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The left panel shows the beam in 3-D space. The top panel shows the amplitude/intensity profile of the beam and the bottom panel shows the phase of the electric field.

The following visualisation shows Hermite-Gaussian (HG) mode solutions to the paraxial wave equation. The field amplitude at any plane along the beam axis is proportional to \[U(x, y) \propto H_n H_m \exp(-i (n + m) \arctan(z/z_R)) \] where \(H_n\) are the Hermite polynomials, \(z\) is the distance from the beam focus, \(z_R\) is the Rayleigh range and \(n\) and \(m\) are the mode order parameters.