We study theoretically a generation of vortices by phase imprinting in trap
ped Bose-Einstein condensates. Phase imprinting is achieved by passing a sh
ort off-resonance laser pulse through an appropriately designed absorption
plate, and impinging it on a condensate. We answer the fundamental question
how the circulation and the vortex are introduced into the system. We disc
uss the possibility of multiple vortex arrays creation. Using multiple abso
rption plates we show that genuine vortex arrays and vortex-antivortex conf
igurations can be created in a controlled way. We discuss vortex dynamics a
nd interactions in such configurations. Various methods of vortex detection
based on interference combined with Bragg scattering technique are also an
alyzed.