  Hermite-Gaussian (HG) laser modes are a complete set of solutions to the
free-space paraxial wave equation in Cartesian coordinates and represent a
close approximation to physically-realizable laser cavity modes. Additionally,
HG modes can be mode-multiplexed to significantly increase the information
capacity of optical communication systems due to their orthogonality. Since,
both cavity tuning and optical communication applications benefit from a
machine vision determination of HG modes, convolution neural networks were
implemented to detect the lowest twenty-one unique HG modes with an accuracy
greater than 99%. As the effectiveness of a CNN is dependent on the diversity
of its training data, extensive simulated and experimental datasets were
created for training, validation and testing.
