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The Journal of Chemical Physics

Cooperative ultrafast nonlinear optical response of molecular nanostructures

Ningjun Wang, Vladimir Chernyak, Shaul Mukamel

Published Feb 15, 1994• 16 citations
Publisher

Abstract

The stationary nonlinear reflection and the time resolved four wave mixing signal from a molecular monolayer are calculated using Green function techniques. Cooperative resonant nonlinear response found in small aggregates suggests the existence of coherence size of order of optical wavelength. A new peak in the nonlinear reflection spectrum is predicted, which is missed by the local field approximation. For an infinite two dimensional molecular monolayer with transition dipole moments in the lattice plane, the momentum-dependent two exciton decay rate is found to be larger than the sum of the single exciton radiative decay rates, as predicted by the local field approximation.

DOI
10.1063/1.466495

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The stationary nonlinear reflection and the time resolved four wave mixing signal from a molecular monolayer are calculated using Green function techniques. Cooperative resonant nonlinear response found in small aggregates suggests the existence of coherence size of order of optical wavelength. A new peak in the nonlinear reflection spectrum is predicted, which is missed by the local field approximation. For an infinite two dimensional molecular monolayer with transition dipole moments in the lattice plane, the momentum-dependent two exciton decay rate is found to be larger than the sum of the single exciton radiative decay rates, as predicted by the local field approximation.
The nonlinear susceptibility ${\mathrm{\ensuremath{\chi}}}^{(3)}$ and the four-wave mixing signal from assemblies of molecules with nonoverlapping charge distributions and an arbitrary geometry are calculated using Green's-function techniques. At low molecular density and under off-resonant excitation we recover the local-field approximation. The role of retarded interactions and cooperative spontaneous emission in the electrodynamics of confined excitons in molecular quantum wells is discussed.
We study the nonlinear optical response of molecular assemblies consisting of coupled two-level molecules with arbitrary geometry including inhomogeneous broadening and exciton dephasing. An analytical expression for the third-order optical susceptibility is derived based on a certain closure of the equation-of-motion hierarchy. An exact expression for the third-order response of small crystalline aggregates with exciton population relaxation is derived, and used to show that for low relaxation rate \ensuremath{\Gamma} the cooperative part of the nonlinear response scales as ${\mathrm{\ensuremath{\Gamma}}}^{\mathrm{\ensuremath{-}}1/2}$ in d=1, and up to logarithmic corrections, as ${\mathrm{\ensuremath{\Gamma}}}^{\mathrm{\ensuremath{-}}1}$ in d=2 and 3. We show that cooperative enhancement is caused by exciton scattering. This is to be contrasted to other cooperative effects such as superradiance, which are related to the size of molecular coherence domains and therefore scale as ${\mathrm{\ensuremath{\Gamma}}}^{\mathrm{\ensuremath{-}}\mathit{d}/2}$. In a numerical study for dipole-dipole interactions in d=1, 2, and 3 dimensions we find that the local-field approximation is valid only in selected cases, and in general fails to reproduce the magnitude and the resonance structure of ${\mathrm{\ensuremath{\chi}}}^{(3)}$.
The performance of approximate theories for the collective nonlinear optical response of assemblies of interacting molecules is investigated by comparing their predictions to exact calculations. To this end, the nonlinear absorption coefficient of linear molecular aggregates with energetic disorder is studied with the aid of Monte Carlo simulations. It is shown that the well-known local-field approximation (LFA) cannot describe the near-resonance nonlinear absorption spectrum for disorder values up to the nearest-neighbor intermolecular interactions; surprisingly, it is found that the validity of the LFA does not at all improve with growing disorder. By contrast, the ``excitonic two-level system'' approximation, in which each collective one-photon transition (Frenkel exciton) of the assembly is treated as an independent two-level system, turns out to describe the collective nonlinear response of the aggregates in a much better way and, moreover, rapidly improves for growing disorder values. It is shown that both models correctly describe the linear optical response and that, within the framework of the LFA, a close connection exists between the rotating-wave approximation and the Heitler-London approximation.
We observe ultrafast and large nonlinear optical responses of a semiconductor thin film where excitons are weakly confined and their center-of-mass motion is quantized. The observed degenerate four-wave mixing (DFWM) signal of a GaAs double-hetero-structure layer exhibits an anomalous thickness-dependence, and is much enhanced at the thickness of 110nm. The decay time of the response is the order of ps, which depends on the thickness of the layer and on the number of the layer. These phenomena are elucidated by the theory of the nonlocal interaction between excitonic states and the light beyond the long wavelength approximation regime. The enhancement at the thickness is due to the size-resonant enhancement of the internal field with a nano-scale spatial structure, where the second quantized level of the exciton center-of-mass motion mainly contributes to the large response at the thickness. We, furthermore, demonstrate ultrafast response in a reflective type nonlinear polarization rotation switch with the 110nm thick three double-hetero. The signal intensity of 20% for the reflective pulse was obtained at a pump intensity of 10nJ/cm2, and the decay time is 1.5ps at low temperatures. These results provide a novel design of a semiconductor structure in order to obtain both large and ultrafast nonlinear response that is suitable for device application.
In nanostructures with a high excitonic coherence, the interplay between the spatial structure of the excitonic wavefunction and that of the radiation field plays an essential role, causing drastic size effects in the optical response, such as size-resonant enhancement of the radiative decay rate and the nonlinear response and the interchange of quantized levels. This article discusses such peculiar optical effects based on the theoretical treatment beyond the long-wavelength approximation and demonstrates the possibility of designing novel photofunctions with the explicit use of the spatial structures of the radiation field.