I have a question in Electromagnetics, precisely about non-uniform plane waves. In the lecture, the professor made a strange assumption, he first used two of Maxwell's equations to get an expression for E and H (which he called E1 and H1). Then he used the remaining two to derive what he called E2 and H2. He also defined the complex wave number k. Then he stated that if alpha (the attenuation) was zero, the wave would be a uniform plane wave (Okay I understand this, but ..) then he said that if alpha was not zero and alpha was perpendicular (why perpendicular? why not just "at an angle"?) to beta, the wave is a non-uniform plane wave. Okay, I think I understand the meaning of giving alpha and beta directions. I also understand that if there is an angle between them, then planes of constant phase wouldn't coincide with planes of constant amplitude. Therefor the wave wouldn't be uniform. Meaning, any plane of constant phase would contain points of different amplitudes. What I don't understand is what he calls E1, E2, H1, H2. How can Maxwell's equations give different values for the same quantity!? I know that the four equations are not independent, but can they contradict? What “is” E1 and E2? And which is the one that's actually there in space? Another question, k is a complex vector, I understand. But I can't imagine it's orientation in space when alpha and beta aren't in the same direction. I know that the wave propagates – by definition – in the direction of beta. But what about k? What “is” k?? if k = (3 + 2j) ax + (1 – 5j) ay + (4 + 10j) az for example. How would such a quantity point in space? I uploaded the part of the lecture I talked about. Thanks in advance!