electromagnetism - Modes in waveguides

What is the meaning of Modes in waveguide? With what physical property of the Electromagnetic wave does it deal with? I have just started with parallel plane waveguide and in that case the constant m- was called Mode of the guide so was curious to know the physical significance of it, other than being a constant in the solution of the Differential Equation. I have also heard about single and multimode fibers in optical communication. Are they the same?

Answer

The modes of a waveguide refer to the distribution of the electrical and magnetic fields across the cross-section of the waveguide.

The electric field going to (roughly) zero at high-conductivity surfaces (like the inner and outer conductor of a coaxial line) places boundary conditions on the differential equations describing the waveguide behavior. This leads to patterns in the way the fields distribute themselves across the waveguide area. If a certain E/M field pattern can propagate along the waveguide without changing, we call that a mode of the waveguide.

Generally there will be only one propagating mode at low frequencies, and additional modes will be able to propagate as the signal frequency increases.

The waveguide modes are important because different modes tend to propagate at different rates along the z-axis of the waveguide. Generally you want to operate a waveguide at a frequency where only a single mode is supported. At higher frequencies, a single pulse input into the guide might exit the other end highly distorted due to the different propagation velocities of the different modes.

Different mode structures can also create reflections at the connection between two transmission lines, even if both transmission lines have the same characteristic impedance.

I have also heard about single and multimode fibers in optical communication. Are they the same?

Yes, it's essentially the same. Of course, the frequencies at play are very different. And the boundary conditions are created by changes in dielectric constant of the material rather than conductive surfaces.