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I am currently studying Optics, fifth edition, by Hecht. Chapter 2.11 Twisted Light says the following:

enter image description here Such beams have what’s called an azimuthal ($\phi$) phase dependence. Looking down the central axis toward the source the phase changes with angle, just as the time on a clock face changes with the angle $\phi$ between the vertical 12–6 line and the minute hand. If a component-wave peak occurs at 12, as in Fig. 2.32, a trough might occur directly beneath the axis at 6. Examine the diagram carefully, noticing that as it goes from 12 to 1 to 2 to 3 and so on the wavelets advance. Their phases are all different on the slice; they’re each shifted successively by $\pi/6$. The disc-shaped slice cuts across the beam but it is not a surface of constant phase, and the overall disturbance is not a plane wave. Still the component sinusoids (all of wavelength $\lambda$) are correlated and all of their peaks lie along a spiral. enter image description here

What is meant by the component sinusoids being "correlated"? Does that mean that, since we know that the the wavelet phases shift successively by $\pi/6$, we can determine a relationship for how other wavelets would relate to any one?

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It sounds like you have the right idea. If I understand the description, I believe the correlation means that the component sinusoids in the beam have a fixed phase relationship to each other. This means that the surface of constant phase will be a fixed shape, a helix in this case. If the wavelets were not correlated, then you would have a scrambled surface of constant phase. As you moved from wavelet to wavelet, the phase would change randomly and you would lose the helix structure.

I hope this helps.

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