On the far field in the Lorenz-Mie theory and T-matrix formulation

The far field within the context of the Lorenz-Mie theory and the T-matrix formulation is usually expressed on the basis of the asymptotic properties of vector spherical waves. The radiation condition is taken into account by employing proper vector spherical functions as the expansion basis of the scattered field. The asymptotic behavior of the Hankel function is obtained from differential equations. The asymptotic far field can also be obtained from the Kirchhoff surface integral equation, in which the radiation condition has been implemented when it is derived from the Maxwell equations. This note is to present an explicit establishment of the relationship between the asymptotic far field and the near field in the Lorenz-Mie theory and the T-matrix formulation through the Kirchhoff surface integral.