tailieunhanh - Wave Propagation 2010 Part 11

Tham khảo tài liệu 'wave propagation 2010 part 11', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 292 Wave Propagation where Lv cos0 qI cos0 in v cos0 vm Ym -1 2 qI cos0 - associated Legendre functions of the 2-nd kind. Fig. 4. Geometry of excitation of hemispherical reflector by electric current ring Consider one-connected area D on complex surface Y and distinguish points Y1 Y2 . Ym for this surface as solutions of Neumann boundary condition for Green function. In every point of the area D function r is univalent analytic function except points Y1 Y2 . Ym where it has simple poles. Let us place the field source on the concave hemisphere surface kr ka . Using Cauchy expression present 2 as a sum of waves and integral with contour that encloses part of the poles Y satisfactory to the condition ka Y ka - ka1 3 and describing the geometrical optic rays field. In the distance from axis of symmetry Ym0 1 the contour integral is given as -2 kã sin0 Jv 1 2 kr íi v 1 2 ổ ổ n 2 e i v 1 2 ổ-ổ v kr 3 J sin0 0 JV 1 2 kar The sign at index exponent corresponds for 0 0 and the sign - for 0 0 . A factor sin0 sin0 1 2 explains geometrical value of increasing of rays by double concave of the hemispherical reflector with comparison to cylindrical surface. First component in contour integral correspond a brighten point at the distance part of the ring with electrical current second component - brighten point at the near part of the ring. Additional phase n 2 is interlinked with passing of rays through the axis caustic. In the focal point area Ym0 1 the contour integral can be written as -4 n 2 1 2 ka 1 2 0sin0 v 1 2 2 1 20 Jv 1 2 kr i v 1 2 0 1 4 d 3 2J J1 v 1 2 0 e av . kr 3 2 sin0 0 Vv v 1 Ji 1 2 ka In accordance with a stationary phase method the amplitude and phase structure of the field in tubes of the rays near a caustic can be investigated. The distribution of the radial component of the electrical field E along axis of the hemisphere with radius of curvature a 22 5cm for uniform distribution field on the aperture 0 n 2 has two powerful interferential maximums at the wave