  Gamma-rays from pulsars can be efficiently attenuated in their magnetospheres
via the mechanism of single-photon pair production and also the exotic QED
process of photon splitting, which become prolific in fields approaching the
quantum critical value of $B_{cr}=4.41\times 10^{13}$ Gauss. Recently we have
published results of our modelling of strongly-magnetized $\gamma$-ray pulsars,
which focused on the escape or attenuation of photons emitted near the pole at
the neutron star surface in dipole fields, in a Schwarzschild metric. We found
that pair production and splitting totally inhibit emission above around 10--30
MeV in PSR1509-58, whose surface field is inferred to be as high as
$0.7B_{cr}$. Our model pulsar spectra are consistent with the EGRET upper
limits for PSR1509-58 for a wide range of polar cap sizes. Here we review the
principal predictions of our attenuation analysis, and identify how its
powerful observational diagnostic capabilities relate to current and future
gamma-ray experiments. Diagnostics include the energy of the gamma-ray turnover
and the spectral polarization, which constrain the estimated polar cap size and
field strength, and can determine the relative strength of splitting and pair
creation.
