Single-Course English 5 ECTS

Waveguide optics

Overall Course Objectives

To establish a solid understanding of the physical and technological background for optical waveguides and components for the control of a broad spectrum of light, from the visible to THz frequencies. Optical circuits are expected to become of great importance for future engineers within areas such as telecommunication, sensors and computer architecture. Optical fibers already play a crucial role within long-distance signal transmission, and are increasingly used as sensors, in laser systems, and for signal processing. This course gives a thorough understanding of optical fibers, an introduction to integrated optical and plasmonic circuits, and a discussion of elementary THz technology. The course constitutes a solid platform for further work (e.g. masters projects) within these fields.

Learning Objectives

  • Describe the structure of modal fields in in optical fibres with a parabolic index profile, and write down expressions for the intermodal dispersion.
  • Estimate the number of guided modes in step-index optical fibers, as well as dispersion, effective area and bend loss, for given values of core radius and index contrast.
  • Describe the structure, guidance mechanisms and applications of photonic crystal fibers, write down the single-mode criterion and estimate dispersion and effective area for standard index-guiding crystal fibers.
  • Describe the structure, modal fields, propagation losses and applications of various types of hollow-core fibers.
  • Discuss prism- and grating-assisted coupling of light to surface plasmon polaritons, as well as prism-assisted beamsplitting in the THz regime.
  • Derive equations for reflection and transmission in fiber-integrated Bragg gratings. Sketch solutions for uniform Bragg gratings, as well as chirped and apodized gratings.
  • Set up full vectorial equations for electromagnetic waves in optical fibers. Describe the weak-guidance approximation, and the scaling laws it entails.
  • Formulate equations controlling the incoupling of light in waveguides. Use modal coefficient formalism to argue for symmetry conservation in tapers.
  • Derive coupled-mode equations for directional couplers, and sketch their solutions. Describe the dependence of the coupling coefficient on the waveguide structure.
  • Describe the properties of surface plasmon polaritons (SPP). Set up the wave equation describing SPP, and outline the dispersion diagram for SPP waves at air/metal interfaces.
  • Describe waveguidance of broadband signals in the THz range,the properties of dispersion-free as well as dispersive metallic waveguides, and loss mechanisms for THz waves in waveguides.

Course Content

Starting from Maxwell’s equations, the fundamental principles for localization and manipulation of light are established. Dielectric waveguides, their geometries and mutual coupling, will be discussed. Furthermore, plasmonic waveguides and metallic waveguides for THz radiation are introduced. The course gives an introduction to the building blocks of optical circuits, such as passive waveguides, Bragg gratings and couplers. Microstructured optical fibers and their bandgap effects are also introduced. The course contains excursions to danish companies, thus giving a good impression of the ongoing activities within the field.

Recommended prerequisites

10036/31400/34020/34021, Knowledge of Maxwells field equations, and the electromagnetic wave equation. Knowledge of vector mathematics, calculus, and differential equations.


See course in the course database.





13 weeks




DTU Lyngby Campus

Course code 34041
Course type Candidate
Semester start Week 5
Semester end Week 19
Days Fri 8-12

7.500,00 DKK