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Astron. Astrophys. 349, 243-252 (1999)

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2. Optical properties of dust

The two sets of quantities that are used to describe optical properties of solids are the real and imaginary parts of the complex refractive index [FORMULA] and the real and imaginary parts of the complex dielectric function (or relative permittivity) [FORMULA] = [FORMULA] + [FORMULA]. These two sets of quantities are not independent, the complex dielectric function [FORMULA] is related to the complex refractive index, m, by [FORMULA] and [FORMULA], when the material is assumed to be non-magnetic ([FORMULA]). Reflection and transmission by bulk media are best described using the complex refractive index, m, whereas absorption and scattering by particles which are small compared with the wavelength are best described by the complex dielectric function, [FORMULA].

The problem of evaluating the expected spectral dependence of extinction for a given grain model (i.e. assumed composition and size distribution) is essentially that of evaluating the extinction efficiency [FORMULA]. It is the sum of corresponding quantities for absorption and scattering; [FORMULA]. These efficiencies are functions of two quantities; a dimension-less size parameter [FORMULA] (where [FORMULA] the grain radius and [FORMULA] the wavelength) and a composition parameter, the complex refractive index m of the grain material. [FORMULA] and [FORMULA] can therefore be calculated from the complex refractive index using Mie theory for any assumed grain model. The resulting values of total extinction can be compared with observational data.

A limit case within the Mie theory is the Rayleigh approximation for spherical particles. This approximation is valid when the grains are small compared to the wavelength, [FORMULA] and in the limit of zero phase shift in the particle ([FORMULA]). In the Rayleigh approximation the extinction by a sphere in vacuum is given as:

[EQUATION]

2.1. Measuring methods of optical properties

A proper application of Mie theory to experimental data requires that the samples are prepared such that the particles are quite small (usually sub-micrometer), well isolated from one another, and that the total mass of particles is accurately known.

In order to obtain single isolated homogeneous particles, the grains are often dispersed in a solid matrix. Small quantities of sample are mixed throughly with the powdered matrix material e.g. KBr or CsI. The matrix is pressed into a pellet which has a bulk transparency in the desired wavelength region. Some of the problems with this technique are that there is a tendency for the sample to clump along the outside rim of the large matrix grains and that the introduction of a matrix, which has a refractive index different from vacuum, might influence the band shape and profile. This matrix effect can be a problem for comparisons of laboratory measurements with astronomical spectra (Papoular et al. 1998; Mutschke et al. 1999).

By measuring the sample on a substrate (e.g. quartz, KBr, Si or NaCl) using e.g. an infrared microscope, the matrix effect can nearly be avoided since the sample is almost fully surrounded by a gas (e.g. air, Ar or He). But the amount of material in the microscopic aperture remains unknown, which is an important disadvantage of this method. Therefore, these measurements are not quantitative but they reveal the shape of the spectrum nearly without a matrix effect (Mutschke et al. 1999).

A major problem of both methods is clustering of the grain samples either during the production of the particles or within the matrix or on the substrate. Clustering can cause a dramatic difference in the optical properties (Huffman 1988). A way to avoid this problem is to perform the optical measurements on a polished bulk sample. For the determination of both n and k two or more measurements on bulk samples are required. This might be done either by a transmission and a reflection measurement, or by two reflectance measurements determinations at different angles or with different polarisations. Since the real part, n, of the refractive index, m, is determined by the phase velocity and the imaginary part, k, by the absorption, a transmission measurement easily fixes k. The Kramers-Kronig relations can be applied in order to obtain the optical constants for grain measurements. The real part of the refractive index can be expressed as an integral of the imaginary part (see e.g. Bohren & Huffman 1983).

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© European Southern Observatory (ESO) 1999

Online publication: August 25, 1999
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