Nonlinear optical response of cofacial phthalocyanine dimers and trimers

The effects of intermacrocycle interactions on the second hyperpolarizabilities 〈γ(−ω;ω,−ω,ω)〉 of cofacial phthalocyanine dimers and trimers are studied. A theoretical analysis is presented based on the Frenkel exciton model for a chain of three level molecules. Using a simplified analysis in the static and near-resonant regimes we identify two mechanisms which lead to enhancements in the dimer or trimer value of 〈γ(−ω;ω,−ω,ω)〉 over that of the monomer. The first mechanism is a disruption of the balance between type I and type II terms in the sum over states expression for the second hyperpolarizability tensor γkjih(−ω;ω,−ω,ω), caused by weak intermacrocycle interactions. The second is a near-resonance enhancement of the type II terms due to an intermacrocycle interaction induced shift in the monomer derived two-photon allowed states towards twice the laser photon energy. This analysis is in good agreement with recent degenerate four wave mixing experiments [SPIE Proc. 2527, 61 (1995)] which showed a strong enhancement of 〈γ(−ω;ω,−ω,ω)〉 for SiPcO oligomers as a function of the number of macrocycles. Our calculations suggest that the first mechanism is responsible for the 25-fold monomer to dimer enhancement measured in this system, and that the additional 4-fold enhancement found in going from the dimer to the trimer is primarily the result of the second mechanism.