Publication
Theory of resolution limit
A Mathematical theory of computational resolution limit in one dimension, Ping Liu and Hai Zhang, Applied and Computational Harmonic Analysis, to appear, 2021.
A Theory of Computational Resolution Limit for
Line Spectral Estimation, Ping Liu and Hai Zhang, IEEE Transactions on Information Theory, 67(7), 2021.
A Mathematical Theory of Computational Resolution Limit in Multi-dimensional Spaces, Ping Liu and Hai Zhang, Inverse Problems 37, 104001, 2021.
Theory of topological material
Mathematical theory for topological photonic materials in one dimension, Junshan Lin and Hai Zhang, Journal of Physics A: Mathematical and Theoretical, 55, 495203, 2022.
Bulk-interface correspondences for one dimensional topological materials with inversion symmetry, Guo Chuan Thiang, Hai Zhang, Proceedings of the Royal Society A, 479:20220675, 2023.
Dirac points for the honeycomb lattice with impenetrable obstacles,
Wei Li, Junshan Lin, Hai Zhang, SIAM Journal on Applied Mathematics, 2023.
Mathematical theory for the interface mode in a
waveguide bifurcated from a Dirac point,
Jiayu Qiu, Junshan Lin, Peng Xie, Hai Zhang, submitted.
arXiv:2304.10843v1.
Theory of metamaterial: a case study using resonant bubbles
Double-negative acoustic metamaterials, Habib Ammari, Brian Fitzpatrick, Hyundae Lee, Sanghyeon Yu and Hai Zhang, Quarterly of Applied Mathematics, 77(4), 2019, 767-791, 2019.
Bloch waves in bubbly crystal near the first band gap: a high-frequency
homogenization approach,
with H. Ammari and H. Lee, SIAM Journal on Mathematical Analysis, 51-1, 45-59, 2019.
Subwavelength phononic bandgap opening in bubbly media,
with H. Ammari, B. Fitzpatrick, H. Lee and S. Yu, Journal of Differential Equations, 5610-5629, 263, 2017.
A mathematical and numerical framework for bubble meta-screens,
with H. Ammari,
B. Fitzpatrick, D. Gontier and H. Lee, SIAM Journal on Applied Mathematics, 1827-1850, 77(5), 2017.
Minnaert resonances for acoustic waves in bubbly media,
with H. Ammari,
B. Fitzpatrick, D. Gontier and H. Lee, Annales de l'Institut Henri Poincare: Analyse Nonlineaire, 1975-1998, 35, 2018.
Plasmonic sensing
Sensitivity of resonance frequency in the detection of thin layer using nano-slit structures, Junshan Lin, Sang-Hyun Oh and Hai Zhang, IMA Journal of Applied Mathematics, 86 (1), 146-164, 2021.
Reconstructing fine details of small objects by using plasmonic spectroscopic data. Part II: The strong interaction regime,
with Habib Ammari, Matias Ruiz and Sanghyeon Yu,
SIAM Journal on Imaging Sciences, 11(3), 1931-1953, 2018.
Reconstructing fine details of small objects by using plasmonic spectroscopic data,
with Habib Ammari, Matias Ruiz and Sanghyeon Yu,
SIAM Journal on Imaging Sciences, 1-23, 11, 2018.
Shape reconstruction of nanoparticles from their associated plasmonic resonances,
with H. Ammari, M. Putinar, M. Ruiz and S. Yu, Journal de Mathematiques Pures et Appliquees, 23-48, 122, 2019.
Plasmonic resonances
Photonic bandgap phenomenon in a metal-dielectric periodic structure, with Fadil Santosa, Research in the Mathematical Sciences, 7(3), 2020.
Mathematical analysis of surface plasmon resonance by a nano-gap in the plasmonic metal, with Junshan Lin, SIAM Math. Anal, 51(6), 4448-4489, 2019.
An integral equation method for numerical computation of plasmonic resonances in a narrow metallic slit,
with J. Lin, J. Comput. Phy., 385, 75-105, 2019.
Field expansions for systems of strongly coupled plasmonic nanoparticles,
Habib Ammari, Matias Ruiz, Sanghyeon Yu and Hai Zhang,
SIAM Journal on Numerical Analysis, 56(4), 2029-2044, 2018.
The plasmonic resonances of a bowtie antenna,
with Eric Bonnetier, Charles Dapogny and Faouzi Triki,
Analysis in Theory and Applications, 85-116, 35 (1), 2019.
Characterization of the essential spectrum of the Neumann-Poincare
operator in 2D domains with corner via Weyl sequences,
with E. Bonnetier, Revista Matematica Iberoamericana, 35 (3), 925-948, 2019.
Mathematical and numerical framework for metasurfaces using thin layers of periodically distributed plasmonic nanoparticles,
with H. Ammari, M. Ruiz, W. Wu and S. Yu,
Proceedings of the Royal Society A. 472: 20160445, 2017.
Mathematical analysis of plasmonic resonances for nanoparticles: the full Maxwell equations,
with H. Ammari, M. Ruiz and S. Yu, Journal of Differential Equations, 261 (2016), 3615-3669.
Mathematical analysis of plasmonic nanoparticles: the scalar case,
with Habib Ammari, Pierre Millien and Matias Ruiz,
Archive on Rational Mechanics and Analysis, 224, 597-658, 2017.
Theory of Fano resonance: a case study using slit structures
Fano resonance for a periodic array of perfectly conducting narrow slits, with Junshan Lin and Stephen P Shipman, SIAM Journal on Applied Mathematics, 80(5), 2045-2070, 2020.
Fano resonance in metallic grating via strongly coupled subwavelength resonators, Junshan Lin and Hai Zhang,
European Journal of Applied Mathematics, 2020.
Theory of extraordinary optical transmission through holes in metallic structure
Mathematical theory for electromagnetic scattering resonances and field enhancement in a subwavelength annular gap,
Junshan Lin, Wangtao Lu, Hai Zhang, SIAM Journal on Multiscale Modeling and Simulation, 2023.
Scattering by a periodic array of subwavelength slits II: surface bound state, total transmission and field enhancement in homogenization regimes,
with J. Lin, SIAM Journal on Multiscale Modeling and Simulation, 16(2), 954-990, 2018.
Scattering by a periodic array of subwavelength slits I: field enhancement in the diffraction regime,
with J. Lin, SIAM Journal on Multiscale Modeling and Simulation, 16(2), 922-953, 2018.
Scattering and field enhancement of a perfect conducting narrow slit,
with J. Lin, SIAM Journal on Applied Mathematics, 951-976, 77(3),
2017. [pdf].
Theory of super-resolution and super-focusing in resonant media
Sub-wavelength focusing of acoustic waves in bubbly media,
with H. Ammari, B. Fitzpatrick, D. Gontier and H. Lee,
Proceedings of the Royal Society A, 473: 20170469, 2017.
Effective medium theory for acoustic waves in bubbly fluids near Minnaert resonant frequency,
with H. Ammari, SIAM Journal on Mathematical Analysis, 3252-3276, 49(4), 2017.
Super-resolution in high contrast media,
with Habib Ammari, Proceedings of the Royal Society A, 471, 2015.
A mathematical theory of super-resolution by using a system of sub-wavelength Helmholtz resonators,
with Habib Ammari, Comm.Math.Physics, 337 (1), 2015.
Super-resolution techniques/algorithms in imaging
IFF: A Super-resolution algorithm for
Multiple Measurements,
Zetao Fei, Hai Zhang, submitted. arXiv:2303.06617v1.
A measurement decoupling based efficient
algorithm for super-resolving point sources with a
multi-cluster structure,
Ping Liu, Hai Zhang, submitted. arXiv:2204.00469v1.
Sensitivity of resonance frequency in the detection of
thin layer using nano-slit structures, Junshan Lin, Sang-Hyun Oh and Hai Zhang,
IMA Journal of Applied Mathematics, 86 (1), 146-164, 2021.
A super-resolution imaging approach via subwavelength hole resonances, Junshan Lin and Hai Zhang, Physical Review Applied, 14 (3), 034066, 2020.
Inverse problems (uniqueness and stability)
Stability for the lens rigidity problem,
with Gang Bao, Archive on Rational Mechanics and Analysis, 1127-1160, 225(3), 2017. [pdf].
Stability analysis for magnetic resonance elastography,
with Habib Ammari and Alden Waters, Journal of Mathematical Analysis and Applications, 919-931, 430 (2015).
Sensitive analysis of an inverse problem for the wave equation with caustics,
with Gang Bao, JAMS, 953-981, 27(2014).
Unique determination of periodic polyhedral structures by scattered electromagnetic fields
II: the resonance case,
with Gang Bao and Jun Zou, Tran.A.M.S, 1333-1361, 366(3)(2014).
Unique determination of periodic polyhedral structures by scattered electromagnetic fields,
with Gang Bao and Jun Zou, Tran.A.M.S, 4527-4551, 363(2011).
Recovery of polyhedral obstacles by a single far field measurement,
with Hongyu Liu and Jun Zou, J. Math. Phys, 50(2009).
High frequency wave propagation
A convergent multiscale Gaussian beam parametrix for wave equations,
with Gang Bao, Jianliang Qian and Lexing Ying, Comm.P.D.E, 38(2013).