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This study is devoted to theory and first realization of a helical distributed feedback (DFB) laser. The theory emphasizes the group theoretic aspects of helical and linear periodic DFB lasers. It is demonstrated that the dispersion relations of the helical DFB modes are neither periodic nor necessarily symmetric with respect to the propagation constant. Nevertheless, DFB effects exist in helical as well as in linear periodic laser structures. Finally, the first experimental realization of a helical DFB laser is described.