  We have developed an apparatus to search for the higher-order Lorentz
violation in photons by measuring the resonant frequency difference between two
counterpropagating directions of an asymmetric optical ring cavity. From the
year-long data taken between 2012 and 2013, we found no evidence for the light
speed anisotropy at the level of $\delta c/c \lesssim 10^{-15}$. Limits on the
dipole components of the anisotropy are improved by more than an order of
magnitude, and limits on the hexapole components are obtained for the first
time. An overview of our apparatus and the data analysis in the framework of
the spherical harmonics decomposition of anisotropy are presented. We also
present the status of the recent upgrade of the apparatus.
