Waveguide optics

• 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.

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.

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