Theorem_circular_polarization_coeff.tex

%
% Copyright © 2018 Peeter Joot.  All Rights Reserved.
% Licenced as described in the file LICENSE under the root directory of this GIT repository.
%
\maketheorem{Circular polarization coefficients.}{thm:polarizationRewrite:700}{
The time domain representation of the field in \cref{eqn:polarization_circular:160} can be stated in terms of the total phase as
\begin{equation*}
F = \lr{ 1 + \Be_3 } \Be_1 \lr{ \alpha_\txtR e^{i\phi} + \alpha_\txtL e^{-i\phi} },
\end{equation*}
where
\begin{equation*}
\begin{aligned}
\alpha_\txtR &= \inv{2}\lr{ c_1 + i c_2 } \\
\alpha_\txtL &= \inv{2}\lr{ c_1 - i c_2 }^\dagger,
\end{aligned}
\end{equation*}
where \( c_1, c_2 \) are the 0,2 grade multivector representation of the Jones vector coordinates from \cref{dfn:polarizationRewrite:680}.
} % theorem