Fast algorithm and surface integral equations for two-dimensional materials modeling

Meng, Lingling

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Description

Title

Fast algorithm and surface integral equations for two-dimensional materials modeling

Author(s)

Meng, Lingling

Issue Date

2021-04-21

Director of Research (if dissertation) or Advisor (if thesis)

Chew, Weng Cho

Doctoral Committee Chair(s)

Chew, Weng Cho

Committee Member(s)

• Kudeki, Erhan
• Schutt-Aine, Jose E.
• Zhu, Wenjuan

Department of Study

Electrical & Computer Eng

Discipline

Electrical & Computer Engr

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Fast multipole algorithm
• Two-dimensional materials
• Surface integral equations
• Structured light
• Second-harmonic generation
• Radiative heat transfer.

Abstract

In this dissertation, a wide-band two-dimensional (2D) fast multipole algorithm (FMA) with a novel diagonalization form is presented. The conventional diagonalization of 2D FMA can be derived based on the interpretation of Parseval's theorem. The performance of FMA in the twilight zone (between the low-frequency and high-frequency regimes) is not good enough. By scaling special functions and applying discrete Fourier transform (DFT), the multipole expansions with dense matrices can be transformed to diagonal matrices with stable accuracy. Therefore a broadband 2D FMA with high efficiency and accuracy is achieved with a multi-level scheme. Then a metasurface platform to generate structured light at second harmonics is proposed with transition metal dichalcogenide (TMDC) flakes. With the aid of the electric field integral equation and impedance boundary condition, the surface currents on TMDC flakes can be calculated at fundamental frequencies. By applying three-fold rotational symmetry of the quadratically nonlinear susceptibility of TMDC monolayer, radial (or azimuthal) polarization and orbital angular momentum can be generated at second harmonics with linearly polarized and circularly polarized incident waves at the fundamental frequency, respectively. Finally, the radiative heat transfer between two graphene-wrapped objects with arbitrary shapes is studied by a fluctuating-surface current formulation derived from surface integral equations with impedance boundary conditions. The surface conductivity of graphene can be tuned by the temperature, chemical doping or electrical gating. The near-field thermal radiation can be enhanced due to graphene plasmonics in the terahertz regime. Off resonance, the graphene coating has a shielding effect on the dielectric bodies containing fluctuating-current sources. This formulation can be extended to the multi-body problem and other two-dimensional materials.

Graduation Semester

2021-05

Type of Resource

Thesis

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N/A.

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