Research project

Superresolution hidden in the far-field and spatial-spectral transformations

Objectives: The project is aimed at demonstrating the possibility of recovering information about sub-wavelength-sized objects from an optical far-field spectral imaging measurement, after a spatial-spectral transformation is realised in the near-field with help of a hyperbolic metamaterial. It concerns the development of photonic nanostructures, MEMS-based measurement techniques and algorithms for super resolving compressive microscopic imaging in the far-field. It is motivated by the recent progress in several fields, including: i) the introduction of alternative indirect optical measurement techniques known as single-pixel detection, with simplified optical architectures and extended computational requirements based on the theory of compressive sensing, ii) the development of optical metamaterials with an effective hyperbolic dispersion capable of preserving extremely high spatial spectrum harmonics during propagation, as well as on the currently well established capability of nanospheres to focus light into nanojets, iii) on the emerging concepts of microscopic super-resolving imaging with spatial-spectral transformations. The project will contribute to each of these research domains. The detailed objectives are to i) develop and test algorithms for the reconstruction of near-field information from the far field broadband information only, ii) to develop optimized hyperbolic metamaterials for spatial-spectral transformations, iii) to develop nanostructures for evanescent-to-propagating wave coupling, iv) to experimentally validate the indirect measurement with spatial-spectral intermixing with a hyperbolic metamaterial for the first time.

Methodology: The 24 month project will be realized at the Faculty of Physics, University of Warsaw by 6 researchers, including 3 working 100% time on the project (one post-doc and 2 PhD students). The subject of the project is well situated in the field of expertise of the research group on compressive sensing, optical metamaterials, super-resolution and electromagnetic modelling. The work-plan is split into 5 research tasks related to the development of i) single-pixel measurement methods for spectrometry, ii) compressive methods for spectral imaging , ii) of hyperbolic metamaterials, and to the iii) analysis and tailoring of the transformation properties of hyperbolic metamaterials, and to the iv) experimental analysis of spectral-spatial intermixing, and the v) development of new sampling methods for compressive imaging. Experimental techniques used will include PVD thin layer deposition, SEM/AFM surface characterization, spectral analysis and microscopic imaging. Simulations of the metamaterial will include finite-difference-time-domain modelling and scattering matrix frequency-domain modelling, while the compressive signal reconstruction will include l1-norm and total-variation minimization with use of open-source optimization toolboxes. Walsh-Hadamard based, noiselet-based and Morlet-wavelet-based sampling will be investigated.

Impact: Realization of the project aims at bringing first experimental results of super-resolving compressive imaging with a hyperbolic metamaterial used to implement a spatial-spectral transformation for the measurement conducted in the far field. A better understanding of the spatial-spectral transformations obtained in a realistic and lossy hyperbolic metamaterial will be gained. Novel microscopic compressive single-pixel spectral imaging techniques will be developed. The understanding of single-pixel imaging techniques, in particular those involving spatial-spectral intermixing, will be improved, paving a way to the development of novel engineering techniques in the future. Reconstruction algorithms will be developed for the restoration of a hyperspectral image from a set of projections over spatially and spectrally modulated patterns with various sampling protocols. The algorithms for the restoration of near-field information from the far-field measurement will be developed.