CANCELLATION OF SIZE-LINEAR TERMS IN THE 3RD-ORDER NONLINEAR SUSCEPTIBILITY - FRENKEL EXCITONS IN A PERIODIC CHAIN

For a system of noninteracting Frenkel excitons in a one-dimensional lattice of size N with periodic boundary conditions, the third-order optical susceptibility ‡(3) has been calculated rigorously in a nonlocal form with arbitrary dependence on external-field frequencies. Among the various terms in ‡(3) (per unit volume), those explicitly proportional to N in the long-wavelength approximation have been shown to cancel out completely for arbitrary N. The remaining terms, including the effect of nonlocality, reduce to the well-known result of a two-level system in the limit of vanishing transfer energy. There remain N-dependent factors in ‡(3), with different functional forms for even and odd N, but they all approach unity in the limit of large N. © 1990 The American Physical Society.