Abstract:Ribbon lattices are kind of transition systems in between one and two dimensions, and their study is crucial to understand the origin of different emerging properties. In this work, we study a Lieb ribbon lattice and the localization–delocalization transition occurring due to a reduction of lattice distances (compression) and the corresponding flat band deformation. We observe how above a critical compression ratio the energy spreads out and propagates freely across the lattice, therefore transforming the syst… Show more
“…For , the three FB states reduce to a profile with only two large amplitude at their center, which may favour localization. This suggests the possibility of a dynamical transition around , which can be mediated by a change in coupling constants, something that could be triggered, for example, by mechanical forces 35 or by morphological changes during learning in neuronal systems 36 . Figure 2 ( a ) Spectrum vs for a dendritic system with alternated spines [see Fig.…”
The capacity of a physical system to transport and localize energy or information is usually linked to its spatial configuration. This is relevant for integration and transmission of signals as performed, for example, by the dendrites of neuronal cells. Inspired by recent works on the organization of spines on the surface of dendrites and how they promote localization or propagation of electrical impulses in neurons, here we propose a linear photonic lattice configuration to study how the geometric features of a dendrite-inspired lattice allows for the localization or propagation of light on a completely linear structure. We show that by increasing the compression of the photonic analogue of spines and thus, by increasing the coupling strength of the spines with the main chain (the “photonic dendrite”), flat band modes become prevalent in the system, allowing spatial localization in the linear – low energy – regime. Furthermore, we study the inclusion of disorder in the distribution of spines and show that the main features of ordered systems persist due to the robustness of the flat band states. Finally, we discuss if the photonic analog, having evanescent interactions, may provide insight into linear morphological mechanisms at work occurring in some biological systems, where interactions are of electric and biochemical origin.
“…For , the three FB states reduce to a profile with only two large amplitude at their center, which may favour localization. This suggests the possibility of a dynamical transition around , which can be mediated by a change in coupling constants, something that could be triggered, for example, by mechanical forces 35 or by morphological changes during learning in neuronal systems 36 . Figure 2 ( a ) Spectrum vs for a dendritic system with alternated spines [see Fig.…”
The capacity of a physical system to transport and localize energy or information is usually linked to its spatial configuration. This is relevant for integration and transmission of signals as performed, for example, by the dendrites of neuronal cells. Inspired by recent works on the organization of spines on the surface of dendrites and how they promote localization or propagation of electrical impulses in neurons, here we propose a linear photonic lattice configuration to study how the geometric features of a dendrite-inspired lattice allows for the localization or propagation of light on a completely linear structure. We show that by increasing the compression of the photonic analogue of spines and thus, by increasing the coupling strength of the spines with the main chain (the “photonic dendrite”), flat band modes become prevalent in the system, allowing spatial localization in the linear – low energy – regime. Furthermore, we study the inclusion of disorder in the distribution of spines and show that the main features of ordered systems persist due to the robustness of the flat band states. Finally, we discuss if the photonic analog, having evanescent interactions, may provide insight into linear morphological mechanisms at work occurring in some biological systems, where interactions are of electric and biochemical origin.
A major challenge in inverse design of optical splitters is to efficiently reach platform nonspecific designs constrained to multiple functional requirements: arbitrary splitting ratio, low insertion loss, broad bandwidth and small footprint. While the traditional designs fail to fulfill all these requirements, the more successful nanophotonic inverse designs require substantial time and energy resources per device. Here, we present an efficient inverse design algorithm that provides universal designs of splitters compliant with all above constraints. To demonstrate the capabilities of our method, we design splitters with various splitting ratios and fabricate 1 × N power splitters in a borosilicate platform by direct laser writing. The splitters show zero loss within the experimental error, competitive imbalance of <0.5 dB and broad bandwidth in the range 20 − 60 nm around 640 nm. Remarkably, the splitters can be tuned to achieve different splitting ratios. We further demonstrate scaling of the splitter footprint and apply the universal design to silicon nitride and silicon-on-insulator platforms to achieve 1 × 5 splitters with the footprints as small as 3.3 µm × 8 µm and 2.5 µm × 10.3 µm, respectively. Owing to the universality and speed of the design algorithm (several minutes on a standard PC) our approach renders 100 greater throughput than nanophotonic inverse design.
Flat bands – single-particle energy bands – in tight-binding lattices, aka networks, have attracted attention due to the presence of macroscopic degeneracies and their sensitivity to perturbations. They support compact localized eigenstates protected by destructive interference. This makes them natural candidates for emerging exotic phases and unconventional orders. In this review we consider the recently proposed systematic ways to construct flat band networks based on symmetries or fine-tuning. We then discuss how the construction methods can be further extended, adapted or exploited in presence of perturbations, both single-particle and many-body. This strategy has lead to the discovery of non-perturbative metal-insulator transitions, fractal phases, nonlinear and quantum caging and many-body nonergodic quantum models. We discuss what implications these results may have for the design of fine-tuned nanophotonic systems including photonic crystals, nanocavities, and metasurfaces.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
