Since the launch of the Fermi/LAT gamma-ray telescope, several hundred radio-loud gamma-ray pulsars have been detected, many belonging to millisecond pulsars but some also to the young pulsar population (spin periods longer than 30 ms). Observing simultaneously pulsed radio and gamma-ray emission from these stars helps to constrain the geometry and radiation mechanisms within their magnetosphere and to localize the photon production sites.

In this presentation we show how time-aligned gamma-ray light curve fitting of young and millisecond pulsars constrains their magnetospheric configuration, namely the magnetic axis and line-of-sight inclination angles. To this end, we assume a dipolar force-free magnetosphere where radio photons emanate from high altitudes above the polar caps and gamma-rays originate from the pulsar striped wind region. Further constraints were obtained from radio polarization measurements, if available, following the rotating vector model, including aberration and retardation effects.

We find a good agreement between our emission model and the time-aligned single- or double-peaked gamma-ray pulsar observations. We deduce the magnetic inclination angle and the observer line-of-sight with respect to the rotation axis within a small error bar. We are currently extending our analysis to the thermal and non-thermal X-ray emission using observations from NICER, NuSTAR, RXTE and XMM. Moreover the recent launch of the IXPE polarimeter is opening a new window to better understand the physics of the X-ray mechanisms and propagation within the magnetosphere. In a last part, we discuss the strength of pulsar population synthesis to put constraints on the neutron star evolution properties, from their birth place to their current position.