  Vortex structure of $d_{x^2-y^2}$-wave superconductors is microscopically
analyzed in the framework of the quasi-classical Eilenberger equations. If the
pairing interaction contains an $s$-wave ($d_{xy}$-wave) component in addition
to a $d_{x^2-y^2}$-wave component, the $s$-wave ($d_{xy}$-wave) component of
the order parameter is necessarily induced around a vortex in
$d_{x^2-y^2}$-wave superconductors. The spatial distribution of the induced
$s$-wave and $d_{xy}$-wave components is calculated. The $s$-wave component has
opposite winding number around vortex near the $d_{x^2-y^2}$-vortex core and
its amplitude has the shape of a four-lobe clover. The amplitude of
$d_{xy}$-component has the shape of an octofoil. These are consistent with
results based on the GL theory.
