# Gadget to realize arbitrary polarization transformation on a higher order Poincar\'e sphere

## TL;DR

This paper introduces a novel gadget capable of performing arbitrary polarization transformations on a higher order Poincaré sphere, overcoming limitations of existing methods and combining holonomic and non-holonomic elements.

## Contribution

The paper presents the first gadget that enables arbitrary polarization transformations on a higher order Poincaré sphere, integrating elements from different topological index spaces.

## Key findings

- Gadget achieves transformations between any two points on the higher order Poincaré sphere.
- The device combines holonomic and non-holonomic polarization elements.
- It overcomes previous limitations of polarization transformation devices.

## 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.