Localized modes in a two-dimensional lattice with a pluslike geometry.

Area of Science:

• Photonics
• Condensed Matter Physics
• Nonlinear Optics

Background:

• Photonic lattices with flat bands exhibit unique light localization properties.
• Engineered lattices are crucial for developing novel optical devices and simulating quantum systems.
• Understanding nonlinear effects in flat-band systems is key to controlling light propagation.

Purpose of the Study:

• To investigate the existence and stability of localized modes in a 2D photonic lattice with a square plaquette in a dodecagon.
• To analyze the impact of nonlinearity on compact eigenmodes within the flat band.
• To explore the formation of new localized modes in induced band gaps.

Main Methods:

• Analytical investigation of the lattice eigenvalue spectrum.
• Numerical simulations to study nonlinear mode dynamics and stability.
• Analysis of intersite coupling ratios to engineer band gap structures.

Main Results:

• The lattice exhibits one flat band and four dispersive bands.
• Tailoring coupling ratios induces band gaps, nesting the flat band.
• Nonlinearity destabilizes compact modes, creating localized modes in gaps via self-trapping.
• Several families of nonlinear localized modes in gaps were shown to be stable.

Conclusions:

• The proposed photonic lattice supports stable nonlinear localized modes.
• Light self-trapping is the primary mechanism for mode localization in this system.
• This model serves as a platform for studying artificial flat-band systems, with applications in ultracold atoms, electronic networks, and polariton condensates.