More Like this

1. A duality between scattering poles and transmission eigenvalues in scattering theory

   https://doi.org/10.1098/rspa.2020.0612  

   Cakoni, Fioralba; Colton, David; Haddar, Houssem (December 2020, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   null (Ed.)

   In this paper, we develop a conceptually unified approach for characterizing and determining scattering poles and interior eigenvalues for a given scattering problem. Our approach explores a duality stemming from interchanging the roles of incident and scattered fields in our analysis. Both sets are related to the kernel of the relative scattering operator mapping incident fields to scattered fields, corresponding to the exterior scattering problem for the interior eigenvalues and the interior scattering problem for scattering poles. Our discussion includes the scattering problem for a Dirichlet obstacle where duality is between scattering poles and Dirichlet eigenvalues, and the inhomogeneous scattering problem where the duality is between scattering poles and transmission eigenvalues. Our new characterization of the scattering poles suggests a numerical method for their computation in terms of scattering data for the corresponding interior scattering problem. 

   more » « less
2. An algorithm for computing scattering poles based on dual characterization to interior eigenvalues

   https://doi.org/10.1098/rspa.2024.0015  

   Cakoni, Fioralba; Haddar, Houssem; Zilberberg, Dana (June 2024, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   We present an algorithm for the computation of scattering poles for an impenetrable obstacle with Dirichlet or Robin boundary conditions in acoustic scattering. This paper builds upon the previous work of Cakoni et al. (2020) titled ‘A duality between scattering poles and transmission eigenvalues in scattering theory’ (Cakoni et al. 2020 Proc. A. 476, 20200612 (doi:10.1098/rspa.2020.0612)), where the authors developed a conceptually unified approach for characterizing the scattering poles and interior eigenvalues corresponding to a scattering problem. This approach views scattering poles as dual to interior eigenvalues by interchanging the roles of incident and scattered fields. In this framework, both sets are linked to the kernel of the relative scattering operator that maps incident fields to scattered fields. This mapping corresponds to the exterior scattering problem for the interior eigenvalues and the interior scattering problem for scattering poles. Leveraging this dual characterization and inspired by the generalized linear sampling method for computing the interior eigenvalues, we present a novel numerical algorithm for computing scattering poles without relying on an iterative scheme. Preliminary numerical examples showcase the effectiveness of this computational approach. 

   more » « less
3. Simultaneous measurements of forward Thomson scattering and rotational Raman scattering in a weakly ionized plasma

   https://doi.org/10.1364/OPTCON.474339  

   He, Zichen; Ranganathan, Rajagopalan_V; Froedge, D_T; Zhang, Zhili (January 2023, Optics Continuum)

   This paper demonstrates a simultaneous Thomson scattering and rotational Raman scattering spectroscopy in a weakly ionized plasma in air. Thomson scattering was collected in the forward scattering direction, in order to compress the relative spectra width of Thomson scattering from the plasma. Simultaneous measurements of rotational Raman scattering were obtained in the same direction, which was not affected by the collection angles. The measurements thus yielded electron temperature (T_e) and electron number density (n_e) as well as gas temperature in a weakly ionized atmospheric pressure plasma. The separation of rotational Raman scattering and Thomson scattering occurred when the scattering angle decreased to 20 degrees in the plasma, where the air temperature was found to be 150 ± 25 °C, and electron temperature of the plasma was 0.587 ± 0.087 eV, and electron number density was (1.608 ± 0.416) × 1021 m-3. The technique could be used for various plasma and combustion diagnostics in realistic engineering environments. 

   more » « less
4. Holographic particle localization under multiple scattering

   https://doi.org/doi:10.1117/1.ap.1.3.036003  

   Tahir, W.; Tian, L.; Kamilov, U. (January 2019, SPIE journal)

   We introduce a computational framework that incorporates multiple scattering for large-scale three-dimensional (3-D) particle localization using single-shot in-line holography. Traditional holographic techniques rely on single-scattering models that become inaccurate under high particle densities and large refractive index contrasts. Existing multiple scattering solvers become computationally prohibitive for large-scale problems, which comprise millions of voxels within the scattering volume. Our approach overcomes the computational bottleneck by slicewise computation of multiple scattering under an efficient recursive framework. In the forward model, each recursion estimates the next higher-order multiple scattered field among the object slices. In the inverse model, each order of scattering is recursively estimated by a nonlinear optimization procedure. This nonlinear inverse model is further supplemented by a sparsity promoting procedure that is particularly effective in localizing 3-D distributed particles. We show that our multiple-scattering model leads to significant improvement in the quality of 3-D localization compared to traditional methods based on single scattering approximation. Our experiments demonstrate robust inverse multiple scattering, allowing reconstruction of 100 million voxels from a single 1-megapixel hologram with a sparsity prior. The performance bound of our approach is quantified in simulation and validated experimentally. Our work promises utilization of multiple scattering for versatile large-scale applications. 

   more » « less
5. From non-scattering to super-scattering with Mie-tronics

   https://doi.org/10.1364/PRJ.503182  

   Barati Sedeh, Hooman; Litchinitser, Natalia M. (March 2024, Photonics Research)

   Electric anapoles, arising from the destructive interference of primitive and toroidal electric dipole moments, have recently emerged as a fundamental class of non-scattering sources. On the other hand, super-scattering states represent the opposite regime wherein the scattering cross-section of a subwavelength particle exceeds the single-channel limit, leading to a strong scattering behavior. Here, we demonstrate that the interplay between the topology of light and the subwavelength scatterer can lead to these two opposite responses within an isolated all-dielectric meta-atom. In particular, we present the emergence of a new non-scattering state, referred to as hybrid anapole, which surpasses conventional electric dipole anapoles by achieving a remarkable 23-fold enhancement in the suppression of far-field radiation and almost threefold enhancement in the confinement of electromagnetic energy inside the meta-atom. We also explore the role of particle orientation and its inversion symmetry in the scattering response and predict the possibility of switching between non-scattering and super-scattering states within the same platform. The presented study elucidates the role of light and matter topologies in the scattering response of subwavelength meta-atoms, uncovering two opposite regimes of light-matter interaction and opening new avenues in applications such as nonlinear optics and spectroscopy. 

   more » « less