Theoretical study of the interparticle interaction of nanoparticles randomly dispersed on a substrate

Metal nanoparticles exhibit the phenomenon of localized surface plasmon resonance (LSPR) due to the collective oscillation of their conduction electrons, which is induced by external electromagnetic radiation. The finite-differential time-domain (FDTD) method is widely used as an electromagnetic field analysis tool for nanoparticles. Although the influence of interparticle interactions is taken into consideration in the FDTD calculation for the plural particles configuration, the FDTD calculation of a random configuration is very difficult, particularly in the case of non-spherical particles. In this study, a theoretical calculation method incorporating interparticle interactions on a substrate with various particle shapes and sizes on a subwavelength scale is developed. The interparticle interaction is incorporated following FDTD calculation with an isolated single particle. This is explained systematically using a signal flow graph. Moreover, the mirror image effect of the substrate and the retardation effect are also taken into account in this method. The validity of this method is verified by calculations for simple arrangements of nanoparticles. In addition, it is confirmed that the method can improve the accuracy of predicted experimental results for Au nanoparticles prepared by the sputtering method, in terms of the plasmon peak wavelength. This method may enable the design of LSPR devices by controlling nanoparticle characteristics, such as the size, shape, and distribution density