能量速度与相速之间关系的讨论

The relationship between energy-velocity and phase-velocity

Brillouin于 1 932年引出了能量传输速度的概念。 1 947年Rytov在波包群速度概念的基础上 ,证明了在无吸收介质中群速度与能量传播速度之间的关系。本文对能量传播速度公式中的平均能量密度及能量平均通量密度用瞬时物理量来代替 ,从而把能量速度的概念推广到包括静电磁场在内的普遍情况。另一方面 ,考虑到电场和磁场是电磁张量的不同分量 ,认为存在这样一种坐标变换 :即原坐标系中有能量速度 ,而在新坐标系中无能量速度。本文具体地找到了这样一种变换 ,且证明了在无吸收介质中上述新旧两个坐标系之间的相对速度就是能量速度。由能量速度与相速之间的关系说明了能量速度是区别于相速、群速的更一般的物理概念。

Brillouin introduced the concept of energy-transportation velocity in 1932. Rytov proved the relation of group-velocity and energy-transportation velocity in non-absorption medium on the basis of group-velocity concept in 1947. In this paper, instant physics-quantity is used to replace average energy density and average influx density in the formula of energy-transportation velocity, so that the concept of energy-velocity is introduced into steady electromagnetic field. On the other hand, considering that electric field and magnetic field are different quantity in electromagnetic tensor, we think there exits a kind of coordinate-transformation: energy-velocity existing in old coordinate but not in the new coordinate. This transformation proved that relative velocity between old coordinate and new coordinate in non-absorption medium is energy-velocity. From the relation of energy-velocity and phase-velocity, we can prove that energy-velocity is different from phase-velocity and group-velocity. Further study on it helps to understand the principle of eaergy_transpertation in complicate problems of electronagnetic filed.