Superoscillatory field features with evanescent waves

We show how to obtain optical fields possessing superoscillatory features by superposing the evanescent tails of waves undergoing total internal reflection at a plane dielectric interface. In doing so, we essentially extend the definition of superoscillations to functions expressed as a continuum of slowly decaying exponentials, while not necessarily being bandlimited in the standard (Fourier) sense. We obtain such functions by complexifying the argument of standard bandlimited superoscillatory functions with a strictly positive spectrum. Combined with our recent method for superoscillations with arbitrary polynomial shape, the present approach offers flexibility for locally shaping the evanescent field near dielectric interfaces for applications such as particle or atom trapping.