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Register a new userLocalization transition in three-dimensional stealthy hyperuniform disordered systems
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Added by
Fabrizio Sgrignuoli
Publication date
2021
fields
Physics
and research's language is
English
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The purpose of this work is to understand the fundamental connection between structural correlations and light localization in three-dimensional (3D) open scattering systems of finite size. We numerically investigate the transport of vector electromagnetic waves scattered by resonant electric dipoles spatially arranged in 3D space by stealthy hyperuniform disordered point patterns. Three-dimensional stealthy hyperuniform disordered systems (3D-SHDS) are engineered with different structural correlation properties determined by their degree of stealthiness $chi$. Such fine control of exotic states of amorphous matter enables the systematic design of optical media that interpolate in a tunable fashion between uncorrelated random structures and crystalline materials. By solving the electromagnetic multiple scattering problem using Greens matrix spectral method, we establish a transport phase diagram that demonstrates a clear delocalization-localization transition beyond a critical scattering density that depends on $chi$. The transition is characterized by studying the Thouless number and the spectral statistics of the scattering resonances. In particular, by tuning the $chi$ parameter, we demonstrate large spectral gaps and suppressed sub-radiant proximity resonances, facilitating light localization. Moreover, consistently with previous studies, our results show a region of the transport phase diagram where the investigated scattering systems become transparent. Our work provides a systematic description of the transport and localization properties of light in stealthy hyperuniform structures and motivates the engineering of novel photonic systems with enhanced light-matter interactions for applications to both classical and quantum devices.
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Hyperuniform disordered photonic materials (HDPM) are spatially correlated dielectric structures with unconventional optical properties. They can be transparent to long-wavelength radiation while at the same time have isotropic band gaps in another frequency range. This phenomenon raises fundamental questions concerning photon transport through disordered media. While optical transparency is robust against recurrent multiple scattering, little is known about other transport regimes like diffusive multiple scattering or Anderson localization. Here we investigate band gaps, and we report Anderson localization in two-dimensional stealthy HDPM using numerical simulations of the density of states and optical transport statistics. To establish a unified view, we propose a transport phase diagram. Our results show that, depending only on the degree of correlation, a dielectric material can transition from localization behavior to a bandgap crossing an intermediate regime dominated by tunneling between weakly coupled states.
We present the first detailed numerical study in three dimensions of a first-order phase transition that remains first-order in the presence of quenched disorder (specifically, the ferromagnetic/paramagnetic transition of the site-diluted four states Potts model). A tricritical point, which lies surprisingly near to the pure-system limit and is studied by means of Finite-Size Scaling, separates the first-order and second-order parts of the critical line. This investigation has been made possible by a new definition of the disorder average that avoids the diverging-variance probability distributions that plague the standard approach. Entropy, rather than free energy, is the basic object in this approach that exploits a recently introduced microcanonical Monte Carlo method.
An ultra-broadband transverse magnetic (TM) pass hyperuniform disordered photonic crystal (HUDPC) polarizer is proposed and demonstrated on a silicon-on-insulator platform. Propagation of the transverse electric mode is blocked by three combined effects, including the photonic bandgap (PBG) effect, diffusive (non-resonant) scattering, and bandedge resonances. Specially, the designed 30-dB bandwidth in polarization extinction ratio (PER) of 265 nm is much larger than the spectral width of the PBG (149 nm) due to using the bandedge resonances. The TM mode is in the subwavelength regime of the HUDPC and thus has a low insertion loss (IL). An ultrawide 30-dB bandwidth in PER of 210 nm (1.44-1.65 um) is experimentally demonstrated in a 12.9-um-long HUDPC polarizer with spectrally averaged PER of 39.6 dB and IL for the TM mode of 1.1 dB (IL = 0.6 dB at 1.55 um). The HUDPC polarizers can be an excellent candidate for ultra-broadband polarization filtering in the silicon photonic platform.
We present a numerical study of electromagnetic wave transport in disordered quasi-one-dimensional waveguides at terahertz frequencies. Finite element method calculations of terahertz wave propagation within LiNbO$_{3}$ waveguides with randomly arranged air-filled circular scatterers exhibit an onset of Anderson localization at experimentally accessible length scales. Results for the average transmission as a function of waveguide length and scatterer density demonstrate a clear crossover from diffusive to localized transport regime. In addition, we find that transmission fluctuations grow dramatically when crossing into the localized regime. Our numerical results are in good quantitative agreement with theory over a wide range of experimentally accessible parameters both in the diffusive and localized regime opening the path towards experimental observation of terahertz wave localization.
The Anderson delocalization-localization transition is studied in multilayered systems with randomly placed interlayer bonds of density $p$ and strength $t$. In the absence of diagonal disorder (W=0), following an appropriate perturbation expansion, we estimate the mean free paths in the main directions and verify by scaling of the conductance that the states remain extended for any finite $p$, despite the interlayer disorder. In the presence of additional diagonal disorder ($W > 0$) we obtain an Anderson transition with critical disorder $W_c$ and localization length exponent $ u$ independently of the direction. The critical conductance distribution $P_{c}(g)$ varies, however, for the parallel and the perpendicular directions. The results are discussed in connection to disordered anisotropic materials.
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