Quantum confinement and superradiance of one-dimensional self-trapped Frenkel excitons

It is known that in one-dimensional (1D) molecular crystals with finite length 2L << lambda (lambda is the optical wavelength) an overwhelming part of the total oscillator strength is concentrated in the lowest excitonic state and it is equal to F-1 congruent to 0.85f(o)(2L/a), where f(o) is the oscillator strength of a monomer and a is the lattice constant. This leads to the superradiance from the lowest excitonic state and its domination in the absorption spectrum of the crystal. We show that self-trapping of excitons destroys this simple picture so that it takes place only for short chains with length 2L small compared to the length 2l(o) of self-trapping. For long enough chains the value of F-1 does not increase with growth of L, as it occurs in linear case, but tends to the saturation limit F-1 congruent to 5f(o)(l(o)/a). The oscillator strength of the next bright state also tends to the same limit with growth of L, but it takes place only at the length L > 9l(o), and analogous relations are true for the following bright states. Contrary to the case of infinite chain, where only one self-trapped state exists, in the chains of finite length several self-trapped states can arise, number of which depends on the length of the chain. We consider also the influence of quantum confinement and self-trapping on the superradiance of 1D molecular crystals. (C) 1999 Elsevier Science B.V. All rights reserved.