Section: 12 | Optical Properties of Selected Inorganic and Organic Solids |
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The table 'Refractive Index n, Extinction Coefficient k, and Reflectivity at Normal Incidence R.* The Incident Light Is Characterized by Energy E, Wavenumber ν̅, and Wavelength λ' has one or more different columns and 837 more rows than appear in the book.
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 The recommended form of citation is: John R. Rumble, ed., CRC Handbook of Chemistry and Physics, 103rd Edition (Internet Version 2022), CRC Press/Taylor & Francis, Boca Raton, FL. If a specific table is cited, use the format: "Physical Constants of Organic Compounds," in CRC Handbook of Chemistry and Physics, 103rd Edition (Internet Version 2022), John R. Rumble, ed., CRC Press/Taylor & Francis, Boca Raton, FL.

# OPTICAL PROPERTIES OF SELECTED INORGANIC AND ORGANIC SOLIDS

L. I. Berger

Optical properties of materials are closely related to their dielectric properties. The complex dielectric function (relative permittivity) of a material is equal to

ε(ω) = ε′(ω) – jε″(ω),

where ε′(ω) and ε″(ω) are its real and imaginary parts, respectively, and ω is the angular frequency of the applied electric field. For a non-absorbing medium, the index of refraction is n = (εμ)1/2, where μ is the relative magnetic permeability of the medium (material); in the majority of dielectrics, μ ≅ 1.

For many applications, the most important optical properties of materials are the index of refraction, the extinction coefficient, k, and the reflectivity, R. The common index of refraction of a material is equal to the ratio of the phase velocity of propagation of an electromagnetic wave of a given frequency in vacuum to that in the material. Hence, n ≧ 1. The optical properties of highly conductive materials like metals and semiconductors (at photon energy range above the energy gap) differ from those of optically transparent media. Free electrons absorb the incident electromagnetic wave in a thin surface layer (a few hundred nanometers thick) and then release the absorbed energy in the form of secondary waves reflected from the surface. Thus, the light reflection becomes very strong; for example, highly conductive sodium reflects 99.8% of the incident wave (at 589 nm). Introduction of the effective index of refraction, neff = (ε′)1/2 = n – jk, where ε′ = ε – jδ/ω εo, δ is the electrical conductivity of the material in S/m, and εo = 8.8542·10–12 F/m is the permittivity of vacuum, allows one to apply the expressions of the optics of transparent media to the conductive materials. It is clear that the effective index of refraction may be smaller than 1. For example, n = 0.05 for pure sodium and n = 0.18 for pure silver (at 589.3 nm). At very high photon energies, the quantum effects, such as the internal photoeffect, start playing a greater role, and the optical properties of these materials become similar to those of insulators (low reflectance, existence of Brewster’s angle, etc.).

The extinction coefficient characterizes absorption of the electromagnetic wave energy in the process of propagation of a wave through a material. The wave intensity, I, after it passes a distance x in an isotropic medium is equal to

I = I0exp(–αx),

where I0 is the intensity at x = 0 and α is called the absorption coefficient. For many applications, the extinction coefficient, k, which is equal to

$k=\alpha \frac{\lambda }{4\pi },$

where λ is the wavelength of the wave in the medium, is more commonly used for characterization of the electromagnetic losses in materials.

Reflection of an electromagnetic wave from the interface between two media depends on the media indices of refraction and on the angle of incidence. It is characterized by the reflectivity, which is equal to the ratio of the intensity of the wave reflected back into the first medium to the intensity of the wave approaching the interface. For polarized light and two non-absorbing media,

$R=\frac{{\left({N}_{1}-{N}_{2}\right)}^{2}}{{\left({N}_{1}+{N}_{2}\right)}^{2}},$

where N1 = n1/cosθ1 and N2 = n2/cosθ2 for the wave polarized in the plane of incidence, and N1 = n1cosθ1 and N2 = n2cosθ2 for the wave polarized normal to the plane of incidence; θ1 and θ2 are the angles between the normal to the interface in the point of incidence and the directions of the beams in the first and second medium, respectively. The reflectivity at normal incidence in this case is

R = [(n1n2)/(n1 + n2)]2

For any two opaque (absorbing) media, the normal incidence reflectivity is

$R=\frac{{\left({n}_{1}-{n}_{2}\right)}^{2}+{k}_{2}^{2}}{{\left({n}_{1}+{n}_{2}\right)}^{2}+{k}_{2}^{2}}.$

In the majority of experiments, the first medium is air (n ≈ 1), and hence,

$R=\frac{{\left(1-n\right)}^{2}+{k}^{2}}{{\left(1+n\right)}^{2}+{k}^{2}}.$

The data on n and k in the following table are abridged from the sources listed in the references. The reflectivity at normal incidence, R, has been calculated from the last equation. For convenience, the energy E, wavenumber ν̅, and wavelength λ are given for the incidence radiation.

## Refractive Index n, Extinction Coefficient k, and Reflectivity at Normal Incidence R.* The Incident Light Is Characterized by Energy E, Wavenumber ν̅, and Wavelength λ

 Compound E/eV ν̅/cm –1 λ/μm n na nc k ka kc R Ra Rc Continued on next page... Crystalline Arsenic Selenide (As2Se3) - [Ref. 1] As2Se3 2.194 17700 0.565 0.30 As2Se3 2.168 17480 0.572 0.25 As2Se3 2.141 17270 0.579 0.20 As2Se3 2.123 17120 0.584 0.17 As2Se3 2.098 16920 0.591 0.13 As2Se3 2.094 16890 0.592 0.26 As2Se3 2.091 16860 0.593 0.26 As2Se3 2.073 16720 0.598 0.10 0.23 As2Se3 2.060 16610 0.602 0.20 As2Se3 2.049 16530 0.605 0.079 0.17 As2Se3 2.036 16420 0.609 0.15 As2Se3 2.023 16310 0.613 0.12 As2Se3 2.013 16230 0.616 0.050 As2Se3 2.009 16210 0.617 0.097 As2Se3 2.000 16130 0.620 0.082 As2Se3 1.987 16030 0.624 0.063 As2Se3 1.977 15940 0.627 0.031 As2Se3 1.974 15920 0.628 0.051 As2Se3 1.962 15820 0.632 0.038
 *Indices a and c relate to the radiation electric field parallel to the a and c axes of the crystal, respectively.

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