Trong chương này, chúng tôi sẽ thảo luận về vấn đề truyền sóng trong môi trường với pháp luật tùy tiện của sự phụ thuộc permittivity phối hợp, có nghĩa là, chúng tôi sẽ cho rằng permittivity có dạng ε = ε (r) trong trường hợp thông thường. Chậm sự biến đổi không gian của permittivity được giả định là tương tự như xấp xỉ (WKB) Wentzel-Kramers-Brillouin thực hiện trong Chương 3. Chúng tôi giả định một lần nữa một thay đổi nhỏ của permittivity ở quy mô bước sóng | 4 Geometrical Optics Approximation EQUATIONS OF GEOMETRICAL OPTICS APPROXIMATION In this chapter we will discuss wave propagation problems in a medium with an arbitrary law of permittivity coordinate dependence that is we will assume that the permittivity has the form e e r in the common case. The spatial variation slowness of the permittivity is assumed to be similar to that for the Wentzel-Kramers-Brillouin WKB approximation carried out in Chapter 3. We assume again a small change of permittivity at the wavelength scale. This property can be expressed as the inequality v ln e k. As in the WKB method we will utilize a solution to Maxwell s equations in the form of the asymptotic Debye series E eik-ỹitì H e-ý . á it The value V is referred to as the eikonal value. We arrive at the system of connected equations vv X H 0 e E 0 0 vv X E 0 -H 0 0 vvxH1 eE1 - V X H0 vvxE1 -H1 - VX E0 after substitution of the Debye series in Maxwell s equations members of the same degree of k are equal to each other. Zero-order equations are a system of homogeneous linear algebraic equations. For the purpose of their nontrivial solution it is necessary to reduce the determinant to zero. This requirement leads to the equation for V the eikonal equation . We can obtain this equation fairly simply if H0 is expressed through E0 also we must take into account the mutual orthogonality of vectors E0 H0 and vv that follows from 85 2005 by CRC Press 86 Radio Propagation and Remote Sensing of the Environment the equations of the zero-order approximation. Now we can easily show that the eikonal equation may be written down in the form The value Vv 2 e. Ọ kv represents the radiowave phase in the zero approximation and eikonal v in engineering terminology represents the electrical length passed by the wave. We assume that the phases of components E0 and H0 do not depend on coordinates in the approximation. Furthermore in this approximation these vectors are believed to be .
