Waves in composites and metamaterials

Welcome to this learning project about Waves in composites and metamaterials!

Learning Project Summary

• Project code:
• Suggested Prerequisites:
  • Partial differential equations
  • Introduction to Elasticity
  • Electromagnetism
• Time investment: 6 months
• Portal:Engineering and Technology
• School:Engineering, Mathematics
• Department:Mechanical Engineering, Electrical Engineering
• Stream: Applied mathematics
• Level: Graduate

Content summary

This course is an introduction to metamaterials and composites and how they interact with electromagnetic and elastic waves.

The content of these notes is based on the lectures given by Prof. Graeme W. Milton (University of Utah) in Spring 2007.

The author of these Wikiversity notes has, in addition to transcribing the lectures given in class, added to the content of the course by expanding on the details. The notes have subsequently been corrected and modified by several other anonymous authors. However, some errors still remain and the reader is urged to check the calculations before using any of the results.

Goals

This learning project aims to give the student the basic tools needed to start working on metamaterials and waves in composites.

Contents

Lessons

• Lecture 1: Rainbows
• Lecture 2: Airy theory
• Lecture 3: Maxwell equations in media
• Lecture 4: Fresnel equations
• Lecture 5: Perfect lenses and negative density materials
• Lecture 6: Anisotropic mass and generalization
• Lecture 7: Elastodynamics and electrodynamics
• Lecture 8: Acoustic metamaterials and negative moduli
• Lecture 9: Fading memory and waves in layered media
• Lecture 10: Airy solution and WKB solution
• Lecture 11: TE waves in multilayered media
• Lecture 12: Continuum limit and propagator matrix
• Lecture 13: Waves in layered media and point sources
• Lecture 14: Point sources and EM vector potentials
• Lecture 15: Mie theory and Bloch theorem
• Lecture 16: Bloch waves and the quasistatic limit
• Lecture 17: Bloch waves in elastodynamics and bubbly fluids
• Lecture 18: Duality relations and phase interchange identity in laminates
• Lecture 19: Backus formula for laminates and rank-1 laminates
• Lecture 20: Hierarchical laminates and Hilbert space formalism
• Lecture 21: Effective tensors using Hilbert space formalism
• Lecture 22: Transformation-based cloaking in electromagnetism
• Lecture 23: Transformation-based cloaking in mechanics
• Lecture 24: Willis equations for elastodynamics

Readings and other resources

• An Introduction to Metamaterials and Waves in Composites, B. Banerjee, 2011, CRC Press, ISBN 1439841578.