Higher-order Poincar\'e Spheres and Spatio-Spectral Poincar\'e Beams

The study of fundamental optics effects has been stimulated through the increasing ability to structure light in all its degrees of freedom (DOFs) in sophisticated but simple experimental settings. However, with such an increase in experimental capabilities, it has also become important to study theoretical descriptions for a more intuitive understanding of the underlying concepts. Here, we introduce a visual representation of light that is structured in its transverse space, frequency, and polarization in the form of a higher-order Poincar\'e sphere and discuss interesting links to its fundamental counterpart. We further leverage this connection to discuss and experimentally generate light possessing all possible polarization states across its spatio-spectral shape, which we term spatio-spectral Poincar\'e beams. By invoking all DOFs of light in the powerful description of higher-order Poincar\'e spheres, our work can pave the way for a deeper understanding and beneficial application of structured light as a powerful tool in optics.