Abstract
We experimentally realize fractal-like photonic lattices by use of the cw-laser-writing technique, thereby observing distinct compact localized states (CLSs) associated with different flatbands in the same lattice setting. Such triangle-shaped lattices, akin to the first generation Sierpinski lattices, possess a band structure where singular non-degenerate and nonsingular degenerate flatbands coexist. By proper phase modulation of an input excitation beam, we demonstrate not only the simplest CLSs but also their superimposition into other complex mode structures. Our experimental and numerical results are corroborated by theoretical analysis. Furthermore, we show by numerical simulation a dynamical oscillation of the flatband states due to beating of the CLSs that have different eigenenergies. These results may provide inspiration for exploring fundamental phenomena arising from the interplay of fractal structure, flatband singularity, and real-space topology.
Highlights
The concept of flatband, as developed in condensed matter physics to describe certain geometrically frustrated lattices, was introduced into the realm of photonics by making an analogy between the electronic hopping and photonic coupling[1,2,3,4]
We show by numerical simulation a dynamical oscillation of the flatband states due to beating of the compact localized states (CLSs) that have different eigenenergies
Such CLSs have been realized in a number of experiments, including photonic Lieb lattices established by femtosecond laser-writing in glass[6, 7] and flatband Lieb and Kagome lattices optically induced in nonlinear crystals[8,9,10]
Summary
The concept of flatband, as developed in condensed matter physics to describe certain geometrically frustrated lattices, was introduced into the realm of photonics by making an analogy between the electronic hopping and photonic coupling[1,2,3,4]. Endeavors towards understanding the CLS completeness and Bloch wave singularities have unveiled the existence of unconventional flatband states – the noncontractible loop states (NLSs), as a manifestation of singular flatbands and nontrivial real-space topology[18,19,20,21,22] Despite those efforts, most of research has focused on lattices with a flatband that is not isolated but rather “crossed” or “touched” by a dispersive band, such as Kagome and Lieb lattices. One is singular nondegenerate and the other two are nonsingular degenerate, which is of particular interest since such a lattice structure, never been realized experimentally in any system before, can serve as a platform to explore the interplay between fractal structure, flatband singularity, and nontrivial topology We measure both the intensity pattern and phase structure associated with the CLSs of each flatband, along with discussion about their superposition to form more complex localized structures or undergo dynamical oscillations
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