Photons in communications theory

Question

In engineering communications theory we switch between time and frequency domain interpretations. If a pulse centered at frequency F is shot out of a transmitter, it's limited time duration implies that it will have a bandwidth B (at 3dB drop off) but really a bunch of frequencies with intensities dropping off.

If it was a pure tone of frequency F, it will have infinite duration.

I don't get how this translates to the photon interpretation. How is it that we say the TX fired a pulse of some duration at frequency F? Did we really create photons at a whole bunch of frequencies centered around F?

I apologize if the question seems unclear.

Trying to understand connection between the on paper continuous time and frequency domain representations and discrete photon representations.

Answer 1

The short answer is yes. In fact it can even become limiting in optical communications systems.

The best and easiest example is a femtosecond laser. In fact to measure sure the pulse width of a femtosecond laser you can use a spectrometer to measure the spectrum convert that spectrum measured in wavelength into frequency and then use the Fourier transform to find how femtoseconds wide your pulse is. Just like in communication systems the best pulse you can get is a Fourier transform limited Gaussian pulse.

If you think a very fast telecommunications system operating at 80 GHz your pulse will be ‘wider’ due to side bands. If I recall correctly , this is one of the limitations of how close you can put wavelengths together in a dense wavelength division multiplexing optical fiber communications system.

If you look at coherence of different light sources it also comes into play. Fourier transform spectroscopy, Michelson interferometer and other instruments for example also essentially are using coherent nature of light as a electromagnetic wave.

Most detectors don’t use the coherent nature of light. Instead of acting like an antenna an electron is excited from the conduction band to the valence band and that process is proportional to the Intensity of the light instead of the electric field.

However for single photon detection you can heterodyne or homodyne the photon with a local oscillator. This hard to do well because of stability issues but works similar to radio waves.

Answer 2

In communication engineering at radio frequencies, the number of photons we could have counted (had we the time, resources and inclination) that make up a macroscopic signal pulse of electromagnetic radiation is so very, very huge and the energy carried by a single photon of, say, typical radio frequency wavelength is so very, very small that for purposes of calculation it is a waste of time to model the process with discrete photons and a convenient and perfectly accurate shortcut to model the process using EM waves with a certain frequency, amplitude, duration, and bandwidth instead.

I know that this is not a simple and direct answer to your question; the point I want to make is that trying to switch between analyzing a signal in terms of single photons and analyzing a signal in the frequency domain using fourier series isn't useful.