Dispersion model Lorentz

To select suitable dispersion model, such Sellimeier model, Cauchy model, Lorentz model, Drude model, effective medium approximation (EMA) model etc., for each layer. Which dispersion model should be selected for a certain layer depends on the specific type of the film and we will discuss later in detail. In the model, some parameters are known and the others are unknown. The unknown parameters will be determined through mathematical inversion method. 

We now want to study the consequences of such a model with respect to the optical properties of a composite medium. For such a purpose, we will consider the phenomenological Lorentz-Drude model, based on the classical dispersion theory, in order to describe qualitatively the various components [20]. Therefore, a Drude term defined by the plasma frequency and scattering rate, will describe the optical response of the bulk metal or will define the intrinsic metallic properties (i.e., Zm((a) in Eq.(6)) of the small particles, while a harmonic Lorentz oscillator, defined by the resonance frequency, the damping and the mode strength parameters, will describe the insulating host (i.e., /((0) in Eq.(6)). 

When applied to spatially extended dynamical systems, the PoUicott-Ruelle resonances give the dispersion relations of the hydrodynamic and kinetic modes of relaxation toward the equilibrium state. This can be illustrated in models of deterministic diffusion such as the multibaker map, the hard-disk Lorentz gas, or the Yukawa-potential Lorentz gas [1, 23]. These systems are spatially periodic. Their time evolution Frobenius-Perron operator... 

Using a four-phase model consisting of ambient/simple grade/film/ substrate, we fit the data to obtain the dispersion of optical constants for each films in the range of 1.55-6.53 eV. The Cauchy model was used as a model for the substrate and fixed during the fitting. The Cody-Lorentz (CL) model [14] was used as a model for the film. 

It is often assumed, although without actual proof, that there exists a definite proportionality between the molecular and the macroscopic relaxation times. A relation between r and r could only be established if the actual field acting on the molecule were known. Equation 27 is obtained if this field is identified either with the external or with the Lorentz internal field. In the first case the macroscopic relaxation time is identical with the molecular one. In the second case r is proportional to t. If Onsager s model is used,88 it may be shown that in first approximation, the cavity field G is itself subject to dispersion ... 

In SAXS studies of a real sample, all the lamellar layers or stacks are oriented at random with respect to the incident beam therefore the intensity function /(g)obs which corresponds to the measured intensity shows spherical symmetry [20]. However, when using theoretical one-dimensional models (where the lateral width of the lamellae is much greater than the periodicity), the dispersion intensity is calculated assuming that the lamellar stacks are correctly oriented (perpendicular) with respect to the incident beam [21]. This implies that the observed intensity (with spherical symmetry) should be corrected to a perpendicular intensity to the lamellar stacks. Because of this, the Lorentz factor that is described for lamellar systems is also used. 

Metals are denoted as fi ee-electron metals if most of the electronic and optical properties are due to the conduction electrons alone. Examples are Al, Mg, and alkali metals. The dispersion of the optical constants of the fi ee-electron metals is described by the Drude model [72], which can be regarded as a special case of the Lorentz model (1.3.3°) when the restoring (bounding) force is equal to zero, and hence the resonance frequency of free carriers, a>o = -JWfm (here, m is electron mass), is also equal to zero, damping force y results... 

FIGURE 5.34 Modeling the dynamical diffraction by means of the Lorentz and Laue centers along the Poynting vectors (Saip) associated to the branches of dispersion surface after Birau and Putz (2000). 

A critical point in method A is the not exactly known refractive index n or, in terms of the Drude-Lorentz model, 800 of PEG in the infrared region, because it enters the spectrum calculation but cannot be determined with sufficient accuracy from the spectral fit. Changes of 800 have, other things being equal, opposite effects on ATR reflectivities calculated for bulk material and thin films on metal, respectively. In the present calculation, 8qo = 2.10 (n = 1.45) was used, somewhat smaller than the value np = 1.46 reported in the literature [18] in order to take into account the optical dispersion [19] in an approximate manner. 

The Lorentz oscillator model is a classical model which is usually used to describe the dispersion relation of semiconductor and crystalline materials. [6, 7, 67, 68] On the basis of this model, the dielectric function is usually expressed as... 

Simple Spectral Method [23] In the simple spectral method, a model dielectric response function is used. It combines a Debye relaxation term to describe the response at microwave frequencies with a sum of terms of classical form of Lorentz electron dispersion (corresponding to a damped harmonic oscillator model) for the frequencies from IR to UV ... 

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