消失场的能量关系及WKBJ分析法

Energy Relations of Evanescent Fields and the WKBJ Method

对于电磁波在均匀媒质中的传播,至少有3种不同机制会使场阻抗产生电抗性分量——有耗媒质中的平面波、电离气体中的平面波、导波模式;因而使人们关注微波在有耗媒质(例如半导体)和等离子体中的传播,关注电磁波在截止频率以下的波导中的情况。在上述情形中,方向相反的两个贮能场会因相互作用从而产生一个净功率流,亦即纯消失态的入射场和反射场会产生能量流,即使分开来看各个场均未携带有功功率。本文从不同角度论述了这一概念。以光纤为对象讨论了光的射线理论及二者的结合运用,这时其效果将是最好。指出了区分光纤中的漏模和折射波辐射的方法。E.Schrdinger对波动力学作出了最大贡献;Schrdinger方程(SE)不仅用在微观粒子分析中,也能处理宏观科学问题,例如光纤。数学物理问题中的许多微分方程归结为ξ2ψ″+p2ψ=0,本文论述了由Wentzel、Kramers、Bril-louim、Jeffreys提出的近似方法在缓变折射率光纤分析中的应用,方法适用于SE的求解。

There are three different mechanisms at least well known to produce a reactive component of the field impedance of a EM-wave propagated in a homogeneous medium——plane wave in a dissipative medium,plane wave in an ionised gas,guided wave modes.In particular,attention is called to microwave propagation in a lossy medium（such as a semiconductor）,in plasma,and in a waveguide operated below cutoff.In each of these cases,the storage fields of oppositely directed travelling waves may interact to produce a net flow of power,i.e.the incident and reflected fields of purely evanescent character interact to produce a flow of energy,even though each field separately carries no power.In this paper,the optical fiber is target of discussion,the ray theory is allied with another method——the wave modes theory.We give good results in analysis.Then,we can strictly distinguish between the two different types of radiation：the leaky modes and the refraction waves.It is well known,E.Schrdinger was the greatest contribution scientist of Wave Mechanics.The Schrdinger Equation（SE） not only can treat the movement of microscopic particles,but also can analysed some of the macroscopic scientific problems,such as the optical fiber.Many differential equations occurring in mathematical physics are reducible to the from ξ2ψ″＋p2ψ=0.In the present paper,the approximate method of Wentzel、Kramers、Brillouim and Jeffreys is applied to the graded refraction indexoptical fiber,and the method is devised for adapting the solutions to the case of quantum wave equation（SE）.