Abstract : it is observed that the sommerfeld ' s formula for a progressive spherical wave is not covariant with respectro the rotation of the coordinate system . it contains complex partial waves that are not physical . the standing wave representation of the same formula is shown to be covariant and physical . it is applied to solve the boundary value problem of fiber optics . the radiation modes as well as the guided normal modes are obtained in closed forms . the intensity distribution in various modes is obtained . it is remarked that the mode of critical refraction is missing 文摘:说明了球面行波的索末菲公式在坐标转动下不协变.证明了球面波的驻波表示是协变的，因而是一个物理的关系式，故适用于圆柱坐标中各类波动方程的定解问题.作为一个例，应用于光纤光学，导出了受导简正模和辐射模的表达式，以及各模式的强度分布
