Mathematical analysis of whispering gallery modes in graded index optical micro-disk resonators Stéphane Balac, Monique Dauge, Yannick Dumeige, Patrice Féron and Zoïs Moitier Eur. Phys. J. D, 74 11 (2020) 221 Published online: 01 November 2020 DOI: 10.1140/epjd/e2020-10303-5