Gadget to realize arbitrary polarization transformation on a higher order Poincaré sphere

Abstract: Designing a single element for all polarization transformations on a Poincar\'e sphere is impossible due to practical limitations and hence a combination of few standard wave-plates are used to construct a gadget. With this gadget it is possible to realize a polarization transformation between any two points on the Poincar\'e sphere. There is no such gadget available to perform arbitrary polarization transformation on a higher order Poincar\'e sphere. We present one gadget here in which the nature of polarization transformations by its elements is a mixture of holonomic and non-holonomic, since the elements belong to two different polarization topological index spaces.