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The so-called spin is circular polarization of light,that is the electric field rotates in either direction normal to propagation

Is it known or is there any theory about how fast the field rotates? does it make a circle in a second or in the time the oscillation takes place (or even less)? In other word does a $10^{12}\,\mathrm{Hz}$ photon spins $100$ times less than a $10^{14}\,\mathrm{Hz}$ one? Is there an explanation why the 'spin' is always $1\cdot h$ for all frequencies?

EDIT

does the direction of the spin alternate as the field goes from plus to minus and viceversa?

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This is correct. Circular polarisation results from photon spin. This was experimentally proven by Beth in 1935. There is however a problem. Electromagnetic spin is incompatible with gauge invariance. This problem is usually not discussed in lectures and text books. An exception is Jackson, Electrodynamics, which touches on the topic in some problem in some advanced chapter (7.19).

If you want to know more read my peer reviewed paper on the subject. I opted to abandon gauge invariance for this very reason. I proved that this leads to a fully accurate and elegant theory of electromagnetism. See https://arxiv.org/abs/physics/0106078. The work of Beth is in ref. 15.

As to you question the rotation frequency is equal to the oscillation frequency. All angular momentum is quantized in units of $\hbar$. The reason is unknown.

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    $\begingroup$ How can circular polarization result from photon spin when circular polarization exists classically and spin does not? $\endgroup$ – G. Smith Nov 2 at 18:14
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    $\begingroup$ Does this Wikipedia article explain why the quantization is what it is? $\endgroup$ – Aaron Stevens Nov 2 at 18:22
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    $\begingroup$ The question did not ask about gauge invariance, yet this answer is mostly about that. $\endgroup$ – G. Smith Nov 2 at 18:41
  • $\begingroup$ @G.Smith Circular polarization is a classical limit of a large number of photons with the same direction of spin. This fact explains how transverse waves are possible without a medium (aether). Spin and polarization are the same physics described by two different mathematical models, classical and quantum. $\endgroup$ – safesphere Nov 2 at 18:43
  • $\begingroup$ @safesphere Classical EM exists independently and does not have to be regarded merely as the classical limit of QED. $\endgroup$ – G. Smith Nov 2 at 18:45

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