High-order Poincaré sphere with flower modes possessing orbital angular momentum

A laser cavity composed of a cylindrical mirror and a gain medium is used to generate scalar flower modes possessing orbital angular momentum. We proposed a new complex modes by using a hemi-cylindrical cavity or spatial light modulator to generate superposition of vector Laguerre-Gaussian modes and vector flower modes. The generated vector fields possessing not only orbital angular momentum but polarization properties which correspond to the specific point on a higher-order Poincare sphere. This work paves the way to cavity laser in several applications.