Intense harmonics generation with customized photon frequency and optical vortex

An optical vortex with orbital angular momentum (OAM) enriches the light and matter interaction process, and helps reveal unexpected information in relativistic nonlinear optics. A scheme is proposed for the first time to explore the origin of photons in the generated harmonics, and produce relativistic intense harmonics with expected frequency and an optical vortex. When two counter-propagating Laguerre-Gaussian laser pulses impinge on a solid thin foil and interact with each other, the contribution of each input pulse in producing harmonics can be distinguished with the help of angular momentum conservation of photons, which is almost impossible for harmonic generation without an optical vortex. The generation of tunable, intense vortex harmonics with different photon topological charge is predicted based on the theoretical analysis and three-dimensional particle-in-cell simulations. Inheriting the properties of OAM and harmonics, the obtained intense vortex beam can be applied in a wide range of fields, including atom or molecule control and manipulation.