Our aim is to transpose the polarization control by mechanical stress, usually applied to single-mode fibers, to the (TM(01), TE(01), HE(21)(ev), HE(21)(od)) annular mode family. Nevertheless, the quasi-degeneracy of these four modes makes the situation more complex than with the fundamental mode HE(11). We propose a simple device based on periodic perturbation and mode coupling to produce the radially polarized TM(01) mode or at least one of the four modes at the extremity of an arbitrarily long fiber, the conversion to TM(01) mode being achievable by classical crystalline plates.