Evanescent waves

In optics, evanescent waves are formed when sinusoidal wavess are (internally) reflected off an interface at an angle greater than the critical angle so that total internal reflection occurs.

"Evanescent" means "tending to vanish", which is appropriate because the intensity of evanescent waves decays exponentially (rather than sinusoidally) with distance from the interface at which they are formed.

Source: http://www.andrew.cmu.edu/user/dcprieve/Evanescent%20waves.htm