  We report on the theory and experimental generation of a class of
diffraction-attenuation-resistant beams with state of polarization (SoP) and
intensity that can be controlled on demand along the propagation direction.
This is achieved by a suitable superposition of Bessel beams, whose parameters
are systematically chosen based on closed-form analytic expressions provided by
the Frozen Waves (FWs) method. Using an amplitude-only spatial light modulator,
we experimentally demonstrate three scenarios. In the first, the SoP of a
horizontally polarized beam evolves to radial polarization and is then changed
to vertical polarization, with the beam intensity held constant. In the second,
we simultaneously control the SoP and the longitudinal intensity profile, which
was chosen such that the beam's central ring can be switched-off over
predefined space regions, thus generating multiple foci with different SoP and
at different intensity levels along the propagation. Finally, the ability to
control the SoP while overcoming attenuation inside lossy fluids is shown
experimentally for the first time in the literature (to the best of our
knowledge). Therefore, we envision our proposed method to be of great interest
for many applications, such as optical tweezers, atom guiding, material
processing, microscopy, and optical communications.
