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Дата изменения: Fri Nov 19 12:07:03 2010 Дата индексирования: Mon Oct 1 23:21:45 2012 Кодировка: Поисковые слова: р п р п р п р п р п р п р п р п |
On the optical characterization of media
|
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(1) |
The parameter i in Eq.(1) describes the optical properties of
the medium where radiation propagates. The quantity
is called
the complex refractive index, its real part
is equal to the ratio
of the velocity of electromagnetic radiation in vacuum to
the phase velocity of radiation in the medium, and its imaginary part
characterizes the decrease of the radiation intensity in the medium
because of absorption.
The refractive index and the extinction coefficient
of a medium are functions of
the frequency, and in the case of anisotropic media
and
also depend on the direction of radiation propagation
.
In the last case the values of
and
are tensors of the second order.
The intensity of radiation in a medium is proportional
to and its absorption is described by the Bouguer-Lambert-Beer law.
According to this law, the intensity of light
after its propagation through a material slab of the thickness
is connected with the initial intensity
as follows:
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(2) |
The value
being the ratio of the intensity
absorbed by the slab to the incident one is called the absorption
coefficient.
From Eqs.(1)-(2) one obtains the expression for the absorption
coefficient
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(3) |
To characterize absorption by a medium, one also uses the quantity
100 (in percent) being the ratio of the intensityof the transmitted
radiation to that of the incident one and called
the transmission coefficient (or transmittance).
For values of , to describe the optical properties
one often uses the quantity
called the
optical density.
The optical constants and
allow one to estimate not only
transmittance and absorption of radiation, but also its reflection
at the border of two media. To calculate the reflection coefficient
(or reflectance) from the values of
and
for two bordering
media and the incidence angle
one can usitilize the Fresnel formula.
Note that the values of the transmission (
), absorption (
) and
reflection (
) coefficients, which characterize the properties of a
sample, are connected
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(4) |
In the electromagnetic theory one often uses not and
, but
the dielectric functions (or permittivity) defined as
. As it follows from its definition,
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(5) |
In an anisotropic medium, the permittivity is a symmetrical tensor and
can be transformed to the main axes
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(6) |
According to the optical properties, crystals are divided in 3 groups:
For single-axis crystals, the coinciding values of the refractive index are called the refractive index of the ordinary ray, the third principal refractive index is the principal refractive index of the extraordinary ray.
Like isotropic media, crystals are characterized not only by
the refractive indices, but also by the absorption indices that
can be combined in a tensor complex refractive index
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(7) |
The theory of interaction of light with a material that
accounts for the frequency dependence of the optical
functions
was developed by Lorentz and Drude.
Despite the difference with the contemporary quantum-mechanical
approach, the results of this classical theory remain
formally valid and correctly describe the main features of the
process of interaction of radiation with a medium.
A material medium in the classical theory is described by
a set of harmonic oscillators characterized by the eigenfrequency ,
the oscillator strength
and the damping
. Using the
Maxwell equations for electromagnetic radiation and
the equations of the classical mechanics for description of
oscillator charge motion, one can obtain the expression for
the frequency dependence of the dielectric permittivity
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(8) |
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(9) |
Denoting the high-frequency dielectric permittivity by
,
the expression for
can written via
and
being the frequencies of the longitudal and transversal oscillations of
crystal lattice, respectively.
Taking into account the damping of the oscillations
(
and
), allowing one to
describe the anharmonicity, the dielectric permittivity is
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(10) |
For more information on the optical constant theory we refer the reader to the chapter of the classical C.F.Bohren & D.R.Huffman book [1] and a recent good textbook by M.Fox [2]. Some technical aspects of obtaing the optical constants are described briefly in another chapter of the book [1] and in more detail, e.g., in the books edited by E.D.Palik [3,4,5].
The optical constants for atmospheric aerosols are well presented in the HITRAN database (see http://www.hitran.com). Those for materials of astronomical interest are collected by us in the JPDOC database (http://www.astro.spbu.ru/JPDOC). This WWW database includes references to the papers where the optical constants were measured or calculated and original data obtained in the laboratory of the Friedrich Schiller University, Jena. A description of the JPDOC is given in [6,7].
(After V.M.Zolotarev)