Numerical methods and their applications to solve Maxwell’s equations made it possible to study the light propagation and interaction with complex structures with nano-scale feature sizes consisting of thin-film stacks of multiple materials with complex optical properties. When using numerical methods and constructing numerical models, it is important to be able to estimate the error and to formulate a stability condition. Additionally, to establish the validity of the results of computation convergence tests are needed.
Statistical modelling is the basis of predictive data analytics. In this course we discuss some of the basics of numerical and statistical analysis as it applies to FDTD and related methods.
Key concepts covered include:
- Free and forced damped harmonic oscillator
- Numerical analysis: finite difference model of the simple harmonic oscillator
- Accuracy, stability and convergence of numerical algorithms
- Classical physics derivation of theoretical dielectric permittivity models from free-electron cloud oscillation for metals explaining bulk plasmons
- Green’s function for the damped harmonic oscillator
- Numerical Green’s function formulation and applications (Advanced)
- Statistical modelling for predictive analytics