The Lagrangian for electromagnetic waves shows that its energy has a kinetic part as well as a potential part (just like everything else). The potential part only exists in a medium whereas in the vacuum all energy in electromagnetic waves are kinetic.
Similar formulation exists for mechanical (e.g. elastic) waves. In this case, I understand easily that the kinetic energy is simply the intensity of shaking/amplitude of waves (e.g. in an earthquake) whereas the potential energy is the so-called strain energy which is basically just the potential energy associated for a spring.
Returning back to electromagnetic waves, I can understand that the kinetic energy is, again, the amplitude of the waves that is manifested by e.g. light brightness or heat (which originates from the motion/collision of particles). However, I am having a hard time thinking of an intuitive interpretation for potential energy for electromagnetic waves. I only know that this only exists in non-vacuum space. So, what is the potential energy for all the electromagnetic waves we create here on earth, which are traveling in the air that is non-vacuum. Are there examples of familiar electromagnetic waves that does not have (or have very little) kinetic energy but is purely all potential energy?