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Omran Abbas, Qurrat-Ul-Ain Nadeem, Loïc Markley, Anas Chaaban

The reflection characteristics of a reconfigurable intelligent surface (RIS) depend on the phase response of the constituent unit cells, which is necessarily frequency dependent. This paper investigates the role of an RIS constituting unit cells with different phase-frequency profiles in a wide-band orthogonal frequency division multiplexing (OFDM) system to improve the achievable rate. We first propose a mathematical model for the phase-frequency relationship parametrized by the phase-frequency profile's slope and phase-shift corresponding to a realizable resonant RIS unit cell. Then, modelling each RIS element with $b$ control bits, we propose a method for selecting the parameter pairs to obtain a set of $2^b$ phase-frequency profiles. The proposed method yields an RIS design that outperforms existing designs over a wide range of user locations in a single-input, single-output (SISO) OFDM system. We then propose a low-complexity optimization algorithm to maximize the data rate through the joint optimization of (a) power allocations across the sub-carriers and (b) phase-frequency profile for each RIS unit cell from the available set. The analysis is then extended to a multi-user multiple-input single-output (MISO) OFDM scenario. Numerical results show an improvement in the coverage and achievable rates under the proposed framework as compared to single-slope phase-frequency profiles.

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Cael Warner, Loïc Markley, Kenneth J. Chau

The polarization density of a broadband electrodynamic lattice-Boltzmann method (ELBM) is generalized to represent frequency-dispersion of materials interacting with electromagnetic waves. The frequency-dependent refractive index and extinction coefficient are modeled using complex-conjugate pole-residue pairs in an auxiliary-differential-equation (ADE). Electric and magnetic fields are evaluated on a single lattice, ensuring a stable numerical solution up to the Nyquist limit. The electric and magnetic fields from the ELBM are compared with the electric and magnetic fields from the finite-difference-time-domain (FDTD) method. Accurate transmittance of a 100 nm silver slab is extracted from the transmitted power spectrum of a broadband Dirac-delta wave-function for photon energies ranging from 0.125-5 eV. Given this capability, the ELBM with an ADE is an accurate and computationally efficient method for modeling broadband frequency-dispersion of materials.

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