Applied Electromagnetics for Metamaterial Design

1) Review of basic electromagnetic concepts
Electro- and magneto-statics, introduction to Maxwell equations, connection to circuit theory (capacitors, inductors), the wave equation in Cartesian coordinates, uniform and non-uniform plane waves, leaky waves, polarization decomposition, boundary conditions.

 

2) Wave scattering and propagation
Scattering at interfaces and homogeneous slabs, potentials, antenna theory (single antenna and antenna arrays), temporal and spatial dispersion, bi-anisotropy and chirality.

 

3) Electromagnetic theorems
Duality, volume equivalent currents, surface equivalence, energy conservation (Poynting theorem), momentum conservation (Maxwell stress tensor, forces and torques), reciprocity (Lorentz and Onsager-Casimir theorems), scalability of the wave equation, Krames-Kronig relations

 

4) Multipolar theory
Primitive Cartesian multipoles, symmetrization and detracing operations, irreducible multipoles, toroidal moments, anapole state, spherical multipoles, multipolar decomposition from the far-field and the near-field, Mie theory, Kerker effects.

 

5) Spatial symmetries in electromagnetics
Properties of the fields under reflection, rotation and parity operations, relation to multipolar effective material parameters, design strategies based on spatial symmetry breaking

 

6) 1D and 2D periodic systems
Diffraction gratings, subwavelength gratings, Rayleigh and Wood anomalies, guided mode resonances, Bravais lattices, conical diffraction

 

7) Homogenization of metamaterials
Effective medium theory, boundary conditions for metasurfaces, effective surface susceptibility modeling and synthesis

 

8) Field control strategies
Polarization control via wave-plates (birefringence) and chirality. Phase control via Gires-Tournois effect, electric and magnetic mode resonances, Pancharatnam-Berry effect, Detour phase. Generalized Snell law and perfect refraction.

 

9) Numerical python scripts
Several python scripts will be implemented during the course. This include a transfer matrix method script to model multilayer homogeneous and uniform slabs. A Fourier based angular propagation method for modeling the propagation of electromagnetic waves. A Mie scattering script for calculating cross-sections of spheres. A rigorous-coupled wave analysis (RCWA) script for simulating multilayer non-uniform 1D and 2D structures. Hologram generation using Gerchberg-Saxton algorithm.