A photonic basis for deriving nonlinear optical response

The last 30 years have witnessed an ever-growing application of computational chemistry for rationalizing the nonlinear optical (NLO) responses of organic chromophores. More specifically, quantum chemical calculations proved highly helpful in gaining fundamental insights into the factors governing the magnitude and character of molecular first hyperpolarizabilities (β), be they either intrinsic to the chromophore molecular structure and arising from symmetry, chemical substitution, or π-electron delocalization, or induced by external contributions such as the laser probe or solvation and polarization effects. Most theoretical reports assumed a rigid picture of the investigated systems, the NLO responses being computed solely at the most stable geometry of the chromophores. Yet, recent developments combining classical molecular dynamics (MD) simulations and DFT calculations have evidenced the significant role of structural fluctuations, which may induce broad distributions of NLO responses, and even generate them in some instances.This Account presents recent case studies in which theoretical simulations have highlighted these effects. The discussion specifically focuses on the simulation of the second-order NLO properties that can be measured experimentally either from Hyper-Rayleigh Scattering (HRS) or Electric-Field Induced Second Harmonic Generation (EFISHG). More general but technical topics concerning several aspects of the calculations of hyperpolarizabilities are instead discussed in the Supporting Information.Selected examples include organic chromophores, photochromic systems, and ionic complexes in the liquid phase, for which the effects of explicit solvation, concentration, and chromophore aggregation are emphasized, as well as large flexible systems such as peptide chains and pyrimidine-based helical polymers, in which the relative variations of the responses were shown to be several times larger than their average values. The impact of geometrical fluctuations is also illustrated for supramolecular architectures with the examples of nanoparticles formed by organic dipolar dyes in water solution, whose soft nature allows for large shape variations translating into huge fluctuations in time of their NLO response, and of self-assembled monolayers (SAMs) based on indolino-oxazolidine or azobenzene switches, in which the geometrical distortions of the photochromic molecules, as well as their orientational and positional disorder within the SAMs, highly impact their NLO response and contrast upon switching. Finally, the effects of the rigidity and fluidity of the surrounding are evidenced for NLO dyes inserted in phospholipid bilayers.

The nonlinear optical (NLO) response of photonic materials plays an important role in the understanding of light-matter interaction as well as pointing out a diversity of photonic and optoelectronic applications. Among the recently studied materials, 2D-LTMDs (bi-dimensional layered transition metal dichalcogenides) have appeared as a beyond-graphene nanomaterial with semiconducting and metallic optical properties. In this article, we review most of our work in studies of the NLO response of a series of 2D-LTMDs nanomaterials in suspension, using six different NLO techniques, namely hyper Rayleigh scattering, Z-scan, photoacoustic Z-scan, optical Kerr gate, and spatial self-phase modulation, besides the Fourier transform nonlinear optics technique, to infer the nonlinear optical response of semiconducting MoS2, MoSe2, MoTe2, WS2, semimetallic WTe2, ZrTe2, and metallic NbS2 and NbSe2. The nonlinear optical response from a thermal to non-thermal origin was studied, and the nonlinear refraction index and nonlinear absorption coefficient, where present, were measured. Theoretical support was given to explain the origin of the nonlinear responses, which is very dependent on the spectro-temporal regime of the optical source employed in the studies.

Metal-terminated graphene nanoribbons (M-GNRs) with planar tetra-coordinate carbons (PtC) are investigated theoretically for a third-order nonlinear optical (NLO) response by using the sum-over-states (SOS) method. The third order NLO polarizability, two-photon absorption (TPA) and nonlinear reflectivity are investigated within the third-harmonic generation (THG) or degenerate four-wave mixing (DFWM) processes. The origins of third order NLO polarizability and TPA are analyzed in terms of the charge transfer process, which indicates that tetra-coordinate carbons in M-GNRs have an important role in the third-order NLO response. The dynamic nonlinear reflectivity of the M-GNR presents a resonant characteristic due to the large third order NLO polarizability. Moreover, the third order NLO polarizability and TPA cross section values increase as the ribbon size increases in the low frequency region of incident light, which indicates that their NLO properties can be tailored by controlling the ribbon size. This paper aims to shed light on the design of NLO properties and understanding of the NLO response mechanisms of graphene related materials.

Surface functionalization of Si6Li6 cluster with superalkalis to achieve high nonlinear optical response: A DFT study

Herein, we examined the nonlinear optical properties of thia[7&8]circulenes (1-18). Circulenes are the building blocks of various nanomaterials such as graphene, nanotubes, and fullerenes. Many studies on circulenes have focused on the aromaticity of circulenes, but less attention has been paid on optoelectronics properties. Carbon atoms of the [7&8]circulenes are replaced with multiple sulfur atoms to designed thia[7&8]circulenes (1-18). These circulenes (1-18) are thermodynamically, kinetically, and chemically stable. Nonlinear optical (NLO) response is evaluated through static and frequency-dependent first and second hyperpolarizability values. The static first hyperpolarizability (βo) of these compounds ranges between 0.00 and 496 au. The frequency-dependent coefficients for all thia[7&8]circulenes show remarkable enhancement at 532 and 1064nm, respectively. The nonlinear refractive index is increased up to 1.13 × 10-14 au for circulene 9 at 532nm. These findings successfully demonstrated that nonlinear optical response of thia[7&8]circulenes can be increased by decorating multiple sulfur atoms. The unsymmetrical distribution of sulfur atoms is more effective in enhancing nonlinear optical response.

The realization of tunable nonlinear optical (NLO) responses in a single nano-/micro-structure is extremely important. However, in lack of effective ways to integrate multiple performances, it still faces severe limitations during applications. Herein, we demonstrate a wavelength-dependent NLO micro-structure based on host-guest metal-organic framework (MOF) materials through encapsulating linear dye molecules into periodic one-dimensional (1D) channels. The confinement to non-centrosymmetric polar dye molecules enhances the second-/third-order NLO responses of the hybrid crystals, causing obvious two-photon luminescence (TPL), second harmonic generation (SHG) and third harmonic generation (THG) responses in the as-prepared composites. The highly ordered structures of MOFs impart spatial regulation on the linear dye molecules to realize orientation alignment, resulting in the polarized anisotropy emission. NIR-to-NIR (NIR, near-infrared region) two-photon pumped lasing is realized with the natural whispering gallery mode resonance cavities of MOFs under the excitation of a 1200-nm fs laser. Furthermore, tunable NLO properties such as TPL, SHG and THG are achieved through switching the incident excitation wavelength from 800 to 1500 nm. Such hybrid materials with tunable NLO responses may open a new avenue toward designing multifunctional NLO devices in the future.

The NLO properties of hybrid materials based on molybdate/hexamolybdate derivatives: A theoretical perspective for electro-optic modulation

Chapter 11 - Nonlinear optics and photonics applications of two-dimensional materials

As a kind of novel organometallic complexes, the cyclopentadienylcobalt (CpCo) linear [4]phenylene complexes (4 = number of benzene rings) display efficient switchable nonlinear optical (NLO) response when CpCo reversibly migrates along the linear [4]phenylene triggered by heating or lighting. In this paper, the second-order NLO properties for CpCo linear [4]phenylene complexes were calculated by using the density functional theory (DFT) methods with four functionals. All of the functionals yield the same order of βtot values: 1<2<4<3. The effect of solvent on second-order NLO properties has been studied using polarized continuum model (PCM) in the tetrahydrofuran (THF) solution. The solvent leads to a slight enhancement of the NLO responses for the studied complexes relevant to their NLO responses in vacuo. The electronic absorption spectra were investigated by the TDDFT methods. The TDDFT calculations indicate that the maximum absorption peaks of complexes 2–4 in the near-infrared spectrum area show the bathochromic shift together with a decreasing intensity compared to complex 1. We have also found that the cobalt (Co) atom acts as a donor in all the organometallic complexes and the d → π* and π → π* charge transfer (CT) transitions contribute to the enhancement of second-order NLO response. Furthermore, two experimentally existing complexes 1 and 3 are found to have a large difference in βtot values. It is our expectation that this difference may stimulate the search for a new type of switchable NLO material based on CpCo linear [4]phenylene complexes.FigureThe second-order NLO properties of the cyclopentadienylcobalt (CpCo) linear [4]phenylene complexes were investigated by density functional theory (DFT) method, and complexes 1 and 3 display switchable NLO responses.

We fabricated Au nanoparticles on the surface of TiO2 by photo-reduction method. The structural property of film is investigated using transmission electron microscopy technique. The surface plasmon resonance absorption peaks of TiO2 and Au-TiO2 were recorded using Shimadzu (UV-2450) UV-visible spectrophotometer. The work function of films was measured by scanning Kelvin probe microscopy (SKP5050) from KP technology, United Kingdom. The nonlinear optical refractive index and nonlinear optical absorption coefficient of Au-TiO2 nanocomposites were simultaneously measured using z-scan technique. The nonlinear optical response of Au-TiO2 nanocomposites is due to pure electronic transfer effects in Au nanoparticles. The observed nonlinearity is due to the dielectric constant of Au, which is due to the surface plasmon resonance and surface polarization between Au nanoparticles and TiO2. The dielectric constant of Au shows maximum value at 532 nm wavelength (2.33 eV). Surface plasmon resonance effect of Au nanoparticles is directly related to the metal dielectric constant, therefore it is increased. The increase in surface plasmon rsonance of Au-TiO2 nanocomposites can be observed from UV-visible absorption spectra. The optical nonlinearity depends strongly on the dielectric constant of Au. Therefore, the optical nonlinearity increases with the increase in surface plasmon resonance peak. The absorption peak of surface plasmon resonance at 544 nm is inversely proportional to the work function. Therefore, we can say that the Au dopant decreases the work function that effectively increases the surface plasmon resonance absorption peak at 544 nm, so that the nonlinear response is enhanced. The systematic change in the work function with Au concentration plays a major role in optical nonlinearity. The estimated optical nonlinearity was found to increase from 3.80&times;10-6 to 9.69&times;10-6 esu with increase in Au concentrations from 0 to 1.0x10-2 mole. This observed increment in nonlinearity is due to the enhancement of local electric field created by excitation of surface plasmon resonance that affects the work function. Therefore, the surface plasmon resonance and work function help in tuning the optical nonlinearity. The tunable nonlinear optical response of the Au-TiO2 nanocomposites may find applications in nonlinear optics at wavelength 532 nm and the development of materials for generating the higher order harmonics.

We present first-principles calculations of the nonlinear optical (NLO) response of a Ni/Cu(001) bilayer. The calculations are based on the full potential linearized augmented plane wave (FLAPW) method with the additional implementation of spin–orbit coupling (SOC). On the basis of this set of eigenstates the magneto-optical transition-matrix elements are evaluated. Using the surface-sheet model the optical reflection properties are determined for the cases of the magnetization vector perpendicular to the surface (polar magneto-optical configuration (MOC)) and for the in-plane magnetization (longitudinal MOC). The nonlinear optical susceptibility tensor elements χ(2) ijk for different magnetization directions as well as the spectral dependence of χ(2) ijk, the resulting intensities, and Kerr angles are presented for the Ni/Cu(001) bilayer. The results show that the magnetic tensor elements of the χ(2) ijk tensor are smaller than the nonmagnetic ones by only one order of magnitude, confirming the important role of magnetic properties in the NLO response.

Nanoscale nonlinear optics is limited by the inherently weak nonlinear response of conventional materials and the small light-matter interaction volumes available in nanostructures. Plasmonic excitations can alleviate these limitations through subwavelength light focusing, boosting optical near fields that drive the nonlinear response, but also suffering from large inelastic losses that are further aggravated by fabrication imperfections. Here, we theoretically explore the enhanced nonlinear response arising from extremely confined plasmon polaritons in few-atom-thick crystalline noble metal films. Our results are based on quantum-mechanical simulations of the nonlinear optical response in atomically thin metal films that incorporate crucial electronic band structure features associated with vertical quantum confinement, electron spill-out, and surface states. We predict an overall enhancement in plasmon-mediated nonlinear optical phenomena with decreasing film thickness, underscoring the importance of surface and electronic structure in the response of ultrathin metal films.

Nonlinear optical responses of carbon quantum dots anchored on graphene oxide hybrid in solid-state transparent monolithic silica gel glasses

The topological Weyl semimetals (WSMs) with peculiar band structures exhibit novel nonlinear optical enhancement phenomena, even for light at optical wavelengths. While many intriguing nonlinear optical effects are constantly uncovered in type‐I WSMs, few experimental works focuse on basic nonlinear optical properties in type‐II WSMs. Here a static and time‐resolved second harmonic generation (SHG) is performed on the 3D type‐II WSM candidate β‐WP2. Although β‐WP2 exhibits extremely high conductivity and a high carrier density (≈1021 cm−3), the SHG is unscreened by conduction electrons, and a rather strong SHG response is observed, comparing with non‐topological polar metals. Additionally, the time‐resolved SHG experiment traces ultrafast symmetry switch and reveals that polar metal β‐WP2 tends to form an inversion symmetric metastable state after photo‐excitation. Intense femtosecond laser pulse can optically drive symmetry switch and tune nonlinear optical response on ultrafast timescales although the interlayer coupling of β‐WP2 is very strong. These findings are illuminating for the polar metal nonlinear optics and provide a new perspective for future ultrafast topological optoelectronic devices.

Density functional theory (DFT) calculations are used to analyze the change in nonlinear optical (NLO) response, electronic and geometric properties of the Li based superalkalis doped C24 nanocage. It was observed that the adsorption of Li4N, Li3O and Li2F superalkalis on C24 nanocage results in thermodynamically stable isomers (A-F). The energy gap between the highest occupied and the lowest unoccupied molecular orbitals (GH-L) is reduced after superalkalis doping on carbon (C24) nanocage. Density of states spectra depict the strong contribution of superalkalis in HOMOs of the considered complexes. Natural bond orbital (NBO) charge analysis showed that the charge is being transferred from superalkali toward C24 nanocage. The values of polarizability (α o ) and hyperpolarizability (β o ) showed that doping of superalkalis on C24 has a significant effect on its NLO response, resulting in a considerable increase in values of α o and β o . Li4N@C24 isomer E showed the highest β o value of 6470.74 au. Time dependent density functional theory (TD-DFT) calculations are implemented to analyze the absorption spectra. This research provides unique and highly efficient superalkalis doped C24 isomers for their applications in future electronic devices.