# 04- Quasi-disordered structures with 2D and 3D complete photonic bandgaps with arbitrary small refractive-index contrast

**Source**: https://www.cs.tum.de/spp1839/projects/2nd-period-2018-2021/04.html
**Parent**: https://www.cs.tum.de/spp1839/projects.html

In
this project we investigate 2D and 3D quasi-disordered structures which
can be considered as a new kind of distributed photonic quasicrystals.
We envisage these to have a complete photonic bandgap even for
arbitrarily small refractive-index contrasts. While the structures
appear completely disordered and lack any discernible symmetry, they
actually possess a long-range order along with a high degree of symmetry
giving them unique properties. The dielectric
distribution of this material is mathematically obtained by a
superposition of sinusoidal gratings with random orientation and random
phase. If the number of gratings used for the
generation of the structure is optimized, the individual bandgaps of the
gratings can overlap to form a complete and isotropic photonic bandgap.
Additionally, the formation of the isotropic bandgap leads to low group
velocities at its edges for all directions. Therefore, a strong
enhancement of the emission of a source immersed in the structured
medium can be observed at these frequencies.

The main objective of this
project is to show that even for very low refractive-index contrasts a
complete photonic bandgap can be found with the structuration scheme we
propose. We want to show a conclusive theory how to obtain the optimal
structure parameters (refractive-index contrast, number of gratings,
size) for the maximal opening of the bandgap. This theory is to be
proven by simulations of 2D and 3D structures. In a systematic numerical
study simulations should also reveal the sensitivity of the
refractive-index contrast minimally required for a complete photonic
bandgap on various kinds of defects, thus indicate practical limitations
stronger than the theoretical ones. Based on our approach, we envisage
realizing a complete 3D bandgap for a refractive-index contrast as low
as 1.55:1 (polymer/air) or 1.43:1 (glass/air). The quasi-disordered
structures will be manufactured in 2D and 3D and characterised for their
transmission and reflection properties. 

Our
approach can be used to control spontaneous and stimulated emission in
2D and 3D structures with a low refractive-index contrast. Our novel
distributed quasicrystals can therefore widen the range of materials
available for the realization of photonic bandgaps and thus can pave the
way for new applications. The results will also be interesting beyond
the photonic community, as the proposed approach extends the theory of
quasicrystals and localisation phenomena in electronic, mechanical and
other wave systems.

## Contributors

Prof. Manfred Eich

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Dr. Alexander Petrov

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Lukas Maiwald

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