Multiplicative resonant enhancement of chemical detection

Optical resonances can increase the sensitivity of measurements to material perturbations and also accelerate photochemical reactions. Here, we show that these two effects can be combined multiplicatively, to enhance the detection via weak or low-concentration photochemical reactions far beyond what could previously be attained. For an optical resonance with quality factor $Q$, the sensitivity of our detection scheme is enhanced by $\ensuremath{\sim}{Q}^{2}$ (where $\ensuremath{\sim}$ denotes approximate proportionality), as demonstrated by both theoretical arguments and numerical simulations of a simple optical-grating resonance coupled with reaction-diffusion equations. Such an approach opens a door to further improvements by careful design of the resonance: even a three-parameter optimization of the grating resonance yields an additional $\ensuremath{\approx}7$ times improvement.