Spin-Orbit Coupling in Optical Microcavities

Open-access Fabry-Perot microcavities are versatile tools that can resonantly trap light and thereby enhance light-matter interaction by the Purcell effect. The paraxial description predicts that the eigenmodes of such cavities are Hermite-Gaussian <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$HG_{nm}$</tex> modes that are characterized by a longitudinal quantum number <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$q$</tex> and a transverse order <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N=n+m$</tex> and that modes with the same <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(q,N)$</tex> labels are frequency degenerate in a rotation-symmetric cavity. But optical cavities with mirror radii and cavity lengths of only a few wavelengths don't operate in the paraxial limit. We will show that the eigen modes of such cavities are more complicated superpositions of HG-modes, superpositions with intriguing polarization patterns due to optical spin-orbit coupling. We will also demonstrate and quantify the role of other mode-shaping effects, like non-paraxial corrections to the propagation and astigmatic and spherical aberrations of the concave mirror.