Today I read "Structural correlations in Gaussian random wave fields," an old PRE by Freund and Shvartsman. The authors analytically found the existence of correlations between the amplitude and phase gradients in random electromagnetic fields commonly known as speckle. Notably, while the amplitude and phase are not correlated at certain points, the amplitude is correlated to the gradient of the phase. Higher amplitudes usually are found with smaller phase gradients and vice-versa.
What's not clear to me is if this treatment works for vector fields or only scalar fields. Notably, I'm not sure what phase means for a random vector field.
Perhaps the authors make the assumption that the components of the vector are independent and thus a scalar treatment is sufficient, but I'm not sure that this is so.
A "lab notebook" about my life in science, programming, and philosophy.
