  In this paper, we study the nonlinear optical bistability (OB) in a
symmetrical multilayer structure. This structure is constructed by embedding a
nonlinear three-dimensional Dirac semimetal (3D DSM) into a solution filled
one-dimensional photonic crystal Fabry-Perot cavity. OB stems from the third
order nonlinear conductivity of 3D DSM and the local field of resonance mode
could enhance the nonlinearity and reduce the thresholds of OB. This structure
achieves the tunability of OB due to that the transmittance could be modulated
by the Fermi energy. OB threshold and threshold width could be remarkably
reduced by increasing the Fermi energy. Besides, it is found that the OB curve
depends heavily on the angle of incidence of the incoming light, the structural
parameters of the Fabry-Perot cavity, and the position of 3D DSM inside the
cavity. After parameter optimization, we obtained OB with a threshold of 106
V/m. We believe this simple structure provides a reference idea for realizing
low threshold and tunable all optical switching devices. Keywords: Optical
bistability, Dirac semimetal, Fabry-Perot cavity.
