Novel Materials, Hyperuniformity & Photonics

C. Vanoni, B.L. Altshuler, P.J. Steinhardt, S. Torquato

Effective delocalization in the one-dimensional Andersaon model with stealthy disorder
arXiv:2509.13502 (2025)

We present numerical simulations of disordered stealthy hyperuniform layered media along 1D ranging up to 10,000 thin slabs of high-dielectric constant separated by intervals of low dielectric constant that show no apparent evidence of Anderson localization of electromagnetic waves or deviations from transparency for a continuous band of frequencies — in apparent violation of the standard lore that disorder in 1D causes all states to be localized.

M. Klatt, P.J. Steinhardt, S. Torquato

Transparency versus Anderson localization in one-dimensional disordered stealthy hyperuniform layered media
arXiv:2507.22377 (2025)

We present numerical simulations of disordered stealthy hyperuniform layered media along 1D ranging up to 10,000 thin slabs of high-dielectric constant separated by intervals of low dielectric constant that show no apparent evidence of Anderson localization of electromagnetic waves or deviations from transparency for a continuous band of frequencies — in apparent violation of the standard lore that disorder in 1D causes all states to be localized.

C. Vanoni, P.J. Steinhardt, S. Torquato

When does hyperuniformity lead to uniformity across length scales?
arXiv:2507.20831 (2025)

Disordered hyperuniform systems are distinguished by strong suppression of large-scale density fluctuations. In this paper, we explore the degree to which the uniformity can extend to intermediate and small length scales.

C. Vanoni, J. Kim, P.J. Steinhardt, S. Torquato

Dynamical properties of particulate composites derived from ultradense stealthy hyperuniform sphere packings
Physical Review E, 112 015406 (2025)

Disordered hyperuniform systems are distinguished by strong suppression of large-scale density fluctuations. In this paper, we explore the degree to which the uniformity can extend to intermediate and small length scales.

W. Man, M. Megans, P.J. Steinhardt,  P.M.  Chaikin

Experimental measurement of the photonic properties of icosahedral quasicrystals
Nature 436 (2005) 993

First construction and characterization of a three-dimensional (icosahedral) photonic quasicrystal

M. C. Rechtsman, H.-C. Jeong, P.M. Chaikin, S. Torquato, P.J. Steinhardt

Optimized structures for photonic quasicrystals
Phys. Rev. Lett. 101(2008) 073902

Finding the quasicrystal patterns with optimal band gap properties for different symmetries

M. Florescu,, S. Torquato, P.J. Steinhardt

Hyperuniformity of quasicrystals
Phys. Rev. B 95 (2017) 054119

First paper to show how to formally extend theconcept of hyperuniformity to quasicrystals

E.C. Oguz,, J.E.S. Socolar, P.J. Steinhardt, S. Torquato

Complete band gaps in two-dimensional photonic quasicrystals
Phys. Rev. 80 (2009) 155112

First construction and characterization of two-dimensional photonic quasicrystals

C. Line, P.J. Steinhardt, S. Torquato

Light Localization in Local Isomorphism Classes of Quasicrystals
Phys. Rev. Lett. 120 (2018) 247401

First construction and characterization of two-dimensional photonic quasicrystals

M. Florescu,, S. Torquato, P.J. Steinhardt

Designer disordered materials with large, complete photonic band gaps
PNAS 106 (2009) 20658

First construction and characterization of Hyperuniform Disordered solids (HUDS) with complete photonic bandgaps

W. Man, M Florescu, K. Matsuyama, P, Yadak, G. Nahal, S. Hashemizad, E. Williamson, P.J. Steinhardt, S. Torquato, and P.M. Chaikin

Photonic band gap in isotropic hyperuniform disordered solids with low dielectric contrast
Optics Express 21 (2013) 19972

First empirical evidence of isotropic bandgaps

W. Man, M. Florescu, E.P. Williamson, Y. He, S.R. Hasehmizad,  B.Y.C. Leung,
D.R. Liner, P.J. Steinhardt, S. Torquato and P. Chaikin

Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids
PNAS 110 (2013) 15886
First waveguides constructed and tested in a HUDS photonic solid

M. Klatt, P.J. Steinhardt, S. Torquato

Gap Sensitivity Reveals Universal Behaviors in Optimized Photonic
Crystal and Disordered Networks
Phys. Rev. Lett. 127 (2021) 037401

First discovery of universal behavior of gap sensitivity (derivative of gap with respect to dielectric contrast) spanning crystalline and disordered networks

M. Klatt, P.J. Steinhardt, S. Torquato

Wave propagation and band tails of two-dimensional disordered systems in the thermodynamic limit
Phys. Rev. Lett. 127 (2021) 037401

Introduction of a computational method for determining band gaps and band tails in increasingly large samples used to show that, among the wide range of disordered network heterostructures studied, only stealthy hyperuniform networks sustain complete band gaps in the large sample limit

M. Hejna, PJS and S. Torquato

Nearly-Hyperuniform Network Models of Amorphous Silicon
Phys. Rev. B87 (2013) 245204
Simulation of nearly-hyperuniform phase of amorphous silicon, a potential 3d solids with complete band gaps

R. Xie, G.G. Long, S.J. Wiegand, S.C. Moss, T. Carvalho, S. Roorda, M. Hejna, P.J. Steinhardt

Hyperuniformity in amorphous silicon based on the measurement of the infinite-wavelength limit of the  structure factor   PNAS 110 (2013) 13250
Empirical evidence for nearly-hyperuniform amorphous silicon