I am having trouble understanding the concept of 'frequency' of a signal in an electrical sense in a wire vs the concept of 'frequency' in the electromagnetic sense in a fibre optic cable. Are these the same thing? The electricity travelling through a wire is not the same physical concept as the electromagnetic wave travelling through a fibre optic cable, right?
Do we treat them the same when we calculate the Shannon limit? I.e. can I look at the range of optical frequencies (wavelengths) that can be transmitted through an optic fibre and compare it to the range of electrical frequencies that can be transmitted through a wire, and compare them?
How does generating pulses of light compare to encoding signals with voltage changes?
Best Answer
Strictly speaking, to James Clerk Maxwell they're all the same thing. Discarding bizarre quantum witchcraft, Maxwell's equations applied rigourously work from DC to cosmic rays, it's just we normally use approximations when dealing with various slices of the spectrum.
Broadly, there are three frequency ranges we deal with in electronics:
Low frequency: where we can assume the wavelengths of the signals are much larger than both the structures we use to transmit them and the devices we use to process them. In this case, the signal generally stays confined to the conductor, and we also don't have to worry about reflections in circuits.
Radio frequency and microwave: There's essentially two cases here. From a few MHz up to around 1 GHz or so, the wavelengths are on the same scale as the lengths of conductor we use to ferry them around. In this case, we have to start to worry about reflections and applying our transmission line equations. Interestingly, the signals involved on the higher end of the scale don't travel in the conductor - for example, a signal on coaxial cable is predominately travelling as a wave in the gap between the core and the sheath. This is why the choice of cladding material can change a cable's velocity factor. Above 1GHz or so (microwave scale), things start to get more annoying, because your wavelength starts to approach the scale of the devices you use to process the signal. This usually requires serious FEM modeling to address.
Optical frequency: Once the frequencies get high enough, the wavelengths are so small that we can start using optical approximations like Snell's law. On this scale, transmission is actually easier than RF calculations-wise, but the engineering that goes into device engineering is much harder.
All three cases above agree with Maxwell's equations, they just use their own simplifications where necessary.
EDIT: I completely missed the second part of your question. I suppose, yes, theoretically you could modulate light up to the shannon limit, but the electronics to achieve that don't exist and might never exist due to the physical challenges involved. Most fiber systems use something called Wavelength Division Multiplexing. Essentially, each channel is assigned a wavelength (a color) and then pulsed to encode a digital signal. This way, you can pack many channels onto a single fiber. You might think of this as the fiber equivalent to frequency division multiplexing. Previously, only one wavelength was used, but the invention of a black magic device called an Erbium Doped Fiber Amplifier made WDM possible.