   ## Optical design and Simulation

Lecturer:

Courses:

Credite points:

• 5 CP (lecture + exercises + exam; module: Vertiefung B1, Experimentalphysik B1)

Examination:   oral

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). 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 the industry standard optical design software package ZEMAX. 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.

11.4. Introduction to calculating ray propagation through lenses, apertures, etc in Matlab/Python / paraxial imaging, simple components / ABCD matrices

18.4. Simulating plane wave interference and diffraction in Matlab/Python

25.4. Scalar diffraction theory: propagation of Gaussian beams: the FFT approach

2.5. Scalar theory of diffraction: direct integration vs. finite difference method. Splitting and mixing beams; Interpolation; Zernike Polynomials

9.5. Examples: Twyman-Green Interferometer / Michelson Interferometer

16.5. Zemax I: Basic definitions and handling of Zemax

23.5. Zemax II: Geometric aberrations: ray tracing, aberration theory, primary aberrations, chromatic aberrations

30.5. Zemax III: Optical Systems

6.6. Zemax IV: wave aberrations, wave optics, Optical Systems correction/optimization

13.6. CST I: Basic definitions and handling of CST (ev. Meep?)

20.6. First steps in nanooptics: Mie theory

27.6. Overview of Maxwell solvers: Boundary element method, FDTD, Multiple scattering techniques, …

4.7. CST/Lumerical I: Geometry modelling, parametrization of dielectric response, source definition

11.7. CST/Lumerical II: Mie scatterer, plasmon polaritons, absorption and scattering

18.7. CST/Lumerical III: Quantum coupling phenomena in nanooptics

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