Optimizing Plasmonic Grating Sensors for Limit of Detection Based on a Cramer-Rao Bound

We explore the impact of the geometrical features such as the period, duty cycle, thickness on the performance of a metal-dielectric plasmonic grating sensor. The sensor is designed to operate at the wavelength of 850 nm for water-monitoring applications. Limit of detection (LOD) is chosen as the performance metric for the optimization of the sensor design. The LOD metric is based on a Cramer-Rao bound (CRB) and offers a theoretical lower limit on the estimation uncertainty of the spectral shift in the proposed sensor. We show that the lowest values of LOD correspond to grating designs, which result in step-like spectral features. An optimum grating design corresponds to gold stripes that are 160 nm thick and 456 nm wide on glass where the stripes are separated by 74 nm. Although our study is focused on a particular design and application, our methods and observations are applicable to a wide range of plasmonic grating sensor designs.