In ground based high frequency (HF) radio pumping experiments, absorption of ordinary (O) mode pump waves energises the ionospheric plasma, producing optical emissions and other effects. Pump-induced or natural kilometre-scale field-aligned density depletions are believed to play a role in self-focussing phenomena such as the magnetic zenith (MZ) effect, i.e., the increased plasma response observed in the direction of Earth's magnetic field. Using ray tracing, we study the propagation of ordinary (O) mode HF radio waves in an ionosphere modified by density depletions, with special attention to transmission through the radio window (RW), where O mode waves convert into the extraordinary (X, or Z) mode. The depletions are shown to shift the position of the RW, or to introduce RWs at new locations. In a simplified model neglecting absorption, we estimate the wave electric field strength perpendicular to the magnetic field at altitudes normally inaccessible. This field could excite upper hybrid waves on small scale density perturbations. We also show how transmission and focussing combine to give stronger fields in some directions, notably at angles close to the MZ, with possible implications for the MZ effect. In a separate study, we consider electromagnetic (e-m) beams with helical wavefronts (i.e., twisted beams), which are associated with orbital angular momentum (OAM). By applying geometrical optics to each plane wave component of a twisted nonparaxial e-m Bessel beam, we calculate analytically the shift of the beam's centre of gravity during propagation perpendicularly and obliquely to a weak refractive index gradient in an isotropic medium. In addition to the so-called Hall shifts expected from paraxial theory, the nonparaxial treatment reveals new shifts in both the transverse and lateral directions. In some situations, the new shifts should be significant also for nearly paraxial beams.