Dielectric refractive index

Figure 1. The effective refractive index (upper plot) and attenuation (lower plot) of a surface plasmon as a function of wavelength for a surface plasmon at the interface between gold and a non-dispersive dielectric (dielectric refractive index n = 1.32).

Figure 2. Distribution of the magnetic field intensity of a surface plasmon at the interface between gold and dielectric (refractive index of the dielectric - 1.32) in the direction perpendicular to the interface (x-y plane) for the wavelength of 850 nm.

Fig. 6 Penetration depth of a surface plasm on into the metal upper plot) and dielectric (lower plot) as a fimction of wavelength for a surface plasmon propagating along the interface of gold and a dielectric (refractive index 1.32)...

Fig. 5 Instrumental contribution to sensitivity S0r/Sn f as a fimction of wavelength for SPR sensors with angular modulation and prism coupler or grating coupler and three different grating periods. Prism-hased sensor configuration BK7 glass prism, gold film, and a non-dispersive dielectric (refractive index 1.32). Grating-based sensor configuration a non-dispersive dielectric (refractive index 1.32) and gold grating...

Grating-based sensor configm-ation a non-dispersive dielectric (refractive index... 

If the scattering particles are in a dielectric solvent medium with solvent refractive index Uq, we can define the excess... 

The Hamaker constant can be evaluated accurately using tire continuum tlieory, developed by Lifshitz and coworkers [40]. A key property in tliis tlieory is tire frequency dependence of tire dielectric pennittivity, (cij). If tills spectmm were tlie same for particles and solvent, then A = 0. Since tlie refractive index n is also related to f (to), tlie van der Waals forces tend to be very weak when tlie particles and solvent have similar refractive indices. A few examples of values for A for interactions across vacuum and across water, obtained using tlie continuum tlieory, are given in table C2.6.3. 

Solvents exert their influence on organic reactions through a complicated mixture of all possible types of noncovalent interactions. Chemists have tried to unravel this entanglement and, ideally, want to assess the relative importance of all interactions separately. In a typical approach, a property of a reaction (e.g. its rate or selectivity) is measured in a laige number of different solvents. All these solvents have unique characteristics, quantified by their physical properties (i.e. refractive index, dielectric constant) or empirical parameters (e.g. ET(30)-value, AN). Linear correlations between a reaction property and one or more of these solvent properties (Linear Free Energy Relationships - LFER) reveal which noncovalent interactions are of major importance. The major drawback of this approach lies in the fact that the solvent parameters are often not independent. Alternatively, theoretical models and computer simulations can provide valuable information. Both methods have been applied successfully in studies of the solvent effects on Diels-Alder reactions. 

Table 5.19 Refractive Index, Viscosity, Dielectric Constant, and Surface Tension...

VISCOSITY, SURFACE TENSION, DIELECTRIC CONSTANT, DIPOLE MOMENT, AND REFRACTIVE INDEX... 

Temp., °C Refractive index, Viscosity, mN Dielectric constant, e Surface tension, mN s ... 

Under the same conditions. Maxwell s theory of radiation shows that the refractive index and the relative dielectric constant are simply related by... 

Equations (10.17) and (10.18) show that both the relative dielectric constant and the refractive index of a substance are measurable properties of matter that quantify the interaction between matter and electric fields of whatever origin. The polarizability is the molecular parameter which is pertinent to this interaction. We shall see in the next section that a also plays an important role in the theory of light scattering. The following example illustrates the use of Eq. (10.17) to evaluate a and considers one aspect of the applicability of this quantity to light scattering. 

Table 5. Dielectric Constants and Refractive Indexes of Parylenes...

Antireflection coatings are used over the silicon surface which, without the coating, reflects ca 35% of incident sunlight. A typical coating consists of a single layer of a transparent dielectric material with a refractive index of ca 2, which is between the index of siUcon and ait or cover material. Materials such as titanium dioxide, tantalum pentoxide, Ta20, or siUcon nitride, Si N, ca 0.08-p.m thick are common. The coating and a physically textured... 

Polarizability Attraction. AU. matter is composed of electrical charges which move in response to (become electrically polarized in) an external field. This field can be created by the distribution and motion of charges in nearby matter. The Hamaket constant for interaction energy, A, is a measure of this polarizability. As a first approximation it may be computed from the dielectric permittivity, S, and the refractive index, n, of the material (15), where is the frequency of the principal electronic absorption... 

Values in parentheses are estimates. Values for band gaps decrease with increasing temperature, whereas values for the static dielectric constant and long wavelength refractive index increase with increasing temperature. 

The bulk density of cellulose acetate varies with physical form from 160 kg/m (10 lb /ft ) for soft dakes to 481 kg/m (30 lb /fT) for hammer-milled powder, whereas the specific gravity (1.29—1.30), refractive index (1.48), and dielectric constant of most commercial cellulose acetates are similar. 

The dielectric constant is a measure of the ease with which charged species in a material can be displaced to form dipoles. There are four primary mechanisms of polarization in glasses (13) electronic, atomic, orientational, and interfacial polarization. Electronic polarization arises from the displacement of electron clouds and is important at optical (ultraviolet) frequencies. At optical frequencies, the dielectric constant of a glass is related to the refractive index k =. Atomic polarization occurs at infrared frequencies and involves the displacement of positive and negative ions. 

It is thus seen that for polymers in which polarisations other than electronic ones are negligible (i.e. P = P ) the dielectric constant is equal to the square of the refractive index Table 6.2). 

The lowest dielectric constant (1.83-1.93) of any known plastics material. (It is to be noted that this is in spite of the fact that the dielectric constant is more than the square of the refractive index, indicating that polarisations other than electronic polarisations are present—see Section 6.3). 

It should be noted that low-loss spectra are basically connected to optical properties of materials. This is because for small scattering angles the energy-differential cross-section dfj/dF, in other words the intensity of the EEL spectrum measured, is directly proportional to Im -l/ (E,q) [2.171]. Here e = ei + iez is the complex dielectric function, E the energy loss, and q the momentum vector. Owing to the comparison to optics (jqj = 0) the above quoted proportionality is fulfilled if the spectrum has been recorded with a reasonably small collection aperture. When Im -l/ is gathered its real part can be determined, by the Kramers-Kronig transformation, and subsequently such optical quantities as refraction index, absorption coefficient, and reflectivity. 

As shown in Fig. 7, a large increase in optical absorption occurs at higher photon energies above the HOMO-LUMO gap where electric dipole transitions become allowed. Transmission spectra taken in this range (see Fig. 7) confirm the similarity of the optical spectra for solid Ceo and Ceo in solution (decalin) [78], as well as a similarity to electron energy loss spectra shown as the inset to this figure. The optical properties of solid Ceo and C70 have been studied over a wide frequency range [78, 79, 80] and yield the complex refractive index n(cj) = n(cj) + and the optical dielectric function... 

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