Individual forms for specific polarizations

It is possible to transform this expression into a form which contains the polar and azimuthal angles 0 and O as defined in the tilted coordinate frame of Fig. 1.15. Applying spherical trigonometry, one then has the following relation between these angles 

Similarly, one obtains for completely linearly polarized light with the electric field vector along the y-direction (note cos = sin 0 sin O) 

The angular distribution pattern for completely right- or left-circularly polarized 

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