Isolas in four-wave mixing optical bistability

Optical bistability based on the cross-interaction of two counterpropagating plane waves in a Kerr-like medium is considered. It is shown that the "input-output" characteristics of such a system have not only multivalued hysteretic response (which was demonstrated by Winful and Marburger in 1980), but also multiple isolated branches (so called isolas) with nonhysteretic jumps from these branches to the main curve (but not vice versa). The isolas were found both in the case in which the problem can be solved analytically (particularly for electrostriction mechanism of optical nonlinearity) and in the general case of arbitrary light-induced anisotropy.