Optical Waveguide Theory

Course L.048.24019 / L.048.92038, academic year 2023/2024, summer semester 2024. The course is part of the Master curricula for Electrical Engineering and Electrical Systems Engineering of the Faculty of Electrical Engineering, Computer Science, and Mathematics at the University of Paderborn. Besides students that follow the Engineering tracks, also students from other areas, where phenomena related to electrodynamics play a role, are most welcome. The course language will be English. Lecturer: Manfred Hammer.

• We meet for the first lecture on Wednesday, April 10, at 09:15 in room P1.5.01.4.
• Following a request from the participants, the meetings on Wednesdays have been shifted to Thursday afternoon. The table below shows the updated schedule.
• In week 22 we'll meet for a lecture on Tuesday, 28.05. at 09:15, as an exception.

Dielectric optical waveguides constitute key-elements of present-day integrated optical / photonic circuits. This course provides an introduction to their theoretical background, and, as such, a sound basis for further, more specific, modelling, simulation, and design work, as well as for experimental activities in the field.

Contents

• Photonics / integrated optics, dielectric waveguides: introductory examples, motivation.
• Brush up on mathematical tools.
• Maxwell equations, survey of different formulations; classes of simulation tasks.
• Normal modes of dielectric optical waveguides, orthogonality, completeness, scattering matrices, reciprocal circuits.
• Examples for dielectric optical waveguides (multilayer slabs, integrated channels, optical fibers), bent waveguides, whispering gallery resonances.
• Coupled mode theory, conventional codirectional, and hybrid analytical / numerical variant, perturbations of optical waveguides.
• Optional, brief remarks on: boundary conditions, initial value problems (beam propagation method), waveguide discontinuities (BEP/QUEP simulations), photonic crystal waveguides & fibers, plasmonic waveguides.

This course will not strictly follow a textbook. Most of our material, however, can be found, if not in a standard introduction to classical electrodynamics, then in slightly more specialized textbooks on optical waveguide theory or integrated optics. Examples are

• C. Vassallo, Optical Waveguide Concepts, Elsevier, Amsterdam (1991),
• K. Okamoto, Fundamentals of Optical Waveguides, Academic Press, San Diego, USA (2000), second and third editions are available,
• R. März, Integrated Optics: Design and Modeling, Artech House, Norwood, USA (1995),
• A.W. Snyder, J.D. Love, Optical Waveguide Theory, Chapman and Hall, London, UK (1983).

At the moment only a preliminary distribution of topics over lectures exists, which may be subject to change, depending on the progress of the course.

Schedule

Our weekly procedure consists of lectures (14×) and tutorials / exercises classes (7×), from week 15, April 10, until week 29, July 18, mostly on Thursdays, in the time slots 09:15 - 10:45 and 14:15 - 15:45 (Thu), in the seminar room P1.5.01.4 / P1.5.01.5 in the TET-corridor. The prospective schedule (irregularities are mostly caused by public holidays, and by absence / conference attendance of the lecturer) is as follows:

All sheets, as far as provided, are tentative; there is a chance that the contents will be adapted before the lecture, very briefly before the lecture, or, if mistakes are discovered, even after the lecture. Cummulative .pdfs of the sheets used in all lectures are available, in original and compactified form. Note that, along with the sheets used for the separate classes, these are likely to change. In addition to the sheets, the lectures will rely heavily on a traditional blackboard; it is recommended that students take notes.

In addition to the regular sheets, handwritten (…) lecture notes are available for further reference, originating frome the online summer semester 2020. These cover reasonably well the material that would have been discussed during the lectures, also those parts (like more elaborate derivations, blackboard) that are not explicitly on the sheets.

Organization

The lectures will be accompanied by bi-weekly homework assignments. These intend to deepen the topics of the lecture, to fill in omitted details, and to apply and extend the theory. While a discussion on the topics of the homework is encouraged, the problems are to be solved and the solutions to be written down individually. Solutions are to be handed in (on paper) at the beginning of the lecture indicated by the dots in the table above, at the latest. Earlier submissions are always welcome. The solutions will be (roughly) corrected and (roughly) graded. The problems will then be discussed in detail in the following exercises class. Each student is supposed to be able to explain her or his solutions, and each student should regularly present an answer to (part of) a problem. The bi-weekly tutorials will be an occasion to raise questions on the topics of the course, to ask for specific hints on homework problems, and to continue with the solutions. This obviously requires the students to have studied the problems in advance. The course closes with an oral examination.

(11.04.2024)