Nonlocal theory of the third-order nonlinear optical response of confined excitons

A nonlocal formalism of the nonlinear optical-response field has been developed, in which the additional-boundary-condition theory for linear response has been extended. In this theory, Maxwell's equations in terms of site-represented susceptibility up to the third order are solved. Calculations using this theory have been performed for a one-dimensional Frenkel exciton model with hard-wall boundary conditions. As a result, it has been made clear that the nonlocal effect appears in the spectra even when the system size is much smaller than the relevant light wavelengths. This is recognized as a clear difference between the results of fully nonlocal calculations and those obtained using the long-wavelength approximation. This result indicates that the local description is not sufficient when studying the nonlinear response of mesoscopic systems.