Mode conversion via reflected stepped phase plate in relativistic systems

The mode conversion efficiency (CE) of the relativistic Laguerre–Gaussian (LG) laser is researched in detail within the context of current petawatt laser facilities. The topological charge, radial integer, laser central wavelength, laser bandwidth, and the design of reflective phase plate are integrated into a unified equation in theory. It is found that the vortex laser mode can be expanded as a series of LG modes, with calculations indicating that the LG10 mode predominates, constituting ∼78% of the total mode distribution. Our analysis reveals that mode CE tends toward a saturation value as the number of steps of the reflective phase plate increases. The 32-step phase plate utilized in relativistic systems is fine enough to obtain a higher CE for LG10 mode lasers, which is also verified in three-dimensional particle-in-cell simulations. This research holds promise for optimizing the design of reflective phase plates to enhance the conversion efficiency of intense LG lasers, thereby facilitating broader applications in intense vortex laser technologies.