Modern optics and photonics relies to a large extent on numerical simulation for design and fabrication. Based on an elementary introduction of geometrical and physical optics and solutions of the electromagnetic wave equation the course will provide hands-on experience with state-of-the-art simulation tools (Python, ZEMAX, CST, Lumerical, or others).
The course starts by introducing analytical methods (paraxial optics, ABCD matrix method) implemented using high-level programming languages (e.g. Python) to demonstrate the basics of calculating the propagation of plane electromagnetic waves through space and across interfaces. The coherent superposition of waves and their propagation leading to interference and diffraction phenomena will then be covered quantitatively. These properties will then be expanded to the more complex case of Gaussian wave propagation using scalar diffraction theory. The simulation of free space propagation in this context will be discussed to cover differences between Fast Fourier Transform methods, direct integration and the finite difference method. This sets the ground for the optimization of complex optical systems in a optical design software package (Optalix or similar). Here, geometric aberrations, Zernike coefficients, wave aberrations, and physical optics modeling will be discussed.
So far, field variations in the vicinity of nanostructures with an extent of about one wavelength were neglected. On these scales the full Maxwell’s equations need to be solved for a given geometry. In the last section of the lecture interactions and optical phenomena on the nanoscale will be covered by solving Maxwell's equations for discretized complex geometries.
- Introduction to calculating ray propagation through lenses, apertures, etc in Python, paraxial imaging, simple components, ABCD matrices
- Simulating plane wave interference and diffraction in Python
- Scalar diffraction theory: propagation of Gaussian beams: the FFT approach
- Scalar theory of diffraction: direct integration vs. finite difference method.
- Splitting and mixing beams; Interpolation; Zernike Polynomials
- Examples: Twyman-Green Interferometer / Michelson Interferometer
- Optical design software: Basic definitions and handling, geometric aberrations: ray tracing, aberration theory, primary aberrations, chromatic aberrations, optical systems, wave aberrations, wave optics, optical systems correction/optimization
- First steps in nanooptics: Mie theory
- Overview of Maxwell solvers: Boundary element method, FDTD, Multiple scattering techniques, …
- CST: Basic definitions and handling, Geometry modelling, parametrization of dielectric response, source definition, Mie scatterer, plasmon polaritons, absorption and scattering
- Quantum coupling phenomena in nanooptics
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