132
7 Modeling of the Optical Characteristics Fibrillar Structure
The obtained results make it possible to determine the optical properties of the
tissue, they are also useful for the diagnosis of early changes tissues.
Thus becomes important to use the mathematical modeling of physical processes
proceeding in biological samples of different types in conditions of laser irradiation.
The problem consists of several parts. In the first part, we consider the problem
of light scattering on a system of parallel dielectric cylinders, modeling collagen
fibers. In the second part we consider the problem of reflection of a Gaussian beam
with an arbitrary cross-section plane wave from a smoothly irregular layer modeling
biological tissue with fibrillar structure. In the third part of the numerical simulations
we investigate the question of electrical characteristics of the biological sample.
7.2 Scattering on a Parallel Cylinders
In this section, we consider the distribution of polarized radiation in multiple scattering media the example of the dermis.
The structure of the dermis are collagen fibers, consisting of parallel beams of an
average thickness 50–100 nm, connected by glycosaminoglycans and proteoglycans
[4], then applied to the analysis of the effect of the morphological characteristics
of multiple scattering in randomly inhomogeneous media with fibrillar structure
regarded in the modeled medium that consists of parallel dielectric cylinders with
identical refraction complex coefficient are n cyl and radius a.
In this case, the cylinders are distributed in an isotropic dielectric medium with
a complex refractive refraction are n o . The distance between the cylinder and the
wavelength incident radiation are comparable and we believe that the cylinders are
oriented along the Z -axis.
Let the cylinders at an angle θ be incident by the plane polarized wave in this
case, the Cartesian coordinate system O X ZY is used as a fixed reference system, ϕ
is the azimuthal angle. We consider only the simple harmonic time dependence of
the angular frequency ω, and the factor exp(−iωt) is omitted.
Note that cylindrical coordinates of primary field incident wave are E, H admits
a representation as superposition of electric and magnetic fields types.
Thus in solving the problem, we consider two cases of the polarization of the
incident wave. Note that the scattered on the cylinders field can be found, depending
on the polarization primary field through the magnetic U and the electric V Hertz
potential. In this case, the values potentials U , V associated with the vector E, H by
the following relations:
E =
i
k
× × ×(e z U ) + + × (e z V ),
(7.1)
H = −n o ×(e z U ) +
i
k
× × ×(e z V )
(7.2)
7 Modeling of the Optical Characteristics Fibrillar Structure
The obtained results make it possible to determine the optical properties of the
tissue, they are also useful for the diagnosis of early changes tissues.
Thus becomes important to use the mathematical modeling of physical processes
proceeding in biological samples of different types in conditions of laser irradiation.
The problem consists of several parts. In the first part, we consider the problem
of light scattering on a system of parallel dielectric cylinders, modeling collagen
fibers. In the second part we consider the problem of reflection of a Gaussian beam
with an arbitrary cross-section plane wave from a smoothly irregular layer modeling
biological tissue with fibrillar structure. In the third part of the numerical simulations
we investigate the question of electrical characteristics of the biological sample.
7.2 Scattering on a Parallel Cylinders
In this section, we consider the distribution of polarized radiation in multiple scattering media the example of the dermis.
The structure of the dermis are collagen fibers, consisting of parallel beams of an
average thickness 50–100 nm, connected by glycosaminoglycans and proteoglycans
[4], then applied to the analysis of the effect of the morphological characteristics
of multiple scattering in randomly inhomogeneous media with fibrillar structure
regarded in the modeled medium that consists of parallel dielectric cylinders with
identical refraction complex coefficient are n cyl and radius a.
In this case, the cylinders are distributed in an isotropic dielectric medium with
a complex refractive refraction are n o . The distance between the cylinder and the
wavelength incident radiation are comparable and we believe that the cylinders are
oriented along the Z -axis.
Let the cylinders at an angle θ be incident by the plane polarized wave in this
case, the Cartesian coordinate system O X ZY is used as a fixed reference system, ϕ
is the azimuthal angle. We consider only the simple harmonic time dependence of
the angular frequency ω, and the factor exp(−iωt) is omitted.
Note that cylindrical coordinates of primary field incident wave are E, H admits
a representation as superposition of electric and magnetic fields types.
Thus in solving the problem, we consider two cases of the polarization of the
incident wave. Note that the scattered on the cylinders field can be found, depending
on the polarization primary field through the magnetic U and the electric V Hertz
potential. In this case, the values potentials U , V associated with the vector E, H by
the following relations:
E =
i
k
× × ×(e z U ) + + × (e z V ),
(7.1)
H = −n o ×(e z U ) +
i
k
× × ×(e z V )
(7.2)