Fano Resonance Sensor with Ultra-High Spectral Resolution in a Metallic Waveguide

High-resolution optical sensing typically relies on complex, high-finesse interferometers, limiting the scalability and cost-effectiveness of extreme precision metrology. We propose a simple, compact alternative: a metallic-boundary waveguide containing a single point dielectric impurity, operated near its cutoff frequency. This device achieves ultra-high spectral resolution by exploiting Fano resonance, arising from the quantum-optical interference between the waveguide's continuous modes and a quasi-bound state induced by the local impurity. For analytical modeling, we employ the Impurity D Function (IDF), an approach previously confined to quantum mechanical scattering, demonstrating its first application in an integrated optical system. Our analysis shows that the spectral resolution (R) scales powerfully with the geometry, specifically R~(e/w)^-12, where (e/w) is the impurity-to-waveguide ratio. This translates directly into an extremely sensitive strain gauge, with transmission linearity T=1/2+Ry near the 50% working point (y is the mechanical strain). We calculate that for a practical ratio of (e/w)~1%, the device yields a resolution of R~10^20, confirming its potential to measure mechanical strains smaller than 10^-21 using a fundamentally simple, integrated platform.