Second-harmonic generation by radially polarized laser beam propagating in homogeneous plasma

This study presents an investigation of second-harmonic generation (SHG) resulting from interaction of radially polarized laser beam propagating in homogeneous, unmagnetized plasma. Lorentz force and continuity equations have been used to derive the radial and axial current density components. Further, using these densities in the wave equation leads to analytical expressions for the SHG field amplitudes. These amplitudes exhibit periodic oscillations along the propagation axis, characterized by detuning length dependent on plasma density and laser parameters. Radial and axial contributions to SHG are found to be highly enhanced near the beam axis due to the Gaussian beam profile of the laser. The analytical findings are validated using Fourier-Bessel particle-in-cell (FBPIC) simulations. Notably, unlike linearly or circularly polarized beams which require either inhomogeneous or magnetized plasma, radially polarized beams facilitate efficient harmonic generation in homogeneous unmagnetized plasmas.