Size Dependence Of X/sup (3)/ For Frenkel Excitons In A Periodic Chain

In order to study the size dependence of x
₍₃₎
for a confined electronic system, we have investigated a system of non-interacting Frenkel excitons in a periodic (N-atom) linear chain, which allows us an exact treatment of x(a) in nonlocal form for arbitrary frequencies of external fields. The nonlinearity of this system arises from the Pauli exclusion principle which forbids two excitons to sit on a same site. The analytic expression of x
^{(3), obtained for arbitrary N after the summation over the internal quantum number for two-exciton states, shows the absence of N as a multiplication factor. This is due to the cancellation of the terms which, in the long wavelength approximation, give rise to factors proportional to N. The N-dependence, described differently for even and odd N, is contained in factors which tend to be unity for large N. A numerical study for a particular case of pump-probe type nonlinear effect in a long wavelength approximation shows the following result: [11 Im[x(3)] contains a size enhancement for a limited region of N. (2) the range of such N is determined by the magnitudes of exciton transfer energy and the relaxation times. In comparison with the local 2-level system, the exciton transfer effect brings about a remarkable change in x(3), both in its spectral shape and magnitude.}