Fig . S1a represents the theoretical momentum - space polaritonic dispersion of the ring with a diameter of 3 m , in good agreement with the experimental data of Fig . 1c of the text . The polaritonic energy separates into multiple discrete coupled orbital modes ( COMs ) . This is obtained from a Fourier transform of the wavefunction ( , , ) into the energy domain in reciprocal space ( , , ) . Theoretically , the reciprocal - space dispersion is given by = | ( , , = 0)| 2 , which is a function of and E at = 0 .