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

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

Determination of the direct band-gap energy of InAlAs matched to InP by photoluminescence excitation spectroscopy

A series of InxAl1-xAs samples (0.51≪x≪0.55)coherently grown on InP was studied in order to measure the band-gap energy of the lattice matched composition. As the substrate is opaque to the relevant photon energies, a method is developed to calculate the optical absorption coefficient from the photoluminescence excitation spectra. The effect of strain on the band-gap energy has been taken into account. For x=0.532, at 14 K we have obtained Eg0=1549±6 meV

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

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

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

Variational principles for nonlinear dynamical systems

A variational method for Hamiltonian systems is analyzed. Two different variationalcharacterization for the frequency of nonlinear oscillations is also suppliedfor non-Hamiltonian systems

Nonlinear models and small sample performance of the generalized method of moments

In this paper I explore the issue of nonlinearity (both in the datageneration process and in the functional form that establishes therelationship between the parameters and the data) regarding the poorperformance of the Generalized Method of Moments (GMM) in small samples.To this purpose I build a sequence of models starting with a simple linearmodel and enlarging it progressively until I approximate a standard (nonlinear)neoclassical growth model. I then use simulation techniques to find the smallsample distribution of the GMM estimators in each of the models.

Use of NIR spectroscopy and multivariate process spectra calibration methodology for pharmaceutical solid samples analysis

Accomplish high quality of final products in pharmaceutical industry is a challenge that requires the control and supervision of all the manufacturing steps. This request created the necessity of developing fast and accurate analytical methods. Near infrared spectroscopy together with chemometrics, fulfill this growing demand. The high speed providing relevant information and the versatility of its application to different types of samples lead these combined techniques as one of the most appropriated. This study is focused on the development of a calibration model able to determine amounts of API from industrial granulates using NIR, chemometrics and process spectra methodology.

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

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.