Abschlussarbeiten - Master
Modellierung und Simulation von Photonischen Strukturen
Art der Abschlussarbeit
Master
Autoren
- Zhang, Ran
Betreuer
- Prof. Dr.-Ing. Andreas Richter
- Dr.rer.nat. Enrico Langer
- Dr.-Ing. Andreas Voigt
Abstract
As a part of this work, the models of periodic photonic structures “photonic crystals”
were built. With the Simulations, the dependence of the photonic properties on the
physical and geometric parameters was ascertained.
First, the generating of the photonic band structure was theoretically analyzed. By the
method “Plane-Wave- Expansion (PWE)”, the electric and magnetic fields were
calculated with the Maxwell-equations. The mathematical models for photonic crystals
of two materials, air and dielectrics, were constructed using the Bloch’s and Brillouin’s
theories.
Using the base of the mathematical models, the influence of the dielectric filling factor,
the lattice angle (symmetry) and the dielectric constant on the photonic band structures
or bandgaps was investigated. In the simulations of the structures made of the material
silicon (dielectric constant: 12), the desired bandgaps are created with a filling factor
between 0.1 and 0.4. The increased filling factor leads to a movement of the band gaps
into the lower frequency range. The simulations showed that the dielectric constants of
the dielectrics also strongly affect the bandgaps. Furthermore, it has been found that,
with a higher dielectric constant, most band gaps become broader and lie in deeper
frequency ranges. Moreover, more bandgaps with higher frequency may be produced
as the dielectric constant increases. The influence of the lattice angle is not as strong as
that of the filling factor and the dielectric constant. For a determined lattice constant,
the bandgaps of the hexagonal structure are larger than those of the square structure.
But this difference is not very clear.
In addition, the periodic structure of a observed special fossil specimen was modeled
as a monoclinic lattice and simulated to determine the optical properties. The simulation
does not result a total band gap, but some small band gaps for the visible light in certain
directions have been determined in this work. Thus, it is possible that these ancient
creatures looked differently colored at different angles.
were built. With the Simulations, the dependence of the photonic properties on the
physical and geometric parameters was ascertained.
First, the generating of the photonic band structure was theoretically analyzed. By the
method “Plane-Wave- Expansion (PWE)”, the electric and magnetic fields were
calculated with the Maxwell-equations. The mathematical models for photonic crystals
of two materials, air and dielectrics, were constructed using the Bloch’s and Brillouin’s
theories.
Using the base of the mathematical models, the influence of the dielectric filling factor,
the lattice angle (symmetry) and the dielectric constant on the photonic band structures
or bandgaps was investigated. In the simulations of the structures made of the material
silicon (dielectric constant: 12), the desired bandgaps are created with a filling factor
between 0.1 and 0.4. The increased filling factor leads to a movement of the band gaps
into the lower frequency range. The simulations showed that the dielectric constants of
the dielectrics also strongly affect the bandgaps. Furthermore, it has been found that,
with a higher dielectric constant, most band gaps become broader and lie in deeper
frequency ranges. Moreover, more bandgaps with higher frequency may be produced
as the dielectric constant increases. The influence of the lattice angle is not as strong as
that of the filling factor and the dielectric constant. For a determined lattice constant,
the bandgaps of the hexagonal structure are larger than those of the square structure.
But this difference is not very clear.
In addition, the periodic structure of a observed special fossil specimen was modeled
as a monoclinic lattice and simulated to determine the optical properties. The simulation
does not result a total band gap, but some small band gaps for the visible light in certain
directions have been determined in this work. Thus, it is possible that these ancient
creatures looked differently colored at different angles.
Schlagwörter
-
Berichtsjahr
2017