Vector spherical wave functions integral representations

Applications of the extinction theorem and Huygens principle yield the null-field equations (2.6) and the integral representations for the scattered field coefficients (2.16). Taking into account that the electromagnetic fields propagating in an isotropic, chiral medium can be expressed as a superposition of vector spherical wave functions of left- and right-handed type (cf. Sect. 1.3), we represent the approximate surface fields as... 

To derive the expression of the reflection matrix we use the integral representations for the radiating vector spherical wave functions... 

As in the scalar case, integral and series representations for the translation coefficients can be obtained by using the integral representations for the vector spherical wave functions. First we consider the case of regular vector spherical wave functions. Using the integral representation (B.26), the relation r = 0 + T" ) and the vector spherical wave expansion... 

Passing to the radiating vector spherical wave functions we consider the integral representation (B.28) and the relation r = ro + ri. For ri > ro, this representation can written as... 

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