Quasi-normal mode expansion as a tool for the design of nanophotonic devices

Many nanophotonic devices rely on the excitation of photonic resonances to enhance light-matter interaction. The understanding of the resonances is therefore of a key importance to facilitate the design of such devices. These resonances may be analyzed by use of the quasi-normal mode (QNM) theory. Here, we illustrate how QNM analysis may help study and design resonant nanophotonic devices. We will in particular use the QNM expansion of far-field quantities based on Riesz projection to design optical antennas.

Stability of the S-essential spectra on a Banach space

In this paper, we give the characterization of S-essential spectra, we define the S-Riesz projection and we investigate the S-Browder resolvent. Finally, we study the S-essential spectra of sum of two bounded linear operators acting on a Banach space.

Transfer of Fourier Multipliers into Schur Multipliers and Sumsets in a Discrete Group

We inspect the relationship between relative Fourier multipliers on noncommutative Lebesgue– Orlicz spaces of a discrete group and relative Toeplitz-Schur multipliers on Schatten–von- Neumann–Orlicz classes. Four applications are given: lacunary sets, unconditional Schauder bases for the subspace of a Lebesgue space determined by a given spectrum , the norm of the Hilbert transformand the Riesz projection on Schatten–von-Neumann classes with exponent a power of 2, and the norm of Toeplitz Schur multipliers on Schatten–von-Neumann classes with exponent less than 1.