  We report the measurement of hyperfine splitting in the $7d$ $^{2}D_{3/2}$
state of $^{133}$Cs using high resolution Doppler-free two-photon spectroscopy
in a Cs vapor cell. We determine the hyperfine coupling constants $A =
7.3509(9)$ MHz and $B = -0.041(8)$ MHz, which represent an order of magnitude
improvement in the precision. We also obtain bounds on the magnitude of the
nuclear magnetic octupole coupling constant $C$. Additionally, we measure the
ac Stark shift of the $6s$ $^{2}S_{1/2} \rightarrow 7d$ $^{2}D_{3/2}$
transition at 767.8 nm to be $-49 \pm 5$ Hz/(W/cm$^2$), in agreement with
theoretical calculations. We further report the measurement of collisional
shift [$-32.6 \pm 2.0$ kHz/mTorr] and pressure broadening for the individual
hyperfine levels of the $6s$ $^{2}S_{1/2} \rightarrow 7d$ $^{2}D_{3/2}$
transition. These measurements provide valuable inputs for analysis of
systematic effects in optical frequency standards based on the cesium $6s$
$^{2}S_{1/2} \rightarrow 7d$ $^{2}D_{3/2}$ two-photon transition
