The Real Refractive Index

The real and imaginary parts of the complex refractive index are related by a mathematical expression called the Kramers-Kronig transform and one can be calculated from the other. The Kramers-Kronig transform for calculating the real refractive index from the imaginary part is defined as  

The output from the Kramers-Kronig transform is the real refractive index spectrum minus the average real refractive index, hereafter referred to as Ukk  

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The considerations before refer to the non-absorbing case when and n are real quantities. In order to characterize the optical properties completely absorption must be included. This can be achieved by taking the optica] and dielectric functions to be complex quantities comprising two real figures each. The (real) refractive index n is complemented by the real absorption index k to constitute the complex refractive index... 

For the weak oscillator the shapes of all graphs related to h and e are symmetrical with respect to the resonance frequency, pairwise similar, and no distinctive wavenumber shift is found. The reflectance spectrum resembles closely the dispersion anomaly of the (real) refractive index. The spectral variations of the components of the dielectric function are... 

For the strong oscillator the n and k spectra are asymmetric. The shift of the k maximum away from the resonance frequency is particularly obvious. In such a case a reliable representation of the vibrational structure cannot be derived from transmittance spectra and thus, from the absorption index k alone. Another peculiarity of the strong oscillator is the spectral range where the (real) refractive index is below unity. This renders... 

V indicates the principal value) are applied to a function F = F + F" (Bode, 1950 Smith, 1985 Hopfe et al., 1981). Such so-called dispersion relations exist between the (real) refractive index and the absorption index. Dedicated software programs are available, also specially for (infrared) spectroscopic purposes (Hopfe, 1989), a generalization for oblique incidence on layered systems was given by Grosse and Offermann (1991). 

The above relationships (Figure 1.10) show that the optical pigment properties depend on the particle size D and the complex refractive index n = n (1 - i/c), which incorporates the real refractive index n and the absorption index k. As a result, the reflectance spectrum, and hence the color properties, of a pigment can be calculated if its complex refractive index, concentration, and particle size distribution are known [1.40]. Unfortunately, reliable values for the necessary optical constants (refractive index n and absorption index k) are often lacking. These two parameters generally... 

Figure 2 The scattering problem illustrated for a spheroidal particle with orientation e and effective refractive index = n — i k. The surrounding medium is nonabsorbing, with the real refractive index ne, The speed of light within the medium is c = Co/r e, where Cq is the speed of light in vacuum. The incident plane wave has frequency v (ie, wavelength X = dv) and a wave vector collinear to o. A propagation direction of the radiation scattered by the particle is denoted as a. 0 is the angle between a and co. ...

Fig. 4.1-163 ZnSe. Numerically calculated spectral dependence of the real refractive index n and the extinction coefficient k (solid lines). The filled circles (n) and open circles (k) are experimental data [1.140]...

Fig.tr.1-175 CdSe, hex, cub. The real refractive index n(E) and the extinction coefficient k E), forming the complex refractive index n (E) = n E) + ik E), for both hexagonal and cubic CdSe. The circles represent experimental data, the solid lines numerically calculated energy dependences [1.150]... 

Like the real refractive index, the imaginary refractive index is also a dimensionless quantity. For pure materials, is given by... 

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