Orbital-Angular-Momentum Selection Rules and Channel-Resolved Control of High-Order Harmonic Generation in Solids Driven by Laguerre-Gaussian Fields

Vortex-beam-driven high-order harmonic generation (HHG) in solids offers a promising route to producing attosecond light pulses carrying orbital angular momentum (OAM). Here, we numerically investigate HHG from a two-dimensional periodic potential driven by Laguerre-Gaussian (LG) fields with circular polarization, orthogonally polarized two-color configurations, and counter-rotating bicircular polarization. By combining energy conservation with the conservation of OAM and spin angular momentum (SAM), while explicitly incorporating the symmetry of the crystal, we develop a photon-channel framework to interpret harmonic selection rules and OAM-transfer pathways. For a circularly polarized single-color LG field, the topological charge of the q-th harmonic increases linearly with the harmonic order. In bicircular fields, by contrast, the allowed OAM channels are jointly determined by the numbers of photons absorbed from the two driving components, their respective SAM and OAM, and the crystal symmetry. For an orthogonally polarized two-color field with equal component amplitudes, the dominant channel also leads to an approximately linear increase in the harmonic topological charge with harmonic order. Varying the relative field amplitudes modifies the weights of competing multiphoton channels, thereby enabling switching between discrete OAM states at a fixed harmonic order. These results elucidate the interplay among photon-channel competition, angular-momentum transfer, and crystal symmetry in HHG in solids, and establish a potential route toward tunable attosecond structured-light sources.