MIT OpenCourseWare

Browse materialsMIT 18.369 · Spring 2008

Mathematical Methods in Nanophotonics

Subjects: Algebra · Linear Algebra · Mathematics · Physics · Quantum Mechanics

Art: Anonymous painter,15th century, Westerner and Arab practicing geometry 15th century manuscript, 15th… · Public domain

Instructor: Prof. Steven G. Johnson
Term: Spring 2008
Level: Graduate
What's inside: 6 problem sets · 1 reading · 13 other files · 6 web pages
Materials open: MIT OCW

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About this course

Source: MIT OpenCourseWare 18.369 Mathematical Methods in Nanophotonics, Spring 2008, Prof. Steven G. Johnson — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.

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Grouped by section, as MIT organized them. Not sequenced or ordered.

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MIT OpenCourseWare, Prof. Steven G. Johnson, 18.369 Mathematical Methods in Nanophotonics, Spring 2008.

License: CC BY-NC-SA 4.0 · Edition: Spring 2008 · Open the original course on OCW ↗

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Mathematical Methods in Nanophotonics

Before you start

What's here, and what isn't

Not included here

Materials by section

Readings

Assignments

Exams

Tools

Lecture 1: Maxwell’s equations and linear algebra

Lecture 2: Modes of a metal box and mirror symmetry

Lecture 3: Symmetry groups, representation theory, and eigenstates

Lecture 4: Translational symmetry, waves, and conservation laws

Lecture 5: Total internal reflection and the variational theorem

Lecture 6: Discrete translations and Bloch’s theorem MPB demo

Lecture 7: Bloch’s theorem, time reversal, and diffraction

Lecture 8: Photonic band gaps in 1d, perturbation theory

Lecture 9: 1d band gaps, evanescent modes, and defects

Lecture 10: Waveguides and surface states, omni-directional reflection

Lecture 11: Group velocity and dispersion

Lecture 12: 2d periodicity, Brillouin zones, and band diagrams

Lecture 13: Band diagrams of 2d lattices, symmetries, and gaps

Lecture 14: Triangular lattice, complete gaps, and point defects

Lecture 15: Line and surface defects in 2d, numerical methods introduction

Lecture 16: Conjugate-gradient, finite-difference time-domain (FDTD) method

Lecture 17: More FDTD: Yee lattices, accuracy, Von-Neumann stability

Lecture 18: Perfectly matched layers (PML), filter diagonalization

Lecture 19: 3d photonic crystals and lattices

Lecture 20: Haus coupled-mode theory, resonance, and Q

Lecture 21: Coupled-mode theory with losses, splitter / bend / crossing / filter devices

Lecture 22: Bistability in a nonlinear filter, periodic waveguides

Lecture 23: Photonic-crystal slabs: gaps, guided modes, waveguides

Lecture 24: Cavities in photonic-crystal slabs Photonic-crystal fibers

Lecture 25: Hollow-core and solid-core photonic-bandgap fibers