Complex refractive indices

The complex refractive index, r, comprises a real and an imaginary part which are denoted n and k respectively. The relation between these terms is concisely given by 

The real and imaginary parts of the complex refractive index govern important characteristics of a material s interactions with light and are discussed in more detail in the next sections. 

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Internal redection starts by consideration of an interface between two media, a denser transparent medium with refractive index n, and a rarer medium with a complex refractive index (= where is the absorption coefficient of the medium) as shown in Figure 23. If of the rarer... 

Attenuated total reflection, on which atr—ftir is based, occurs when the rarer medium is absorbing and is characterized by a complex refractive index (40). The absorbing characteristics of this medium allow coupling to the evanescent field such that this field is attenuated to an extent dependent on k. The critical angle in the case of attenuated total reflection loses its meaning, but internal reflection still occurs. Thus, if the internally reflected beam is monitored, its intensity will reflect the loss associated with the internal reflection process at the interface with an absorbing medium. 

Using the complex refractive index N = n + iK where i =- f—1 and Kis the absorption coefficient, the reflectivity R of metals and alloys is given by ... 

For thin-film samples, abrupt changes in refractive indices at interfrees give rise to several complicated multiple reflection effects. Baselines become distorted into complex, sinusoidal, fringing patterns, and the intensities of absorption bands can be distorted by multiple reflections of the probe beam. These artifacts are difficult to model realistically and at present are probably the greatest limiters for quantitative work in thin films. Note, however, that these interferences are functions of the complex refractive index, thickness, and morphology of the layers. Thus, properly analyzed, useful information beyond that of chemical bonding potentially may be extracted from the FTIR speara. 

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... 

Figure 11. Imaginary part of complex refractive index for polystyrene...

The approximate picture of a transparent electrochemical interface is rather far from the actual situation. Nevertheless, the Fresnel equations are valid also for absorbing media, if one uses the complex refractive indexes, Nk ... 

Del Villar, I. Mafias, I. R. Arregui, F. J. Achaerandio, M., Nanodeposition of materials with complex refractive index in long period fiber gratings, J. Lightwave Technol. 2005, 23, 4192... 

The real part of this nnmber is the normal refractive index n = c/v(c and v being the speed of light in vacnnm and in the medium, respectively). The imaginary part of the complex refractive index, k, is called the extinction coefficient. It is necessary to recall here that both magnitndes, n and k, are dependent on the frequency (wavelength) of the propagating wave co,N = N(co). 

Allen et a/. (1991) performed these computations for 1-octadecene droplets, and they measured the evaporation rate of the droplets as a function of laser power. To determine the absolute irradiance /, of the laser beam, they also measured the force on the particle exerted by the laser beam using the techniques discussed above. The photon pressure force is given by Eq. (87), which involves the complex refractive index. The real component of the refractive index n was determined from optical resonance measurements, and the imaginary component was obtained iteratively. That is, they assumed a... 

Table III shows that the experimental and predicted evaporation rates are in good agreement at all beam intensities. There is some inconsistency at the highest power levels. It was difficult to maintain the droplet in the center of the laser beam at the highest power level, and the measured evaporation rate is somewhat low as a result of that problem. Additional computations demonstrate that the predicted evaporation rate is quite sensitive to the choice of the imaginary component of N, so the results suggest that this evaporation method is suitable for the determination of the complex refractive index of weakly absorbing liquids. For strong absorbers, the linearizations of the Clausius-Clapeyron equation and of the radiation energy loss term in the interfacial boundary condition may not be valid. In this event, a numerical solution of the governing equations is required. The structure of the source function, however, makes this a rather tedious task.

Sokolik, I. N., A. V. Andronova, and T. C. Johnson, Complex Refractive Index of Atmospheric Dust Aerosols, Atmos. Environ., 27A, 2495-2502 (1993). 

The real and imaginary parts of the complex refractive index satisfy Kramers-Kronig relations sometimes this can be used to assess the reliability of measured optical constants. N(oj) satisfies the same crossing condition as X(w) N (u) = N( — u). However, it does not vanish in the limit of indefinitely large frequency lim JV(co) = 1. But this is a small hurdle, which can be surmounted readily enough by minor fiddling with JV(co) the quantity jV(co) — 1 has the desired asymptotic behavior. If we now assume that 7V( ) is analytic in the top half of the complex [Pg.28]

The rate at which electromagnetic energy is removed from the wave as it propagates through the medium is determined by the imaginary part of the complex refractive index. If the irradiances I0 and lt (or rather their ratio) are measured at two different positions z = 0 and z = h, then a, and hence k, can be obtained in principle from the relation... 

Table 4.1 Scattering Coefficients for a Water Droplet in Air with Size Parameter x = 3 and Complex Refractive Index m = 1.33 + 10 8...

There are two sets of quantities that are often used to describe optical properties the real and imaginary parts of the complex refractive index N = n + ik and the real and imaginary parts of the complex dielectric function (or relative permittivity) e = c + ie". These two sets of quantities are not independent either may be thought of as describing the intrinsic optical properties of matter. The relations between the two are, from (2.47) and (2.48),... 

We must reemphasize that the real and imaginary parts of the complex dielectric function (and the complex refractive index) are not independent. Arbitrary choices of c and <" (or n and k) do not necessarily correspond to... 

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