Tight focusing of plane waves from micro-fabricated spherical mirrors

We derive a formula for the light field of a monochromatic plane wave that is truncated and reflected by a spherical mirror. Our formula is valid even for deep mirrors, where the aperture radius approaches the radius of curvature. We apply this result to micro-fabricated mirrors whose size scales are in the range of tens to hundreds of wavelengths, and show that sub-wavelength spot sizes can be achieved. This opens up the possibility of scalable arrays of tightly focused optical dipole traps without the need for high-performance optical systems.