When light is an equal mix of all visible frequencies, we call it white light.
By analogy, sound that is a mix of all audible frequencies is called white noise.
For sound, there is an additional concept of Brownian noise, also called red noise, whose name derives from the "random walks" of particles undergoing Brownian motion. Brown noise sounds "smoother" and lower pitched (think ocean waves) than white noise (think hard rain), due I would assume to its less extreme shifts in frequency.
So, by direct analogy: Brownian light should also exist.
Since light is a transverse wave with polarization states not found in compression-only sound waves, I surmise that at least three distinct forms of Brownian light are possible:
Brownian-frequency light (BF light)
Brownian-polarization light (BP light), and
Brownian-frequency-and-polarization light (BFP light), in which the random walk takes place within a space where frequency and polarization are orthogonal axes.
Surprisingly, none of the ideas show up readily on a Google or Google Scholar search.
While that could be due to general recognition that noise types apply to any form of signal, one might think that the special case of human-visible would merit some special attention. Also, since the polarization and frequency-plus-polarization variants of Brownian state walks are not immediately obvious when starting from the sound analogy, they would need to be called out explicitly for light.
So, does anyone know if these ideas exist already and have been studied?
Is there a way generate BF, BP, or BFP light, e.g. with lasers?
Might the variants of Brownian light have any useful or interesting properties, e.g. for optical communications or signal encryption?
And finally: Humans can't see polarization, but they can certainly see frequencies. So, what would Brownian frequency light look like? I'm guessing red due to the way the Brownian spectrum is weighted. Perhaps that is why Brownian noise is also called "red noise"?