3D Polarization: theory and measurement – 3DPol

Many modern photonic applications involve light that is strongly focused or confined, where the three components of the electric field at each point are significant. The standard 2D polarization formalism and the associated experimental tools become inadequate in these situations, in which a 3D polarization description is required. This project will provide theoretical and experimental advances in the description and measurement of 3D polarization and its spatial distribution, including the topological features it forms. It has two main goals:

1) to elaborate a consistent, general and intuitive theoretical formalism to describe 3D polarization, both full and partial, and to apply this theory to the description and design of fields displaying interesting and/or useful topological polarization features;
2) to implement and apply novel, robust and efficient experimental techniques for generating and measuring 3D polarization distributions, both in the full and partially polarized regimes, capable of surpassing the limitations of current.

The project is composed of three research work packages:

The first work package will be dedicated to the theoretical aspects of the project. Its first goal is to propose new, intuitive representations for the local state of polarization, which involves eight degrees of freedom. These representations should inherit the many properties of the Poincaré sphere for 2D polarization, namely its simple representation of local polarization transformations, its connection to geometric phase, and its unified description for full and partial polarization. They should also provide a natural framework to understand topological features of extended polarization distributions. This connection will be exploited to design new types of fields whose polarizations span complete subspaces of polarization (e.g. Skyrmions).
These tools can open the door to the design and characterization of fields that efficiently couple light to nanostructures, as well as to nanofabrication and nanomanipulation applications.
The second work package regards two novel methods for the efficient and accurate measurement of extended distributions of 3D polarization. These two methods involve very different physical principles and are valid for different situations.
The first method consists on imaging the field scattered by a 2D array of nanoparticles, each of which reports on the local state of 3D polarization of the field. The retrieval of the 3D polarization distribution relies on imaging the nanoparticles (in darkfield or brightfield modes) by using a spatially-varying birefringent mask at the Fourier plane to encode the 3D polarization information onto the shape of the images of each nanoparticle. This approach should be able to resolve the variation of 3D polarization well below a micron.
The second method is appropriate for slower 3D polarization variations but over much larger fields of view and is hence relevant for more extended nonparaxial field distributions with arbitrary wavefront deformations. Its operating principle is the interaction of the field with a liquid crystal layer, whose internal structure captures the features of the measured field.
The third work package regards the design and implementation of spatially-varying birefringent masks. This has two goals: the generation of 3D polarization distributions, and the Fourier-plane filter that encodes 3D polarization in the point-spread function used in the first measurement technique in the second work package. For both, liquid-crystal-based technologies will receive particular attention given their compactness, high transmissivity and reconfigurability. These devices will be implemented to match as well as possible optimal solutions that will be found theoretically.

The combined theoretical and experimental advances in 3DPol will lead to many new insights into the behavior of optical fields in situations relevant to modern nanophotonic applications.