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Transverse modes have a field vector normal to the direction of propogation and are determined by the geometry of the laser or waveguide cavity and any limiting apertures. Waveguide modes are characterized as TE (transverse electric) with the electric vector normal, and TE (transverse magnetic) with the magnetic vector normal. In general, laser modes that do not have wall boundary conditions are designated TEM (transvers electric magnetic) with both vectors normal to the direction of propogation. The lowest order mode is the Gaussian TEM00. The appearance that higher-order modes take depends upon whether the limiting apertures are circular or rectancular. The three lowest-order modes for a circularly symmetric cavity are shown below
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The higher order the mode, the smaller the beam diameter (for a given geometry), the lower the divergence, and the smaller the M2 value (M2 = 1 for a pure TEM00 beam). The higher order the mode, the more uniform the beam cross-section. Very high-order-mode beams have a top-hat shape
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