Abstract
A numerical optimization technique of a three-dimensional (3D) SERS substrate with finite element analysis is proposed. Using the optical reciprocity theorem, we have shown that instead of the well-known local field enhancement criterion, it is more correct to use the Purcell factor as an objective function that determines the quality of the SERS substrate. This allows us to take into account the detail inhomogeneity of local fields in an arbitrary three-dimensional structure containing multiple emitters. We have theoretically shown that employment of a 3D CNT structure as a nanoparticle substrate instead of a nanoparticle monolayer allows one to achieve the enhancement of the SERS signal.
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