We demonstrate a method for fabricating sapphire rib waveguides with femtosecond laser micromachining technology. Finite difference beam propagation method (FD-BPM) is applied to design sapphire rib waveguides. We explore the process of etching on a sapph
Vortex harmonics with fractional average orbital angular momentum are generated when a relativistic fractional vortex beam is incident on and reflected from an over-dense plane plasma target. A two-step model is presented to explain the far-field patterns