Gap solitons and soliton trains in finite-sized two-dimensional periodic and quasiperiodic photonic crystals

We demonstrate the existence of the gap solitons and soliton trains in finite-sized two-dimensional periodic nonlinear photonic crystals by using the mutiple-scattering approach with an iterative scheme. In 12-fold symmetric nonlinear quasicrystals, we also demonstrated the existence of symmetric, regular gap solitons, asymmetric single-soliton states, and two-solitons states. We revealed that the existence of symmetric, regular gap solitons in a 12-fold quasicrystal is limited by the geometrical size of the hexagon that forms the core of the dodecahedral cell, which is the building block of the quasicrystal.