  We study monochromatic, scalar solutions of the Helmholtz and paraxial wave
equations from a field-theoretic point of view. We introduce appropriate
time-independent Lagrangian densities for which the Euler-Lagrange equations
reproduces either Helmholtz and paraxial wave equations with the
$z$-coordinate, associated with the main direction of propagation of the
fields, playing the same role of time in standard Lagrangian theory. For both
Helmholtz and paraxial scalar fields, we calculate the canonical
energy-momentum tensor and determine the continuity equations relating "energy"
and "momentum" of the fields. Eventually, the reduction of the Helmholtz wave
equation to a useful first-order Dirac form, is presented. This work sheds some
light on the intriguing and not so acknowledged connections between angular
spectrum representation of optical wavefields, cosmological models and physics
of black holes.
