Abstract
Collinear degenerated four-wave mixing can demonstrate optical bistability with hysteretic response.1 For this system, we predict the existence of multistable isolated nonhysteretic branches of solution (so-called isolas). We consider two optical beams with the same frequency counterpropagating along the z axis in a Kerrlike medium. Their total electric field is E = [E1 exp (ikz) + E2 exp(−ikz)] exp(−iωt), where E1 and E2 are the vectorial envelope of forward and backward waves, respectively. The influence of the Kerrlike medium enters through the nonlinear polarization2 PNL = χ [AE(E · E*) + BE*(E · E)], where χ is a constant of nonlinear interaction for a single linearly polarized plane wave; A and B(A + B= 1) are dimensionless constants dependent on the particular mechanism of nonlinearity. The wave equations3 for the electric fields Ej(j = 1,2) in general can be solved in terms of an elliptic integral. For special cases B=0 (which corresponds to the electrostriction mechanism of nonlinearity) and B = 0.5, analytical solutions can be found. Both analytical solutions (for B = 0 or B = 0.5) and numerical solutions4 (for other values of B) exhibit a new remarkable feature of optical multi-stability in four-wave mixing: the existence of multiple isolated branches of solutions (isolas), the total number of which depends on the intensity of the waves. The results of these calculations are shown at Figs. 1 and 2 for the case when one of the beams (e.g., the second one) is circularly polarized at the plane of incidence.
© 1986 Optical Society of America
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