Lightwave Engineering

7	Propagation and Focusing of the Beam

The propagation of a beam can be classified as a propagation in free space (or in a homogeneous medium) and a propagation in a guided structure.

Free-space propagation can be described as propagation by diffraction of light, whereas propagation of light in a waveguide can be explained by the eigenmode expansion of the waveguide. In this chapter, we will discuss the propagation of light in a dielectric medium with a homogeneous, isotropic dielectic constant e, including vacuum.

7.1  GAUSSIAN BEAM

The propagation of light as an electromagnetic wave exactly satisfies the following vector wave equation, which is derived from Maxwell’s equations:

${\Delta }^{2}E-{\mu }_0\epsilon \frac{{\partial }^{2}E}{\partial t^2}=0.$

(7.1)

Here, with the propagation direction ...