Electromagnetic scattering and absorption of multilayered spheres illuminated by a plane wave or a shaped beam are important issues because of the extensively applications. However, computation of the internal fields suffers from several difficulties, especially when the sphere contains strongly-absorbing layers. In the paper, reformulation of expressions of electromagnetic fields are made, by replacing the unnormalized associated Legendre functions and the Riccati-Bessel functions with the normalized associated Legendre functions and the ratios of Riccati-Bessel functions. Thus, the beam shape coefficients and the Mie coefficients are redefined. An improved recurrence algorithm is presented for calculating the redefined Mie coefficients and numerical calculations are performed for exemplifying the algorithm. It is numerically shown that the reformulation of expressions rescales the involved quantities into the reasonable ranges for machine calculation and the modified algorithm is robust, reliable and efficient.

由于广泛的应用，由平面波或成形光束照射的多层球体的电磁散射和吸收是重要的问题。但是，内部场的计算存在许多困难，特别是当球体包含强吸收层时。在本文中，通过用规范化的关联勒让德函数和Riccati-Bessel函数的比率代替未归一化的关联勒让德函数和Riccati-Bessel函数，重新形成了电磁场的表达式。因此，光束形状系数和米氏系数被重新定义。提出了一种改进的递归算法，用于计算重新定义的米氏系数，并进行了数值计算以举例说明该算法。