Simulations of the interaction of very intense short
pulse lasers with solid density plasmas have indicated
that there may be very high magnetic fields and electron
temperatures in the vicinity of the focal spot. We investigate
the propagation of an incident electromagnetic wave under
these conditions, both analytically and by means of a particle
code, and show that the evanescence length of the wave
field in a highly overdense plasma may be much greater
than is usually supposed. This effect could be important
in understanding the penetration of energy into the overdense
region and the particle heating and acceleration which
takes place there.