A nonlinear theory for the optical properties of gold nanorods at various aspect ratios is used to calculate the refractive index sensitivity of surface plasmon resonance (M) which is found to be 100 to 1000 nm/RIU and proportional to the aspect ratio (R). Based on Gans theory, the calculated figure of merit, defined by the ratio of M and the resonance spectral width, has a range of 1.0 to 10 and has a maximum value at the optimum aspect ratio of 3.5 to 4.5. Numerical results are fit for analytic equations for the peak wavelength and sensitivity showing their nonlinear dependence on the surrounding medium refractive index (n) and R. The calculated optimal condition for the figure of merit provides useful guideline for the design of biosensors.
Jui-Teng Lin, Jui-Teng Lin,
"Nonlinear optical theory and figure of merit of surface plasmon resonance of gold nanorods," Journal of Nanophotonics 5(1), 051506 (1 January 2011). https://doi.org/10.1117/1.3543815