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Laser Physics

Drastic size effects in light-matter interactions due to long-range excitonic coherence

Hajime Ishihara

Published Feb 1, 2006• 0 citations
Publisher

Abstract

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.

DOI
10.1134/s1054660x06020046

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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.
We derive a rigorous theory of the interaction between photons and spatially extended excitons confined in quantum dots in inhomogeneous photonic materials. We show that beyond the dipole approximation, the radiative decay rate is proportional to a nonlocal interaction function, which describes the interaction between light and spatially extended excitons. In this regime, light and matter degrees of freedom cannot be separated and a complex interplay between the nanostructured optical environment and the exciton envelope function emerges. We illustrate this by specific examples and derive a series of important analytical relations, which are useful for applying the formalism to practical problems. In the dipole limit, the decay rate is proportional to the projected local density of optical states, and we obtain the strong and weak confinement regimes as special cases.
The optical response of radiatively coupled semiconductor multiple-quantum-well structures is investigated theoretically. It is shown that the transverse optical field leads to a coupling of exciton states within each well which causes a radiative decay and a mixing of excitonic resonances. Simultaneously, the field-induced long-ranged coupling between different wells leads to collective effects that are very sensitive to the detailed geometry of the structure. For a quantum-well spacing equal to an integer multiple of half the optical wavelength inside the medium, it is predicted that the collective effects cause a stimulated decay of electronic excitations that should be observable in either transmission or reflection geometry. On the other hand, in a quarter wavelength structure, the light-induced coupling causes an interwell energy transport and a splitting of the excitonic resonances, that should be observable as quantum beats in the time-resolved transmitted or reflected signal.
We study the size dependence of the nonlinear response of weakly confined excitons for the size region beyond the long wavelength approximation regime. The observed degenerate-four-wave mixing signal of GaAs thin layers exhibits an anomalous size dependence, where the signal is resonantly enhanced at a particular thickness region. The theoretical analysis elucidates that this enhancement is due to the size-resonant enhancement of the internal field with a spatial structure relevant to the nondipole-type excitonic state. These results establish the formerly proposed new type of size dependence of nonlinear response due to the nonlocality induced double resonance.
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 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.