Vector spherical wave functions radiating

The surface fields ei i and hi i are the tangential components of the electric and magnetic fields in the domain bounded by the closed surfaces Sx and 52. Taking into account the completeness property of the system of regular and radiating vector spherical wave functions on two enclosing surfaces... 

To compute the T matrix of the two-particles system and to derive a scattered-field expansion centered at the origin O of the global coordinate system we use the Stratton-Chu representation theorem for the scattered field Eg in Dg. In the exterior of a sphere enclosing the particles, the expansion of the approximate scattered field in terms of radiating vector spherical wave functions reads as... 

The scattered field is expanded in terms of radiating vector spherical wave functions... 

Returning to the scattering problem of a particle near an arbitrary infinite surface, we see that our analysis is complete if, according to Step 1, we are able to represent the plane electromagnetic wave and the radiating vector spherical wave functions and as integrals over vector plane waves. 

The superscript T stands for the regular vector spherical wave functions while the superscript 3 stands for the radiating vector spherical wave functions. It is useful to note that for n = m = 0, we have mI q = = 0. Mi, ,... 

In the far-held region, the asymptotic behavior of the spherical Hankel functions for large value of the argument yields the following representations for the radiating vector spherical wave functions [40] ... 

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... 

For ri < ro, we represent the radiating vector spherical wave functions as... 

The regular and radiating spherical vector wave functions can be expressed as integrals over vector spherical harmonics [26]... 

The following theorems state the completeness and linear independence of the system of regular and radiating spherical vector wave functions on two enclosing surfaces. 

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