Variational calculation of vibrational linear and nonlinear optical properties

A variational approach for reliably calculating vibrational linear and nonlinear optical properties of molecules with large electrical and/or mechanical anharmonicity is introduced. This approach utilizes a self-consistent solution of the vibrational Schrödinger equation for the complete field-dependent potential-energy surface and, then, adds higher-level vibrational correlation corrections as desired. An initial application is made to static properties for three molecules of widely varying anharmonicity using the lowest-level vibrational correlation treatment (i.e., vibrational Møller-Plesset perturbation theory). Our results indicate when the conventional Bishop-Kirtman perturbation method can be expected to break down and when high-level vibrational correlation methods are likely to be required. Future improvements and extensions are discussed

Linear and nonlinear optical properties of Si nanocrystals in SiO2 deposited by plasma-enhanced chemical-vapor deposition

Linear and nonlinear optical properties of silicon suboxide SiOx films deposited by plasma-enhanced chemical-vapor deposition have been studied for different Si excesses up to 24¿at.¿%. The layers have been fully characterized with respect to their atomic composition and the structure of the Si precipitates. Linear refractive index and extinction coefficient have been determined in the whole visible range, enabling to estimate the optical bandgap as a function of the Si nanocrystal size. Nonlinear optical properties have been evaluated by the z-scan technique for two different excitations: at 0.80¿eV in the nanosecond regime and at 1.50¿eV in the femtosecond regime. Under nanosecond excitation conditions, the nonlinear process is ruled by thermal effects, showing large values of both nonlinear refractive index (n2 ~ ¿10¿8¿cm2/W) and nonlinear absorption coefficient (ß ~ 10¿6¿cm/W). Under femtosecond excitation conditions, a smaller nonlinear refractive index is found (n2 ~ 10¿12¿cm2/W), typical of nonlinearities arising from electronic response. The contribution per nanocrystal to the electronic third-order nonlinear susceptibility increases as the size of the Si nanoparticles is reduced, due to the appearance of electronic transitions between discrete levels induced by quantum confinement.

Field-induced coordinates for the determination of dynamic vibrational nonlinear optical properties

Three conjugated organic molecules that span a range of polarity and valence-bond/charge transfer characteristics were studied. It was found that dispersion can be insignificant, and that adequate treatment can be achieved with frequency-dependent field-induced vibrational coordinates (FD-FICs)

Nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties by means of electrical property expansions: Application to HF, CH4, CF4, and SF6

Electrical property derivative expressions are presented for the nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties. For CF4 and SF6, as opposed to HF and CH4, a term that is quadratic in the vibrational anharmonicity (and not previously evaluated for any molecule) makes an important contribution to the static second vibrational hyperpolarizability of CF4 and SF6. A comparison between calculated and experimental values for the difference between the (anisotropic) Kerr effect and electric field induced second-harmonic generation shows that, at the Hartree-Fock level, the nuclear relaxation/infinite frequency approximation gives the correct trend (in the series CH4, CF4, SF6) but is of the order of 50% too small

Variational calculation of static and dynamic vibrational nonlinear optical properties

The vibrational configuration interaction method used to obtain static vibrational (hyper)polarizabilities is extended to dynamic nonlinear optical properties in the infinite optical frequency approximation. Illustrative calculations are carried out on H2 O and N H3. The former molecule is weakly anharmonic while the latter contains a strongly anharmonic umbrella mode. The effect on vibrational (hyper)polarizabilities due to various truncations of the potential energy and property surfaces involved in the calculation are examined

Basis set and electron correlation effects on initial convergence for vibrational nonlinear optical properties of conjugated organic molecules

The level of ab initio theory which is necessary to compute reliable values for the static and dynamic (hyper)polarizabilities of three medium size π-conjugated organic nonlinear optical (NLO) molecules is investigated. With the employment of field-induced coordinates in combination with a finite field procedure, the calculations were made possible. It is stated that to obtain reasonable values for the various individual contributions to the (hyper)polarizability, it is necessary to include electron correlation. Based on the results, the convergence of the usual perturbation treatment for vibrational anharmonicity was examined

Surface characterization techniques for determining the root-mean-square roughness and power spectral densities of optical components

Surface topography and light scattering were measured on 15 samples ranging from those having smooth surfaces to others with ground surfaces. The measurement techniques included an atomic force microscope, mechanical and optical profilers, confocal laser scanning microscope, angle-resolved scattering, and total scattering. The samples included polished and ground fused silica, silicon carbide, sapphire, electroplated gold, and diamond-turned brass. The measurement instruments and techniques had different surface spatial wavelength band limits, so the measured roughnesses were not directly comparable. Two-dimensional power spectral density (PSD) functions were calculated from the digitized measurement data, and we obtained rms roughnesses by integrating areas under the PSD curves between fixed upper and lower band limits. In this way, roughnesses measured with different instruments and techniques could be directly compared. Although smaller differences between measurement techniques remained in the calculated roughnesses, these could be explained mostly by surface topographical features such as isolated particles that affected the instruments in different ways.

Treatment of nonlinear optical properties due to large amplitude anharmonic vibrational motions: umbrella motion in NH3

A general reduced dimensionality finite field nuclear relaxation method for calculating vibrational nonlinear optical properties of molecules with large contributions due to anharmonic motions is introduced. In an initial application to the umbrella (inversion) motion of NH3 it is found that difficulties associated with a conventional single well treatment are overcome and that the particular definition of the inversion coordinate is not important. Future applications are described

Initial convergence of the perturbation series expansion for vibrational nonlinear optical properties

Initial convergence of the perturbation series expansion for vibrational nonlinear optical (NLO) properties was analyzed. The zero-point vibrational average (ZPVA) was obtained through first-order in mechanical plus electrical anharmonicity. Results indicated that higher-order terms in electrical and mechanical anharmonicity can make substantial contributions to the pure vibrational polarizibility of typical NLO molecules

Design of surface forces apparatus for tribology studies combined with nonlinear optical spectroscopy

We describe the design, calibration, and performance of surface forces apparatus with the capability of illumination of the contact interface for spectroscopic investigation using optical techniques. The apparatus can be placed in the path of a Nd-YAG laser for studies of the linear response or the second harmonic and sum-frequency generation from a material confined between the two surfaces. In addition to the standard fringes of equal chromatic order technique, which we have digitized for accurate and fast analysis, the distance of separation can be measured with a fiber-optic interferometer during spectroscopic measurements (2 Å resolution and 10 ms response time). The sample approach is accomplished through application of a motor drive, piezoelectric actuator, or electromagnetic lever deflection for variable degrees of range, sensitivity, and response time. To demonstrate the operation of the instrument, the stepwise expulsion of discrete layers of octamethylcyclotetrasiloxane from the contact is shown. Lateral forces may also be studied by using piezoelectric bimorphs to induce and direct the motion of one surface.

Mesophyll conductance to CO2 and leaf morphological characteristics under drought stress during Quercus ilex L resprouting

• Quercus ilex L., the dominant species in Mediterranean forests and one with a great capacity for resprouting after disturbances, is threatened by the expected increase in fire frequency and drought associated with climate change. • The aim of this study was to determine the contribution of photosynthesis limitants, especially mesophyll conductance (gmes ) during this species’ resprouting and under summer drought. • Resprouts showed 5.3-fold increased gmes and 3.8-fold increased stomatal conductance (gs) atmidday with respect to leaves of undisturbed individuals. With increased drought, structural changes (decreased density and increased thickness) in resprouts contributed to the observed higher photosynthesis and increased gmes. However, gmes only partially depended on leaf structure, and was also under physiological control. Resprouts also showed lower non-stomatal limitations (around 50% higher carboxylation velocity (Vc,max) and capacity for ribulose-1,5-bisphosphate regeneration (Jmax)). A significant contribution of gmes to leaf carbon isotope discrimination values was observed. • gmes exhibits a dominant role in photosynthesis limitation in Q. ilex and is regulated by factors other than morphology. During resprouting after disturbances, greater capacity to withstand drought, as evidenced by higher gmes , gs and lower non-stomatal limitants, enables increased photosynthesis and rapid growth.

New delay-dependent stability criteria for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations

The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range dependent, and distributeddelay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs) and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method

Suboptimal filtering and nonlinear time scale transformation for the analysis of multiexponential decays

Multiexponential decays may contain time-constants differing in several orders of magnitudes. In such cases, uniform sampling results in very long records featuring a high degree of oversampling at the final part of the transient. Here, we analyze a nonlinear time scale transformation to reduce the total number of samples with minimum signal distortion, achieving an important reduction of the computational cost of subsequent analyses. We propose a time-varying filter whose length is optimized for minimum mean square error

On the consequences of misspecifing assumptions concerning residuals distribution in a repeated measures and nonlinear mixed modelling context

In this paper we describe the results of a simulation study performed to elucidate the robustness of the Lindstrom and Bates (1990) approximation method under non-normality of the residuals, under different situations. Concerning the fixed effects, the observed coverage probabilities and the true bias and mean square error values, show that some aspects of this inferential approach are not completely reliable. When the true distribution of the residuals is asymmetrical, the true coverage is markedly lower than the nominal one. The best results are obtained for the skew normal distribution, and not for the normal distribution. On the other hand, the results are partially reversed concerning the random effects. Soybean genotypes data are used to illustrate the methods and to motivate the simulation scenarios