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Fundamentals of Photonics

or Introduction to Lightwave Technologies (ILT)

This course is taught during the Spring semester at the Department of Electrical and Computer Engineering of Aarhus University. It is part of the Photonics teaching portfolio.

Objectives of the course:

After this course the student should be familiar with the essential role photonics plays and will play in the world and in the field of electrical engineering in particular.
The main objective of the course is to acquaint the student with the fundamentals of optics and quantum mechanics and to show how these relate to the field of photonics and its applications. This will be achieved by revisiting and/or introducing the fundamentals of classical optics and quantum mechanics. Principles that are of key importance for the field of photonics will then be discussed in more detail and application examples will be given.

Learning outcomes and competences:

The participants must at the end of the course be able to:

  • understand fundaments of photonics, as rooted in both optics and quantum electronics;
  • understand how fundamental optics and quantum mechanics relate to the broad field of photonics;
  • analyze quantitatively basic optical and photonic elements;
  • understand how photonics impacts the field of electrical engineering.

ECTS credits: 5

Course coordinator: Nicolas Volet

Compulsory programme: Active participation.

Prerequisites: Electromagnetism, Optics.

Course assessment:
Oral exam based on a research paper.
Seven-point grading scale. External co-examination.

Where and when?

  • At AU-ECE, Building 5125 ("Edison", Finlandsgade 22)
    – Mondays 12:00–14:00 in Room 120
    Exercises + lab demos: 
    – Thursdays 10:00–12:00 in Room 423

Course contents

The course starts with a review of classical optics, including Maxwell’s equations, geometrical optics and Gaussian beams. This theory will be applied to practical cases, such as mirrors, interferometers, resonators, gratings, optical fibers and waveguides for optical chips. The second part of the course will focus on the basics of quantum mechanics and how light interacts with matter. The diode laser will be discussed in detail as a specific and important example of light-matter interaction. Furthermore, throughout the course the relevance of photonics to the field of electrical engineering will be highlighted by illustrative examples, such as optical memory, imaging technologies, and close integration with electronics for sensors and telecommunication and interconnect networks.

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

  • Part 1 (Sessions 1–7) introduces different topics of optics.
  • Part 2 (Sessions 8–15) focusses more on the integrated part.

Part 1

1. Electric and magnetic fields (Jan. 29 + Feb. 1)
Recap on complex numbers and differential operators.
Maxwell's equations and complex fields.
Fourier decomposition, separation of variables and trial solution.
Pulses, small-signal modulation and continuous-wave (cw) operation.
Wavenumber, attenuation coefficient and effective refractive index. 
Expressions for the electric field.

2. Direction of propagation (Feb. 5 + 8)
Constitutive relations. Helmholtz’ equation. 
Relative directions of the fields.
Poynting vector, time average.
Intensity and optical power.
Walk-off effect.
Boundary conditions. Snell's law.
Total internal reflection. Evanescent field.

3. Interface between materials (Feb. 12 + 15)
Transverse polarizations.
Coefficients of reflection and transmission.
Fresnel's relations.
Brewster's angle. Phase jumps.
Thin films: antireflection (AR) coating, bandpass filter, distributed Bragg reflector (DBR).
Goos-Hänchen effect.

During the exercice session on Thursday (Feb. 15), we will use the software EMode Photonix.
Information on how to get started can be found here.
Please go through the information provided at this link and install the license.

4. Gaussian waves (Feb. 19 + 22)
Dispersion relation and paraxial wave equation. Material refractive index.
Gaussian solution. Rayleigh length. Beam waist and divergence. Gouy's phase.
Effective beam area. M-squared parameter.

5. Generation of light (Feb. 26 + 29)
Incandescence and blackbody radiation.
Planck's spectrum, Wien's law.
Foundations of quantum mechanics.
Spontaneous and stimulated emission.
Wavelength conversion.

  • Booklet: TBC
  • Slides: PDFPPT
  • Exercises: SOL

National Optics Congress in Odense: Feb. 27 + 28
Great opportunity to network with #photonics companies on the beautiful campus of University of Southern Denmark (SDU).
––> For students: all expenses paid for the conference experience including transport and accommodation.

6. Wavelength conversion (March 4 + 7)
Second-harmonic generation.
Optical frequency combs.

––> March 8 (Friday): deadline to submit group abstracts

Guest lecture from Asger Sellerup Jensen, Senior Market Development Manager & Head of Quantum at NKT Photonics
Video: MPG

Internship and project day: March 8 (Friday)
Starting at 7:45 in Building 5122, Room 122.
See this LinkedIn post.

7. Optical spectrum (March 11 + 14)
Ensemble average. Wiener-Khintchine theorem.
Phase noise, frequency noise and intrinsic linewidth.
Lorentzian spectrum of an ideal laser.
Flicker noise and dither tones.

––> Feedback on submitted abstracts

7b. Polarization of light
Polarization ellipse. State of polarization.
Stokes parameters.
Polarizers and waveplates.
Müller matrices.

  • Booklet: PDF
  • Slides: PDFPPT
  • Exercises: Lab session

8. Modes in optical fibers, part 1 (March 18 + 21)
Dispersion relation.
Characteristic equation and effective index.
Single-mode condition.

Research day: March 20 (Wednesday)
Pitches starting at 12:30 in Peter Bøgh Andersen Auditory in Building 5335.
Poster session starting at 13:30 in Building 5122, Room 122.

Introduction to Integrated Nonlinear Photonics (March 22)

March 25 – 29: no teaching at AU (Easter)

Part 2

** April 1 (Monday): public holiday (Easter Monday), no teaching **

––> April 4 (Thursday): group presentations

9. Modes in optical fibers, part 2 (April 8 + 11)
Intensity distribution.
Hybrid modes.
Electric mode profiles.

––> April 12 (Friday): deadline to submit individual abstracts

Introduction to Photodetection (April 11)

10. Multiplexing (April 15 + 18)
Wavelength division multiplexing (WDM).
Splitters and combiners.

––> Feedback on submitted abstracts: PDFPPT

  • Booklet: TBC
  • Slides: PDFPPT
  • Exercises: PDF

11. Directional couplers and interferometers (April 22 + 25)
Directional couplers and supermodes. Phase-matching condition.
Mach-Zehnder interferometers (MZIs).
Multi-mode interference (MMI) couplers.
Optical hybrids and coherent receivers.

Teacher: Asger

12. Ring resonators (April 29 + May 2)
Transmission spectrum. Critical coupling.
Quality factor. Effective phase shift.
Applications: filters, mirrors, isolators, optical frequency combs, and all-optical switches.

Teacher: Pedro

13. Phase modulation (May 6)
Electro-optic effects. Pockels cells.
Electro-optic modulators (EOMs). Generation of sidebands.

Teacher: Jeppe

** May 9 (Thursday): public holiday (Ascension Day), no teaching **

  • Booklet: PDF
  • Slides: PDF – PPT
  • Exercises: PDF

14. Last session (May 13 + 16)

Teacher: Asger / Jeppe / Pedro

Course evaluation

––> May 16 (Thursday): individual presentations (rehearsal)

Course evaluation

We hope you enjoyed this course, and we want to improve next semester.
Please take a few minutes to answer this Google survey (anonymous).

Nick, Asger, Jeppe, and Pedro

Simulation exercises

For numerical simulations of modes in waveguides, we will use the software EMode Photonix.
Information on how to get started can be found here.

Exam: June 24, 2024 (Monday)

A design study involving one or more research papers about optical technologies.

  • April 12, 2024 (Friday): deadline to submit your abstract (100 words)
  • May 16, 2024 (Thursday): individual presentations (rehearsal)

For those that would like to attend the exam, please send your abstract to Nicolas Volet by email before the above deadline.

The exam is oral, and the duration is 20 min.
We ask you to prepare a presentation for 10 min, leaving 10 min for questions.
At the exam, there will be a co-examiner external to AU.


The 7-point grading scale is used for the assessment.

  • The highest grade is 12, and corresponds to:
    "an excellent performance displaying a high level of command of all aspects of the relevant material, with no or only a few minor weaknesses"
  • The minimum grade for passing the exam is 2, and corresponds to:
    "a performance meeting only the minimum requirements for acceptance"

How to choose a topic for the design study?

Below are applications notes on recent hot topics in photonics. They are meant to provide a brief entry point for a broad audience.

Other links

Other useful links are provided below.

RP Photonics Encyclopedia
An encyclopedia of optics and optoelectronics, laser technology, optical fibers, nonlinear optics, optical communications, imaging science, optical metrology, spectroscopy and ultrashort pulse physics.

An American privately held optical equipment company. In addition to their products, Thorlabs' website contains technical resources that include tutorials, application notes, white papers, lab facts, etc.

European Photonics Industry Consortium (EPIC)
A not-for-profit association that serves the photonics community through a regular series of workshops, market studies and partnering.
EPIC also manages the website Jobs in Photonics.

The largest collection of peer-reviewed optics and photonics content.


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

Slides and other files are available at this SharePoint site.