 |
|
where K is the propagation constant at the carrier frequency of the optical signal, p
is the length of one period or round trip, and the integral is over the transverse coordinates at the reference or input plane.
The function K is commonly called the propagation kernel, since the field
E (1)(x, y) after one propagation step can be obtained from the initial field E (0)(x0, y0) through the operation of the linear kernel or "propagator" K(x, y, x0, y0).
By setting the condition that the field, after one period, will have exactly the same transverse form, both in
phase and profile (amplitude variation across the field), we get the equation
|
|
|
where Enm represents a set of mathematical eigenmodes, and gnm a corresponding set of eigenvalues. The eigenmodes are referred to as transverse cavity modes, and, for stable resonators, are closely approximated by Hermite-gaussian functions, denoted by TEMnm.
The lowest order, or "fundamental" transverse mode, TEM00 has a gaussian intensity profile, shown in the figure below, which has the form
|
|
|
|
Gaussian beam intensity profile
|
In this section we will identify the propagation characteristics of this
lowest order solution to the propagation equation. In the next section,
Real-World Beams we will discuss the propagation characteristics of
higher-order modes, as well as beams that have been distorted by
diffraction, or various anisotropic phenomena.
|
