  Synchrotron radiation is widely considered as the origin of the pulsed
non-thermal emissions from rotation-powered pulsars in optical and X-ray bands.
In this paper, we study the synchrotron radiation emitted by the created
electron and positron pairs in the pulsar magnetosphere to constrain on the
energy conversion efficiency from the Poynting flux to the particle energy
flux. We model two pair creation processes, two-photon collision which
efficiently works in young $\gamma$-ray pulsars ($\lesssim10^6$ yr), and
magnetic pair creation which is the dominant process to supply pairs in old
pulsars ($\gtrsim10^6$ yr). Using the analytical model, we derive the maximum
synchrotron luminosity as a function of the energy conversion efficiency. From
the comparison with observations, we find that the energy conversion efficiency
to the accelerated particles should be an order of unity in the magnetosphere,
even though we make a number of the optimistic assumptions to enlarge the
synchrotron luminosity. In order to explain the luminosity of the non-thermal
X-ray/optical emission from pulsars with low spin-down luminosity $L_{\rm
sd}\lesssim10^{34}$ erg s$^{-1}$, non-dipole magnetic field components should
be dominant at the emission region. For the $\gamma$-ray pulsars with $L_{\rm
sd}\lesssim10^{35}$ erg s$^{-1}$, observed $\gamma$-ray to X-ray and optical
flux ratios are much higher than the flux ratio between curvature and the
synchrotron radiations. We discuss some possibilities such as the coexistence
of multiple accelerators in the magnetosphere as suggested from the recent
numerical simulation results. The obtained maximum luminosity would be useful
to select observational targets in X-ray and optical bands.
