tailieunhanh - Electromagnetic Waves Propagation in Complex Matter Part 2

Tham khảo tài liệu 'electromagnetic waves propagation in complex matter part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | The Generalized Solutions of a System of Maxwell s Equations for the Uniaxial Anisotropic Media 7 which satisfy the equation A k0 0 ỗ r . 23 On the other hand we can obtain Eqn. 23 after application of the inverse Fourier transformation from Eqn. 12 . Thus the general solution of the system of stationary Maxwell s equations for a three-dimensional unbounded isotropic media was deduced by means of solely one fundamental solution 0. Hence the solution preserves the same form concerning the fundamental solution 0 for two-dimensional and one-dimensional problems. The useful forms of the fundamental solutions are adduced below by means of Fourier transformations 0 x y kz w 4H01 ựk0 kfựx2 y2 two-dimensional case exp ih y 0 kx y kz w 2ih h ựk0 k2 k2 const one-dimensional case . Electrodynamic potentials and Hertz vector It should be noted that all electrodynamic quantities of isotropic media can be expressed by function 0 including the electrodynamic potentials and Hertz vector. By designating the scalar potential ty and vector potential A ty 1 0 p A P0P 0 j 24 the solution 18 or 20 can be presented in known form by vector potential E Vty iwA H p0y 1V X A. 25 It should be noted that physical sense of Lorentz gauge of potentials consists in the charge conservation law 21 indeed VA i w 0 y0ụty P0P 0 Vj iwp 0. 26 Similarly by designating Hertz vector n iw 0 1j 0 27 solution 18 can be written as E VV k0 n VXV X n i 0 w - 1j H i 0 W V xn. 28 It is easy to take notice that the relation between the electrodynamic potentials and Hertz potential is A iw 0 p0pn ty Vn. 29 8 Electromagnetic Waves Propagation in Complex Matter 3. The generalized solutions of Maxwell equations for the uniaxial crystal The exact analytical solutions of Maxwell s equations are constructed by means of method of generalized functions in vector form for unlimited uniaxial crystals Sautbekov et al. 2008 . The fundamental solutions of a system of Maxwell s equations for uniaxial crystals are obtained.