  Space-time description of pulsed laser radiation by means of coherent states
is presented. The corresponding displacement operator contains space dependent
annihilation and creation operators, not the "standard" operators corresponding
to mode decomposition of the electromagnetic field. This allowed for a direct
description of space and time dependence of the electromagnetic field of the
pulse. The main characteristics of the pulse is its profile in the wave-vector
space. It determines space-time structure of expectation values of the
electromagnetic field carried by the pulse, and the distribution of photon
modes as well. Determination of the latter required transition from the
space-time, or field description to the photon mode approach. Expectation
values of the electric field of a Gaussian pulse propagating in the z-direction
and linearly polarized in the x-direction are presented graphically in the form
of contour plots in the x-z plane. Apart of the dominant x-component electric
field has a small longitudinal component in the z-direction. The dominant
component of the magnetic field in the y-direction is acompannied by small
components in z- and x-directions. The plane wave limit of the pulse can be
implemented by shrinking transverse width of the profile to zero (transverse
spatial extension goes to infinity), while keeping the photon density constant.
One can then retrieve standard plane wave form of the pulse also in the dipole
approximation.
