By Shung-Wu Lee (auth.), Y. T. Lo, S. W. Lee (eds.)

ISBN-10: 146156459X

ISBN-13: 9781461564591

ISBN-10: 1461564611

ISBN-13: 9781461564614

Techniques according to the strategy of modal expansions, the Rayleigh-Stevenson enlargement in inverse powers of the wavelength, and likewise the strategy of moments answer of critical equations are primarily limited to the research of electromagnetic radiating buildings that are small by way of the wavelength. It for that reason turns into essential to hire approximations according to "high-frequency innovations" for appearing a good research of electromagnetic radiating platforms which are huge by way of the wavelength. the most flexible and beneficial high-frequency thoughts is the geometrical idea of diffraction (GTD), which used to be built round 1951 via J. B. Keller [1,2,3]. a category of diffracted rays are brought systematically within the GTD through a generalization of the suggestions of classical geometrical optics (GO). in response to the GTD those diffracted rays exist as well as the standard incident, mirrored, and transmitted rays of pass. The diffracted rays within the GTD originate from sure "localized" areas at the floor of a radiating constitution, reminiscent of at discontinuities within the geometrical and electric homes of a floor, and at issues of grazing occurrence on a delicate convex floor as illustrated in Fig. 1. particularly, the diffracted rays can input into the cross shadow in addition to the lit areas. hence, the diffracted rays completely account for the fields within the shadow area the place the cross rays can't exist.

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**Sample text**

The field components for the (m,n)th mode calculated from (82) and (83) are (105a) (105b) Ht = Cmn Ymn. kZ z X a mn + k. mn Ymn Z Z C- X A- t'mn (105c) (105d) where amn x) sin(n; y) - Y(r:n) sin(r: x) cos ( n; y) ] e-jy",,,z = [x(n;) cos(r:n n Pmn = (-Ykn)[ x + Y( n;) (106a) (m;) cos(r:n x) sin(n; y) sin(r:n n; x) cos( y) ] e-jy",,,z (l06b) In particular, the nonzero field components of the dominant TEJO mode are (107a) (107b) H z :Jl) e-m,,z . 1- ( -na )2 ClOcos (-x a (107c) For the field component traveling in the -z direction we change the sign of Ymn in (103) through (107).

17. A periodic structure illuminated by an incident plane wave. (a) Side view . (b) Top view. incident plane wave described in (22). The plane wave propagates in the direction k = k i , where ki = k(x sin 80 cos CPo + Ysin 80 sin CPo + Zcos ( 0 ) (93) The problem at hand is to find a field representation for the scattered field in the unbounded space (outside of the periodic slab). Due to the periodic nature of the structure and the uniformity of the incident field, the scattered field can be expressed in terms of Floquet space harmonics.

The formula in (73) can be expressed in a different form. 3/llogcos(OEI2)1 where the log is of base 10. 3/1 log cos(OHI2) 1 are much less than one radian, (75) is (76) where ()E and 0H are expressed in degrees. Another directivity formula, which is similar to (76), is based on the approximation that D == 4:rr/n, where n is the solid angle extended by the main beam at the half-power level. Using a further approximation that n == ()EOH, we obtain (77) where ()E and 0H are expressed in degrees. Formulas similar to (76) and (77) exist in the literature, and the coefficients in the numerator usually fall in the range from 27900 to 41300 (see [5,6]).

### Antenna Handbook: Theory, Applications, and Design by Shung-Wu Lee (auth.), Y. T. Lo, S. W. Lee (eds.)

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