The discussion focuses on the conditions under which one can replace the del operator and the time derivative with the expressions ik and -iω in electromagnetic equations. This substitution is valid when the electromagnetic equations are linear and Cartesian coordinates are used, allowing for the decomposition of solutions into plane waves. However, in media where the conductivity tensor is generally nonlinear, this approximation holds true only for small amplitudes of electromagnetic waves, particularly in plasma physics. For large amplitudes, this technique is not applicable.
PREREQUISITESPhysicists, electrical engineers, and students studying electromagnetism and plasma physics, particularly those interested in wave propagation and linearity in electromagnetic equations.
Khashishi said:This works when the electromagnetic equations are linear and you are using Cartesian coordinates. In this case, you can decompose the solution into a sum of plane waves.
In media, the conductivity tensor is generally NOT linear, but it can be approximately linear for small amplitudes of electromagnetic waves. In plasma physics, we often solve for small amplitude plane wave solutions using this technique, but it isn't valid for large amplitudes.