  Results of a simulation of synchrotron-self Compton (SSC) emission from a
rotation-powered pulsar are presented. The radiating particles are assumed to
be both accelerated primary electrons and a spectrum of electron-positron pairs
produced in cascades near the polar cap. They follow trajectories in a slot gap
using 3D force-free magnetic field geometry, gaining pitch angles through
resonant cyclotron absorption of radio photons, radiating and scattering
synchrotron emission at high altitudes out to and beyond the light cylinder.
Full angular dependence of the synchrotron photon density is simulated in the
scattering and all processes are treated in the inertial observer frame.
Spectra for the Crab and Vela pulsars as well as two energetic millisecond
pulsars, B1821-24 and B1937+21 are simulated using this model. The simulation
of the Crab pulsar radiation can reproduce both the flux level and the shape of
the observed optical to hard X-ray emission assuming a pair multiplicity of
$M_+ = 3 \times 10^5$, as well as the very-high-energy emission above 50 GeV
detected by MAGIC and VERITAS, with both the synchrotron and SSC components
reflecting the shape of the pair spectrum. Simulations of Vela, B1821$-$24 and
B1937+21, for $M_+$ up to $10^5$, do not produce pair SSC emission that is
detectable by current telescopes, indicating that only Crab-like pulsars
produce significant SSC components. The pair synchrotron emission matches the
observed X-ray spectrum of the millisecond pulsars and the predicted peak of
this emission at 1 - 10 MeV would be detectable with planned Compton
telescopes.
