Can an EM wave be both circularly polarized and horizontally polarized at once?

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Can an electromagnetic wave be both circular polarized and horizontal or E polarized at the same time?
 
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It can be a mix, such as 60% plane, 40% circular.
 
A circular polarized wave has both horizontal and vertical polarization, is this correct?
 
Completely circularly polarized light can be decomposed into two orthogonal linear components in quadrature. In general, any pure polarization state can be decomposed into two orthogonal basis states (linear, circular, elliptical, etc).