Looking at Optics at a New Angle: it's Magic!

The magic angle −54.7356°- is manifested in solid state and nuclear physics as an angle for which certain properties are optimized. We show that this angle plays a role in optics per se. We find that an azimuthally polarized vortex has maximum focused intensity and spin density for a narrow input ring aperture subtended by this angle. We hope this research will entice the optical community to seek other phenomena optimizing light properties at the magic angle and find its applications.