Purpose The purpose of this paper is to develop a rigorous self-contained formulation for analyzing electromagnetic scattering by grating of plasmonic nanorods. The authors investigate this structure from the viewpoint of the practical application as a refractive index plasmonic sensor. The presented rigorous formulation is accompanied with a neat implementation providing a high computation efficiency and could be considered as an important tool for designing and optimizing compact sensors. Design/methodology/approach Scattering of an incident plane wave by grating made of a periodic arrangement of metal-coated dielectric nanocylinders on a dielectric slab is rigorously investigated using the recursive algorithm combined with the lattice sums technique. As a dielectric slab, the authors consider glass material, which is widely used in experiments, whereas silver (Ag) is used as a low loss metal suitable to excite plasmon resonances. The main advantage of the developed self-contained formulation is that first the authors extract the reflection and transmission matrices of a single planar array from a separate analysis of the grating and the slab and then obtain the scattering characteristics of the whole structure by using a recursive formula. The method is computationally fast. Findings Dependence of the surface plasmon resonance wavelength on the refractive index of the surrounding medium is carefully investigated. The resonance peaks are red-shifted with respect to an increasing refractive index of surrounding medium showing an almost linear behavior. Near field distributions are analyzed at the resonance wavelengths of the spectral responses. Special attention is paid to the formation of the dual-absorption bands because of the excitation of the localized surface plasmons. The authors give physical insight to the coupling between grating and the glass slab. The authors found that a strong enhancement of the field inside the slab occurs when the scattered wave of the grating is phase-matched to the guided modes supported by the slab. Originality/value In the authors’ formulation, they do not use any approximation and it is rigorous and accurate. The authors use their original method. The method is based on the lattice sums technique and uses the recursive algorithm to calculate the generalized reflection and transmission characteristics by grating. Such fast and accurate method is an effective tool apt for designing and optimizing tailored sensors, for e.g. advanced biomedical applications.