14 February 2007 Dome-shaped microresonators and the Born-Oppenheimer method
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Abstract
Numerical studies of the vector electromagnetic fields in plano-concave microresonators have recently revealed that a photonic analogue of spin-orbit coupling can occur in paraxial geometries. Laguerre-Gauss modes with circular polarization are then no longer the correct eigenstates, even if the resonator is axially symmetric. A crucial role in this effect is played by the presence of a boundary (e.g., a Bragg mirror) whose reflectivity at non-normal incidence is polarization-dependent. Aiming for an analytical treatment that can incorporate both form birefringence and non-paraxiality, we explore the Born-Oppenheimer method as an alternative to the paraxial approximation. The conditions for the validity of these two approaches are different, but in a regime where they overlap we show that all the major results of paraxial theory can also be derived from the Born-Oppenheimer method. We discuss how this new approach can incorporate the Bragg stack physics in a way that can overcome the limitations of paraxial theory.
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Jens U. Nöckel, Jens U. Nöckel, David H. Foster, David H. Foster, } "Dome-shaped microresonators and the Born-Oppenheimer method", Proc. SPIE 6452, Laser Resonators and Beam Control IX, 64520V (14 February 2007); doi: 10.1117/12.714306; https://doi.org/10.1117/12.714306
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