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Integrated Nonlinear Photonics

Next edition

During "week 42": October 14 (Monday) – October 18 (Friday), 2024.

This course is part of the Photonics teaching portfolio. It is offered by the Doctoral School of Photonics at EPFL. It is also an official PhD course in Denmark.

Objectives of the course:

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.

Learning outcomes and competences:

At the end of the course, the student should be able to:

  • Explain the main nonlinear optical effects and the main platforms for photonic integration that are available.
  • Make a design study, with a qualitative understanding of the required trade-offs and a quantitative knowledge of the typical component and/or circuit operation parameters.

Prerequisites: Optics, electromagnetism

Compulsory programme:
Active participation, submission of report with design study.

Course assessment:
A project report with a design study

ECTS credits: 3
This includes 30 hours of lectures, and an extra 60 hours for preparation and to work on the design study.

Special comments on this course:
This course is available online or in person at EPFL.

Instructors: Christophe Galland + Nicolas Volet


Monday (Oct. 14) through Friday (Oct. 18).

  • Mornings: from 9:15 to 12:00
  • Afternoons: from 14:15 to 17:00

Detailed program: PDF

Course contents

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).

The content of the course is summarized into several booklets. 
These booklets are meant to be concise and include all mathematical steps.


1. Chief equation 
Background from electromagnetism.
Wave equation for nonlinear optics.
Dispersion relation. Dynamic equation. Chief equation.

2. Second-order nonlinearities
Formalism for second-order nonlinearity.
Coupled-amplitude equations for second-harmonic generation (SHG) and for difference-frequency generation (DFG).

3. Second-harmonic generation (SHG)
Undepleted regime. Condition of perfect phase-matching.
Specific examples in a zincblende waveguide.
Signal power and pump power versus length.

4. Difference-frequency generation (DFG)
Mid-infrared generation.
Numerical examples.

5. Third-order nonlinearities
Chi-3 tensor and symmetries.
Coupled-amplitude equations for third-harmonic generation (THG) and degenerate four-wave mixing.

6. Third-harmonic generation
Numerical examples.

  • Booklet: PDF

Quantum session

7. Nonlinear Schrödinger (NLS) equation
Ring resonators.
Optical Kerr effect. All-optical switches.

Simulation exercises

The exercise sessions involve numerical simulations of modes in waveguides.
We will use the software EMode Photonix, and information on how to get started can be found here.

#1 SHG in GaAs waveguides: PDF – Solutions

Course assessment

A design study, summarized in a 5-page report.

  • November 5, 2023 (Sunday): deadline to submit your abstract (100 words)
  • December 3, 2023 (Sunday): deadline to submit your report (5 pages)

For those that would like a course certificate (and the 3 ECTS), please send your abstract and report to Nicolas Volet by email before the above deadlines.


For registration and inquiries, please send an email to Nicolas Volet.


LaTeX files (for booklets and exercises) are available at this Overleaf project.

Slides and other files are available at this SharePoint site.