystals have attracted many attentions due to the frequency-conversion capability to generate coherent tunable IR laser output for military and civil applications. Chalcogenides as a most popular branch of IR-NLO materials are the competitive candidates owing to their large second-harmonic generation (SHG) coefficient (deff) and broad transmission regions. Currently, how to obtain the non-centrosymmetric (NCS) structure and realize the coexistence of wide energy gap (Eg ≥ 3.0 eV), sufficient deff (≥ 1.0 × AgGaS2), and beneficial phase-matching (PM) feature are the two major challenges faced in this field. The former can be effectively solved through the combination of local asymmetric units and chemical substitution strategy, while for the latter, there is no systematic survey and lack of universally applicable methodology. In this review, 40 IR-NLO chalcogendides are selected based on the aforementioned two challenges and divided into 7 types according to the different chemical components. The composition-structure-performance relationships and the theoretical origin of their IR-NLO properties are summarized systematically. At length, some useful information and development prospects were briefly discussed, which may offer new ideas and promote the discovery of IR-NLO materials with the ideal comprehensive performance.

Zn2BS3Br: An Infrared Nonlinear Optical Material with Significant Dual-Property Enhancements Designed through a Template Grafting Strategy

Developing high-performance infrared nonlinear optical (IR-NLO) materials with high second-harmonic generation (SHG) coefficients (dij) and wide band gaps (Eg) has been a serious challenge owing to the intrinsic negative correlativity between the two key properties. Herein, taking π-delocalized BS3 as core functional motifs (FMs), a template grafting strategy that facilitates dual-property enhancement is proposed and novel thioborates of Zn2BS3Br with target IR-NLO performances are predicted by the first-principles evolutionary algorithm. They not only possess wide band gaps of 3.63–4.05 eV, increasing by 1.0 eV over the benchmark AgGaS2 (AGS, 2.62 eV); moreover, benefiting from the parallel alignments of FMs, five phases exhibit high SHG effects (dij > 1.0 × AGS), particularly I (2.0 × AGS & 3.68 eV) and II (2.2 × AGS & 3.77 eV), in which significant enhancements in dij and Eg can be achieved concurrently, surpassing almost all of the accessible IR-NLO materials. Remarkably, the sufficiently wide band gaps and large birefringence of I and II lead to very short phase-matching wavelengths (λPM = 443.9/370.1 nm), enabling them a dual-waveband application potential, which is rarely found in IR-NLO chalcogenides. In addition, the isomorphic selenides show record high SHG coefficients of 3.8 × AGS in the wide-band-gap range of Eg > 3.0 eV. Therefore, the Zn2BS3Br-family crystals would be promising IR-NLO materials. Profound mechanism explorations conclusively demonstrate the effectiveness of our design strategy.

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.