Photonic crystals for Optical Communication

Modelling of supercells for mode analysis in 2D and 3D

Formulations

• Infinite photonic crystal (full periodicity)
• Supercells (periodicity in one or two directions) with boundary conditions
• Quadratic eigenvalue problem

Discretisation by means of finite elements

• scalar finite elements in 2D with additional bilinearform for the quadratic eigenvalue problem

Eigenvalue problems

Concrete subprojects

• Bandstructure calculation for infinite photonic crystal - linear eigenvalue problem (P.Kauf, K.Schmidt)
• Bandstructure calculation for infinite photonic crystal - quadratic eigenvalue problem (Ch.Engström, D.Kressner)
• Supercell in 2D with quadratic eigenvalue problem (R.Kappeler, K.Schmidt, D.Kressner)
• Supercell in 3D with 2D periodicity
• Supercell in 3D with 1D periodicity

Supercells with stochastic variations in 2D and 3D

• Variation of radius, deviation from perfect periodicity
• Variation of hole shape, derivation of apex from perfect periodicity, angle, underetches

Treatment of large photonic circuits with generalised FEM

• finite crystal in 2D with local 1D periodicity (unit-cell is a stripe)
• finite crystal in 2D with local 2D periodicity
  • cell-problems of super-cells (stripes)
  • cell-problems of unit-cells
• finite crystal in 3D with local 2D periodicity