Absolute Optical Frequency Measurement of the CesiumD1Line with a Mode-Locked Laser

We have measured the absolute optical frequency of the cesium $D_1$ line at 335 THz (895 nm). This frequency provides an important link for a new determination of the fine structure constant $\alpha$. The $D_1$ line has been compared with the fourth harmonic of a methane stabilized He-Ne laser at 88.4 THz ( $3.39\mu \mathrm{m}$). To measure the frequency mismatch of 18.39 THz between $4\times 88.4\mathrm{THz}=354\mathrm{}\mathrm{THz}$ and the $D_1$ line a frequency comb spanning around 244 000 modes of a Kerr-lens mode-locked laser was used. We find 1 167 688 (81) kHz for the hyperfine splitting of the ${6P}_{1/2}$ state and 335 116 048 807 (41) kHz for the hyperfine centroid from which we derive ${\alpha }^{-1\mathrm{}}=137.035\mathrm{}9924\left(41\right)$.