Light Localization in Nonlinear Binary Two-Dimensional Lieb Lattices

• Light localization in photonic lattices (PLs) is a well-known phenomenon which has been investigated during decades. It has been shown that light localization in the linear regime can be achieved by designing PLs with specific geometries, instead of embedding defects or disorder in otherwise periodic lattices [1]. These geometries provide conditions necessary for destructive wave interference, leading to formation of a perfectly flat (dispersionless) energy band. Eigenvectors associated to the flat-band (FB) eigenfrequencies are entirely degenerate and compact states (FB modes) and any superposition of them is nondiffracting. One of the simplest FB lattice patterns is the two-dimensional (2D) Lieb lattice [2,3] in which the primitive cell contains three sites. By appropriate spatial repetition of this fundamental block, it is possible to achieve a FB in the energy spectrum. Light confinement in PLs can also be a consequence of the interplay between nonlinearity and diffraction when these effects cancel each other, leading to formation of solitons. Recently, it has been reported that nonlinearity and “binarism” in quasi-one-dimensional FB systems can increase the range of existence and stability of FB ring modes [4].We model a 2D binary Lieb lattice with nonlinearity of Kerr type and analyse numerically and analytically the existence, stability and dynamical properties of various localized modes found to emerge in spectrum. From the derived dispersion relation we found that binarism does not affect the FB. However, due to the presence of additional periodicity, new gaps occur in the energy spectrum above and below the FB and their widths depend on the ratio between coupling constants. Like in the uniform Lieb lattice, we found eigenmodes in the form of a staggered four-peak “ring” structure, but only under certain conditions which require a particular relation between the field amplitudes in neighbouring sites. In the nonlinear regime, ring modes survive in the uniform Lieb lattice but lose their stability moving away from the FB. On the other hand, nonlinearity destroys the existence of ring solutions in the binary Lieb lattice, leading to a new class of stable localized solutions which can be found in minigaps. As in previous kagome and ladder binary nonlinear strips [4], it is shown that the binarism increases the existence range of stable nonlinear localized solutions.References[1] R. A. Vicencio, M. Johansson, Physical Review A 87, 061803(R) (2013).[2] R. A. Vicencio et al., Physical Review Letters 114, 245503 (2015).[3] D. Leykam, O. Bahat-Treidel, A. S. Desyatnikov, Physical Review A 86, 031805(R) (2012).[4] P. P. Beličev et al., Physical Review E 92, 052916 (2015).

Ämnesord

NATURVETENSKAP  -- Fysik -- Atom- och molekylfysik och optik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Atom and Molecular Physics and Optics (hsv//eng)

Nyckelord

Flat-band systems; Light localization; Nonlinearity

Publikations- och innehållstyp

ref (ämneskategori)

kon (ämneskategori)