Confusion about quantum optic modes -- How to gain intuition? I have started reading some materials on quantum optics and one concept I can't seem to wrap my head around is the concept of a mode. I'd appreciate if someone could point me towards some materials or provide an intuitive explanation for this concept:)
Thanks so much in advance.
 A: The concept of mode is not specific to quantum optics, but it's already present in classical electromagnetism and in other subfields of physics.
In electromagnetics, modes are functions that allow one to decompose the electromagnetic field in a Fourier series. In the language of Hilbert spaces, a set of modes is a (possibly orthonormal) basis for the electromagnetic field. If this basis of functions is adapted to the problem at hand, with its boundary conditions, the problem of determining the evolution (or the propagation) of the field in a linear electromagnetic system is greatly simplified because each mode propagates in space and time with a simple law and in linear media the propagated field equals the sum of the propagated modes. In this sense modes are eigenfunctions of partial differential equations with their boundary conditions.
In other contexts, modes are also called eigenstates or channels.
You can learn more about this in any book discussing electromagnetic transmission lines and cavities, e.g.
J. Schwinger et al., Classical electrodynamics, CRC PRess, 2018.
or, more advanced,
L. B. Felsen et al., Electromagnetic field computation by network methods, Springer, 2009.
