Modal Patterns

To look at the mode patterns, Jim and I placed a fine hair inside the laser cavity and scattered some of the beam.  This caused all modes but one to drop out.  The modes most affected by the scattering were unable to achieve threshold gain.  The shape of the modes depends mostly on the size and curvature of the mirrors at the ends of the cavity.  Solutions for the mode patterns for a Gaussian beam inside the laser cavity include Hermitian polynomials and are of the form:

Here are some images of the patters we observed and a mathematical representation of the mode using Mathematica.

For   n = 4  m = 0:

For n = 1  m= 0:

For n = 3  m= 1:

Other Modes:    (0,1) , (2,0) , (3,0) , (5,0)

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