I'm reading about stationary waves in a cube with side of length $L$. The electric field is described from a vector $E$ where each component is of the type $sin(\frac{\pi}{L}n_{j}x_{j})$ and the author says that if I call $K=\frac{\pi}{L}(n_{1},n_{2},n_{3})$, where $n_{j}$ is natural, I have two polarizations for each $k$, "one for each orthogonal direction' Why?
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$\begingroup$ Could you refer us to the book you are reading? $\endgroup$– abirCommented Apr 2, 2021 at 13:26
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We are free to choose our coordinate system. Thus, let's choose the $z$ direction to be parallel to the wave vector, $\vec k \parallel\vec z$. Since the electro-magnetic field is transverse in nature, we further know that the electric field is perpendicular to the wave vector, $\vec k \perp \vec E$. Thus, we know that $\vec E$ must oscillate in the $xy$-plane. Finally, any oscillation in a plane can be described by the projection onto two independent vectors. These are two polarisations. Does this make sense to you?
