  We find a simple solution to the problem of probe laser light shifts in
two-photon optical atomic clocks. We show that there exists a magic
polarization at which the light shifts of the two atomic states involved in the
clock transition are identical. We calculate the differential polarizability as
a function of laser polarization for two-photon optical clocks based on neutral
calcium and strontium, estimate the magic polarization angle for these clocks,
and determine the extent to which probe laser light shifts can be suppressed.
We show that the light shift and the two-photon excitation rate can be
independently controlled using the probe laser polarization.
