focusing by an arbitrary opening paraboloid mirror and its application in confocal scanning microscopy

Focusing of the plane wave with radially polarized electric field by an arbitrary opening paraboloid mirror is analyzed using a rigorous vectorial diffraction theory, i.e., Stratton-Chu integral. In the vicinity of the focus, far-field approximation conditions are used to simplify the derived integrals with sufficiently high accuracy. It is found that a noticeable deviation of the approximate integral, as characterized by a phenomenon of focal shift, from the exact integral can be observed when the maximum focusing semi-angle α below π/9. For α=π/2, the radial spot size reduces to below 0.40λ if cutting off the central segment, larger than π/4, of the paraboloid mirror. The sharp focusing property of the paraboloid mirror has the potential application in super-resolution confocal scanning microscopy. Specific confocal scanning arrangements are provided and remarked.