SPATIAL CHARACTERISTICS
OF
LASERS
The spatial
distribution of the irradiance of a laser beam is of prime importance in
many applications. For example, laser drilling requires beams of a particular
diameter so that holes of the proper size can be drilled. Laser ranging
requires well collimated
beams that diverge slowly as they travel away from the laser. Almost all
applications require the uniform spatial distribution of irradiance produced by
the Gaussian, or TEM00 mode.
TRANSVERSE
ELECTROMAGNETIC MODES:
Optical
Cavities and Modes of Oscillation, "describe the variations in
the electromagnetic field along the optical
axis of the laser cavity. A complete description of the E-M field requires that variations in
directions perpendicular to the optical axis also be considered.
Electromagnetic field variations perpendicular to the direction of travel of
the wave are called "transverse electromagnetic modes," or
"TEM modes" as shown in Figure 1.
Fig. 1 Transverse electromagnetic modes
Figure 1 illustrates the irradiance patterns produced by
lasers operating in various transverse modes. The generalmode is specified as TEMmn, where m is the number of dark
bands (white areas in Figure 1) crossing the horizontal axis and n is the
number of dark bands (white areas) crossing the vertical axis. Thus, TEM21(Figure 1f) has two vertical bands (shown as
white) crossing the x-axis and one horizontal band (shown
as white) crossing the y-axis.
The
centers of the dark bands (white bands)in the intensity patterns of the TEM modes actually are nodes in the electric
field within the laser cavity. The electric fields of two modes within the
cavity of a vertically polarized laser are depicted in Figure 2. Figure 2a
shows the electric field of the TEM00 mode in a plane perpendicular
to the optical axis of the cavity that contains an antinodeof the longitudinal mode at one instant of time. The electric field is
upward at all points within this plane. The curve drawn on the plane represents
the magnitude of the electric field a