Based on essential-state models for three-photon absorption (3PA), we have investigated the structure-property relationships for stilbene-based dipolar and quadrupolar chromophores. The emphasis lies on the evolution of the 3PA cross section with the degree of ground-state polarization. For dipolar systems, we find a dominant role played by Δμ, which expresses the change in dipole moment between the ground state and the 3PA active excited state. Thus, the strategies usually applied to maximize the second-order polarizability β are also applicable to optimize the 3PA cross section. For quadrupolar systems, the 3PA response is dominated by contributions from channels including various low-lying two-photon allowed states, which limits the applicability of essential-state models. Optimization strategies can be proposed but vary for different ranges of ground-state polarization.
Bibliographical noteFunding Information:
The work in Beijing is partly supported by the NSFC (Grant Nos. 20433070, 10425420, and 20420150034) and the Supercomputing Center of the Chinese Academy of Sciences. The work at Georgia Tech is partly supported by DARPA, by the National Science Foundation (CRIF 04-43564), and by the STC Program of the National Science Foundation under Award No. DMR-0120967. One of the authors (D.B.) is a senior research associate of the Belgian National Science Foundation (FNRS). FIG. 1. Chemical structures of the model systems for a dipolar chromophore (4-dimethylamino- 4 ′ -cyano-E-stilbene), I, and a quadrupolar chromophore ( 4 , 4 ′ -bis(dimethyl)amino- α , β -dicyano-E-stilbene), II, together with an illustration of the system of point charges used to continuously vary the ground-state polarization. FIG. 2. Evolution of the second-order polarizability β (top), the 2PA cross section ( σ 2 ) (middle), and the 3PA cross section ( σ 3 ) obtained from the T -tensor approach and the two-state model (bottom) for molecule I, as a function of BLA. FIG. 3. Evolution of the T -tensor-based 3PA cross section into the first excited states of I with the number of intermediate states: (a) at a large BLA value ( BLA = 0.095 Å ) ; (b) at a small BLA value ( BLA = 0.047 Å ) . σ 3 ( converged ) is the value obtained when including 200 intermediate states. For the sake of clarity, a zoom into the full graph is shown in the inset. FIG. 4. Evolutions of the D ′ and N ′ terms from Eq. (4) (top) and of the transition dipole, M g e , and change in state dipole moment, Δ μ g e , (bottom) in I as a function of BLA. FIG. 5. Evolution of the 2PA (top) and 3PA (bottom) cross sections of molecule II as a function of BLA. For 3PA, the converged results obtained from the T -tensor approach are compared with those calculated using the three-state model [Eq. (5) ]. FIG. 6. Evolution of the 3PA T -tensor cross section into the most dominant excited states for quadrupolar molecule II, with the number of intermediate states at large BLA value ( BLA = 0.087 Å ) (a) and at small BLA value ( BLA = 0.063 Å ) (b). For the sake of clarity, a zoom into the full graph is shown in the inset. FIG. 7. Evolutions of the T ′ and N ′ terms from Eq. (6) in molecule II as a function of BLA.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physical and Theoretical Chemistry