Fabry-Perot microcavity spectra have a fine structure

Abstract

Optical cavities can support many transverse and longitudinal modes. A paraxial scalar theory predicts that the resonance frequencies of these modes cluster in different orders. A non-paraxial vector theory predicts that the frequency degeneracy within these clusters is lifted, such that each order acquires a spectral fine structure, comparable to the fine structure observed in atomic spectra. In this paper, we calculate this fine structure for microcavities and show how it originates from various non-paraxial effects and is co-determined by mirror aberrations. The presented theory, which applies perturbation theory to Maxwell's equations with boundary conditions, proves to be very powerful. It generalizes the effective 1-dimensional description of Fabry-Perot cavities to a 3dimensional multi-transverse-mode description. It thereby provides new physical insights in several mode-shaping effects and a detailed prediction of the fine structure in Fabry-Perot spectra.

Observation of microcavity fine structure

“…Also their degeneracy is lifted by perturbations which are intrinsic to microcavities. This analogy gives accurate predictions [4] that agree with the experiments presented in this paper.…”

“…The analogy of microcavity fine structure to that of atoms is surprisingly fruitful and gives new predictions [4] that agree with experiments. Figure 1 illustrates the perturbations in both systems.…”

“…We experimentally determine the radius of curvature from the transverse mode spacings between each N group, which are equidistant in the paraxial theory [19,20]. A more complete (nonparaxial) description from [4] contains the fine-structure splittings L,…”

“…More aspects of this model are described in Ref. [4] The explicit model for the N = 4 group is shown in Appendix A.…”

“…The relativistic correction in atoms is a quartic p 4 correction to the momentum, which shifts all modes proportional to 2 . As a direct analogy, a nonparaxial momentum correction k 4 ⊥ is required for microcavities with large opening angles [11,17], which also shifts all modes proportional to 2 . In addition, the nonparaxial theory contains a r 4 correction from higher-order Taylor expansions of the mirror and wavefront shape [18].…”