Multifractality of light in photonic arrays based on algebraic number theory

Year: 2020

Authors: Sgrignuoli F., Gorsky S., Britton WA., Riboli F., Dal Negro L.

Autors Affiliation: Boston Univ, Dept Elect & Comp Engn, 8 St Marys St, Boston, MA 02215 USA; Boston Univ, Photon Ctr, 8 St Marys St, Boston, MA 02215 USA; Boston Univ, Div Mat Sci & Engn, 15 St Marys St, Brookline, MA 02446 USA; CNR, Inst Nazl Ott, Via Nello Carrara 1, I-50019 Sesto Fiorentino, Italy; European Lab Nonlinear Spect, Via Nello Carrara 1, I-50019 Sesto Fiorentino, Italy;‎ Boston Univ, Dept Phys, 590 Commonwealth Ave, Boston, MA 02215 USA

Abstract: Many natural patterns and shapes, such as meandering coastlines, clouds, or turbulent flows, exhibit a characteristic complexity that is mathematically described by fractal geometry. Here, we extend the reach of fractal concepts in photonics by experimentally demonstrating multifractality of light in arrays of dielectric nanoparticles that are based on fundamental structures of algebraic number theory. Specifically, we engineered novel deterministic photonic platforms based on the aperiodic distributions of primes and irreducible elements in complex quadratic and quaternions rings. Our findings stimulate fundamental questions on the nature of transport and localization of wave excitations in deterministic media with multi-scale fluctuations beyond what is possible in traditional fractal systems. Moreover, our approach establishes structure-property relationships that can readily be transferred to planar semiconductor electronics and to artificial atomic lattices, enabling the exploration of novel quantum phases and many-body effects.
Emergent multifractality is the object of both fundamental and technology-oriented research. Here, the authors demonstrate and characterize multifractality in the optical resonances of aperiodic arrays of nanoparticles designed from fundamental structures of algebraic number theory.


Volume: 3 (1)      Pages from: 106-1  to: 106-9

More Information: We would like to acknowledge Dr. R. Wang for his contribution during the first stage of this work. We would also like to acknowledge Dr. A. Ambrosio and Dr. M. Tamaglione for their help during the multispectral dark-field measurements performed at the Center for Nanoscale Systems at Harvard University (Cambridge, MA 02138 USA). F.S. acknowledges Dr. F. Scazza for fruitful discussion on the applications of aperiodic lattices on ultracold quantum physics. L.D.N. acknowledges partial support from the Army Research Laboratory under Cooperative Agreement Number W911NF-12-2-0023 for the development of theoretical modeling and of the NSF program Tunable Si-compatible Nonlinear Materials for Active Metaphotonics under Award DMR No. 1709704.
DOI: 10.1038/s42005-020-0374-7

Citations: 8
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