110 http://isa.epfl.ch/imoniteur_ISAP/ itffichecours.txt?path=EPFL.Etu.FicheCours.HeaderFR itffichecours.txt?path=EPFL.Etu.FicheCours.GlobalNav_js fr 2026 943936 6683147 943936 2840683608 2840683608 0 0 Genie electrique et electronique EL STI Faculté des sciences et techniques de l'ingénieur School of Engineering !itffichecours.htm?ww_i_matiere=4543921481&ww_x_anneeAcad=2840683608&ww_i_section=943936&ww_i_niveau=6683147 1696552884 1696552963 2025-2026 LIVRET DE COURS MICRO-449 Applied Electromagnetics for Metamaterial Design Applied Electromagnetics for Metamaterial Design Enseignants Achouri Karim Langue d'enseignement Cursus Génie électrique (edoc)(2025-2026, EDEE 2025-26)
Génie électrique et électronique(2025-2026, EL - Master 2024)
Génie électrique et électronique(2025-2026, EL - Master 2025)
Microtechnique(2025-2026, MT - Master 2024)
Microtechnique(2025-2026, MT - Master 2025)
Photonics minor(2025-2026, Photonics 2025-26)
Photonique (edoc)(2025-2026, EDPO 2025-26)
SemestreOblig.OptionFilières
x
Hx
MA1, MA3x
MA1, MA3xA B
 Crédits 3 Session Hiver Charge 90h Examen Oral Nombre de places Semestre Automne Semaines 14 Heures 3 hebdo
Cours 3 hebdo
Plan d'étude SemestreOblig.OptionFilières
EDEE - Electrical Engineering 2025-26x
EDPO - Photonics 2025-26x
Génie électrique et électronique 2025-26MA1x
Génie électrique et électronique 2025-26MA3x
Microtechnique 2025-26MA1xA B
Microtechnique 2025-26MA3xA B
Minor : Photonics 2025-26Hx
Cursus Sem. Type
Génie électrique et électronique MA1, MA3 Opt.
Génie électrique Obl.
Microtechnique MA1, MA3 Opt.
Photonics minor H Opt.
Photonique Obl.
Remarque . Résumé This course provides the students with the appropriate electromagnetics foundation to understand, model and design metamaterials, especially two-dimensional electromagnetic and optical structures such as metasurfaces. This course covers concepts that apply to both the microwave and optical regimes. Contenu

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.

 Mots-clés

Electromagnetics, wave scattering, multipolar theory, metamaterials

 Compétences requises Concepts importants à maîtriser

Basic knowledge in electromagnetics and python programming

 Acquis de formation A la fin de ce cours l'étudiant.e doit être capable de:
  • Modéliser and design a large array of metamaterial structures performing various operations
  • Utiliser several python scripts to help them design electromagnetic systems
  • Reconnaitre the theoretical concepts behind most contemporary concepts in the field of metamaterials
  • Démontrer how these concepts are derived from Maxwell equations, how they can be used and extended
 Méthode d'enseignement

Ex-cathedra courses and exercises

 Méthode d'évaluation

The concepts discussed during the course will be evaluated via an oral exam at the end of the semester. The students are expected to explain these concepts, their origin and meaning, how they are derived from Maxwell equations and how they can be applied for modeling metamaterials. The students are not expected to remember all formulas by heart.

 Ressources Bibliographie
  1. Rothwell, E.J. and Cloud, M.J., "Electromagnetics", CRC press, 2018.
  2. Paknys, R., "Applied frequency-domain electromagnetics, John Wiley & Sons, 2016.
  3. Kong, J.A., "Theory of electromagnetic waves", John Wiley & Sons, 1975.
  4. Stutzman, W.L. and Thiele, G.A., "Antenna theory and design", John Wiley & Sons, 2012.
  5. Ishimaru, A., "Electromagnetic wave propagation, radiation, and scattering: from fundamentals to applications", John Wiley & Sons, 2017.
  6. Achouri, K. and Caloz, C., "Electromagnetic metasurfaces: Theory and applications", John Wiley & Sons, 2021.
 Liens Moodle Microtechnique, 2025-2026, Master semestre 1 Microengineering, 2025-2026, Master semester 1 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2025-2026 Master semestre 1 MA1 HIVER Master semester 1 MA1 Microtechnique MT Microengineering MT
Microtechnique MT Microengineering MT
A B optionnel optional
3 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Achouri Karim 175309
Microtechnique MT Microengineering MT
. 4543921481 Applied Electromagnetics for Metamaterial Design Applied Electromagnetics for Metamaterial Design 3
Oral Oral Crédit Credits 3 Session hiver Session winter HIV HIV
. Microtechnique, 2025-2026, Master semestre 3 Microengineering, 2025-2026, Master semester 3 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2025-2026 Master semestre 3 MA3 HIVER Master semester 3 MA3 Microtechnique MT Microengineering MT
Microtechnique MT Microengineering MT
A B optionnel optional
3 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Achouri Karim 175309
Microtechnique MT Microengineering MT
. 4543921481 Applied Electromagnetics for Metamaterial Design Applied Electromagnetics for Metamaterial Design 3
Oral Oral Crédit Credits 3 Session hiver Session winter HIV HIV
. Génie électrique et électronique, 2025-2026, Master semestre 1 Electrical and Electronics Engineering, 2025-2026, Master semester 1 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2025-2026 Master semestre 1 MA1 HIVER Master semester 1 MA1 Génie électrique et électronique EL Electrical and Electronics Engineering EL
Génie électrique et électronique EL Electrical and Electronics Engineering EL
optionnel optional
3 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Achouri Karim 175309
Microtechnique MT Microengineering MT
4543921481 Applied Electromagnetics for Metamaterial Design Applied Electromagnetics for Metamaterial Design 3
Oral Oral Crédit Credits 3 Session hiver Session winter HIV HIV
Génie électrique et électronique, 2025-2026, Master semestre 3 Electrical and Electronics Engineering, 2025-2026, Master semester 3 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2025-2026 Master semestre 3 MA3 HIVER Master semester 3 MA3 Génie électrique et électronique EL Electrical and Electronics Engineering EL
Génie électrique et électronique EL Electrical and Electronics Engineering EL
optionnel optional
3 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Achouri Karim 175309
Microtechnique MT Microengineering MT
4543921481 Applied Electromagnetics for Metamaterial Design Applied Electromagnetics for Metamaterial Design 3
Oral Oral Crédit Credits 3 Session hiver Session winter HIV HIV
Génie électrique (edoc), 2025-2026 Electrical Engineering (edoc), 2025-2026 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2025-2026 Génie électrique (edoc) EDEE Electrical Engineering (edoc) EDEE
obligatoire mandatory
3 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Achouri Karim 175309
Microtechnique MT Microengineering MT
. 4543921481 Applied Electromagnetics for Metamaterial Design Applied Electromagnetics for Metamaterial Design 3
Oral Oral Crédit Credits 3 Session hiver Session winter HIV HIV
. Photonics minor, 2025-2026, Semestre automne Photonics minor, 2025-2026, Autumn semester Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2025-2026 Semestre automne H HIVER Autumn semester H Photonics minor MIN_PHOTONICS Photonics minor MIN_PHOTONICS
optionnel optional
3 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Achouri Karim 175309
Microtechnique MT Microengineering MT
. 4543921481 Applied Electromagnetics for Metamaterial Design Applied Electromagnetics for Metamaterial Design 3
Oral Oral Crédit Credits 3 Session hiver Session winter HIV HIV
. Photonique (edoc), 2025-2026 Photonics (edoc), 2025-2026 Ecole polytechnique fédérale de Lausanne EPFL Ecole polytechnique fédérale de Lausanne EPFL 2025-2026 Photonique (edoc) EDPO Photonics (edoc) EDPO
obligatoire mandatory
3 Cours Courses Heure(s) hebdo x 14 semaines Hour(s) per week x 14 weeks H hebdo H hebdo Achouri Karim 175309
Microtechnique MT Microengineering MT
. 4543921481 Applied Electromagnetics for Metamaterial Design Applied Electromagnetics for Metamaterial Design 3
Oral Oral Crédit Credits 3 Session hiver Session winter HIV HIV
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