Ping Liu, Doctor, Department of Mathematics, ETH Zürich

Weiying Zheng, Professor

Mathematical Theories in Super-resolution and Subwavelength Physics

10:10-11:10 December 14(Thursday), Tencent Meeting ID: 585 591 444

In the first part of the talk, we will propose a new concept “computational resolution limit” which reveals the fundamental limits of super-resolving the number and locations of point sources in the imaging problem. We will quantitatively characterize the computational resolution limits by the signal-to-noise ratio, the sparsity of sources, and the cutoff frequency of the imaging system. As a direct consequence, it is demonstrated that l_0 optimization achieves the optimal order resolution in solving super-resolution problems. For the case of resolving two point sources, the resolution estimate is improved to an exact formula, which answers the long-standing question of diffraction limit in a general circumstance.

In the second part of the talk, we will introduce mathematical theories of skin effect and interface modes in a one-dimensional finite chain of subwavelength resonators. We approximate the continuous physical model by a so-called capacitance matrix, which is a 2-Toeplitz matrix. Then through the application of Chebyshev polynomials, we demonstrate the skin effect and the existence of interface modes.