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Caveat: I don't know much about OAM. In my mind, I'm thinking of it as analoguous to CDMA for radio signals, where you can have many different signals occupy the same frequency band, but they correlate to different (orthogonal, ideally) codes, so that adding one more signal shouldn't affect any of the others. In reality, it takes a finite amount of power (energy) to transmit data, and imprecision in your equipment does create some "leaking" between channels.

If you picture a "traditional" signal as a single bar (from a bar graph), and picture OAM as any number of these bars, but splaying out from a center point radially into a circular form, you can see a theoretically infinite number of bars. 360 of them, spaced 1 degree apart, then 720 spaced at half-degree intervals, etc. (As I understand the article, they also spin these at certain speeds, which makes sense for practical reasons, but isn't necessary for the analogy) The problem becomes when your equipment can't distinguish between two neighbouring bars (or the transmitting equipment lets the bars leak, or something about the channel, eg turbulence, confuses matters).

So in mathworld, it may be theoretically infinite, but in the real world we'll hit limits. There will be a limit due to quantum mechanics because energy differences can only be measured to a certain precision. A limit due to physics of noise, and a limit due to what we can practically realize (and all the ugliness of dealing with a planet with a pesky atmosphere and temperature changes).

In a trivialized mathworld, many calculations are useless for the real world. Trivializing the same way, we might as well ignore the capacitance of wires, cross-talk, and general EM noise and claim that wires can transfer at infinite bandwidth. Or say that air has no resistance, therefore we can launch a cannonball into orbit around the earth at roughly sea-level.

This is no different. It's pointless hyperbole.

Both of these analogies are wrong. CDMA is unrelated to OAM. Think of CDMA as a way to trade-off effective bit-rate with signal power, even in noisy environments and a way to minimize cross-signal noise.

What you're describing is a description of polarization.

As to OAM, it's a bit hard to explain because it's difficult to visualize. Think about an ordinary radio wave going back and forth like a sine wave in a single plane. This is linearly polarized light. Now, with the same frequency and phase another photon could also be polarized at a different angle, say 90 deg. to the other photon. However, you can essentially combine both aspects of waves in varying degrees, creating elliptical and circularly polarized waves. You can think of that as the photon "spinning". OAM is on a different scale. Normally we think of light as traveling in purely straight lines other than the wave effects. However, take that model of a rotating photon wave-packet and at a larger scale imagine the photon "in orbit" along a trajectory, taking a cork-screw path.

Circularly polarized light is like a spinning football being thrown. Light with non-zero OAM is like a curve ball (although admittedly the analogy breaks down).

Fair 'nuff, and in general I don't like using analogies, precisely because they are imprecise or break down, as mine did. My main goal was to show that just because you can, in theory, overlay an infinite number of channels, doesn't mean there won't be very real limits on performance.

At first glance, I though OAM sounded like circular polarization with different angular velocities. Now your comment makes me think there's more to it. Maybe someday I'll get back on track for a physics degree, and I'll be able to think through it properly.

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