Exciton coherence-size and phonon-mediated optical nonlinearities in restricted geometries

Abstract

The magnitude of optical nonlinearities of molecular nanostructures is determined by a characteristic coherence-length which controls the cooperativity of the optical response. Equations of motion describing the evolution of the optical polarization coupled to two-exciton variables are derived, and used to calculate the third order optical response (x'~') of a onedimensional molecular crystal or a polymer. We show that the coherence-length is determined by the interplay between intramolecular and intermolecular (nonlocal) nonlinearities and explore the limitations of the local-field approximation. Phonon-mediated exciton-exciton attractive interaction may result in the formation of bound exciton pairs (biexcitons). We show how unbound (two-exciton) as well as biexciton states could readily be observed as resonances in two-photon absorption and third harmonic generation.

Multiple Exciton Coherence Sizes in Photosynthetic Antenna Complexes viewed by Pump−Probe Spectroscopy

“…Equation 15 is the same formula used for the definition of L f (see eq 12), with G mn ( ) replaced by F mn . This quantity gives the length scale on which the density matrix decays along the "antidiagonal" direction, i.e., as a function of n -m. Similar measures has been successfully used in the analysis of off resonant polarizabilities of aggregates, 42,45 conjugated polymers, 46 and semiconductor nanocrystals. 47 Figure 7 displays the thermally equilibrated density matrixes for model I corresponding to 100 K (Figure d) and 300 K (Figure e).…”

Femtosecond four-wave-mixing spectroscopy of interacting magnetoexcitons in semiconductor quantum wells

“…27,28 Effects of dephasing induced by the coupling to phonons have been incorporated for Frenkel exciton systems by using a closed system of equations of motion for ͗B͘ and ͗B † B͘ variables, the latter representing the exciton density matrix. 14,29 The same level of theory for semiconductor systems yields SBE's with dephasing, 18,30-32 which have been successfully applied for the interpretation of ultrafast nonlinear optical phenomena in semiconductors and semiconductor nanostructures. These equations have already been used to analyze the linear and nonlinear optical properties of magnetoexcitons in two 9 and three 10 dimensions.…”

“…26 and 14 were developed subsequently. 17,29 Green-function expressions which represent the combined effects of exciton transport and two-exciton resonances have been developed and applied to various Frenkel exciton systems. [33][34][35][36] In the absence of vibronic coupling the method was extended to molecular aggregates made of three-level molecules, 37 and to semiconductors.…”

Effective Frenkel Hamiltonian for optical nonlinearities in semiconductors: Application to magnetoexcitons

“…The approach of Ref. 43, which deals with coupled equations of motion for oneexciton, two-exciton, and exciton-population variables interpolates between the theories of Refs. 38 and 42; however, it does not describe the combined effects of exciton population relaxation and resonant exciton-exciton scattering.…”