I have no problem with Planck's abstract idea of a photon being a ''quantum of action''. For the helical solenoid model the “hidden rotation” takes 2 forms: the large radius (R) rotation of the photon's helical form around its direction of travel, and the solenoidal rotation within the helical tube (small radius r). Both rotations are inter-related.

The well-known inverse relationship between frequency and wavelength is problematic when it comes to refraction, because here wavelength is shortened (or lengthened) and yet frequency remains the same (energy E = hν [or hf using your notation] is preserved, and thus frequency is unchanged). Thus the velocity of light is considered to change, meaning that the speed of light “c” can only be considered constant in a specified medium but varies by medium.

The helical solenoid model provides a physical explanation (rather than a purely mathematical one) as follows for light moving from a lower refractive index medium to a higher: the helical coil is slightly compressed, effectively increasing the turns per unit length (N), with the length of the coil (as laid out straight) being unchanged. Thus the solenoidal flow of energy, moving at the speed of light in a (proverbial) vacuum, remains unchanged but the linear speed of the overall helical solenoid coil is reduced.

Referring to

''Kind of beautiful'', but with many abstract ideas

The beauty to which I was referring was the helical solenoid model explanation of refraction as expanded upon above. And Science is full of abstract ideas and has greatly benefited from them. Many are called hypotheses or theories: and many being quite speculative and innovative. They are eventually proved or dis-proved by experimentation and further observation.

In the referenced paper I have attempted to address as many experimental results and observations as possible, providing a physical rather than a mathematical explanation: it would be good to have a more substantial mathematical underpinning of the concepts and hopefully that will eventuate (could be a good pet project for a budding mathematician).