We introduce ring lasers with continuous π-phase shifts in the second order distributed feedback grating. This configuration facilitates insights into the nature of the modal outcoupling in an optical cavity. The grating exploits the asymmetry of whispering gallery modes and induces a rotation of the far field pattern. We find that this rotation can be connected to the location of the mode relative to the grating. Furthermore, the direction of rotation depends on the radial order of the whispering gallery mode. This enables a distinct identification and characterization of the mode by simple analysis of the emission beam.