Second harmonic generation in composites of ellipsoidal particles with core–shell structure

We study the enhancement of the second-harmonic generation (SHG) coefficient in a random composite consisting of ellipsoidal particles with a core–shell structure in a linear dielectric host. The material making up the ellipsoidal core is assumed to be dielectric, but with a nonlinear susceptibility for SHG. The coating material is assumed to be metallic with a linear susceptibility. The effective SHG coefficient is derived and its expression is related to various local field factors. The numerical calculations of the effective SHG response per unit volume of nonlinear material can be greatly enhanced at certain frequencies. For coated ellipsoidal particles, the core–shell structure and the particle shape allow for tuning of the resonance through the choice of material parameters and/or the ratio of the core to shell volume fraction and the depolarization factor of the particles.     

Theory of enhanced second-harmonic generation in some artificial materials

We review the recent theoretical investigation on enhanced second-harmonic generation (SHG) in soft nonlinear optical materials based on ferrofluids, graded metallic films, and graded metal-dielectric films of anisotropic particles. The SHG of soft ferrofluid-based nonlinear optical materials possess magnetic-field controllabilities, i.e., magnetic-field-controllable anisotropy, red-shift and enhancement, which are caused to appear by the shift of a resonant plasmon frequency due to the formation of the chains of the coated nanoparticles. Both graded metallic films and graded metal-dielectric films of anisotropic particles can serve as a novel optical material for producing a broad structure in both the linear and SHG response and an enhancement in the SHG signal, due to the local field effects.      

Imaging theory of nonlinear second harmonic and third harmonic generations in confocal microscopy

ItisreportedrecentlythatnonlinearopticalphenomenonofSHGandTHGhasbeenobservedinmanybiologicaltissues[16].SHGandTHGhavebeenusedtoperformthethree-dimensionalimaginginlivingtissuesandhaveattractedmuchattentionrecently.TherearemanyadvantagesofusingSHGandTHGtoperformthethree-dimensionalimaginginlivingtissues,suchasnoninvasiveandnophotobleaching,inadditiontotheimagingpropertiesofmulti-photonfluorescenceimaging[7—9].Firstly,unlikeinthesingle-andmulti-photonfluorescenceprocesses,onlyvirtualstat…     

Linear and nonlinear optical properties of hydrated and dehydrated silica micro-spheres under an electric bias

The linear refractive indices and nonlinear second-order susceptibility of hydrated and dehydrated silica micro-spheres are studied using attenuated total reflectance (ATR) and the second harmonic generation (SHG) method in direct transmission, respectively. A dramatic change of the effective dielectric constant of silica suspension under an electric bias was observed, which is attributed to particle redistribution in the fluid. Dielectric constants of dehydrated silica spheres change slightly under an electric field due to Pockels effect, for which we measure a linear electro-optical coefficient of r₃₃ ∼3.4±0.7 pm/V. The transmission second harmonic generation comes from the third-order susceptibility χ⁽³⁾, which is a coupling of two photons and the electrostatic field induced by the surface –OH charges as characterized by the Gouy-Chapman model. The SH signal from the dehydrated silica vanishes because of the loss of –OH groups on the particle surfaces. Dehydration of silica beads is irreversible. The optical properties of dried silica spheres do not recover their original hydrated state when distilled water is added.     

金属/电介质颗粒复合介质的非线性交流响应

推广T矩阵法来研究二组分颗粒复合介质的非线性交流响应，解析推导出基频、三次及五次谐波频率下的有效线性介电常数及三阶和五阶非线性极化率的解析表达式.当组分颗粒的介电常数为实数时，表达式同以前微扰理论完全一致.进一步数值计算了金属-电介质复合介质的有效非线性交流响应，数值结果表明，体系的三阶、五阶非线性极化率在表面等离子共振频率附近有明显增强，而且，随着体积分数提高，共振峰增强且伴随着共振频率红移现象.还进一步讨论了维度效应对体系非线性交流响应的影响. 关键词： T矩阵方法 复合介质 非线性交流响应     

Plasmon-Assisted Phase-Matched Second- and Third-Harmonic Generation in Single-Negative Heterostructures

Dispersion relations of surface plasmon polaritons （SPPs） in sandwiched optical systems are studied. The system is actually a kind of SPP waveguides, with two kinds of single negative material （SNG） as core and cladding layers, respectively. Since both TM and TE polarized SPPs can be excited in the structure, the dispersion of SPPs becomes more abundant and leads to colorful nonlinear opticM properties. The authors demonstrate the effective phase-matched second and third-harmonic generation （SHG, THG） assisted by the coupled SPPs. A cascaded second-order nonlinear process can Mso be achieved in the structure when the thickness of the core layer is properly selected, leading to the simultaneous SHG and THG. Further investigations show that much easier phase-matching can be fulfilled in the SNG waveguide array. Our results would be of potential use for surface-enhanced frequency conversion device such as light emitters or lasers.     

Second harmonic generations in aperiodic optical superlattices with finite width and in one-dimensional defective photonic crystals made of nonlinear optical materials

The characteristics of the second harmonic generations (SHGs) in homogeneous and inhomogeneous systems are investigated. We consider two kinds of structures: one is aperiodic optical superlattices (AOSs) with homogeneous linear susceptibility and the modulated second-order nonlinear susceptibility; the second is linear and nonlinear susceptibilities both the system with inhomogeneous. We derive a general solution of SHG for the AOS with finite lateral width and of SHG in considering the depletion of the pump light power. We carry out the design of AOSs by using simulation annealing (SA) algorithm and show that the constructed AOSs can implement multiple wavelength SHGs with identical effective nonlinear coefficient at the preassigned wavelengths of incident light. We observe great enhancement of SHGs in the one-dimensional photonic crystals (PCs) with defects consisting of multiple photonic quantum wells made of nonlinear material when the frequency of fundamental wave aims at one of the defect states. We also propose an effective design approach of aperiodically stacked layers of nonlinear material and air in terms of the SA method. The constructed structure can achieve multiple-wavelength SHGs at the preas-signed wavelengths.      

Second order optical susceptibilities in alkali halide crystals due to FA color centers

This paper presents the first calculation of the second order optical nonlinearity of the F_A color center for second harmonic generation (SHG) in KCl:Li crystals. The real and imaginary components of the nonlinear susceptibility evaluated over a wide spectral range enclosing the resonance region of the center show interesting feature. Second harmonics generation and three wave mixing processes are nonlinear optical effects based on the second order susceptibility of materials and are very effective in providing laser radiation over a wide range of wavelengths. The density matrix formalism is employed and the equation of motion is solved by second order perturbation to evaluate the nonlinear susceptibility for SHG. It is found that the system shows large resonance-enhanced second order susceptibilities for color center concentration of 10²³ m⁻³. A scheme of phase matching in terms of anomalous dispersion of the centers is discussed.     

Optical properties of the Au–Ag alloy nanowire coated with an anisotropic shell

The optical properties of the Au–Ag alloy nanowire coated with a cylindrical shell with radial dielectric anisotropy are investigated based on quasistatic theory. Numerical results show that the surface plasmon resonance (SPR) peak is redshifted with increasing the component ratio of Au in the alloy, while the intensity of extinction section at the SPR increases with increasing the component ratio of Ag in the alloy. In addition, as the extent of anisotropy of the shell increases, the extinction section at SPR wavelength decreases and the SPR wavelength is redshifted, but compared with the isotropic shell consisting of comparable dielectric constant materials, the SPR has a distinct blueshift for anisotropic shell. We also find that the field enhancement can be completely concentrated inside the anisotropic shell and the electromagnetic transparency can be exhibited.     

The effective dielectric response of nonlinear coated granular composites

The dielectric response of a nonlinear composite system, which is composed of coated granular cylinders with nonlinear cores and linear shells or with linear cores and nonlinear shells randomly embedded in a linear host matrix, is investigated. For the concentric cylinders with weak nonlinear core and linear shell embedded in a linear host, the system can be replaced by solid cylinders with weak nonlinearity embedded in the same host under certain conditions. One of the linear partially resonant conditions is ϵ_s + ϵ_h = 0, which associated with two linear components can be extended to this nonlinear composite, the equivalent nonlinear solid cylinders have the same dielectric function as the original cores and radii larger than those of the original coating shells. Another is the linear partially resonant condition ϵ_c + ϵ_s = 0, which associated with one linear component and another nonlinear component cannot be extended to this nonlinear composite, but under this condition the nonlinear dielectric response of whole system will still be greatly enhanced. For another case of concentric cylinders with linear cores and nonlinear shells, we cannot find the equivalent nonlinear solid cylinders embedded in the same host, and the nonlinear partially resonant condition cannot be realized.     

Nonlinear optical properties of nanometer-size silver coated polydiacetylene composite vesicles and resulting Langmuir–Blodgett films

Noble metal-coated PDA composite vesicles were expected to increase the effective third-order nonlinear optical susceptibility χ ⁽³⁾(ω), due to the enhancement of the optical electric field induced by localized surface plasmon resonance. Different size (20, 50 and 80 nm) Ag colloidal nanoparticles were coated on the outer surface of polydiacetylene (PDA) vesicles to form PDA/Ag nanocomposite vesicles and the size-dependent effect of Ag colloidal nanoparticles on NLO properties enhancement has been explored. The explanation based on the competition of a size-dependent light-confinement effect and a size-dependent dielectric constant of Ag particles had been presented. Furthermore, these PDA/Ag composite vesicles were successfully immobilized onto the solid substrate by the Langmuir–Blodgett (LB) method and their linear and nonlinear optical properties were characterized, respectively. Obviously, PDA/Ag composite vesicles Langmuir–Blodgett (LB) films promoted the enhancement of the third-order NLO properties.     

Optical properties of a GaAs cone-like quantum dot: Second and third-harmonic generation

In the present work, we have studied numerically the second harmonic generation (SHG) and third harmonic generation (THG) in a cone-like quantum dot. For this purpose, we firstly obtained the energy levels and wave functions of this system. Then, we have used an expression for the SHG and THG by a compact density matrix approach and an iterative procedure. The SHG and THG enhance and shift toward lower energy by increasing the height h and vertex angle α. According to the results it is found that the structural parameters have great influence on the THG in this system.     

Calculated Optical Properties of Dielectric Shell Coated Gold Nanorods

Optical absorption spectra of dielectric shell coated gold nanorods are simulated using the discrete dipole ap- proximation method. The influence of the aspect ratio, shell thickness, dielectric constant of the shell, and surrounding medium on the longitudinal resonance mode is investigated. It is found that the coated dielectric shell does not affect the trend in the dependence of resonance position on the aspect ratio, while it broadens the resonant line width and reduces the sensitivity of plasmon resonance in response to changes of the surrounding medium. F~arthermore, the difference of dielectric constants between the shell and surrounding medium plays an important role in determining the resonance position. The screening effect of the dielectric shell tends to be less apparent for a thicker shell thickness.Optical absorption spectra of dielectric shell coated gold nanorods are simulated using the discrete dipole ap- proximation method. The influence of the aspect ratio, shell thickness, dielectric constant of the shell, and surrounding medium on the longitudinal resonance mode is investigated. It is found that the coated dielectric shell does not affect the trend in the dependence of resonance position on the aspect ratio, while it broadens the resonant line width and reduces the sensitivity of plasmon resonance in response to changes of the surrounding medium. F~urthermore, the difference of dielectric constants between the shell and surrounding medium plays an important role in determining the resonance position. The screening effect of the dielectric shell tends to be less apparent for a thicker shell thickness.     

The nonlinear optical susceptibility and electro-optic tensor of ferroelectrics: first-principle study

The nonlinear optical properties of some ABO₃ materials (BaTiO₃, KNbO₃, LiTaO₃ and LiNbO₃) are studied by density functional theory (DFT) in the local density approximation (LDA) expressions based on first-principle calculations. Our goals are to give the details of the calculations for linear and nonlinear optical properties, including the linear electro-optic (EO) tensor for some ABO₃ structures with oxygen octahedral structures using first-principles methods. These results can then be used in the study of the physics of ferroelectrics, specifically, we present calculations of the second harmonic generation response coefficient X _ijk ⁽²⁾ (−2ω, ω, ω) over a large frequency range for ABO₃ crystals. The electronic linear EO susceptibility X _ijk ⁽²⁾ (−ω, ω,0) is also evaluated below the band gap. These results are based on a series of the LDA calculations using DFT. Results for X _ijk ⁽²⁾ (−ω, ω,0) are in agreement with experiments below the band gap. The results are compared with the theoretical calculations and the available experimental data.     

Vibrational mode assignments for bundled single-wall carbon nanotubes using Raman spectroscopy at different excitation energies

This study establishes a generic fitting approach to assignment of nanotube chiralities based on radial breathing mode frequencies (ω _RBM) of SWCNTs in as-produced bundles. Four laser lines with energies of 2.62 eV, 2.33 eV, 1.88 eV and 1.58 eV were employed. The observed RBM frequencies, ω _RBM, were plotted as a function of the possible diameters, d, as identified from the so-called Kataura plot and reported values of the parameters A and B, where ω _RBM=A/d+B, assuming that SWCNTs resonant at the respective laser frequencies dominate the spectrum. The refined values of A and B, obtained by the best fit of a linear regression between ω _RBM and 1/d, were found to vary significantly for different laser frequencies. This variation is interpreted in terms of the differences in electronic properties of SWCNTs resonant at different frequencies. The assigned nanotubes match well with those identified in the Kataura plot, falling within a resonant line width of ±0.2 eV of the respective laser lines.     

A nanohole in a thin metal film as an efficient nonlinear optical element

The nonlinear optical properties of single nanoholes and nanoslits fabricated in gold and aluminum nanofilms are studied by third harmonic generation (THG). It is shown that the extremely high third-order optical susceptibility of aluminum and the presence of strong plasmon resonance of a single nanohole in an aluminum film make possible an efficient nanolocalized radiation source at the third harmonic frequency. The THG efficiency for a single nanohole in a thin metal film can be close to unity for an exciting laser radiation intensity on the order of 10¹³ W/cm².     

Effects of hydrostatic pressure and temperature on the nonlinear optical properties of semiparabolic plus semi-inverse squared quantum wells

In this study, the effects of hydrostatic pressure and temperature on nonlinear optical rectification(OR), second-harmonic generation(SHG), third-harmonic generation(THG) and the linear,nonlinear, and total optical absorption coefficients(OACs) of a semiparabolic plus semi-inverse squared quantum well(QW) are theoretically investigated. The results show that hydrostatic pressure and temperature have significant effects on the optical properties of semiparabolic plus semi-inverse squared QWs, and that the energy levels and magnitudes of the resonant peaks of OR, SHG, THG, and the total OACs vary according to the shape of the limiting potential, the hydrostatic pressure, and the temperature. It is easily seen that the peak positions of the resonant peaks of OR, SHG, THG, and the total OACs in the semiparabolic plus semi-inverse squared QW show a red shift with increasing hydrostatic pressure, but a blue shift with increasing temperature. Therefore, the magnitude and position of the resonant peaks of OR, SHG, THG,and the total OACs can be adjusted by changing the hydrostatic pressure and the temperature,which promise a new degree of freedom in the tunability of various electro-optical devices.     

Manifestation of nano-sized effects in photoinduced nonlinear optics of CdI2–Cu layered single crystals

The infrared (IR) induced second harmonic generation in the thin CdI₂–Cu crystalline layers was discovered. With decreasing thickness of the CdI₂–Cu crystals up to several nanometers value of second-order nonlinear optical susceptibility d₁₄ (at wavelength λ=2.76 μm) for the output IR-induced SHG significantly increases. For the Cu content about 0.4% the output SHG signal achieves its maximum at the sample thickness below 2 nm. It is important that for the samples with larger film thickness the corresponding changes have substantially different properties. Limitation of the d₁₄ at the larger concentration is probably caused by formation of the Cu clusters limiting the enhancement of the hyperpolarizability for particular cluster as well as total nonlinear dielectric susceptibility.     

On the harmonic analysis of non-linear dielectric effects

We investigate the nonlinear dielectric effects in a polar viscous liquid, propylene carbonate, by analyzing the voltage and current traces obtained for a sinusoidal electric field at a frequency of 1 kHz and field amplitudes as high as 162 kV/cm. The main source of non-linear behavior results from the energy absorbed from the field and is understood quantitatively. However, there is a qualitative difference in the behavior of the field induced change, Δε^′′(E), and the third harmonic amplitude of the current, I_3ω. Although both Δε^′′(E) and I_3ω are considered reliable measures of non-linear behavior, we show here that the third harmonic signal reflects only those non-linear responses that are instantaneous on the time scale of the test frequency.