We investigate one magnetically nonlinear response of antiferromagnetic (AF) films to incident electromagnetic waves, or the reflective optical bi-stability (ROB). Such geometry is used, where the AF anisotropy axis and external static magnetic field both are parallel to the film surfaces and normal to the incident plane. For TE incident waves with the electric component transverse to the incident plane, the ROB of the AF film with the absorption is calculated, but the case of TM incident waves is neglected since no magnetic nonlinearity is induced in this geometry. The bi-stability is completely different in the two resonant-frequency vicinities. Two kinds of bi-stability are found in the higher vicinity, and their features versus incident power are opposite. We also find that there are critical incident angle and critical film thickness for the existence of bi-stability. The bi-stability disappears when the film thickness or incident angle exceeds its critical value. Because the properties of bi-stable reflection sensitively depend on the external field and the incident angle, this bi-stability can be easily modulated by means of changing these quantities.
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