RU2418292C1 - Method for determining chirality of artificial chiral media - Google Patents

Abstract

FIELD: radio engineering. ^ SUBSTANCE: experimental measuring method of chirality of plane-parallel specimen of artificial chiral medium is provided by using scanning microwave radiation with known wave length at specified values of dielectric and magnetic permeabilities of substance. Method is based on recording of turn angle of polarisation plane of microwave radiation of known wave length at passage of plane-parallel specimen of chiral material by means of rectangular E-plane sectoral horn antenna. Chirality parametre of specimen is calculated on the basis of experimentally obtained data as ratio of turn angle of polarisation plane of microwave radiation to module of wave number of this radiation. ^ EFFECT: possibility of determining chirality parametre of material in wide microwave band. ^ 2 dwg

Description

The invention relates to radio engineering, in particular to methods for determining the electrophysical parameters of artificial chiral materials used in the manufacture of reflective coatings, waveguide and radiating structures.

A known optical method for determining the specific rotation of optically active media by measuring the angle of rotation of plane-polarized light in an optically active medium [1].

However, using the indicated optical method, it is impossible to obtain the numerical value of the chirality parameter of artificial chiral materials, but it is possible to measure, for example, the concentration of a naturally occurring optically active substance — sugar in urine, for example, with a saccharimeter.

Modern artificial metamaterials can be created using mirror-asymmetric chiral conductive composites with transverse dimensions much shorter than the microwave wavelength [2]. An artificial chiral medium is a composite material, where periodically arranged and randomly oriented conducting trace elements of a mirror-asymmetric shape are included in a solid dielectric base. As chiral composites, three-dimensional right- and left-handed spirals, strips in the form of the letter S and its mirror equivalent, flat spirals and other elements with the property of mirror asymmetry can be used. Structures including mirror-asymmetric composites are called chiral and are currently being used to create a new class of frequency and polarization-selective microwave devices and to design low-reflectivity coatings of a certain frequency range.

To describe the electrophysical properties of the chiral structure, in contrast to the dielectric, it is necessary to use three material parameters — relative permittivity ε, magnetic permeability µ, and chirality parameter χ [2]. The current waveguide methods for measuring the electrophysical parameters of samples allow us to obtain experimental values of only ε and μ. Modern requirements for the creation of composite metamaterials lead to the need to determine the relative parameter of the chirality of the sample with known values of dielectric and magnetic permeability and thickness. A known theoretical technique for determining the relative chirality parameter of the chiral layer based on flat S-elements [3]. The experimental implementation of the method considered in [3] is not possible.

The material equations of the chiral medium have the form [2]:

и

- напряженности электрической и магнитной составляющих поля, а

и

- их индукции, ε и µ - относительные диэлектрическая и магнитная проницаемости киральной среды; χ - параметр киральности, i - мнимая единица. Верхние знаки соответствуют киральной среде на основе правых форм зеркально асимметричных элементов, а нижние знаки - на основе левых форм.Where

and

- the intensity of the electric and magnetic components of the field, and

and

- their induction, ε and μ are the relative dielectric and magnetic permeabilities of the chiral medium; χ is the chirality parameter, i is the imaginary unit. The upper signs correspond to the chiral medium based on the right forms of mirror-asymmetric elements, and the lower signs correspond to the left forms.

The chirality parameter χ is a connecting element of two second-order differential equations for the vectors of the electric and magnetic fields of microwave radiation in a chiral medium [2]:

- показатель преломления диэлектрической основы киральной среды, k=2π/λ - модуль волнового числа СВЧ-излучения в киральной среде, λ - длина волны этого излучения в киральной среде.Where

is the refractive index of the dielectric base of the chiral medium, k = 2π / λ is the modulus of the wave number of microwave radiation in the chiral medium, λ is the wavelength of this radiation in the chiral medium.

и левокруговой

поляризацией (поля Бельтрами), фиг.1.To separate equations (2), we introduce the electric field strengths with the right-handed

and left

polarization (Beltrami field), Fig. 1.

и левокруговой

поляризацией

. Используя общую связь напряженностей электрического и магнитного полей в электромагнитной волне, можно найти напряженность магнитного поля в этой волне в виде

. Следовательно, связанные дифференциальные уравнения (2) разделяются на два независимых уравнения для электрических полей с правокруговой

и левокруговой

поляризацией:The plane-polarized electric field strength of an electromagnetic microwave wave in a chiral medium is equal to the superposition of electric field intensities with the right-handed

and left

polarized

. Using the general relationship between the electric and magnetic fields in an electromagnetic wave, we can find the magnetic field in this wave in the form

. Consequently, the coupled differential equations (2) are divided into two independent equations for electric fields with a right-handed

and left

polarization:

where k _R = k (n + χ) and k _L = k (n-χ) are the wave numbers of electric fields with right-handed and left-handed polarization in a chiral medium.

Using the general relationship between the wave number and the refractive index of a substance, we find the refractive indices of fields with right-handed and left-handed polarization n _R = n + χ and n _L = n-χ.

Based on phenomenological ideas, Fresnel obtained a formula for calculating the angle of rotation of the plane of polarization of light in an optically active (chiral) medium [4]:

where d is the thickness of the medium, figure 2. The value α = π (n _R -n _L ) / λ is called specific rotation.

Substituting the expressions for n _R and n _L in the Fresnel formula (4), we obtain:

where the specific rotation is α = kχ.

Thus, the physical meaning of the chirality parameter consists in its equality to the specific rotation normalized to the wave number.

, находим из формулы (5) параметр киральности:Given the relationship of the wave number of the electromagnetic wave in vacuum k _vak = 2π / λ _vak , where λ _vak is the wavelength of microwave radiation in vacuum (figure 2), and in the medium

, we find from formula (5) the chirality parameter:

Formula (5) allows us to calculate the chirality parameter of an artificial chiral medium from the measured angle of rotation of the plane of polarization of the wave passing through the chiral sample.

To find the chirality parameter of the sample using a rectangular E-plane sectorial horn antenna 1 [5], a plane-polarized microwave wave of a given length λ _{vac is} sent to a flat chiral sample (figure 2). The microwave wave transmitted through the chiral sample is received by the same horn antenna 2. The plane of polarization of a plane-polarized microwave wave at the input from the chiral sample is determined by rotating the horn antenna 2 around its axis. When the maximum intensity of microwave radiation detected from the horn antenna 2 appears, the angle of rotation of the horn antenna 2 relative to the horn antenna 1 is measured. The angle of rotation between antennas 1 and 2 is equal to the angle of rotation of the plane of polarization φ of a plane-polarized microwave wave of a given length λ _vak when it passes through chiral sample. Using the known data on the values of d, ε, and μ, the chirality parameter χ of the test sample is calculated by formula (6).

The proposed experimental method for measuring the chirality parameter has the following advantages:

1. The chiral sample is in free space, which does not impose restrictions on its transverse dimensions.

2. Measurements can be carried out in a wide range of microwave wavelengths.

3. For measurements it is not necessary to determine the exact power values of the reflected and transmitted through the chiral sample electromagnetic waves.

Information sources

1. Liventsev N.M. Physics course for medical schools. - M.: Higher School, 1974. - 648 p.

2. Neganov V.A., Osipov O.V. Reflective, waveguide and radiating structures with chiral elements. - M.: Radio and Communications, 2006. - 280 p.

3. Boruhovich S.P., Prosvirnin S.L., Schwanecke A.S., Zheludev N.I. Multiplicative measure of planar chirality for 2D meta-materials // Proceedings of the European Microwave Association, 2006. - V.2. - P.89-93.

4. Volkenstein M.V. Biophysics. - M .: Nauka, 1981. - 576 p.

5. Neganov V.A., Tabakov D.P., Yarovoy G.P. Modern theory and practical applications of antennas. - M.: Radio Engineering, 2009 .-- 720 p.

Claims (1)

A method for determining the medium chirality parameter based on recording the angle of rotation of the plane of polarization of a microwave wave in a chiral sample using a rectangular E-plane sectorial horn antenna, characterized in that a numerical value of the angle of rotation of the plane of polarization of a plane-polarized microwave wave of a given length and using a unique the relationship between the angle of rotation of the plane of polarization of a plane-polarized microwave wave, the thickness of the sample of the chiral medium, the relative dielectric and magnetic permeability s chiral environment, the microwave wavelength in vacuo parameter determined chirality.

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