  We report on the generation of coherent phonon polaritons in ZnTe, GaP and
LiTaO$_{3}$ using ultrafast optical pulses. These polaritons are coupled modes
consisting of mostly far-infrared radiation and a small phonon component, which
are excited through nonlinear optical processes involving the Raman and the
second-order susceptibilities (difference frequency generation). We probe their
associated hybrid vibrational-electric field, in the THz range, by
electro-optic sampling methods. The measured field patterns agree very well
with calculations for the field due to a distribution of dipoles that follows
the shape and moves with the group velocity of the optical pulses. For a
tightly focused pulse, the pattern is identical to that of classical Cherenkov
radiation by a moving dipole. Results for other shapes and, in particular, for
the planar and transient-grating geometries, are accounted for by a convolution
of the Cherenkov field due to a point dipole with the function describing the
slowly-varying intensity of the pulse. Hence, polariton fields resulting from
pulses of arbitrary shape can be described quantitatively in terms of
expressions for the Cherenkov radiation emitted by an extended source. Using
the Cherenkov approach, we recover the phase-matching conditions that lead to
the selection of specific polariton wavevectors in the planar and transient
grating geometry as well as the Cherenkov angle itself. The formalism can be
easily extended to media exhibiting dispersion in the THz range. Calculations
and experimental data for point-like and planar sources reveal significant
differences between the so-called superluminal and subluminal cases where the
group velocity of the optical pulses is, respectively, above and below the
highest phase velocity in the infrared.
