Sphere on a substrate

The substrate reflects part of the scattered field back onto the particle and raises the average refractive index around it, so resonances red-shift and broaden, and the field near the contact grows. The calculator includes the substrate's reflections exactly, for any angle of incidence and polarization.

A metal particle a few nanometres above a metal film couples to its own image: the light is squeezed into the gap, giving a very strong, red-shifted gap plasmon. Set a metal substrate and a small gap to compute it.

A narrow, intense beam that forms just behind a dielectric microsphere, narrower than the diffraction limit over a short length. A 3 µm silica sphere on glass at 532 nm concentrates the light about 67-fold (|E|²/|E₀|²).

Any angle of incidence, with s (TE) or p (TM) polarization; p-polarization at oblique incidence has a field component normal to the surface, which drives the gap modes most strongly.