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This theoretical study, deals with the effect of bi-particle interaction onthe surface plasmon resonance (SPR) in a dimer which includes two identicalmetal nanoparticles (NPs). Considering the dipole-dipole interaction in aDrude-like model, an appropriate equation is derived for the permittivity ofeach NP. The restoration force related to the classical confinement originatingfrom the finite size of NPs is considered and an appropriate adjustmentcoefficient is considered for this term through analyzing experimental data.Two different polarizations are considered for the laser beam electric fieldand it is shown that the orientation of electric field has essential role inthe linear optical properties of dimer. Numerical investigation is accomplishedfor a dimer of gold NPs with two different diameters of 4nm and 20nm. For theparallel polarization, dipole-dipole interaction leads to the red-shift of SPRwavelength and increase in its peak value while for the perpendicularpolarization, the absolutely opposite results are derived. For all cases, it isshown that SPR wavelength functionality with respect to the geometric factor$a/d$ (NP radius to the separation) can be presented by a cubic equation thatfits better than an exponential one suggested by the earlier studies whichdemonstrates the dipole-dipole characteristic of the interaction.Qualitatively, our results are in good agreement with the other experimentalstudies.

Analytical approach to the surface plasmon resonance characteristic of metal nanoparticle dimer in dipole-dipole approximation