Nonlinear Optics || Nonlinear Optics in the Two-Level Approximation

摘要： Our treatment of nonlinear optics in the previous chapters has for the most part made use of power series expansions to relate the response of a material system to the strength of the applied optical field. In simple cases, this relation can be taken to be of the form ?P (t) = (cid:2)0χ (1) ?E(t) + (cid:2)0χ (2) ?E(t)2 + (cid:2)0χ (3) ?E(t)3 + · · · . However, there are circumstances under which such a power series expansion does not converge, and under such circumstances different methods must be employed to describe nonlinear optical effects. One example is that of a saturable absorber, where the absorption coefficient α is related to the intensity I = 2n(cid:2)0c|E|2 of the applied optical field by the relation α = α0 / (1 + I /Is), where α0 is the weak-field absorption coefficient and Is is an optical constant called the saturation intensity. We can expand this equation in a power series to obtain α = α0 [1 ? (I /Is) + (I /Is)2 ? (I /Is)3 + · · · ]. However, this series converges only for I < Is, and thus only in this limit can saturable absorption be described by means of a power series of the sort given by Eq. (6.1.1).