The role of Berry's geometric phase in the mode spectrum of a Fabry-Pérot resonator

• Published in: 2011 Conference on Lasers and Electro-Optics Europe and 12th European Quantum Electronics Conference (CLEO EUROPE/EQEC) p. 1
• Main Authors: Pinkse, P. W. H., Koch, M., Hagemann, B., Motsch, M., Zeppenfeld, M., Rempe, G.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.05.2011
• ISBN: 9781457705335; 1457705338
• DOI: 10.1109/CLEOE.2011.5943470

Berry's geometric phase is a universal phenomenon which appears naturally when dealing with three-dimensional rotations. Here we will demonstrate its unexpected role in the high-resolution transmission spectrum of a two-mirror Fabry-Pérot resonator. Using analytical three-dimensional vector solutions to Maxwell's equations in spheroidal coordinates, we have calculated the first-order corrections to eigenmodes and eigenfrequencies in a Fabry-Pérot resonator in the short-wavelength limit. Analogous to atomic spectra, these analytical expressions show the "fine structure" of the spectrum of an optical resonator. Especially for high-order transverse modes with large orbital angular momentum as the one shown in the figure, the consequences are striking, leading to series of intricate mode patterns with Laguerre-Gaussian character split by their total angular momentum.