An exact surface-integral approach for accurate interferometric microscopy of single nanoparticles

We present a half-plane surface-integral equation (SIE) approach for modeling the optical phase response of a single nanowire under phasestepping interferometric (PSI) microscopy. This approach calculates scattered fields exactly from the Helmholtz equation in this 2D problem, obviating the need for ray-optic approximations. It is demonstrated that refractive index metrology is enabled by this method, with precision as low as 7 × 10^-5 possible for current state-of-the-art PSI microscopes. For nanowires of known refractive index, radii as small as 0.001λ are shown to yield a measurable phase signal and are therefore potentially measurable by this approach. Measurements are also demonstrated to be relatively insensitive to the spectral and coherence characteristics of the light source, the illumination conditions, and variations in nanowire cross-section shape. Prospects for measuring both the radius and refractive index simultaneously, and scope for generalizing this approach to arbitrary nanoparticle shapes are discussed.