MATH 7875: Waves in Composites and Metamaterials

These lecture notes are based on a course given by Prof. Grame Milton at the University of Utah. My contribution has been to typeset the notes, draw the figures, and work out the detials of most of the equations.

The entire set of lecture notes is now on Wikiversity. You can find them at

Please send an email to banerjee at [] if you find mistakes in the notes.

-- Biswajit Banerjee - 18 Jan, 2008

o Lecture 1: Rainbows
o Lecture 2: Airy Theory
o Lecture 3: Maxwell's Equations in Media
o Lecture 4: Fresnel's Equations
o Lecture 5: Perfect Lenses and Negative Density Materials
o Lecture 6: Anisotropic Mass and Generalization
o Lecture 7: Elastodynamics and Electrodynamics
o Lecture 8: Acoustic Metamaterials and Negative Moduli
o Lecture 9: Fading Memory/Waves in Layered Media
o Lecture 10: Airy solution and WKB solution
o Lecture 11: TE waves in multilayered media
o Lecture 12: Continuum limit and propagator matrix
o Lecture 13: Waves in layered media and point sources
o Lecture 14: Point sources and EM vector potentials
o Lecture 15: Mie Theory and Bloch's Theorem
o Lecture 16: Bloch Waves and the Quasistatic Limit
o Lecture 17: Bloch Waves in Elastodynamics and Bubbly Fluids
o Lecture 18: Duality Relations/Phase Interchange Identity/Laminates
o Lecture 19: Backus Formula for Laminates/Rank-1 Laminates
o Lecture 20: Hierarchical Laminates/Hilbert space formalism
o Lecture 21: Effective tensors using Hilbert space formalism
o Lecture 22: Transformation-based Cloaking in Electromagnetism
o Lecture 23: Transformation-based Cloaking continued
o Lecture 24: Willis equations for Elastodynamics

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