Related Experiment Video
Updated: Aug 19, 2026

Microwave Photonics Systems Based on Whispering-gallery-mode Resonators
Published on: August 5, 2013
Canonical Hamiltonian formulation of the nonlinear Schrödinger equation in a one-dimensional, periodic Kerr medium
1Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario, Canada M5S 1A7.
Abstract:
A canonical Hamiltonian formulation of the nonlinear Schrödinger equation has been derived in this paper. This formulation governs the dynamics of pulse propagation in a one-dimensional, periodic Kerr medium when the frequency content of the pulse is sufficiently narrow relative to a carrier frequency, and sufficiently far removed from a photonic band gap of the medium. Our Hamiltonian is numerically equal to the energy, and our fields obey canonical commutation relations, so the theory can easily be quantized. We clarify the nature of the conserved quantities associated with simple symmetries.
More Related Videos
11:03An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
08:04Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
Related Concept Videos
The de Broglie Wavelength
The Quantum-Mechanical Model of an Atom
First Law: Particles in One-dimensional Equilibrium
Poisson's And Laplace's Equation
Symmetry in Maxwell's Equations
Differential Form of Maxwell's Equations