evanescentwave

An evanescent wave is an electromagnetic field that is bound to a boundary and decays exponentially with distance from that boundary. Unlike a freely propagating wave, an evanescent field does not carry energy away from the boundary in the normal direction; its amplitude diminishes as a function of distance while the wave’s frequency remains the same.

Evanescent waves commonly arise in total internal reflection. When light in a medium with higher refractive index n1 strikes a boundary with a lower index n2 at an angle θ greater than the critical angle, the transmitted field in medium 2 becomes evanescent. The in-plane component of the wavevector is real, but the perpendicular component is imaginary, leading to an electric field that decays as E(z) ∝ e^{-α z}. The decay constant is α = k0 sqrt(n1^2 sin^2 θ − n2^2), where k0 is the vacuum wavenumber, and the characteristic decay length is δ = 1/α. For optical wavelengths, δ typically ranges from tens to hundreds of nanometers, depending on the frequency and incidence angle.

Evanescent fields also appear in other contexts, such as surface-bound modes in waveguides, near-field optics, and surface plasmon polaritons at metal–dielectric interfaces. In these cases, the field is confined near a surface and decays away from it into both adjoining media.

Applications of evanescent waves include near-field scanning optical microscopy (NSOM/SNOM), which uses the localized evanescent field to achieve sub-diffraction-limited spatial resolution, and attenuated total reflectance (ATR) spectroscopy, which probes thin films by analyzing the interaction of the evanescent field with the sample. They also play a central role in plasmonics and various sensing technologies.