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Decomposing the field scattered by an object into vector spherical harmonics(VSH) is the prime task when discussing its optical properties on moreanalytical grounds. Thus far, it was frequently required in the decompositionthat the scattered field is available on a spherical surface enclosing thescatterer; being with that adapted to the spatial dependency of the VSHs butbeing rather incompatible with many numerical solvers. To mitigate thisproblem, we propose an orthogonal expression for the decomposition that holdsfor any surface that encloses the scatterer, independently of its shape. Wealso show that the orthogonal relations remain unchanged when the radiative VSHused for the expansion of the scattered field are substituted by the VSH usedfor the expansion of the illumination as test functions. This is a key factorfor the numerical stability of our decomposition. As example, we use afinite-element based solver to compute the multipole response of a nanorodilluminated by a plane wave and study its convergence properties.

Decomposition of scattered electromagnetic fields into vector spherical wave functions on surfaces with general shapes