Analytical Model of Artificial Chiral Media:
not Canonical Helixes but Real Spirals
I. V. Semchenko, S. A. Khakhomov and E. A. Fedosenko
Gomel State University, Department of General Physics,
Sovyetskaya Str. 104, 246019, Gomel, Belarus,
fax: 3-75-232-572412, e-mail: isemchenko@gsu.unibel.by
Abstract
At present time various models for description of interaction of electromagnetic waves with artificial
chiral media are used. One of the primary tasks is to calculate the effective parameters of artificial
composite structure, taking into account electric and magnetic properties of host media and chiral
properties of metallic spiral inclusions.
The first possible method is based on use of the integral equations of electromagnetics,
allowing to calculate distribution of current in the separate microspiral and to find the radiated by it
fields [1-3]. Advantage of this method consists of its accuracy, however this method is sufficiently
complex even in the case of the single spiral. It is necessary to take into account that in artificial chiral
media the concentration of metallic spiral inclusions can be sufficiently high and reaches the values of
order 70 per cubic centimeter [4]. To use the method of integral equations in this case is much
difficult in view of significant increasing of problem difficulty.
Second possible method consists in use of mathematical model, according to which the
metallic spiral is considered as a combination of the rectilinear conductor and flat round loop (so
called canonical helix) [2,3,5]. The approximate calculation of components of a polarizability tensor
of separate spiral in electric and magnetic fields of incident wave are possible. After an averaging in
the volume we can determine the effective parameters of artificial chiral media. Defect of this method
is not taking into account a pitch of the spiral, because the helix is considered as a flat loops.
In present paper a possibility to use the spiral model of molecules of material [6] for the
interaction description of electromagnetic waves with the artificial chiral media is shown. On the base
of offered model the numerical evaluation of effective chirality parameter, which is coincides with
experimental data is performed. The optimal pitch of spiral elements of artificial composite media is
calculated, which guarantees the maximum values of average chirality parameter.
An analytical model, allowing to calculate electric dipole moment and magnetic moment,
come up in the spiral under the action of the incident electromagnetic wave is formed.
A comparison of offered model with the earlier known model, in which metallic spiral is
considered as a combination of rectilinear conductor and flat round loops is performed. New model
allows to take into account all geometric parameters of spiral, including the pitch of spiral. The
optimal parameters of spiral under which is observed a maximal transformation of the polarization
of electromagnetic waves, in concrete, the turn of polarization plane on maximum angle are found.
References
[1] Samusenko А.I., Izv. vuzov. Radioelektronika 36, No. 7, P. 64-69, (1993).
[2] Demidchik V.I.,Kornev R.V., Vestnik BGU, Ser.1, No. 2. p.14-16, (2001)
[3] Demidchik V.I., Kukharchik P.D., Kornev R.V., Izv. Gomel. Gos. Univer., No5, p.63-66, (2001).
[4] Kuehl S.A., Grove S.S, Kuehl E., Bingle M., Cloete J.H., Advances in Complex Electromagnetic
Materials, ed. by A. Priou, Kluwer Academic Publishers, 317-332, (1997).
[5] Marriotte F., Tretjakov S. A., Sauviac B., IEEE Anten. and Prop. Mag. 38, No2, p.22-32, (1996).
[6] Kauzmann W. Introduction to quantum chemistry, Moscow, Izdat. inostr. lit., 560p, (1960).