Direct numerical simulations were performed to investigate conditions for the strong effects of photonassisted quantum transport. Transmission probabilities of incident electrons as Gaussian wave packets were calculated for single- and double-barrier structures irradiated by electromagnetic fields that were focused within a finite region j ac . When the period of the ac electromagnetic field is short compared with the time t j ac , which is the traversal time of the electrons in the region of the applied ac field, the transmission probability can be affected by photon emission and photon absorption. The magnitude of these effects strongly depends on the width j ac and the bound-state character of the electrons. These dependences can be understood from the selection rule, which results from the momentum conservation of the electron and photon system. Consequently, we have shown that photon-assisted transport over a single barrier is difficult to achieve in two-dimensional electron-gas devices due to the relatively long screening length. We have demonstrated, however, that the photon-assisted process is significantly enhanced in double-barrier devices due to quasibound-to-extended-state transitions. @S0163-1829~96!02435-6#