Saturated absorption technique used in Potassium microcell for magnetic field sensing

It is demonstrated that the use of a Micrometric Thin ${}^{39}$K vapor Cell (MTC) and Saturated Absorption spectroscopy (SA) allows to form narrow atomic lines in transmission spectrum without unwanted Cross-Over (CO) resonances. Another important feature is the small characteristic magnetic field value $B_0=A_{hf}\mathrm{/}{\mu }_B$ of ${}^{39}$K, significantly smaller than for Rb and Cs. As a consequence, decoupling of $J$ and $I$ can be observed at relatively low magnetic fields $\sim$300 G, which results in the formation of two groups of four well-spectrally-resolved and equidistantly-positioned atomic transitions having the same amplitude (each group corresponds to a given circular polarization ${\sigma }^{\pm }$) which we record using a simple experimental setup with a linearly polarized tunable diode-laser and a longitudinal magnetic field obtained with two permanent magnets. Fabrication of a MTC is much easier than the fabrication of the ${}^{39}$K nanocells used in our previous works. A simple method to determine the magnitude of a wide range of B-fields with a spatial resolution of 30 $\mu$m is presented, which is intrinsically calibrated and does not require a frequency reference.