  Artificially engineered geometric phase optical elements may have tunable
photonic functionalities owing to sensitivity to external fields, as is the
case for liquid crystals based devices. However, a liquid crystal technology
combining high-resolution topological ordering with tunable spectral behavior
remains elusive. Here, by using a magneto-electric external stimulus, we create
robust and efficient self-engineered liquid crystal geometric phase vortex
masks with broadly tunable operating wavelength, centimeter-size clear
aperture, and high-quality topological ordering.
