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   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. 

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2. Reinforced Inverse Scattering

   https://doi.org/10.1137/22M153207X  

   Jiang, Hanyang; Khoo, Yuehaw; Yang, Haizhao (December 2024, SIAM Journal on Scientific Computing)
3. 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. 

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4. Scattering and inverse scattering for the AKNS system: A rational function approach

   https://doi.org/10.1111/sapm.12434  

   Trogdon, Thomas (August 2021, Studies in Applied Mathematics)

   Abstract We consider the use of rational basis functions to compute the scattering and inverse scattering transforms associated with the AKNS (Ablowitz–Kaup–Newell–Segur) system. The proposed numerical forward scattering transform computes the solution of the AKNS system that is valid on the entire real axis and thereby computes a reflection coefficient at a point by solving a single linear system. The proposed numerical inverse scattering transform makes use of a novel improvement in the rational function approach to the oscillatory Cauchy operator, enabling the efficient solution of certain Riemann–Hilbert problems without contour deformations. The latter development enables access to high‐precision computations and this is demonstrated on the inverse scattering transform for the one‐dimensional Schrödinger operator with a potential. 

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5. Joint Time–Frequency Scattering

   https://doi.org/10.1109/TSP.2019.2918992  

   Anden, Joakim; Lostanlen, Vincent; Mallat, Stephane (July 2019, IEEE Transactions on Signal Processing)