  A search for Lorentz violation in electrodynamics was performed by measuring
the resonant frequency difference between two counterpropagating directions of
an optical ring cavity. Our cavity contains a dielectric element, which makes
our cavity sensitive to the violation. The laser frequency is stabilized to the
counterclockwise resonance of the cavity, and the transmitted light is
reflected back into the cavity for resonant frequency comparison with the
clockwise resonance. This double-pass configuration enables a null experiment
and gives high common mode rejection of environmental disturbances. We found no
evidence for odd-parity anisotropy at the level of $\delta c /c \lesssim
10^{-14}$. Within the framework of the Standard Model Extension, our result put
more than 5 times better limits on three odd-parity parameters
$\tilde{\kappa}^{JK}_{o+}$ and a 12 times better limit on the scalar parameter
$\tilde{\kappa}_{\tr}$ compared with the previous best limits.
