Tianyuan Mathematical Center in Northeast China will open the short Course “Resonances for light interaction with subwavelength structures” between Jan 9 – Jan 13, 2023. It is held by Prof. Junshan Lin from Auburn University, USA and Prof. Hai Zhang from The Hong Kong University of Science and Technology, Hong Kong (China). 

一、About the short course

1. Instructors：

Prof. Junshan Lin, Auburn University, USA

Prof. Hai Zhang, The Hong Kong University of Science and Technology, Hong Kong, S.A.R. China

2. Course name：Resonances for light interaction with subwavelength structures

3. Period：Jan 9，2023 – Jan 13，2023

4. Prerequisite knowledge：Ordinary Differential Equations (ODE), Partial Differential Equations (PDE) and numerical analysis.

5.References：

[1] H. Ammari, et al., Mathematical and Computational Methods in Photonics and Phononics, Americal Mathematical Society, 2018

[2] D. Colton and R. Kress, Integral Equation Methods in Scattering Theory, SIAM, 2013

[3] Junshan Lin and Hai Zhang, Scattering and field enhancement of a perfect conducting narrow slit, SIAM Journal on Applied Mathematics, 951-976, 77(3), 2017.

[4] Junshan Lin and Hai Zhang, Scattering by a periodic array of subwavelength slits I: field enhancement in the diffraction regime, Junshan Lin and Hai Zhang, SIAM Journal on Multiscale Modeling and Simulation, 16(2), 922-953, 2018.

[5] Junshan Lin and Hai Zhang, Scattering by a periodic array of subwavelength slits II: surface bound state, total trans- mission and field enhancement in homogenization regimes, SIAM Journal on Multiscale Modeling and Simulation, 16(2), 954-990, 2018.

[6] Junshan Lin, Stephen P Shipman and Hai Zhang, Fano resonance for a periodic array of perfectly conducting narrow slits, SIAM Journal on Applied Mathematics, 80(5), 2045-2070, 2020.

[7] Junshan Lin and Hai Zhang, Fano resonance in metallic grating via strongly coupled subwavelength resonators,
European Journal of Applied Mathematics, 32, 370-394, 2021.

[8] Junshan Lin, Sang-Hyun Oh and Hai Zhang, Sensitivity of resonance frequency in the detection of thin layer using nano-slit structures,  IMA Journal of Applied Mathematics, 86 (1), 146-164, 2021.

[9] Junshan Lin and Hai Zhang, A super-resolution imaging approach via subwavelength hole resonances,  Physical Review Applied, 14, 034066, 2020.

[10] Junshan Lin, Wangtao Lu, and Hai Zhang, Mathematical theory for electromagnetic scattering resonances and field enhancement in an annular subwavelength gap, arXiv:2205.05377v1.

二、Content and schedule

In this series of lectures, we will discuss how to use the layer potential techniques and asymptotic analysis to develop rigorous theories for the various resonances in the light interaction with subwavelength slit structures and their applications in bio-medical sensing and super-resolution imaging.

This course will be structured in 3 parts: 

PART I: Introduction to layer potential. We will give a short introduction to layer potential techniques and the boundary integral equation formulations for wave propagation problems in various cases.

PART II: Anomalous light scattering by subwavelength structures. We will discuss the interesting physics phenomenon of light scattering by subwavelength structures, which include extraordinary optical transmission (EOT) and local field enhancement (LFE). We will apply layer potential techniques to develop rigorous mathematical theories for the EOT and LFE in the context of the subwavelength slit structures in various regimes, which includes a single slit structure, a periodic array of slits.  

PART III: Complementary topics. We will discuss a couple of complementary topics related with the contents of this course which includes: Fano resonances, sensitivity of detect thick structures using the slit structure, a super-resolution technique using the slit structure.  

三、About the Lecturers

1、Prof. Junshan Lin，C Harry Knowles Endowed Associate Professor;  Expert in Applied Mathematics: Applied and Numerical Analysis, Scientific Computation, Mathematical Problems for Waves in Novel Devices and Materials, Inverse Wave Scattering and Imaging, Computational Optimization.

2、Prof. Hai Zhang ，Associate Professor. Expert in Applied Mathematics; Inverse Problems and Imaging, Wave Propagation in Metamaterials and Topological Materials.