Abstract
The discovery of a new type of soliton occurring in periodic systems is reported. This type of nonlinear excitation exists at a Dirac point of a photonic band structure, and features an oscillating tail that damps algebraically. Solitons in periodic systems are localized states traditionally supported by photonic bandgaps. Here, it is found that besides photonic bandgaps, a Dirac point in the band structure of triangular optical lattices can also sustain solitons. Apart from their theoretical impact within the soliton theory, they have many potential uses because such solitons are possible in both Kerr material and photorefractive crystals that possess self-focusing and self-defocusing nonlinearities. The findings enrich the soliton family and provide information for studies of nonlinear waves in many branches of physics.
Highlights
It is well-known that the photonic bandgap of a periodic system can support linear localized modes at a defect
Confinement of waves within a finite area is the basis of all information processing [1,2,3,4]. Such wave trapping is achieved by cavities and waveguides that rely on total internal reflection, or a photonic bandgap, to suppress radiation losses [5, 6]
Nonlinearity creates its own defect by changing its onsite refractive index, so that light is trapped to the defect by photonic bandgaps of the periodic lattices, forming a gap soliton in this case
Summary
It is well-known that the photonic bandgap of a periodic system can support linear localized modes at a defect. Nonlinearity creates its own defect by changing its onsite refractive index, so that light is trapped to the defect by photonic bandgaps of the periodic lattices, forming a gap soliton in this case. The band structure of a photonic crystal formed by a triangular lattice possesses Dirac cones at the corners of the Brillouin zones [14] At these high-symmetry points Maxwell’s equations can be replaced by the Dirac equation, with Ψ being the wave functions of two degenerate Bloch states. The transition to the nonlinear case is effected by replacing the defect by the auto-induced defect created by nonlinearity, a soliton localized mode is found to exist This new specific entity is sustained by the Dirac point rather than photonic bandgaps, so is designated here as Dirac-point soliton.
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