In this work we perform polarization spectroscopy of erbium atoms in a hollowcathode lamp (HCL) for the stabilization of a diode laser to the 401-nmtransition. We review the theory behind Doppler-free polarization spectroscopy,theoretically model the expected erbium polarization spectra, and compare thenumerically calculated spectra to our experimental data. We further analyze thedependence of the measured spectra on the HCL current and the peak intensitiesof our pump and probe lasers to determine conditions for optimal laserstabilization.
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