Notes

These notes introduce the mathematics and optical physics used by PyNLO, covering the basics of Fourier transforms and the linear and nonlinear propagation of light in optical modes.

Topics

• Fourier Transforms
  • The Fourier Family
  • Useful Relationships
  • Numeric Implementation of DFTs
• Linear Optics
  • Maxwell’s Equations
  • Plane Waves
  • Waveguides
• Nonlinear Optics
  • Local Modes
  • Multi-Mode Propagation Equations
  • Single-Mode UPE
  • Numerical Implementation
• Supplementary Material
  • Transverse and Longitudinal Vector Components
  • Transverse and Longitudinal Maxwell’s Equations
  • Derivation of the Multi-Mode Propagation Equations
  • Unit Analysis of the Effective Nonlinear Parameters
  • Relationship Between the Kerr Parameter and the Nonlinear Susceptibility