Absolute Optical Frequency Measurement of the Cesium<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="italic">D</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>Line 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 $\ensuremath{\alpha}$. The ${D}_{1}$ line has been compared with the fourth harmonic of a methane stabilized He-Ne laser at 88.4 THz ( $3.39\ensuremath{\mu}\mathrm{m}$). To measure the frequency mismatch of 18.39 THz between $4\ifmmode\times\else\texttimes\fi{}88.4\mathrm{THz}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}354\mathrm{THz}$ 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 ${\ensuremath{\alpha}}^{\ensuremath{-}1}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}137.0359924(41)$.