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5.4: Propagation of a Uniform Plane Wave in an Arbitrary Direction
https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_II_(Ellingson)/05%3A_Wave_Reflection_and_Transmission/5.04%3A_Propagation_of_a_Uniform_Plane_Wave_in_an_Arbitrary_Direction
In this representation, ${\bf r}$ is the position at which $\widetilde{\bf E}$ is evaluated, $\hat{\bf e}$ is the reference polarization expressed as a unit vector, and ${\bf k}$ is the unit v...In this representation, ${\bf r}$ is the position at which $\widetilde{\bf E}$ is evaluated, $\hat{\bf e}$ is the reference polarization expressed as a unit vector, and ${\bf k}$ is the unit vector $\hat{\bf k}$ in the direction of propagation, times $\beta$ ; i.e.: $\hat{\bf e} = \left(\hat{\bf e}\cdot\hat{\bf x}\right)\hat{\bf x} + \left(\hat{\bf e}\cdot\hat{\bf y}\right)\hat{\bf y} + \left(\hat{\bf e}\cdot\hat{\bf z}\right)\hat{\bf z} \nonumber$

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