Fundamentals and Applications of Metamaterials

Timetable

Lectures (1 h) followed by Exercises (1 h) will be held every Monday, starting on Monday 5 October 2026.

Module aim (aims)

This course introduces the fundamental physical principles of metamaterials, their key applications in photonics, phononics, plasmonics, sensing, and signal processing, and the main methods used for their design, synthesis, and characterization. Specifically, the module aims to explain:

a) Basic principles
Understand the scope, working principles, and research methods of metamaterials, with emphasis on mesoscopic and nanostructured systems fabricated via bottom-up and top-down approaches, and on modern microscopic and spectroscopic characterization techniques.

b) Fundamental theory
Develop familiarity with core concepts from wave mechanics, condensed-matter physics, photonics, and nanotechnology that underpin the operation and applications of metamaterials.

c) Design, synthesis, and characterization
Learn (i) the basic principles of designing and optimizing metamaterials using finite-element calculations, (ii) modern nanofabrication techniques such as nanoparticle self-assembly, electron-beam lithography, photolithography, and focused-ion-beam milling, and (iii) characterization methods including scanning and transmission electron microscopy (SEM, TEM) and Brillouin light scattering.

d) Key concepts
Explore major research directions including photonic crystals and band gaps, plasmonic nanostructures and superlattices, phononic crystals, Bragg and hybridization gaps, disordered and hyperuniform systems, thermal engineering, sensing and signal-processing applications, transducers, modulators, optomechanics, and topological metamaterials.

Pre-requisites in terms of knowledge, skills and social competences (where relevant)

Students are expected to have a good command of English, familiarity with searching and reading scientific literature, and basic skills in mathematics (differentiation and integration). Basic knowledge of classical mechanics (Newton’s laws and mechanical oscillators), as well as introductory electrostatics and optics, is also required.

Syllabus

Week 1: Controlling wave transport with artificial periodic structures. Introduction to nanotechnology and its role in increasing metamaterial operating frequencies. Examples of photonic and phononic metamaterials. Ref. [1] (see reading list)

Week 2: Bottom-up vs. top-down synthesis: nanoparticle self-assembly, electron-beam lithography, photolithography, and focused-ion-beam milling. Structural control at micro- and nanoscale and its impact on metamaterial properties. Ref. [2]

Weeks 3–4: Characterization techniques: SEM, TEM, AFM; Raman and Brillouin light scattering; Raman thermometry, SERS, and momentum-resolved Brillouin spectroscopy with selected metamaterial examples.

Weeks 5–6: Mechanical waves: harmonic oscillator, phonons in 1D monoatomic and diatomic chains, derivation and solutions of the 1D wave equation, dispersion relations and band-gap formation. Ref. [3]

Weeks 7–8: Phononic crystals across length scales; colloidal and lithographically fabricated systems; Lamb modes; types of phononic band gaps; effects of coherence, disorder, and surface roughness. Refs. [1,4,5]

Weeks 9–10: Electromagnetic waves: Maxwell equations, derivation of the optical wave equation, dielectric response, optical properties of materials, and electromagnetism as an eigenvalue problem. Refs. [6,7]

Weeks 11–12: Plasmons: Frohlich resonance of nanoparticles, plasmon modes in nanorods and superstructures, plasmonic superlattices, plasmonic dispersion relationships in nanoparticle chains, plasmonic losses and applications (SERS, photocatalysis, photothermal conversion). Refs. [8,9]

Weeks 13–14: Coupling electromagnetic and mechanical excitations: Surface acoustic waves and SAW devices, microwave signal processing, optomechanics, electrostriction, photoelastic and moving-boundary effects, piezoelectric materials, and optomechanical modulators.

Week 15: Negative refraction in metamaterials, Ref. [10]. One-way transport and phononic diodes. Topological metamaterials: Berry phase and Berry curvature, Chern insulators, and Zak phase, Ref. [1].

Reading list

[1] Journal of Applied Physics, 129(16), 160901 (2021).
https://doi.org/10.1063/5.0042337

[2] Advanced Functional Materials, 30(8), 1904434 (2020).
https://doi.org/10.1002/adfm.201904434

[3] Mechanical Metamaterials. Lecture notes by Sebastian Huber, ETH Zurich.
http://www.cmt-qo.phys.ethz.ch  

[4] Journal of Physics D Applied Physics, 55(19), 193002 (2022).
https://doi.org/10.1088/1361-6463/ac4941

[5] Nano Letters, 16(9), pp. 5661–5668 (2016).
https://doi.org/10.1021/acs.nanolett.6b02305

[6] Griffiths, D. J., Introduction to Electrodynamics, 4th ed., Cambridge University Press.

[7] John D. Joannopoulos, Steven G. Johnson, Joshua N. Winn, and Robert D. Meade, Photonic Crystals: Molding the Flow of Light, Second Edition, Princeton University Press, 2008.

[8] Maier, S. A. Plasmonics: Fundamentals and Applications. New York: Springer, 2007.

[9] Plasmon-induced hot carrier science and technology. Nature Nanotechnology, 10(1), 25–34 (2015). https://doi.org/10.1038/nnano.2014.311

[10] Chapter 16 of the book "The Physics of Solids: Essentials and Beyond" by Economou, E. N. Springer Berlin, Heidelberg (2010).