Reconstructing Fine Details of Small Objects by Using Plasmonic Spectroscopic Data

This paper is concerned with the inverse problem of reconstructing a small object from far field measurements. The inverse problem is severally ill-posed because of the diffraction limit and low signal to noise ratio. We propose a novel methodology to solve this type of inverse problems based on an idea from plasmonic sensing. By using the field interaction with a known plasmonic particle, the fine detail information of the small object can be encoded into the shift of the resonant frequencies of the two particle system in the far field. In the intermediate interaction regime, we show that this information is exactly the generalized polarization tensors associated with the small object, from which one can perform the reconstruction. Our theoretical findings are supplemented by a variety of numerical results. The results in the paper also provide a mathematical foundation for plasmonic sensing

Reconstructing fine details of small objects by using plasmonic spectroscopic data. Part II: The strong interaction regime

This paper is concerned with the inverse problem of reconstructing a small object from far field measurements by using the field interaction with a plasmonic particle which can be viewed as a passive sensor. It is a follow-up of the work [H. Ammari et al., Reconstructing fine details of small objects by using plasmonic spectroscopic data, SIAM J. Imag. Sci., to appear], where the intermediate interaction regime was considered. In that regime, it was shown that the presence of the target object induces small shifts to the resonant frequencies of the plasmonic particle. These shifts, which can be determined from the far field data, encodes the contracted generalized polarization tensors of the target object, from which one can perform reconstruction beyond the usual resolution limit. The main argument is based on perturbation theory. However, the same argument is no longer applicable in the strong interaction regime as considered in this paper due to the large shift induced by strong field interaction between the particles. We develop a novel technique based on conformal mapping theory to overcome this difficulty. The key is to design a conformal mapping which transforms the two particle system into a shell-core structure, in which the inner dielectric core corresponds to the target object. We show that a perturbation argument can be used to analyze the shift in the resonant frequencies due to the presence of the inner dielectric core. This shift also encodes information of the contracted polarization tensors of the core, from which one can reconstruct its shape, and hence the target object. Our theoretical findings are supplemented by a variety of numerical results based on an efficient optimal control algorithm. The results of this paper make the mathematical foundation for plasmonic sensing complete.Comment: 24 pages, 4 figure

Reconstruction of domains with algebraic boundaries from generalized polarization tensors

This paper aims at showing the stability of the recovery of a smooth planar domain with a real algebraic boundary from a finite number of its generalized polarization tensors. It is a follow-up of the work [H. Ammari et al., Math. Annalen, 2018], where it is proved that the minimal polynomial with real coefficients vanishing on the boundary can be identified as the generator of a one dimensional kernel of a matrix whose entries are obtained from a finite number of generalized polarization tensors. The recovery procedure is implemented without any assumption on the regularity of the domain to be reconstructed and its performance and limitations are illustrated

Plasmonic photoconductive terahertz focal-plane array with pixel super-resolution

Imaging systems operating in the terahertz part of the electromagnetic spectrum are in great demand because of the distinct characteristics of terahertz waves in penetrating many optically-opaque materials and providing unique spectral signatures of various chemicals. However, the use of terahertz imagers in real-world applications has been limited by the slow speed, large size, high cost, and complexity of the existing imaging systems. These limitations are mainly imposed due to the lack of terahertz focal-plane arrays (THz-FPAs) that can directly provide the frequency-resolved and/or time-resolved spatial information of the imaged objects. Here, we report the first THz-FPA that can directly provide the spatial amplitude and phase distributions, along with the ultrafast temporal and spectral information of an imaged object. It consists of a two-dimensional array of ~0.3 million plasmonic photoconductive nanoantennas optimized to rapidly detect broadband terahertz radiation with a high signal-to-noise ratio. As the first proof-of-concept, we utilized the multispectral nature of the amplitude and phase data captured by these plasmonic nanoantennas to realize pixel super-resolution imaging of objects. We successfully imaged and super-resolved etched patterns in a silicon substrate and reconstructed both the shape and depth of these structures with an effective number of pixels that exceeds 1-kilo pixels. By eliminating the need for raster scanning and spatial terahertz modulation, our THz-FPA offers more than a 1000-fold increase in the imaging speed compared to the state-of-the-art. Beyond this proof-of-concept super-resolution demonstration, the unique capabilities enabled by our plasmonic photoconductive THz-FPA offer transformative advances in a broad range of applications that use hyperspectral and three-dimensional terahertz images of objects for a wide range of applications.Comment: 62 page

Far-field Super-resolution Chemical Microscopy

Far-field chemical microscopy providing molecular electronic or vibrational fingerprint information opens a new window for the study of three-dimensional biological, material, and chemical systems. Chemical microscopy provides a nondestructive way of chemical identification without exterior labels. However, the diffraction limit of optics hindered it from discovering more details under the resolution limit. Recent development of super-resolution techniques gives enlightenment to open this door behind far-field chemical microscopy. Here, we review recent advances that have pushed the boundary of far-field chemical microscopy in terms of spatial resolution. We further highlight applications in biomedical research, material characterization, environmental study, cultural heritage conservation, and integrated chip inspection.Comment: 34 pages, 8 figures,1 tabl

Shape reconstructions by using plasmon resonances

We study the shape reconstruction of a dielectric inclusion from the faraway measurement of the associated electric field. This is an inverse problem of practical importance in biomedical imaging and is known to be notoriously ill-posed. By incorporating Drude's model of the dielectric parameter, we propose a novel reconstruction scheme by using the plasmon resonance with a significantly enhanced resonant field. We conduct a delicate sensitivity analysis to establish a sharp relationship between the sensitivity of the reconstruction and the plasmon resonance. It is shown that when plasmon resonance occurs, the sensitivity functional blows up and hence ensures a more robust and effective construction. Then we combine the Tikhonov regularization with the Laplace approximation to solve the inverse problem, which is an organic hybridization of the deterministic and stochastic methods and can quickly calculate the minimizer while capture the uncertainty of the solution. We conduct extensive numerical experiments to illustrate the promising features of the proposed reconstruction scheme