The role of short-range order and hyperuniformity in the formation of band gaps in 2D disordered photonic materials

DIPC Seminars

Luis S. Froufe-Perez (Physics Department, University of Fribourg, Switzerland)
Donostia International Physics Center
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The role of short-range order and hyperuniformity in the formation of band gaps in 2D disordered photonic materials **The role of short-range order and hyperuniformity in the formation of band gaps in 2D disordered photonic materials** Physics Department, University of Fribourg, Switzerland. **Abstract** ** ** Photonic Crystals (PCs) have represented a major driving force for the optical materials community for the last three decades. In analogy with solid- state physics, the goal of photonic crystal science and technology is to understand, engineer and fabricate materials with specific light transport and emission properties. Photonic band engineering is at the heart of virtually any application of PCs. In the early stages of the development of the technological capacities to fabricate photonic bandgap structures, it was realized that fabrication defects inhibit the formation of a gap and thus spoil to a large extent the performance of any practical photonic device, up to a point where commercial applications might be practically precluded. Recently however the picture of considering disorder as the limiting factor for the fabrication of photonic band gap materials has changed dramatically. Several groups realized that, indeed, certain types of correlated disorder may be beneficial for the creation of a photonic bandgap. Moreover such amorphous bandgap materials would feature a spatially isotropic gap difficult to attain in a truly crystalline structure. In the pioneering work of M. Florescu and coworkers [1], it was shown that the so called stealthy hyperuniform (HU) disorder can lead the buildup of isotropic photonic bandgaps in two and three [2,3] dimensions . In contrast with the structures studied in [4], it was suggested that crystalline order is not required to obtain a full band gap but local ordering, uniform topology and, importantly, stealth hyperuniformity. Stealth HU is a structural property related to the structure factor S(q) of the disordered system: HU patterns present a vanishing S(q) as q tends to zero, while stealthy HU imposes a much more restrictive constrain to S(q): it exhibits vanishing values over a finite range of values from q=0 up to a critical value qc. Stealthy HU materials can be regarded, to some extent, as the reciprocal space counterpart of the constrains imposed by the hard-sphere (hard-disc in 2D) model in the real space. In this seminar we consider different two dimensional non-polycrystalline disordered systems with different degrees of correlation, and showing both stealthy hyperuniformity or only short range ordering due to random packing in real space. Depending on the topology and exact geometry of the system, it can be shown that an isotropic bandgap emerges for both types of disorder. In particular we consider the build-up of complete band gaps in both TE and TM polarizations in structures where it was believed not to occur. We conclude that any constrain imposed in the accessible degrees of freedom leads to peaks in the radial distribution function or the structure factor and, if placed at appropriate positions, it promotes the emergence of a photonic bandgap provided the scattering strength of the individual building blocks is sufficiently strong. **Bibliography** ** ** [1] M. Florescu, S. Torquato, and P. J. Steinhardt, “Designer disordered materials with large, complete photonic band gaps”, PNAS **106** , 20658–20663 ,2009. [2] S. F. Liew, J-K. Yang, H. Noh, C. F. Schreck, E. R. Dufresne, C. S. O’Hern, and H. Cao, “Photonic band gaps in three-dimensional network structures with short-range order”, Phys. Rev. A **84** , 063818 (2011). [3] N. Muller, J. Haberko, C. Marichy, and F. Scheffold, “Silicon Hyperuniform Disordered Photonic Materials with a Pronounced Gap in the Shortwave Infrared”, Adv. Opt. Mat. **2** , 115–119, 2014. [4] J-K. Yang, C. Schreck, H. Noh, S. F. Liew, M. I. Guy, C. S. O’Hern, and H. Cao, “Photonic-band-gap effects in two-dimensional polycrystalline and amorphous structures”, “Photonic-band-gap effects in two-dimensional polycrystalline and amorphous structures” Phys. Rev. A **82** , 053838, 2010.