We present a complete frequency-domain description of electro-optic (EO) de
tection of terahertz (THz) electromagnetic radiation, including a descripti
on of the ellipsometry technique employed. These frequency-domain results s
how the effect of EO detection of a pulse of THz radiation as the product o
f three spectral filters acting on the complex amplitude spectrum of the TH
z pulse that is entering the EO crystal. For the usual experimental situati
on in which the optical bandwidth of the interrogating light pulse is small
compared with the optical carrier frequency, we obtain an important simpli
fication of our general result for the detected EO signal. When this simpli
fied result is rewritten in the time domain, a more general description of
the previous time-domain picture of EO detection is obtained. (C) 1999 Opti
cal Society of America [S0740-3224(99)00308-2].