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