Biexcitonic nonlinearity in GaAs/GaxAl1−xAs quantum wells and quantum-well wires

The recently reported high excitonic and biexcitonic binding energies in GaAs/${\mathrm{Ga}}_{\mathrm{x}}$ ${\mathrm{Al}}_{1\mathrm{-}\mathrm{x}}$As quantum wells and quantum-well wires suggest the possibility of strong optical nonlinearities around the biexcitonic resonance. We calculate in a simple boson model both absorption and dispersion spectra in GaAs around this resonance for various intensities comparing bulk, quantum-well, and quantum-well-wire structures. An assessment of inhomogeneous line broadening due to a Gaussian distribution of quantum-well-wire radii is also presented.