955 подписчиков
248 видео
Eigenmode expansion: overlap matrices
Laurent series
EX: Time reversal symmetry
Periodic points
Finite difference approximation of derivatives
Chaos in a photonic system
EX: Second form of Bloch's theorem in 3D
The eigenfunctions of a Hermitian operator are orthogonal
A variational form of the Helmholtz eigenvalue problem
Photonic crystals
Bessel's differential equation
EX: Fraunhofer diffraction pattern of circular aperture (Airy disk)
Sensitive dependence on initial conditions
Phase portraits
EX: Laurent series in outer ring
Sinks and sources
Saddle points
Two metal plates and a dielectric walk into a bar...
Stability of linear maps
Continuous systems
Guided modes in the slab waveguide
A recurrence relationship for Bessel functions
Cobweb diagrams
Hermite's differential equation revisited
Functions of a complex variable
Using complex contour analysis to solve integrals with trigonometric functions
The eigenvalues of Θ are positive
Stable and unstable manifold
Dynamical systems
Square lattice of dielectric rods
1D maps and logistic growth
Stability theorem for fixed points
The Lorenz attractor
2D maps - Henon
The irreducible Brillouin zone
Family of logistic maps
The Brillouin zone in 3D
Slab waveguide
EX: The integral of sin(x) / x (part 2)
Series expansion using Hermite polynomials
A generating function for Bessel functions
Non-linear maps and the Jacobian matrix
Fun with commutators
