Intensity patterns for laser transverse modes

The intensities of the modes are shown in false colour - blue is lowest and red is highest. These are like cross sections across the laser beam. Usually people try to get the TEM00 mode because it focusses down into the smallest spot, and it is the most "uniform" (if that is the right word!). TEM00 TEM00
The transverse mode patterns shown are only five of an infinite set of possibilities. Furthermore this is not the only set of possibilities but it is by far the most common. The names of the modes derive from the fact that the waves are transverse; i.e. the electric and magnetic fields are each perpendicular to the direction that the wave travels. At least in air or a vacuum. TEM01 TEM01
"TEM" stands for Transverse Electric Magnetic. The numbers after that tell you how many "zeros" there are in the intensity as you make a cut through the pattern. The TEM00 mode has no zeros in the middle of the distribution in either the horizontal or vertical axes (or any other pair of perpendicular axes) TEM02 TEM02
In the TEM03 distribution there are no zeros in one axis but there are three in the axis perpendicular to that ... and so on it goes. TEM03 TEM03
These pictures were obtained with a small "microchip" Neodymium laser with the Nd3+ions embedded in an Yttrium Vanadate (YVO) host crystal. A small portion of the beam was split off and shone onto a CCD camera to record the intensity distributions. TEM13 TEM13

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