Introduction to Nonlinear Optics


Nonlinear optics is the study of the response of dielectric media to strong optical fields. The fields are sufficiently strong that the response of the medium is, as its name implies, nonlinear. That is, the polarization, which is the dipole moment per unit volume in the medium, is not a linear function of the applied electrical field. This module is on nonlinear optics at the level of a beginning graduate student. The intent of the module is to provide an introduction to the field of nonlinear optics that stresses fundamental concepts and that enables the student to go on to perform independent research in this field.


Chapter 1: The Nonlinear Optical Susceptibility

  • Introduction to Nonlinear Optics
  • Descriptions of Nonlinear Optical Processes
  • Formal Definition of the Nonlinear Susceptibility
  • Nonlinear Susceptibility of a Classical Anharmonic Oscillator
  • Properties of the Nonlinear Susceptibility
  • Time-Domain Description of Optical Nonlinearities
  • Kramers-Kronig Relations in Linear and Nonlinear Optics

Chapter 2: Wave-Equation Description of Nonlinear Optical Interactions

  • The Wave Equation for Nonlinear Optical Media
  • The Coupled-Wave Equations for Sum-Frequency Generation
  • Phase Matching
  • Quasi-Phase-Matching
  • Nonlinear Optical Interactions with Focused Gaussian Beams

Chapter 3: Quantum-Mechanical Theory of the Nonlinear Optical Susceptibility

  • Linear Response Theory

Chapter 4: The Intensity-Dependent Refractive Index

  • Descriptions of the Intensity-Dependent Refractive Index
  • Semiconductor Nonlinearities
  • Concluding Remarks

Chapter 5: Processes Resulting from the Intensity-Dependent Refractive Index

  • Self-Focusing of Light and Other Self-Action Effects
  • Optical Phase Conjugation
  • Optical Bistability and Optical Switching
  • Two-Beam Coupling
  • Pulse Propagation and Temporal Solitons

Chapter 6: Spontaneous Light Scattering and Acoustooptics

  • Features of Spontaneous Light Scattering

Chpter 7: Stimulated Brillouin and Stimulated Rayleigh Scattering

  • Stimulated Scattering Processes

Learning Outcomes

1. Understanding and knowledge in the field of nonlinear optics from the perspective of the nonlinear susceptibility.
2. Understanding and knowledge of propagation light waves through nonlinear optical media by means of the optical wave equation.
3. Understanding and knowledge of linear response theory.
4. Understanding and knowledge of nonlinear refractive index.
5. Understanding and knowledge on spontaneous and stimulated light scattering and on the related topic of acoustooptics.


1. Nonlinear Optics, third edition, Robert W. Boyd, Elsevier,2008
2. The Principles of Nonlinear Optics, Shen, Wiley & Sons 2003
3. The Quantum Theory of Nonlinear Optics, P. D. Drummond & M. Hillery, Cambridge 2014
4. Nonlinear Optical Systems, L. Lugiato, F. Prati & M. Brambilla, Cambridge 2015

External Evaluator

To be announced

Responsible Academic

Dr. Irit Juwiler (SCE), email:

Awarded ECTS