Computational methods for microoptics and photonics 1103-4Fot24
The course:
1. Linear systems; impulse response and the modulation transfer function - application to diffractive optics, and to the development of diffractive and holographic elements.
2. Finite difference method - various discretization schemes; boundary conditions; stability conditions;
3. Fundamentals of the beam propagation method (BPM) - application to the analysis of waveguide elements, and to the determination of the modal structure of optical waveguides.
4. Finite difference time domain method (FDTD).
5. Plane-wave decomposition method - calculation of the modal structure of photonic crystals.
6. Selected applications of numerical methods to the optics of photonic crystal, to analysis of sub-wavelength diffractive gratings, and plasmonic elements.
The exercises have a numerical character and require the knowledge of Python or some other language with similar capabilities eg. Matlab. The oral exam includes a discussion on the numerical work done during the course.
Mode
Prerequisites (description)
Course coordinators
Learning outcomes
The student knows the basic analytical and numerical methods used for modeling optical and photonic structures. They understand the operating principles of the TMM/SMM, FDTD, BPM, RCWA, and PWM methods, as well as the fundamentals of the finite-element method in the context of electromagnetic field analysis. The student is familiar with the Jones and Stokes formalism and the basics of Gaussian beam optics and ABCD matrix theory.
The student is able to apply appropriate modeling methods (TMM/SMM, FDTD, BPM, RCWA, PWM) to the analysis of thin-film, waveguide, and periodic structures. They can compute free-space field propagation, including evaluating diffraction integrals, and model diffractive and polarization optical elements. The student is able to use selected inverse-problem techniques (e.g., compressive sensing, phase retrieval) for the analysis and reconstruction of optical fields.
The student is prepared to critically evaluate the results of numerical simulations and to select appropriate modeling methods for a given photonic problem. They understand the need to further develop their knowledge and skills in modern computational tools used in photonics.
Assessment criteria
Oral exam – includes questions related to the topics covered in the lectures and exercises; it evaluates the student’s understanding of photonic modeling methods and their ability to interpret the results. During the exam, the 10 numerical assignments completed in the exercises are also discussed.
Bibliography
B. Saleh, M. Teich, Fundamentals of Photonics, John Wiley & Sons, wyd. 3, 2019
M. Sadiku, Numerical Techniques in Electromagnetics, CRC Press, 2001
A. Taflove, "Computational Electrodynamics: The Finite-Difference Time-Domain Method", Artech House, 2000
J. Joannopolous, S. Johnson, , J.Winn, R. Meade, Photonic Crystals, Molding the flow of light, 2nd Ed, Princeton Univ. Press, 2008
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: