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This course is part of our Photonics Teaching Program. It is offered by the Doctoral School of Photonics at EPFL. It is also an official PhD course in Denmark.
The objective of the course is to acquaint the students with the principles of nonlinear optics, their use in photonic integrated circuits and the applications of this technology for telecommunication, spectroscopy and metrology.
It introduces the main nonlinear optical effects, related applications, and the material platforms available for photonic integration. It explores the physics of conversion between modes in waveguides. Finally, it applies numerical simulation software to solve design problems.
At the end of the course, the student should be able to:
This course first introduces some fundamentals of light-matter interaction and the most important nonlinear optical effects. Then an overview of relevant photonic devices is presented, including lasers, waveguides and photodetectors. It is discussed how these photonic devices can be considered as building blocks that can be combined into a circuit and which material systems can be used for that.
Emphasis is put on the required trade-offs and the main differences between material systems. A Python-based simulation software is used to illustrate the concept of optical mode, and as a design tool to optimize device parameters to obtain efficient nonlinear processes (such as frequency conversion).
ECTS credits: 3
This includes 30 hours of lectures, and an extra 60 hours for preparation and to work on the design study.
Prerequisites: Prior knowledge of electromagnetism and optics.
Compulsory program: Active participation, submission of report with design study.
Course assessment: A project report with a design study
Special comments on this course: This course is available online or in person at EPFL.
Instructors: Christophe Galland + Nick Volet
During week 41: October 5 (Monday) – October 9 (Friday), 2026.
1. Chief equation
Electromagnetic foundations
Wave equation for nonlinear optics
Optical modes and power normalization
Eigenvalue equation and dispersion relation
Dynamic equation for guided waves
General propagation ("chief") equation
2. Second-order nonlinearities
Second-order nonlinear polarization
Crystal symmetry and nonlinear susceptibility tensors
Nonlinear coupling in integrated waveguides
General coupled-amplitude equations
Second-harmonic generation (SHG)
Difference-frequency generation (DFG)
3. Second-harmonic generation (SHG)
Phase matching
Pump depletion
Nonlinear coupling coefficient
GaAs waveguide design
Mode simulations
Power and phase evolution
4. Difference-frequency generation (DFG)
Phase matching
Coupled power evolution
Phase evolution
AlGaAs waveguide design
Mode simulations
Mid-infrared frequency conversion
5. Third-order nonlinearities
Third-order nonlinear polarization
Symmetry of the third-order susceptibility tensor
Nonlinear coupling between optical modes
Coupled-amplitude equations for third-order interactions
Third-harmonic generation (THG)
Degenerate four-wave mixing (FWM)
6. Third-harmonic generation
Phase matching
Pump depletion and nonlinear energy transfer
Power and phase evolution
Effects of propagation loss
Characteristic nonlinear interaction length
Analytical solutions and power scaling
Quantum session
7. Nonlinear Schrödinger (NLS) equation
Group velocity and group-velocity dispersion
Derivation of the nonlinear Schrödinger equation
Interplay between dispersion and Kerr nonlinearity
Optical solitons
Optical Kerr effect
Power-dependent phase and effective refractive index
Ring resonators and all-optical switches
These optional research supplements extend the guided-mode formalism of the core course to nonlinear interactions involving radiation modes. They document an ongoing theoretical development and are provided in their current form for reference. They are not required for completion of the course.
Radiation directions and the Čerenkov cone
Continuum representation of radiation fields
Dirac-distribution normalization
Longitudinal power flux
Reduced radiation-mode model for rib waveguides
Field profiles in absorbing multilayer structures
Electromagnetic boundary conditions and normalization
Guided-to-radiation-mode nonlinear coupling
Coupled-amplitude equations for the radiation continuum
Longitudinal and transverse phase mismatch
Čerenkov phase-matching condition and emission angle
Nonlinear coupling coefficient
BBO waveguide geometry and crystal orientation
Guided-mode simulations for deep-UV generation
A design study, summarized in a 5-page report.
For those that would like a course certificate (and the 3 ECTS), please send your abstract and report to Nick Volet by email before the above deadlines.
For registration and inquiries, please send an email to Nick Volet.
Slides and other files are available at this SharePoint site.
LaTeX files (for booklets and exercises) are available at this Overleaf project.
