Frequency dependence of scaling exponents of hyperpolarizability in polyenes: A density-matrix renormalization-group approach

Scaling properties of the second-order hyperpolarizability gamma in polyenes are investigated by the Lanczos-based density-matrix renormalization-group scheme. The numerical results suggest that the exponent eta, characterizing the scaling law gamma/(NNeta)-N-chi, is inversely proportional to the incident photon frequency w, The static exponent sets the maximum. The full relation can be cast into an analytical expression as eta(w) = b/(w + a), which allows one to directly compare the results measured at different frequencies and objectively evaluate the nonlinear optical performance of one specific material. The microscopic conditions for this relation are also discussed. [S0163-1829(99)01540-4].