= Polarization of Zeeman components
Viewed perpendicular to the <magnetic field>, the <normal Zeeman effect> has a $\pi$ component with <linear polarization> parallel to the <magnetic field> and two $\sigma$ components polarized perpendicular to it. Along the <magnetic field>, $\pi$ vanishes and the $\sigma$ pair has opposite <circular polarizations>. <Pieter Zeeman> described these geometry-dependent patterns in his lecture.<Light Radiation in a Magnetic Field by Pieter Zeeman>[Light Radiation in a Magnetic Field, University of Maryland mirror PDF p. 3, rectilinear/circular oscillator discussion and cadmium photographs]{ref}
The geometry can be derived from <electric dipole radiation>. Let the observation unit <vector> be $\mathbf n=(\sin\theta,0,\cos\theta)$, with $\theta$ measured from the <magnetic field>. Radiation retains only the transverse part of the oscillating <electric dipole moment> $\mathbf d$:
$$
\mathbf E_{\rm rad}\ \propto\ \mathbf d-\mathbf n(\mathbf n\cdot\mathbf d).
$$
For $\pi$, take $\mathbf d\parallel\hat{\mathbf z}$; its angular <light intensity> factor is $\sin^2\theta$, so it vanishes on axis. For $\sigma^\pm$, use normalized complex dipoles $(\hat{\mathbf x}\pm i\hat{\mathbf y})/\sqrt2$. Their angular factors are $(1+\cos^2\theta)/2$. Projection gives circles on axis, lines at $\theta=\pi/2$, and generally <elliptical polarization> between. These factors assume equal dipole magnitudes; actual line <light intensities> also depend on initial <quantum state populations>, transition strengths and collection geometry. No absolute handedness name is needed: it depends on the viewing and phase conventions.
\Image[/zeeman-viewing-direction-polarization.png]
{title=Viewing direction selects the Zeeman polarization pattern}
{description=Original projection diagram with the magnetic field vertical. The top panels show electric-field traces as seen by transverse and axial observers. The lower plot gives calculated dipole angular factors for equal dipole magnitudes; it is not a measured spectrum or an assumption of equal state populations.}
A transverse <polarizer> can separate $\pi$ from $\sigma$ even before the <spectral line> components are fully resolved. Along the <magnetic field>, a <quarter-wave plate> followed by a <polarizer> converts the two opposite <circular polarizations> into distinguishable linear settings. This explains why polarization analysis carried information beyond a small increase in line width.
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