Third-order Susceptibility Research Articles

Two-dimensional coherent spectrum of interacting spinons from matrix product states

We compute numerically the second- and third-order nonlinear magnetic susceptibilities of an Ising ladder model in the context of two-dimensional coherent spectroscopy by using the infinite time-evolving block decimation method. The Ising ladder model couples a quantum Ising chain to a bath of polarized spins, thereby effecting the decay of spinon excitations. We show that its third-order susceptibility contains a robust spinon echo signal in the weak-coupling regime, which appears in the two-dimensional coherent spectrum as a highly anisotropic peak on the frequency plane. The spinon echo peak reveals the dynamical properties of the spinons. In particular, the spectral peak corresponding to the high-energy spinons, which couple to the bath, is suppressed with increasing coupling, whereas those corresponding to low-energy spinons do not show any significant changes.

Linear and Nonlinear Optical Properties of PVA:SA Blend Reinforced by TiO2 Nanoparticles Prepared by Flower Extract of Aloe Vera for Optoelectronic Applications

In this study, a polyvinyl alcohol–sodium alginate blend, PVA:SA 3:1 (w:w), was doped with different contents of TiO2 nanoparticles (NPs) prepared by aloe vera leaf extract to form the investigated nanocomposites. The nonlinear parameters of third-order susceptibility (χ(3)) and refractive index (n2) were detected by using UV-Vis spectroscopy and Z-scan techniques. Some different optical parameters were also determined, including the refractive index (n), optical dielectric parameters, volume and surface energy loss functions, and some others. The best solar skin protection factor (SSPF) was investigated by 5 wt.% of TiO2 NPs doped in PVA:SA 3:1, which was about 84.6% compared to the corresponding value of the host blend (41%). The studied nanocomposites were examined for their utility in the optical limiting of CUT-OFF laser filters utilizing a continuous He-Ne laser working at 632.2 nm. As a result, our finding demonstrated that TiO2 NPs doped in the host blend of PVA:SA positively influences a laser light blocking for the investigated laser source. Using the estimated gap energies values, different models were used to deduce theoretical values of the linear refractive index (n). The presence of Ti peaks in the EDX spectrum confirmed the doping of TiO2 NPs in the nanocomposites. SEM showed that the TiO2 NPs are homogeneously dispersed through the host blend with some agglomerates. XRD spectra showed that the values of the lattice strain εstr. detected at 2ϴ = 19.78° are 0.058, 0.055, and 0.060, corresponding to 1, 3, and 5 wt.% of TiO2 NPs doped in the PVA:SA blend.

Effective model for studying optical properties of lead halide perovskites

We use general symmetry-based arguments to construct an effective model suitable for studying optical properties of lead halide perovskites. To build the model, we identify an atomic-level interaction between electromagnetic fields and the spin degree of freedom that should be added to a minimally coupled $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ Hamiltonian. As a first application, we study two basic optical characteristics of the material: the Verdet constant and the refractive index. Beyond these linear characteristics of the material, the model is suitable for calculating nonlinear effects such as the third-order optical susceptibility. Analysis of this quantity shows that the geometrical properties of the spin-electric term imply isotropic optical response of the system, and that optical anisotropy of lead halide perovskites is a manifestation of hopping of charge carriers. To illustrate this, we discuss third-harmonic generation.

Excellent Nonlinear Optical Limiting Behavior of Tetra (C60) Lanthanum Phthalocyanine in Solid Poly(methyl methacrylate) Films

This work reports on the exceptional optical limiting performance of a novel D–A-type compound, namely, LaPc-4(C60), wherein the lanthanide phthalocyanine is used as a donor and four C60 are used as acceptors. In addition, phenyl ether bonds were introduced into the molecule, making it semirigid and increasing its solubility. At the same time, the phenyl ether bond could act as a π-electron bridge, which increases the electron transfer pathway, expands the π-conjugated system, and reduces the spatial site resistance of the molecule. Furthermore, the uniform poly(methyl methacrylate) (PMMA) composite film (LaPc-4(C60)/PMMA) was prepared by a simple solution casting method. In comparison with individual C60 or LaPc(CHO)4, both LaPc-4(C60) in solution and in the solid PMMA composite film exhibited larger third-order nonlinear absorption coefficients and lower limiting thresholds at 532 nm. In particular, LaPc-4(C60)/PMMA exhibits huger nonlinear absorption coefficient (2900 cm/GW) and larger third-order susceptibility (4.91 × 10–9 esu), which can be attributed to the synergistic effect of the different non-linear absorption mechanisms and efficient photoinduced electron transfer process between C60 and LaPc.

Third-order optical nonlinearity and multiferroicity of nanoparticles thin films of isovalent rare earth Y3+ ion substituted BiFeO3

Present work reveals the multiferroic and nonlinear optical properties of pristine and Yttrium (Y3+) substituted BiFeO3 nanoparticles synthesized by sol-gel technique, and fabricated thin films of the nanoparticles. The nanoparticles thin films were deposited on glass substrates with an average thickness of 85 nm by the thermal evaporation method in a high vacuum of 10−6 Torr. The structural and morphological studies were done by using XRD, Fullprof, XPS, AFM, FESEM and TEM with SAED. Further BET method was used to find out the surface area, pore size and pore volume of the nanoparticles. The multiferroic properties of Bi1-xYxFeO3 (x = 0.0, 0.5, 0.10, 0.15) have been investigated using VSM (magnetic) and P-E loop tracer (electrical). The doping of magnetic Y3+ions in host BiFeO3 nanoparticles modified and improved the optical, structural, multiferroic properties enormously. Linear optical properties were characterized by UV–Visible, Raman, and Photoluminescence. Third-order nonlinear absorption coefficient (β) and the imaginary part of third-order susceptibility (χi3) of Bi1-xYxFeO3 (x = 0.0, 0.5, 0.10, 0.15) have been investigated using a single beam Z-scan technique with a continuous wave (CW) diode laser of 520 nm wavelength. The films exhibit saturation absorption (SA) behavior and it increases on increasing the Yttrium (Y3+) substitution in BiFeO3. Thus, the NLO behavior of the films makes it an auspicious material for application in optoelectronic devices.

Role of electron-withdrawing groups on nonlinear optical response of conjugated anthracenyl fused rings chalcone: Experimental and DFT study

Conjugated organic molecules may represent the most intriguing topic of study in the Nonlinear Optical field. Herein, two novel chalcones crystals based on anthracene named 3a and 3b are synthesized and recrystallized. The main aim of this study is to investigate the impact electron-withdrawing group substituents on the Nonlinear optical properties of the chalcone derivatives. Characterization studies, X-ray structure and UV–vis analyses were used to conform the optical properties. High precision density functional theory computations were used to examine the geometrical structures, electronic structure, excited state characteristics, global reactivity descriptors, Molecular Electrostatic Potential, and hyperpolarizabilities. The findings show, both compounds stabilize with strong electron-withdrawing group and long conjugation length which directly can be observed as a low energy band gap and high value of third-order susceptibility (χ(3)≈10−7 esu). The study also shows that the presence of the anthracene as electron-donating group at the end terminal of the chalcone could enhance the nonlinearity response and performance.

Hybrid quantum dot-graphene layers with improved optical properties in the terahertz spectrum region

Recently, it has been shown that the graphene plasmonic (GP) effect can enhance the optical properties of quantum dots (QDs) through the Purcell's effect. This can happen when the electromagnetic field is concentrated tightly in a region where the ground state (S-state) and the first excited state (P-state) of electron are present, and the S-to-P transition frequency falls onto the frequency of plasmonic resonance of graphene layers. Here, we use a hybrid composition of graphene layers, consisting of a disk and four L-shaped layers, and a QD aimed to enhance the linear and third-order optical susceptibilities of QD in the terahertz (THz)/far infrared (FIR) spectrum region. Unlike the previous works, where much more graphene layers were used, in this work, we use fewer layers beneath the wetting layer and with a noticeably simpler scheme, we achieve comparable results in transition dipole moments (TDMs) and optical properties. By changing the Fermi's energy of graphene, we could reach 90-fold enhancement for TDM and 8 × 10 3 - and 6 × 10 7 -fold enhancements, respectively, for linear and third-order susceptibilities. Our scheme can noticeably reduce the difficulties in fabricating hybrid graphene-QD systems. • Graphene flakes in nanodisk and L-shaped geometry have been placed in conic-shaped InAs/GaAS quantum dots (QDs). • The emission of QDs has been tuned with graphene plasmonic (GP). • With use of GP effect, S-to-P transition dipole moment (TDM) of QD has been enhanced 120 times. • Linear susceptibility of QD has been multiplied by a factor of 8 × 10 3 . • Third-order susceptibility of QD has been multiplied by a factor of 6 × 10 7 . • GP has been used as a passive method to enhance significantly the optical properties of QDs.

Study of femtosecond nonlinear optical coefficients for Bi doped Se85-xTe15Bix chalcogenide thin films

The present work reports the influence of selenium replacement by bismuth on the nonlinear optical parameters of ternary Se85-xTe15Bix (x=0, 1, 2, 3, 4, 5 atomic %) chalcogenide thin films. Calculation of nonlinear refractive index (n2), two-photon absorption coefficient (β2) and third-order susceptibility (χ (3)) by well known Z-scan technique with femtosecond laser pulses were done. The Z-scan spectra for Se85-xTe15Bix upto Bi= 4 atomic % results in self- focusing behavior of n2 is positive while for Bi=5 atomic % n2 is negative. The behavior of n2 by using different physical parameters are exlpained. The comparison of experimental and theoretical values of n2 with pure silica are also studied. The presence of the valley at focus in open aperture Z-scan graph demonstrates strong reverse saturable absorption. The figure of merit (FOM) for the SeTe-Bi chalcogenide thin films is found to be less than 1 and are beneficial for all-optical switch devices.

Appreciably optimization of PVA/PVP nanocomposite blend for enhanced optoelectronics properties and multifunctional applications

The optical and electrical properties of PVA/PVP were manipulated by optimizing the blend ratio between those polymers. The (40/60) wt.% of PVA/PVP achieved the lowest energy gap and the highest electrical conductivity. After that, the optical and electrical properties of blend films were engineered using Ni(OAc)2 for enhanced optoelectronic properties. The doping impact on the semicrystalline and molecular structures of the prepared blend was investigated. The optical properties of the doped blend films were examined using optical transmission and absorption spectra measurements. The nonlinear optical parameters such as nonlinear refractive index and third-order optical susceptibility were estimated. The prepared films showed a pronounced laser cut-off performance. The electrical properties of the fabricated films showed a tunable behavior with the variation of doping level. The engineered doped polymer blend films exhibited good sensitivity to visible light with promising values of responsivity and specific detectivity ∼5.89 mA/W, and 4.31 × 109 Jones, respectively.

Enhanced non-linear optical properties of porphyrin-based polymers covalently functionalized with graphite phase carbon nitride.

In our work, a flurry of original porphyrin-based polymers covalently functionalized g-C3N4 nanohybrids were constructed and nominated as PPorx-g-C3N4 (x = 1, 2 and 3) through click chemistry between porphyrin-based polymers with alkyne end-groups [(PPorx-C≡CH (x = 1, 2 and 3)] and azide-functionalized graphitic carbon nitride (g-C3N4-N3). Due to the photoinduced electron transfer (PET) between porphyrin-based polymers [PPorx (x = 1, 2 and 3)] group and graphite phase carbon nitride (g-C3N4) group in PPorx-g-C3N4 nanohybrids, the PPorx-g-C3N4 nanohybrids exhibited better non-linear optical (NLO) performance than the corresponding PPorx-C≡CH and g-C3N4-N3. It found that the imaginary third-order susceptibility (Im [χ(3)]) value of the nanohybrids with different molecular weight (MW) of the pPorx group in the nanohybrids ranged from 2.5×103 to 7.0 × 103gmol-1 was disparate. Quite interestingly, the Im [χ(3)] value of the nanohybrid with a pPorx group'sMW of 4.2 × 103gmol-1 (PPor2-g-C3N4) was 1.47 × 10-10 esu, which exhibited the best NLO performance in methyl methacrylate (MMA) of all nanohybrids. The PPorx-g-C3N4 was dispersed in polymethyl methacrylate (PMMA) to prepare the composites PPorx-g-C3N4/PMMA since PMMA was widely used as an alternative to glass. PPor2-g-C3N4/PMMA showed the excellent NLO performance of all nanohybrids with the Im [χ(3)] value of 2.36 × 10-10 esu, limiting threshold of 1.71J/cm2, minimum transmittance of 8% and dynamic range of 1.09 in PMMA, respectively. It suggested that PPorx-g-C3N4 nanohybrids were potential outstanding NLO materials.

Ab initio nonlinear optics in solids: linear electro-optic effect and electric-field induced second-harmonic generation

Second-harmonic generation (SHG), linear electro-optic effect (LEO) and electric-field induced second-harmonic generation (EFISH) are nonlinear optical processes with important applications in optoelectronics and photovoltaics. SHG and LEO are second-order nonlinear optical processes described by second-order susceptibility. Instead, EFISH is a third-order nonlinear optical process described by third-order susceptibility. LEO and EFISH are only observed in the presence of a static electric field. These nonlinear processes are very sensitive to the symmetry of the systems. In particular, LEO is usually observed through a change in the dielectric properties of the material while EFISH can be used to generate a “second harmonic” response in centrosymmetric material. In this work, we present a first-principle formalism to calculate second- and third-order susceptibility for LEO and EFISH. LEO is studied for GaAs semiconductor and compared with the dielectric properties of this material. We also present how it is possible for LEO to include the ionic contribution to the second-order macroscopic susceptibility. Concerning EFISH we present for the first time the theory we developed in the framework of TDDFT to calculate this nonlinear optical process. Our approach permits to obtain an expression for EFISH which does not contain the mathematical divergences in the frequency-dependent second-order susceptibility that caused until now many difficulties for numerical calculations.

Bromine Substitution Effect on Structure, Reactivity, and Linear and Third-Order Nonlinear Optical Properties of 2,3-Dimethoxybenzaldehyde.

The structural and electronic properties of 2,3-dimethoxybenzaldehyde (2,3-DMB), 5-bromo-2,3-dimethoxybenzaldehyde (5-BRB), and 6-bromo-2,3-dimethoxybenzaldehyde (6-BRB) were extensively discussed with emphasis on linear and nonlinear optical responses. The intermolecular interactions were comparatively studied by Hirshfeld surfaces, quantum theory of atoms in molecules (QTAIM), and natural bond orbitals (NBOs), indicating that bromine substitution decreases the H···H and C···H contacts and increases H···Br and Br···Br closed-shell interactions on crystalline arrangements. The frontier molecular orbitals and molecular electrostatic potential map, carried out at the CAM-B3LYP/6-311++G(d,p) level of theory, showed that the kinetic stability occurs in the increasing order 6-BRB < 5-BRB < 2.3-DMB. The bromine atom has a beneficial effect on the nonlinear third-order susceptibility of 2,3-DMB, with theoretical predictions of 89.54 ×10-22 and 83.15 ×10-22 (m/V)2 for 6-BRB and 5-BRB, respectively. These findings were favorably compared with available theoretical and experimental data of other organic crystals that may be promising as NLO materials.

Asymmetric encryption by optical Kerr nonlinearities exhibited by electrochromic NiO thin films.

Herein is analyzed how an electric field can induce a band gap shift in NiO films to generate an enhancement in their third-order optical nonlinearities. An electrochromic effect seems to be responsible for changes in absorbance and modification in off-resonance nonlinear refractive index. The optical Kerr effect was determined as the dominant physical mechanism emerging from the third-order optical susceptibility processes present in a nanosecond two-wave mixing configuration at 532 nm wavelength. Absence of any important multi-photonic absorption was validated by the constant trace of high-irradiance optical transmittance in single-beam mode. The inspection of nonlinear optical signals allowed us to propose an exclusive disjunctive logic gate assisted by an electrochromic effect in an optical Kerr gate. Asymmetric encryption by our XOR system with the influence of a switchable probe beam transmittance and electrical signals in the sample was studied. Immediate applications for developing multifunctional quantum systems driven by dynamic parameters in electrochromic and nonlinear optical materials were highlighted.

SHG in Micron-Scale Layers of Glasses: Electron Beam Irradiation vs. Thermal Poling

In this work, we studied the introduction of second-order optical nonlinearity (SON) into subsurface layer soda-lime and alkali-free flint glasses using two different techniques: electron beam irradiation and thermal poling in an open anode configuration. The experiments showed that thermally poled soda-lime glass and e-beam poled flint glass demonstrated noticeable second-harmonic generation (SHG) with their second-harmonic (SH) signals being close in magnitude. The performed estimates showed that the coincidence in the SH signal intensity in these two glasses cannot be explained in the frames of the model that relates the second-order nonlinear susceptibility with the third-order susceptibility and the “frozen” electric field in glasses (EFISH model). This supposes another mechanism of SON in thermally poled soda-lime glass. We believe that this mechanism is the dipole orientation of entities injected into the soda-lime glass during thermal poling in an open anode configuration.

Nonlinear optical properties of porous monoclinic BiVO4 at 2.3 µm for the passively Q-switching laser

In this work, we report the nonlinear optical response of porous monoclinic bismuth vanadate (m-BiVO4) at 2.3 µm for the first time. We adopted the conventional open/closed aperture (OA/CA) Z-scan techniques to systematically investigate the nonlinear optical (NLO) behavior. The effective nonlinear absorption coefficient βeff was −6.4 ± 0.02 cm MW−1, the nonlinear refractive index n2 was 9.88 ± 0.08 × 10-1 cm2 GW−1, and the NLO third-order susceptibility |χ(3)| was 2.69 × 10-7 esu. These NLO properties allowed it to be used as a fantastic saturable absorber for the generation of mid-infrared (MIR) pulses. As an application, we implemented a passively Q-switched Tm:YAP laser with the prepared porous m-BiVO4 saturable absorber for the first time. A minimum pulse duration of 349 ns and a maximum pulse repetition frequency of 193 kHz were achieved, resulting in a maximum pulse energy of 1.18 µJ. Our findings suggest that the porous m-BiVO4 could provide a route to the MIR optoelectronic applications.

Mass ratio-dependently tunable enhancement of the optical nonlinearities of SnO2/RGO composites

The composite of graphene and semiconductor nanoparticles has attracted increasing interest in the search for novel nonlinear optical materials. Herein, composites of reduced graphene oxide (RGO) and SnO2 nanoparticles with different mass ratios were synthesized via a facile hydrothermal method. The structural morphology and basic physical properties of the SnO2/RGO composites were characterized using TEM, SEM, XRD, Raman, XPS and UV–Vis spectra, indicating that SnO2 nanoparticles were uniformly anchored on the surface of graphene nanosheets through covalent and partial-ionic bonds. The third-order optical nonlinearities of the composites were studied for the first time by the Z-scan technique using a picosecond laser at 532 nm. It was found that the composites demonstrated saturable absorption and positive nonlinear refraction properties, and both were significantly enhanced compared with pure SnO2 nanoparticles and RGO nanosheets, and the enhancement was tunable with the variation of SnO2:GO mass ratio. The maximum saturable absorption coefficient and the third-order susceptibility of the as-prepared SnO2/RGO composites were obtained to be −2.93×10–11 m W−1 and 2.25 × 10–11 esu, respectively. The maximum saturable absorption modulation depth obtained was 10% with the corresponding saturation light intensity of 0.3 GW cm−2. Moreover, the optimised third-order susceptibility of SnO2/RGO was found much greater than many other materials ever studied. Several involved factors contributing to the nonlinearities were discussed. The results propose that the third-order optical nonlinearities of SnO2/RGO and other similarly structured composites can be potentially tuned to meet certain application requirements of nonlinear optical devices by controlling the mass ratio of semiconductor to graphene.

The nonlinear second harmonic generation and third harmonic generation in GaAs/GaAlAs exponentially confined quantum well: Electric and magnetic field effects

The second harmonic generation(SHG) and third harmonic generation(THG) of a GaAs/GaAlAs exponential quantum well(QW) are numerically investigated in the presence of applied electric and magnetic field, which are parallel to the QW growth direction. The eigenvalues and corresponding eigenfunctions of the system are obtained by using the finite difference technique . The expression for the second- and third-order susceptibility is given by the density matrix and iterative approach. It is showed that, the SHG and THG not only depend strongly on quantum confinement, but also the intensity of external fields. We have systematically studied the SHG and THG of different confinement QWs by adjusting the structural parameters, as well as the effects of external electric and magnetic fields. We give the optimal system parameters in which the external field effects play important role.

Ab initio calculation of two-photon absorption in semiconductors

A theoretical derivation of two-photon absorption (2PA) from semiconductors, based on the length gauge analysis and the electron density operator, is formulated; the intraband ${\mathbit{r}}_{i}$ part and the interband ${\mathbit{r}}_{e}$ part of the position operator $\mathbit{r}$ are properly accounted for. Within the independent-particle approximation, the nonlinear third-order susceptibility tensor ${\ensuremath{\chi}}^{\mathrm{a}\mathrm{b}\mathrm{c}\mathrm{d}}(\ensuremath{-}\ensuremath{\omega};\ensuremath{-}\ensuremath{\omega},\ensuremath{-}\ensuremath{\omega},\ensuremath{\omega})$ and the two-photon absorption coefficient are calculated, including the scissors correction needed to correct the well-known underestimation of the local-density-approximation band gap. Using time-reversal symmetry, it is shown that the expression for ${\ensuremath{\chi}}^{\mathrm{a}\mathrm{b}\mathrm{c}\mathrm{d}}(\ensuremath{-}\ensuremath{\omega};\ensuremath{-}\ensuremath{\omega},\ensuremath{-}\ensuremath{\omega},\ensuremath{\omega})$ is finite at $\ensuremath{\omega}=0$, avoiding nonphysical divergences presented in previous calculations when $\ensuremath{\omega}\ensuremath{\rightarrow}0$. Ab initio band structure calculations using different pseudopotential schemes that include spin-orbit coupling are used to calculate the 2PA for several semiconductors, and the calculations are compared with available experimental results for photon energies that are below the optical band gap.

Linear and Nonlinear Optical Properties of a Doubly Clamped Suspended Monolayer Graphene Nanoribbon Nanoresonator

We studied the optical properties of a hybrid structure that was composed of a semiconductor quantum dot and a doubly clamped suspended graphene nanoribbon nanoresonator. We obtained analytical results for the linear and third-order optical susceptibilities of the hybrid system. The spectrum of the linear susceptibility exhibited a single resonance, and its position depended on the value of the on-resonance exciton energy and the exciton–nanoribbon resonator coupling strength coefficient; the amplitude of the resonance was independent of the values of these parameters. The third-order optical susceptibility spectrum exhibited a sharp resonance arising at low frequencies of the probe field, the position of which depended only on the frequency of the fundamental flexural phonon mode. It also presented a broader resonance arising at higher frequencies of the probe field, the position of which was determined both by the coupling strength coefficient and by the exciton frequency; its amplitude depended solely on the exciton–photon coupling strength.

The Investigation of New Phosphate–Titanite Glasses According to Optical, Physical, and Shielding Properties

The melt-quenching approach was used to prepare phosphate–titanite glasses with the composition P2O5-Na2O-CaO-8KF-CaCl2-xTiO2 (where x = 2, 4, and 6) in a mol %. The optical, physical, and shielding properties, such as the mass attenuation coefficient (MAC), half-value layer (HVL), effective electron density (Neff), and effective atomic number (Zeff), of the glasses were investigated at energies ranging between 15 and 200 keV. The shielding parameters were investigated using recently developed software (MIKE). The optical properties were examined using devices such as UV-Vis-NIR spectroscopy over wavelengths ranging between 190 and 2500 nm. The reported results showed that increasing the concentration of TiO2 led to an increase in the density from 2.657 to 2.682 g/cm3 and an increase in the OPD from 66.055 to 67.262 mol/L, while the molar volume (VM) and oxygen molar volume (VO) decreased from 39.21 to 39.101 cm3/mol and from 15.139 to 14.867 cm3/mol, respectively. The energy gap was found to decrease from 3.403 to 3.279 eV when the TiO2 concentration increased. Furthermore, as the surface plasmon resonance of TiO2 increases, so does its third-order susceptibility, non-linear refractive indices, linear attenuation, and mass attenuation. The shielding performance evaluation indicates that the most suitable energy range is between 15 and 50 keV. Based on the results, the PCKNT3 glass sample exhibits the highest attenuation performance of all of the samples tested.