An approximate theoretical model of surface plasmon resonance optical waveguide and fibre-optic sensors

Optical surface plasmon resonance (SPR) excitation can be theoretically depicted and discussed using Fresnel's equations. However, Fresnel's equations cannot explicitly give expressions to reflect the characteristics of SPR systems, especially in SPR optical waveguide and fibre-optic sensors. In this paper a mathematical model based on the approximation proposed by Kretschmann in bulk optics is presented to describe the characteristics of SPR optical waveguide and fibre-optic sensors. The results show that the model keeps high accuracy when used in the area close to the minimum reflection, at which the resonance condition is achieved. This model can be used to analytically estimate the performance of SPR optical waveguide sensors, and SPR fibre-optic sensors in meridional rays approximation.