Pulsed beam propagation in inhomogeneous medium

Pulsed beams (PB) are localized space-time wavepackets that propagate along ray trajectories. This paper deals with general PB solutions in inhomogeneous medium. We derive an approximate form of the time-dependent wave equation (termed the wavepacket equation), valid within a moving space-time window that brackets the wavepacket, and then construct its exact PB solutions. This is done first in a free-space and latter on in a general smoothly varying medium where the propagation trajectories are curved. We also determine the reflection and transmission laws at curved interfaces. These new PBs are related to the so called complex source pulsed beams which are exact solutions in free-space, but they have more general form that admits wavepacket astigmatism and medium inhomogeneity. Since they maintain their wavepacket structure throughout the propagation process they are identified as eigen-wavepacket solutions of the time dependent wave equation