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The rotating vector model and radius-to-frequency mapping in the presence ofmultipole magnetic field in pulsars and magnetars are considered. Anaxisymmetric potential field is assumed. It is found that: (1) The radiationbeam in the case of multipole field is wider than the dipole case. This mayaccount the increasing pulse width at higher frequency of pulsars(anti-radius-to-frequency mapping). (2) The expression for the polarizationposition angle is unchanged. Only the inclination angle {\alpha} and phaseconstant {\phi}_0 will change. The angle between the rotational axis and lineof sight, and the position angle constant {\psi}_0 will not change. Whenfitting the varying position angle of magnetars, these constraints should beconsidered. The appearance and disappearance of multipole field may account forthe changing slope of position angle in the radio emitting magnetar SwiftJ1818.0-1607. Similar but more active process in magnetar magnetospheres mayaccount for the diverse position angle in fast radius bursts.

Rotating vector model and radius-to-frequency mapping in the presence of multipole magnetic field