The intrasubband plasmons in the long-wavelength limit and intersubband plasmons in the zero-wave-vector limit are calculated numerically for the GaAs/AlAs lateral-surface superlattices (LSSLs) with periodically structured interfaces and short lateral periods under normally applied electric fields. Square-root dispersion relations are found for the intrasubband plasmons with the in-plane wave vector qz1 and qy=0. The frequencies of the intrasubband plasmons in the LSSLs are expected to be less than those of plasmons in quantum wells with the same electron densities. Oscillations of the intrasubband-plasmon frequencies as functions of the Fermi level, or equivalently the electron density, are predicted. A sensitive dependence of the intrasubband-plasmon frequencies on the electric fields applied normally to the LSSLs is found, a result that is absent in quantum wells with planar interfaces. The energies of the intersubband plasmons are found to be close to the single-electron transition energies between the two lowest subbands at the center of the first Brillouin zone (FBZ) for the LSSLs with small interface structures and short lateral periods, typically with Lx<200 for the LSSLs we considered. The effects of the electron Coulomb interactions on the optical absorptions of the LSSLs are negligible. The optical absorptions of the LSSLs are dominated by the single-electron transitions across the first subband gap at the edge of the FBZ, if the electron densities are high enough to move the Fermi level into the first subband gaps of the LSSLs. Distinctive and strong intersubband-plasmon- absorption peaks appear in the optical-absorption spectra if the lateral periods of the LSSLs increase, typically if Lx>400 for the LSSLs we considered. The changes of the intersubband-plasmon energies as functions of the interface structures, electron densities, lateral periods of the LSSLs, and electric fields applied normally to the LSSLs are investigated. © 1995 The American Physical Society.