Absorption and emission of radiation by plasmons in two-dimensional electron-gas disks

The theoretical formalism of Ritchie et al. is used to characterize the electromagnetic properties of plasma oscillations in two-dimensional electron-gas disks, such as those produced lithographically in the GaAs-${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As semiconductor heterojunction system. The disks are treated as very thin, oblate spheroids of free-electron gas on the surface of a high-dielectric-constant substrate, and the resonant frequencies are obtained for modes symmetric about the plane of the disk, particularly the lowest-order (dipole) mode. The plasmon fields in this quasi-two-dimensional system are quantized in order to calculate the interaction between the plasmons and the photon field. Closed-form expressions are obtained for the photon absorption cross section and the radiative contribution to the decay width, and the results are compared with those from recent relevant experimental work.