We report time-domain measurements with subpicosecond resolution of optical
tunneling of terahertz electromagentic pulses undergoing frustrated total
internal reflection. Measurements of the transmitted electromagnetic pulses
over a 3 THz bandwidth permits direct determination of frequency-dependent
phase and amplitude changes in both the thin and opaque barrier limits in
a single measurement. A complex frequency response function describing prop
agation through the barrier is developed based upon linear dispersion theor
y and the Fresnel coefficients at complex angles in the optical barrier. Ou
r measurements are in excellent agreement with this theoretical model acros
s the experimentally determined bandwidth; the model makes no assumptions a
bout the beam path through the barrier and has no adjustable parameters. Th
e theory is shown to satisfy the Kramers-Kronig relations, indicating causa
l propagation across the barrier.