  We discuss non-thermal emission mechanism of the Crab-like pulsars with both
a two-dimensional electrodynamical study and a three-dimensional model. We
investigate the emission process in the outer gap accelerator. In the
two-dimensional electrodynamical study, we solve the Poisson equation of the
accelerating electric field in the outer gap and the equation of motion of the
primary particles with the synchrotron and the curvature radiation process and
the pair-creation process. We show a solved gap structure which produces a
consistent gamma-ray spectrum with EGRET observation. Based on the
two-dimensional model, we conduct a three-dimensional emission model to
calculate the synchrotron and the inverse-Compton processes of the secondary
pairs produced outside the outer gap. We calculate the pulse profiles, the
phase-resolved spectra and the polarization characteristics in optical to
$\gamma$-ray bands to compare the observation of the Crab pulsar and PSR
B0540-69. For the Crab pulsar, we find that the outer gap geometry extending
from near the stellar surface to near the light cylinder produces a complex
morphology change of the pulse profiles as a function of the photon energy.
This predicted morphology change is quite similar with that of the
observations. The calculated phase-resolved spectra are consistent with the
data through optical to the $\gamma$-ray bands. We demonstrate that the
10$\sim$20 % of the polarization degree in the optical emissions from the Crab
pulsar and the Vela pulsar are explained by the synchrotron emissions with the
particle gyration motion.
