INTRODUCTION. The problem of interaction of electromagnetic waves with cylindrical objects has been studied for a long time. It is one of the first problems of ...
ISSN 10642269, Journal of Communications Technology and Electronics, 2011, Vol. 56, No. 10, pp. 1193–1196. © Pleiades Publishing, Inc., 2011. Original Russian Text © Shi He, S.N. Shulga, N.G. Kokodity, N.N. Gorobets, V.I. Kiiko, A.Yu. Butrym, Yu Zheng, 2011, published in Radiotekhnika i Elektronika, 2011, Vol. 56, No. 10, pp. 1201–1204.
ELECTRODYNAMICS AND WAVE PROPAGATION
Interaction of Electromagnetic Waves in a Waveguide with Very Thin Wires Shi He, S. N. Shulga, N. G. Kokodity, N. N. Gorobets, V. I. Kiiko, A. Yu. Butrym, and Yu Zheng Received November 1, 2010
Abstract—Absorption and scattering of electromagnetic radiation by thin metal wires in a waveguide are investigated experimentally and theoretically. It is shown that, when the wavelength many times exceeds the diameter of a cylindrical wire, this wire strongly absorbs the radiation and weakly scatters it, and the absorp tion efficiency factor depends on the wavelength only slightly. This phenomenon can be used for developing radiation absorbers in the meterwavelength range. DOI: 10.1134/S1064226911100123
INTRODUCTION The problem of interaction of electromagnetic waves with cylindrical objects has been studied for a long time. It is one of the first problems of electromag netics that was rigorously solved. However, much attention has still been focused on this problem. This is due to numerous applications of the wave diffraction by a cylinder. Thus, the analysis of the diffraction pat tern can provide for information on the dimensions of the cross section of a cylinder, its shape, and the refractive index of its material [1]. The effects occur ring during the interaction of the electromagnetic radiation with dielectric and metal fibers are used for measuring the parameters of this radiation. In study [2], a device employing the pressure of laser emission on a lattice of glass fibers is described. In studies [3, 4], it is shown how lattices of thin metal wires can be used for measuring the power of laser emission and the intensity distribution in the beam. The emission pres sure and absorbed power can be found from a solution to the problem of diffraction by a cylinder. Although the solution to the problem of diffraction of a plane electromagnetic wave by a cylinder is well known and it is described, for example, in studies [5, 6] and monographs [7–9], an unknown effect has recently been discovered: thin metal wires very strongly absorb and scatter the electromagnetic radia tion [10]. 1. WIRES IN FREE SPACE At first, we investigate the influence of the thick ness of a nichrome cylinder on its capability to absorb and scatter the electromagnetic radiation. The effect of strong absorption is illustrated in Fig. 1a, where the absorption efficiency factor is shown as a function of the diameter of a thin nichrome cylinder calculated at three wavelengths (λ1 = 10 cm, λ2 = 5 cm, and λ3 = 3 cm). It is seen from the plots that this factor reaches very large
values (from 400 to 800) for a cylinder whose diameter is several micrometers. Figure 1b shows a similar dependence for the scattering efficiency factor. These effects are observed only for the Е polarization of a wave, i.e., in the case when the electric field is aligned with the axis of the cylinder. The absorption, scattering, and attenuation effi ciency factors are used in numerous studies devoted to investigations of the interaction between the electro magnetic radiation and objects [2–10]. These factors are defined as follows: Qab = Pab/P is the absorption efficiency factor, Qsc = Psc/P is the scattering efficiency factor, and Q = Qab + Qsc is the attenuation efficiency factor. Here, P is the radiation power incident on the cylinder, Pab is the radiation power absorbed by the cylinder, and Psc is the radiation power scattered by the cylinder. Figure 2 shows factors Qab and Qsc as functions of radiation wavelength λ calculated for the cylinder’s fixed diameter. Here, we observe an interesting phe nomenon: when λ Ⰷ D (D standing for the diameter of the cylinder), the cylinder very strongly absorbs radiation and weakly scatters it. Factor Qab does not substantially depend on the wavelength. Probably, this phenomenon can be used for developing radiation absorbers. 2. FORMULATION OF THE PROBLEM The effect of strong absorption by a thin metal wire is experimentally confirmed in study [10], and certain special cases are considered in [11–13]. For example, the case when a thin wire is oriented along the axis of a focused Gaussian radiation beam is investigated in [12, 13]. Experimental investigations of this effect are hampered by the necessity of measuring the power of microwave radiation beams scattered in the space. Therefore, we performed in a waveguide measure ments (that are described in [10]) of absorption with
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Fig. 1. (a) Absorption efficiency factor Qab and (b) scattering efficiency factor Qsc vs. diameter d obtained for a thin nichrome cylinder at the wavelengths (1) λ1 = 10, (2) λ2 = 5, and (3) λ3 = 3 cm.
Qab 5×103
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Fig. 2. Factors (a) Qab and (b) Qsc vs. wavelength λ obtained for the fixed diameters of the cylinder: (1) d1 = 6 µm, (2) d1 = 10 µm, and (3) d1 = 15 µm.
the help of a thin wire. In [14, 15], measurements of radiation absorption and scattering by nichrome wires are described. The wires had a diameter of 15 µm, and the measurements were performed in a frequency band of 3–18 GHz. These measurements were also performed in waveguides, a circumstance that made it possible to monitor the magnitudes of the incident, scattered, and absorbed powers. The measurements confirm that the absorption and scattering efficiency factors of thin wires are very large. However, the wave length dependence of these parameters that has been found in the experiments differs from the character of these dependences determined theoretically and cal culated for a plane wave in free space. Therefore, we performed investigations oriented to the comparison of the experimental and calculated results for the H10 wave in a rectangular waveguide. The computation was performed with the use of the Ansoft HFSS commercial computer code based on the finite element method.
The measurements were performed with the help of R267 reflectometers in the following frequency bands: Frequency, GHz
Waveguide’s cross section, mm
2.8…5.5 6…11 8…12 12…18
25 × 58 12 × 28 10 × 23 8 × 16
The object of measurements was a nichrome wire of a diameter of 15 µm. The wire was enclosed in a 7.5µmthick glass shell. The presence of this shell practically did not affect the process of interaction between the radiation and wire and was disregarded in the computation. The wire was placed in parallel to the waveguide’s narrow wall at the center of the wide wall (at the maximum of the electric field in parallel to the
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INTERACTION OF ELECTROMAGNETIC WAVES (а)
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Fig. 3. Factors (a) Qab and (b) Qsc vs. frequency for a thin nichrome wire of a diameter of 15 µm. The data are measured and cal culated in waveguides of various cross sections: (1) 25 × 58 mm, (2) 12 × 28 mm, and (3) 10 × 23 mm; the solid and dashed curves correspond to the calculation for waveguide and free space, respectively; dots correspond to the experiment for the waveguide.
intensity vector). We measured attenuation L (dB) introduced by the wire into the waveguide and stand ingwave ratio r. From these parameters, we calculated the power transmission and reflection coefficients 2 2 L[dB]/10 and R = ( r − 1) ( r + 1) , respectively. T = 10 3. THE CALCULATION METHOD In order to facilitate the comparison with the com putation performed earlier for a plane wave in free space, we estimated the absorption, scattering, and absorption efficiency factors from the measured quan tities according to the following procedure. When a radiation beam of power P0 is incident on a wire, a portion of the beam’s energy is scattered by the wire and absorbed in it, so that the receiver placed behind the wire receives the power
P = P0 − QPcyl,
(1)
where Pcyl is the power falling on the wire and Q is the attenuation efficiency factor. The division by P0 yields
T =1−Q
Pcyl , P0
(2)
where T = P P0 is the power transmission coefficient. The power falling on the wire is
Pcyl = I 0Db,
(3)
where I0 is the wave intensity at the point of the wire position and D and b are the wire’s diameter and length (the dimension of the waveguide’s narrow wall), respectively. The power of the H10 wave propa gating in the waveguide is coupled with intensity I0 at the center of the wide wall of the waveguide as follows:
(4) P0 = 1 I 0ab, 2 where a is the dimension of the wide wall of the waveguide. The substitution of expressions (4) and (5) into (3) yields the following calculation formula coupling attenuation efficiency factor Q and transmission coef ficient T: (5) Q = (1 − T ) a . 2D Scattering efficiency factor Qsc can be estimated with the help of the approximate formula
R=
QscPcyl . P0
(6)
The numerator is the power scattered by the cylin der. The formula is approximate, because the scattered radiation propagates in all directions, and the reflec tion coefficient takes into account the wave traveling in the waveguide in the backward direction. However, the experiment showed that the error of this formula is 10–20%. Substituting into it expressions (4) and (5), we obtain
Qsc = R a . 2D
(7)
Qab = Q − Qsc.
(8)
4. ANALYSIS OF THE RESULTS Figure 3a presents the results of the computation and experiment for the absorption of the H10 by a wire in waveguides with various cross sections. Figure 3b shows similar results for the scattering efficiency fac
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tor. The following conclusions can be drawn from the analysis of the obtained plots: (i) Efficiency factors Qsc and Qab reach very large values of several hundred. (ii) As the frequency grows, their values decrease. This result follows from the theory and is confirmed by the experiment. (iii) At the same frequency, the scattering and absorption efficiency factors are different in different waveguides. This circumstance is due to the fact that the waveguide mode field can be represented in the form of plane waves propagating at a certain angle to the waveguide’s axis. The angle depends on the ratio of the wavelength to the cutoff wavelength. At the same frequency, this angle is larger for the smaller waveguide, a circumstance that results in a more intensive/longer time interaction between the wave field and the wire. Therefore, the scattering and absorption efficiency factors increase. (iv) The calculated curve for a plane wave in free space (Fig. 3, the dashanddot line) qualitatively cor rectly describes the character of the effect, but the quantitative results substantially differ from the com putation results for the wave in the waveguide despite the similar characters of the fields in the H10 and plane waves. (v) Wires of a micron diameter can be used as effi cient radiation scatterers and absorbers at frequencies below 4 GHz. At higher frequencies, it is necessary to use for this purpose thinner wires of submicron and nanometer diameters. REFERENCES 1. L. P. Lazarev and S. D. Mirovitskaya, Control of Geomet ric and Optic Parameters of a Fiber (Radio i Svyaz’, Mos cow, 1988) [in Russian].
2. N. G. Kokodity, V. F. Efimov, and V. N. Timoshenko, Impul. Fotometriya, No. 7, 65 (1981). 3. A. B. Katrich and A. V. Khudoshin, Prib. Tekh. Eksp., No. 2, 227 (1988). 4. V. M. Kuz’michev and S. N. Pokhil’ko, Metrologiya, No. 8, 22 (1997). 5. J. R. Wait, Canad. J. Phys. 33 (5), 189 (1955). 6. A. C. Lind and J. M. Greenberg, J. Appl. Phys. 37, 3195 (1966). 7. H. C. Hulst, Light Scattering by Small Particles (Wiley, New York, 1957; Inostrannaya Literatura, Moscow, 1961). 8. E. A. Ivanov, Diffraction of Electromagnetic Waves by Two Bodies (Nauka i Tekhnika, Minsk, 1968) [in Russian]. 9. M. Kerker, The Scattering of Light and Other Electromag netic Radiation (Academic, London, 1969). 10. V. M. Kuz’michev, N. G. Kokodity, B. V. Safronov, and V. P. Balkashin, J. Commun. Technol. Electron. 48, 1240 (2003). 11. N. G. Kokodity, J. Commun. Technol. Electron. 51, 175 (2006). 12. A. Akhmeteli, “Efficient Heating of Thin Cylindrical Targets by Broad Electromagnetic Beams I”, http:// arxiv.org/PS_cache/physics/pdf/ 0405/0405091v1.pdf. 13. A. Akhmeteli, “Efficient Heating of Thin Cylindrical Targets by Brood Electromagnetic Beams II”, http:// arxiv.org/PS_cache/physics/pdf/ 0611/0611169v1.pdf . 14. N. G. Kokodity, N. N. Gorobets, V. I. Kliko, et al., in Microwave Engineering and Telecommunication Technol ogies (Proc. 18th Int. Conf. (CriMiKo'2008), Sevastopol, Crime, Ukraine, Sept. 8–12, 2008) (Weber, Sevastopol, 2008), p. 447. 15. He Shi, S. N. Shulga, N. G. Kokodity, et al., in Physics and Technology of Millimeter and Submillimeter Waves (MSMW'2010) (Proc. 7th Int. Kharkov Symp., Kharkov, Ukraine, June 21–26, 2010) (IRPE NAS, Kharkov, 2010), pp. 1–3 (on CD).
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