论文标题
Sommerfeld半空间问题重新审视：短波渐近解决方案
Sommerfeld half-space problem revisited: Short-wave asymptotic solutions
论文作者
论文摘要
提出了一种解决半空间Sommerfeld问题的方法，它使我们能够以Sommerfeld积分的形式获得精确的解决方案及其短波渐近学。首先是通过将Sommerfeld问题减少到将方程式系统求解到傅立叶变换域中介质接口上的表面电流密度的方法进行的。第二个由使用etalon积分的修改后的鞍点法提供。仔细的注意力支付了Sommerfeld积分的集成技术。对于所有类型的波（例如空间，表面和侧面）的任何观察角表达式的均匀定期。通过源场发现了反射和透射空间波的简单渐近表达式，请记住菲涅尔系数。能量通量保护定律检查的空间波的渐近表达。详细分析了表面波的存在问题。对获得的表达式以及适用条件的分析和物理解释进行了。以封闭形式评估的Sommerfeld积分。
A method for solving the half-space Sommerfeld problem is proposed, which allows us to obtain exact solutions in the form of Sommerfeld integrals, as well as their short-wave asymptotics. The first carried out by reducing the Sommerfeld problem to solving a system of equations to surface current densities on an interface of media in the Fourier transform domain. The second is provided by the modified saddle point method using an etalon integral. Careful attention pays the integration technique of the Sommerfeld integrals. The uniformly regular for any observation angles expressions of all types of waves, such as space, surface, and lateral, are obtained. The simple asymptotic expressions for the reflected and transmitted space waves are found via a source field, bearing in mind the Fresnel coefficients. The asymptotic expressions for the space waves checked by the law of conservation of energy flux. The issue of the existence of surface waves analyzed in detail. The analysis and physical interpretation of the obtained expressions, as well as the applicability conditions, are carried out. The Sommerfeld integrals evaluated in closed form.
