Experimental Study of the Field Structure of the Surface Electromagnetic Wave in an Anisotropically Conducting Tape

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1 ISSN -9, Journal of Communications Technolog and Electronics,, Vol. 58, No., pp. 8. Pleiades Publishing, Inc.,. Original Russian Tet R.B. Vaganov, I.P. Korshunov, E.N. Korshunova, A.D. Oleinikov,, published in Radiotekhnika i Elektronika,, Vol. 58, No., pp.. ELECTRODYNAMICS AND WAVE PROPAGATION Eperimental Stud of the Field Structure of the Surface Electromagnetic Wave in an Anisotropicall Conducting Tape R. B. Vaganov, I. P. Korshunov, E. N. Korshunova, and A. D. Oleinikov Institute of Radio Engineering and Electronics, Russian Academ of Sciences (Fraino Branch), pl. Vvedenskogo, Fraino, Moscow oblast, 9 Russia korip@ms.ire.rssi.ru Received August, Abstract It is shown that, in the frequenc band 5. GH, a tape of metal conductors supports slow waves. The field structure of the surface wave in an anisotropicall conducting tape is studied eperimentall. It is found that the electromagnetic field of the tape has three electric and two magnetic components. Intensit distributions of all field components, the slowing factor of the surface wave, and the loss per unit length are measured. DOI:./S995 INTRODUCTION Slow waves in guiding structures ma be of interest in applications where it is required, for eample, to obtain rather intense longitudinal electric fields. Below, it will be shown that a tape with conductance along a chosen direction (below, an anisotropicall conducting band) satisfies this requirement: it supports propagation of surface waves in a wide frequenc band, has low loss, and is rather elastic.. FORMULATION OF THE PROBLEM A planar slowing structure formed b a tape with an arbitrar fied direction of anisotropic conductance was first proposed and analed in []. In this paper, an integral equation for eigencurrents was derived and solved rigorousl with the help of a numerical method; for the case narrow tapes, an analtical solution was obtained. The geometr of such a slowing structure is shown in Fig.. The tape of width a is formed from copper conductors of diameter d, which are placed with period p. Let us anale the structure of the field in a tape with the direction of conductance making the angle Ψ = 9 with ais. All components of the electromagnetic field of the fundamental mode of the surface wave can be epressed in terms of one real function U(, ) []. This function has the meaning of the transverse distribution of component Π of the Hert vector. Function U(, ) is even along coordinate and is continuous across the tape (at =, < a); its partial derivative U is discontinuous on the tape. For the funda- Deceased. mental mode, this function is also even along coordinate : U(, ) = U(, ). () In this case, the electric field has the following components: U(, ) E = ep( ih) k () ( an odd function of ), E = + U(, )ep( ih) k () ( an even function of ), ih U(, ) E = ep( ih ) k () ( an odd function of ), where k = π/λ is the propagation constant in free space, h = π/λ is the propagation constant of the surface wave, λ is the wavelength in vacuum, and Λ is the wavelength of the surface wave. The magnetic field has the following components: H = h U(, )ep( ih)(an even function of ), (5) k H =, () i U(, ) H = ep( ih )(an even function of ). (7) k It follows from epressions (5) (7) and evenness propert () that, in half-spaces < and >, the magnetic-field vector has elliptical polariation with opposite signs of rotation. In the domain ( =, > a), the magnetic field is linearl polaried and is directed along the ais. As was noted in [], the fundamental 8

2 EXPERIMENTAL STUDY OF THE FIELD STRUCTURE OF THE SURFACE 9 p H E a d Ψ E H E Fig.. Geometr of the anisotropicall conducting surface-wave line. mode of an anisotropicall conducting tape eists at arbitraril low frequencies. Orientation of field components (5) (7) in the coordinate sstem of the tape is shown in Fig.. Let us consider the technique of performed studies and the results of these studies.. SLOWING FACTOR OF THE SURFACE WAVE IN THE ANISOTROPIC TAPE AND THE LOSS PER UNIT LENGTH Slow waves can propagate along an anisotropicall conducting tape. For these waves, propagation constant h is larger than wave number k; in this case, the slowing factor of the surface wave is described b the ratio γ= hk λλ. (8) For eperimental studies, two tapes with anisotropic conductance were manufactured. One tape was made of a special material with conductors having the diameter d =. mm. The conductors were placed between Dacron and polethlene laers with the period p.5 mm. The other tape was made of conductors with the diameter d =.7 mm, which were sealed between polethlene laers with the period p.5 mm. The width of both tapes a 8 mm and the length of each tape is about m. The dependence of slowing factor γ on frequenc f = c/λ (where c is the velocit of light in vacuum) was studied with the use of the laout shown in Fig.. The data obtained with both tape specimens were found to be rather close; therefore, below, we discuss the results obtained for the first specimen. Tape is ecited b component E of the field of the fundamental mode of rectangular waveguide ; the tape plane is parallel to the narrow wall of the waveguide. Forward surface wave propagates along the tape from the waveguide end to reflector and reflected wave 5 propagates in the opposite direction. Thus, standing-wave conditions are implemented in the tape. Short Γ-shaped oscillator is ecited b component E of the tape eigenmode. The signal from the output of this oscillator enters microwave detector 7 and, afterwards, is recorded b oscilloscope 8. Moving the oscillator along the ais, it is possible to determine the distance between adjacent minima of the standing wave l min, which, as is well known, is Λ/. The studies results are presented in Fig., where values of γ are plotted along the vertical ais, values of ka are plotted along the horiontal ais, and corresponding frequencies f = kc/π are plotted along the upper horiontal ais. The figure contains also eperimental points obtained from rigorous calculation [] and calculation data obtained in the approimation of small values of parameter ka. These data were obtained on the basis of Eq. () from [], which is valid at small ka and Ψ = π/: γka ( ) ( )ln h J ka + kaj ka. = k The solution of this equation for h/k is h J( ka) γ= + ep, k ( χka) kaj( ka) (9) () where J n (ka) is the Bessel function of the first kind of order n and χ.78 is the Euler constant. As seen JOURNAL OF COMMUNICATIONS TECHNOLOGY AND ELECTRONICS Vol. 58 No.

3 VAGANOV et al Fig.. Laout for implementation of standing-wave operating conditions: () anisotropicall conducting tape, () rectangular waveguide, () forward wave, () end reflector, (5) reflected wave, () Γ-shaped probe, (7) detector, and (8) recorder. from the figure, eperimental and numerical results are in good agreement. Let us estimate loss q in the studied surface-wave line from the obtained eperimental data. Using the ratio of measured field intensities at the maimum and I min the minimum of the standing wave, ν = =., I ma we obtain that, for a length of measured tape section of m, q db/m. γ(ka) f, GH ka Fig.. Slowing factor of the surface wave as a function of ka: () eperiment, () rigorous calculation, () approimate calculation for small ka, and () envelope of eperimental values.. ANALYSIS OF INTENSITY DISTRIBUTIONS OF ELECTRIC COMPONENTS OF THE FIELD OF THE SURFACE WAVE The laout for measuring the intensit distributions of electric-field components in tape is shown in Fig.. Sensors of the field of propagating wave are short wire probes,, and 5 placed parallel to corresponding field components. Minimum distance Δ between the probes and the tape plane is ~ mm. Electric signals from the probes pass through microwave detector and enter recorder 7. Intensit distributions along coordinates and of three electricfield components, E (); E (); E (); E (); E (), and E (), were studied. The measurement results are shown in Figs. 5 and. As seen from Fig. 5, intensities of all field components decrease more than fivefold as the distance to the tape surface becomes mm (.Λ, see the upper horiontal ais) along the ais, and the greatest rate of decrease corresponds to component E. Vertical lines in Fig. at = ± mm mark positions of the tape edges. As seen, the field of component E is most localied, and intensities of all components decrease more than tenfold at a distance of 5 mm from the tape center. Note that the behavior of distributions in Fig. corresponds to epressions () (); i.e., components E and E are described b odd functions and component E is describe b an even function.. ANALYSIS OF INTENSITY DISTRIBUTIONS OF ELECTRIC COMPONENTS OF THE FIELD OF THE SURFACE WAVE The laout for measuring the intensit distributions of magnetic-field components in the tape is shown in JOURNAL OF CJOURNAL OF COMMUNICATIONS TECHNOLOGY AND ELECTRONICS Vol. 58 No.

4 EXPERIMENTAL STUDY OF THE FIELD STRUCTURE OF THE SURFACE Δ E () E () 7 E () 5 Fig.. Laout for measuring the intensit distributions of electric components of the field of the surface wave: () plane of the anisotropicall conducting tape; () forward wave; (,, and 5) sensors of field components E, E, and E, respectivel; () detector; and (7) recorder.. /Λ /Λ I(), rel. units.. I(), rel. units , mm , mm Fig. 5. Intensit distributions I e () of electric components of the filed of the surface wave as functions of transverse coordinate : () E (), () E (), and () E (). Fig.. Intensit distributions I e () of electric components of the filed of the surface wave as functions of transverse coordinate : () E (), () E (), and () E (). Fig. 7. As in Fig., tape supports surface wave, which propagates along the ais. In order to ensure traveling-wave conditions, matched load is placed at the tape end. Component E of the surface wave ecites Γ-shaped probe of the output receiver. Probe is placed near the maimum of distribution E (Fig. ). JOURNAL OF COMMUNICATIONS TECHNOLOGY AND ELECTRONICS Vol. 58 No.

5 VAGANOV et al. H H H H H 9 8 E 7 5 Fig. 7. Laout for measuring the intensit distributions of magnetic components of the field of the surface wave: () plane of the anisotropicall conducting tape; () forward wave; () matching load; () receiving probe for component E ; (5) detector; () recorder; and (7, 8, and 9) sensors of field components H, H, and H, respectivel. I(), rel. units /Λ , mm Fig. 8. Readings of the recorder for the case when sensors of magnetic-field components H and H move along the () () ais: () E E and () E () () E. The electric signal of this probe enters detector 5 and, afterwards, output recorder. In this case, intensit distributions of magnetic components were studied with the help of the socalled perturbation method. Let us describe the essence of this method. Data on the analed intensities of field components are measured as perturbations of the response recorded b the receiver installed at the output of the surface-wave line, rather than the responses of the field probe. These perturbations are caused b interaction between a passive magnetic sensor and the corresponding component of the magnetic field. A sandwich of two so-called modified broken rings (MBRs) [] with oppositel oriented radial slots was used as passive sensors of the magnetic field. The MBR sensors were manufactured on a clad dielectric film with the use of the printed-circuit technolog. The outer diameter of the rings was ~5 mm, the width along the radius was about.7 mm, and the thickness of the dielectric film was. mm. Dotted arrows in Fig. 7 show the direction of spatial scanning of the rings. Ring 7, whose plane is perpendicular to vector H, creates resonant scattering at the operating frequenc f. GH. Ring 8, whose plane JOURNAL OF CJOURNAL OF COMMUNICATIONS TECHNOLOGY AND ELECTRONICS Vol. 58 No.

6 EXPERIMENTAL STUDY OF THE FIELD STRUCTURE OF THE SURFACE I(), rel. units /Λ is perpendicular to vector H, behaves similarl. Sensors 7 9 in Fig. 7 are shown b outline drawings. Resonant power etraction performed b rings 7 and 8 causes simultaneous weakening of all three field components. Receiving probe at the output end of the surface-wave line is ecited b field component E, which is weakened b perturbing influence of rings 7 and 8, and the degree of this weakening varies as the rings move along the ais. Curves depicting the readings of recorder (Fig. 7) during motion of rings 7 and 8 along the ais are shown in Fig. 8. Curve corresponds to variations in the intensit of component E under the influence of resonance scattering E () ( ) of ring 7 ecited b component H. Curve illustrates the behavior of the intensit of component E under the influence of resonance scattering E () ( ) of ring 8 ecited b component H. It follows from the aforesaid that the degree of influence of responses of rings 7 and 8 to component E is proportional to the amplitudes of components H () and H (). When the rings are shifted beond the tape ( > mm), their influence is minimal and, vice versa, when the rings are placed at the tape ais, i.e., at the maima of H () and H (), their influence is maimal. In view of these considerations, curves in Fig. 8 can be transformed to normalied distributions [H ()] and [H ()], which are shown in Fig. 9. Here,, mm Fig. 9. Intensit distributions I m () of magnetic components of the filed of the surface wave as functions of transverse coordinate : () H () and () H (). vertical lines = ± mm mark positions of the tape edges. Note that the procedure described above was also used in the stud of the influence of ring sensor 9 (see Fig. 7) ecited b component H (). It has been found that, as the sensor moves along the ais, variations in the intensit of component E are almost absent. Thus, as follows from epressions (5) (7), intensit variations of magnetic components of the field of the surface wave are described b even functions of coordinate and component H is absent. CONCLUSIONS An anisotropicall conducting tape is a guiding structure supporting slow surface waves. Guiding properties of two tape specimens composed of copper conductors with diameters of. mm and.7 mm have been studied. The tape width is 8 mm and the tape length is about m. In the frequenc band.5 5. GH, the slowing factor of the surface wave varies from.8 to.. The power loss in the tape is about db/m. The electromagnetic field in the tape has three electric components and two magnetic components. It has been shown eperimentall that intensit distributions of components E () and E () are described b odd functions, whereas the intensit distribution of component E () is described b an even function. Intensit distributions of all electric components rather rapidl decrease along the ais and decrease approimatel tenfold at a distance to the tape surface of mm (.Λ). Intensit distributions of magnetic components H () and H () are described b even functions and decrease b more than db at a distance of mm beond the tape edges. Magnetic component H is almost absent in the tape. ACKNOWLEDGMENTS We are grateful to A.D. Shatrov for his interest in this stud and useful discussions. REFERENCES. E. N. Korshunova, I. P. Korshunov, A. N. Sivov, and A. D. Shatrov, J. Commun. Technol. Electron., 9 (998).. I. P. Korshunov, E. N. Korshunova, A. N. Sivov, and A. D. Shatrov, J. Commun. Technol. Electron. 5, 5 (7).. R. Marques and F. Medina, R. Rafii-El-Idrissi, Phs. Rev. B 5, (). JOURNAL OF COMMUNICATIONS TECHNOLOGY AND ELECTRONICS Vol. 58 No.

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