Delivery and focusing
of radiation requires a variety of optical
elements such as waveguides and mirrors or lenses. Heretofore, they
were used separately, the former for radiation delivery, the latter
for focusing. Here, we show that cylindrical multimode waveguides
can both deliver and simultaneously focus radiation, without any external
lenses or parabolic mirrors. We develop an analytical, ray-optical
model to describe radiation propagation within and after the end of
cylindrical multimode waveguides and demonstrate the focusing effect
theoretically and experimentally at terahertz frequencies. In the
focused spot, located at a distance of several millimeters to a few
centimeters away from the waveguide end, typical for focal lengths
in optical setups, we achieve a more than 8.4× higher intensity
than the cross-sectional average intensity and compress the half-maximum
spot area of the incident beam by a factor of >15. Our results
represent
the first practical realization of a focusing system consisting of
only a single cylindrical multimode waveguide, that delivers radiation
from one focused spot into another focused spot in free space, with
focal distances that are much larger than both the radiation wavelength
and the waveguide radius. The results enable design and optimization
of cylindrical waveguide-containing systems and demonstrate a precise
optical characterization method for cylindrical structures and objects.