We theoretically investigate the absorption bistability behavior of a nanostructure consisting of a vanadium dioxide (VO2) layer grown on top of a one-dimensional photonic crystal. The proposed structure is illuminated by a continuous wave pump laser, resulting in heat generation within the VO2 layer, and a subsequent phase transition which drastically affects the optical response of the nanostructure. We solve a multiphysics problem containing electromagnetism and thermodynamics in order to show that the optically induced transitions in the VO2 layer can lead to a bistable response in the nanostructure over some ranges of incident intensities during the VO2 heating and cooling modes. Interestingly, when the laser is well set up for an appropriate wavelength, the high contrast of two absorption values in the hysteresis loop indicates bistability and the possibility of achieving near-unity absorption. For example, considering 1025 nm, we get bistability over 1.182 W/cm2
