Selective reflection from a Potassium atomic layer with a thickness as small as $lambda /13$

We demonstrate that a method using the derivative of the selective reflection signal from a nanocell is a convenient and robust tool for atomic laser spectroscopy, achieving a nearly Doppler-free spectral resolution. The recorded linewidth of the signal from a potassium-filled cell, whose thickness $ell$ lies in the range $350-500$ nm, is 18 times smaller than the Doppler linewidth ($sim 900$ MHz full width at half maximum) of potassium atoms. We also show experimentally a sign oscillation of the reflected signals derivative with a periodicity of $lambda/2$ when $ell$ varies from 190 to 1200~nm confirming the theoretical prediction. We report the first measurement of the van der Waals atom-surface interaction coefficient $C_3 = 1.9pm 0.3$ kHz$cdotmu$m$^3$ of potassium $4S_{1/2} rightarrow 4P_{3/2}$ transitions with the nanocells sapphire windows, demonstrating the usefulness and convenience of the derivative of selective reflection technique for cell thicknesses in the range $60 -120~$nm.