*— Course "Optical Waveguide Theory", University of Paderborn, Germany, Summer 2023 —*

**A ** |
Photonics / integrated optics, theory: Maxwell equations; dielectric waveguides & circuits: phenomena, introductory examples. |

**B ** |
Brush up on mathematical tools: vector calculus, Fourier transform, differential equations, linear problems with homogeneity along a coordinate, a little variational calculus. |

**C ** |
Maxwell equations, survey of different formulations, time and frequency domain, interfaces, energy and power flow, material properties, dispersion. |

**D ** |
Classes of simulation tasks: scattering problems, time and frequency domain, mode analysis, resonance problems; spatial dimensions / symmetry; scalar, quasi-vectorial approximations; initial value problems (beam propagation method, brief); boundary conditions (brief). |

**E ** |
Normal modes of dielectric optical waveguides: governing equations, symmetry properties, polarization, classification, orthogonality, completeness properties; mode superpositions: power evaluation; (super-) mode interference. |

**F ** |
Examples for dielectric optical waveguides: multilayer slab waveguides, channel waveguides of rib- or strip-type (effective index model), optical fibers, complex waveguides (loss/gain, leakage). |

**G ** |
Waveguide discontinuities (BEP/QUEP simulations, brief), examples, scattering matrices, reciprocal circuits. |

**H ** |
Bent optical waveguides: general, 2D, examples, field displacement, radiation losses; whispering gallery resonances; circular integrated optical microresonators. |

**I ** |
Conventional (codirectional) coupled mode theory, parallel optical channels: parametrized models, derivation of CMT equations by means of reciprocity techniques / from a variational principle; perturbation theory for optical waveguides. |

**• ** |
Hybrid analytical / numerical coupled mode theory (Graduate lecture). |

**J ** |
A touch of photonic crystals; a touch of plasmonics. |

**• ** |
Oblique semi-guided waves |

**A-J ** |
Lectures A-J (one file). |