Optimized bifocal conic section mirrors for single-wavelength sized focusing

Compressing all the energy of a laser pulse into a spatiotemporal focal cube edged by the laser center wavelength will realize the highest intensity of an ultra-intense ultrashort laser facility, which is called as the 3 regime or the 3 laser. Conic sections with two foci that can be used as secondary focusing mirrors to reduce the focal spot size from several wavelengths to one wavelength. We investigate the optimal focusing conditions for ellipse mirrors and propose hyperbola mirrors - another important conic section also with two foci - for single-wavelength sized focusing, which can also produce the same reduced minimum focal spots as ellipse mirrors.