Advanced computational Methods in Nano-optics

Teacher : Alexey Shcherbakov (ITMO University – St Petersburg)

This lecture covers the following topics:

  • Elements of the complexity theory and algorithms. Fast Fourier Transform and related topics.
  • Selected topics of the matrix analysis. Krylov subspace methods for solution of large linear algebraic equation systems and eigenvalue problems.
  • Fast algorithms for special type matrices and applications in the volume integral methods and the coupled dipole approximation. Spectra of nanoparticle aggregations.
  • Sparse matrices and their application in the finite-difference and finite element methods.
  • Calculation and analysis of band diagrams and dispersion curves, and overview of related physical phenomena.
  • Advanced numerical integration and differentiation.
  • Methods of solution to the 1D arbitrary potential tunneling problem. Anderson localization.
  • Resonances in physical systems. Fano resonances in nanooptics. Perfect optical absorbers.
  • Surface integral methods in the wave diffraction and scattering theory. Enhancement of local electromagnetic fields.
  • Modal methods. Mie theory and Waterman T-matrix. Multiple scattering.
  • Overview of the effective medium approximations in optics. Analytic results and numerical approaches.

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