Observation of localized flat-band modes in a quasi-one-dimensional photonic rhombic lattice

Abstract

We experimentally demonstrate the photonic realization of a dispersionless flat-band in a quasione-dimensional photonic lattice fabricated by ultrafast laser inscription. In the nearest neighbor tight binding approximation, the lattice supports two dispersive and a non-dispersive (flat) band. We experimentally excite superpositions of flat-band eigen modes at the input of the photonic lattice and show the diffractionless propagation of the input states due to their infinite effective mass. In the future, the use of photonic rhombic lattices, together with the successful implementation of a synthetic gauge field, will enable the observation of AharonovBohm photonic caging.Introduction The dynamics of electrons in a crystal reveals many interesting phenomena that depend on the lattice geometry, external fields, presence of disorders and inter-particle interactions. The propagation of light waves across a photonic lattice, a periodic array of coupled optical waveguides, mimics the time evolution of the electronic wavefunction in a periodic potential. Due to this mapping, the photonic analogue of various solidstate-phenomena [1][2][3][4][5] can be realized in the system of engineered waveguide-arrays. As with cold atoms in optical lattices [6][7][8], this artificial system allows us to engineer and access a desired Hamiltonian, and hence acts as a powerful platform for the study of various complex quantum mechanical effects in a clean environment. Indeed photonic lattices are ideal systems to study various effects in the absence of undesired excitations such as phonons in a real solid.

Simple method to construct flat-band lattices

“…This point is very interesting because aperiodical systems will present no dispersive bands at all, but could present full FBs composed of different states. Therefore, the disorder could promote localization in the form of destructive interference of plane waves (Anderson localization [4,5]) or due to a local geometric phase cancellation (FB localization [15,21,22]). As our criterion does not depend on the periodicity, but on the discreteness of the system (miniarray geometry), we can compose an aperiodical system as a sequence of different mini-arrays connected by several connector sites.…”

“…In these quasi-1D or 2D systems, a complete band (not only a section of it) is completely flat, implying zero dispersion and not diffraction at all for the states belonging to this band. Diamond [15], Stub [16], Sawtooth [17,18], Kagome [19,20] or Lieb [21][22][23] lattices are some examples of recent explored FB systems, in diverse physical contexts. These examples show the diversity of fabrication techniques and impressive possibilities for creating, in principle, any wished lattice.…”

Photonic zero-energy modes in a metal-based Lieb lattice

“…diffraction-free image transmission [3][4][5], Aharonov-Bohm photonic cages [6][7][8], and edge states [9,10]. Currently, there are three main ways to achieve the artificial photonic flat-band lattices, including exciton-polaritons in structured micropillars [11][12][13][14][15][16], waveguide arrays [9,[17][18][19][20][21], and metamaterials [22][23][24]. The first two ways obtain the energy bands through the tight-binding (TB) approximation, while the third way is based on a coupled oscillator model.…”

Solitary Electromagnetic Waves in a Weakly Nonlinear Rhombic Waveguide Array

“…A rhombic waveguide array ( Fig.1) is the example of the discrete medium where the photon spectrum has one flat band and two usual bands [10,11]. In the linear case existence of the localized flat band modes in the rhombic waveguide array was experimentally demonstrate [12,13]. Recent review devoted to the optical system with a flat band is [14].…”