Performance optimization of bi-metallic surface plasmon resonance based sensors with silicon layer using poynting vector analysis

摘要

We have proposed a formula to calculate the optimum thickness of Silicon (a high-index dielectric) which is introduced in a conventional bi-metallic surface plasmon resonance (SPR) sensor to enhance the sensitivity. This formula has been derived from the penetration depth analysis of the 'instantaneous Poynting vector' in a five-layer bi-metallic sensor structure. This formula is shown to be different from the conventional penetration depth formula of the "average Poynting vector" (intensity) which is discussed in many textbooks on optics. We have applied this formula to optimize the design parameters of a bi-metallic sensor consisting of prism-silver-gold-analyte (H_2O) in Rretschmann configuration with an adjustable Si layer for various combinations of Ag/Au thicknesses to yield maximum sensitivity. The optimum thickness of any high-index dielectric layer which is used in SPR based sensors for the sensitivity enhancement can be calculated from the proposed formula and the values match very well with the experimental results already reported in the literature. Also, the optimum thickness derived using the proposed formula is found to yield the maximum sensitivity of an SPR sensor when computed using the Transfer Matrix Method (TMM) analysis. The analysis of the shape of the SPR curves for the proposed bi-metallic sensor is also done. From the paper, we can conclude that the study of the instantaneous Poynting vector plays an important role in understanding the working of optical devices which are based on the phenomenon of evanescent coupling. The analysis done in this paper can be extended to calculate the design parameters of other evanescently coupled optical devices, such as directional couplers and TE/TM polarizers.