Laser Modes
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The fundamental TEM00 mode is only one of many transverse
modes that satisfy the round-trip propagation criteria described in the section on
Gaussian Beam Propagation
. The figure below shows examples of the primary lower-order
Hermite-Gaussian (rectangular) solutions to the propagation equation.
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Low-order Hermite-gaussian resonator modes |
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Note that the subscripts n and
m in the Eigenmode TEM
nm are correlated to the number of
nodes in the x and
y directions. In each case, adjacent
lobes of the mode are 180° out of phase. The propagation equation can also be written in cylindrical form in terms of radius (r) and angle (f). The eigenmodes (Erf) for this equation are a series of axially symmetric modes, which, for stable resonators, are closely approximated by Laguerre-Gaussian functions, denoted by TEMrf. For the lowest order mode, TEM00, the Hermite-Gaussian and Laguerre-Gaussian functions are identical, but for higher order modes, they differ significantly, as shown in the figure below. |
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Low-order axisymetric resonator modes |
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The mode, TEM01*, also known as the "bagel" or "doughnut"
mode, is considered to be a superposition of the Hermite-Gaussian
TEM10 and TEM01 modes, locked in phase
quadrature. In real-world lasers, the Hermite-Gaussian modes predominate since strain, slight misalignment, or contamination on the optics tends to drive the system toward rectangular coordinates. Nonetheless, the Laguerre-Gaussian TEM10 "target" or "bulls-eye" mode is clearly observed in well-aligned gas-ion and helium neon lasers with the appropriate limiting apertures. |
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| Optics Guide Copyright 2002 Melles Griot Inc. |