Photon Polarization
//Bead Panel// from a baby carrier, Bahau people. Borneo 19th century, 40 x 19 cm. From the Teo Family collection, Kuching. Photograph by D Dunlop.
Bead Panel from a baby carrier, Bahau people. Borneo 19th century, 40 x 19 cm. From the Teo Family collection, Kuching. Photograph by D Dunlop.

Let some photon $\, \gamma$ be characterized by a repetitive chain of events noted by $\, \Psi^{\gamma} = \left( \sf{\Omega}_{\sf{1}}, \sf{\Omega}_{\sf{2}}, \sf{\Omega}_{\sf{3}} \ \ldots \ \right)$. By definition photons are anti-symmetric particles, so $\sf{\Omega}$ can be parsed into two sets of quarks $\mathcal{A}_{\LARGE{\circ}}$ and $\mathcal{A}_{\LARGE{\bullet}}$ that are out of phase anti-particles of each other. Since they are anti-particles, these two sets have opposing radius vectors $\overline{\rho} \left( \mathcal{A}_{\LARGE{\circ}} \right) =- \, \overline{\rho} \left( \mathcal{A}_{\LARGE{\bullet}} \right)$. So their magnetic and electric radii have the same absolute values

$\rho_{m} = \left| \; \rho_{m}\left(\mathcal{A}_{\LARGE{\circ}} \right) \vphantom{\left(\mathcal{A}_{\LARGE{\circ}} \right)^{2}} \, \right| = \left| \; \rho_{m}\left( \mathcal{A}_{\LARGE{\bullet}} \right) \vphantom{\left(\mathcal{A}_{\LARGE{\circ}} \right)^{2}} \, \right|$

$\rho_{e} = \left| \; \rho_{e}\left(\mathcal{A}_{\LARGE{\circ}} \right) \vphantom{\left(\mathcal{A}_{\LARGE{\circ}} \right)^{2}} \, \right| = \left| \; \rho_{e}\left( \mathcal{A}_{\LARGE{\bullet}} \right) \vphantom{\left(\mathcal{A}_{\LARGE{\circ}} \right)^{2}} \, \right|$

Note that these are the radii of $\mathcal{A}_{\LARGE{\circ}}$ and $\mathcal{A}_{\LARGE{\bullet}}$ only, not for the photon as a whole. Nonetheless, we use them to characterize $\, \gamma$ by defining $\vartheta$ the polarization angle of the photon by

$\begin{align} \vartheta \equiv \arcsin{ \frac{\ \ \ \rho_{e}}{\sqrt{\rho_{m}^{2} + \rho_{e}^{2} \ \vphantom{\Sigma^{Sigma}} } } } \end{align}$ $0^{\large{\circ}} \le \vartheta \le 90 ^{\large{\circ}}$

Photons may be classified by this angle as noted in the accompanying table.

$\vartheta$ Polarization Type
$0^{ \large{\circ}}$ linear along the magnetic axis
$10^{ \large{\circ}} \sim 30^{ \large{\circ}}$ elliptically polarized
$45^{ \large{\circ}}$ a circularly polarized photon
$60^{ \large{\circ}} \sim 80^{ \large{\circ}}$ elliptically polarized
$90^{ \large{\circ}}$ linear along the electric axis


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