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Why we always consider the direction of propagation of EM wave along $z$-axis also rotation along $z$-axis in discussing many physics phenomenon? Does it helps in simplification of expressions or something else?

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You have to pick some direction. Why pick $\frac{\sqrt{2}\hat x-\sqrt{3}\hat y+4\hat z}{\sqrt{21}}$ when you can pick something simple like $\hat z$?

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It is often not stressed enough that the physical system comes first and then we introduce the coordinates, not the other way around. It's not that the EM wave propagates along the $z$-axis, but, instead, we choose to name the direction of the EM wave propagation "$z$-axis".

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