  We investigate the fusion cross sections of light nuclei in the presence of
linearly polarized intense laser fields. By combining the Coulomb-Volkov
solutions with the complex spherical square-well nuclear potential, we derive
an explicit formulation of the multiphoton cross section in a self-consistent
manner. Our analysis is specifically focused on deuteron-triton (DT) and
proton-boron (p$^{11}{\rm B}$) fusion reactions, both of which have garnered
widespread attention. The theoretical results reveal that, under conditions of
longer laser wavelengths and lower incident particle kinetic energies, a few
thousands of photons can participate in the fusion reactions, resulting in a
substantial enhancement of fusion cross sections by almost ten orders of
magnitude. We elucidate the multiphoton mechanism underlying these findings and
discuss their implications.
