Abstract
A new type of waveguide lattice that relies on the effect of bandgap guidance, rather than total internal reflection, in the regions between the waveguide defects is proposed. Two different setting, for low index and high index defects are suggested. We analyze the linear bandgap and diffraction properties of such lattices. In the nonlinear regime the Kerr effect can counteract diffraction leading to the formation of gap lattice solitons. Interestingly enough, in the case of low index defects, stable soliton solutions are localized in the low index areas. This finding challenges the widely accepted idea that stable solitons can be sustained in high refractive index regions. In addition, in the case of high index defects, the coupling coefficient can become negative. Physical settings where the linear and nonlinear properties for bandgap lattices can be experimentally realized are presented.
Highlights
The field of linear and nonlinear dynamics in periodic optical systems recently attracts considerable attention
This finding challenges the widely accepted idea that stable solitons can be sustained in high refractive index regions
We proposed a new type of waveguide lattice that relies on the effect of bandgap guidance, rather than total internal reflection, in the regions between the waveguide defects
Summary
The field of linear and nonlinear dynamics in periodic optical systems recently attracts considerable attention. As a direct result of CMT the n discrete eigenvalues will form the first n bands of the complete band structure In this regime, linear modes (residing inside the bands) and nonlinear waves or solitons (residing either in the infinite bandgap or in the Bragg resonances or finite bandgaps) will be localized inside the high index regions. In the present work we propose that that by engineering the bandgap properties one can attain lattices whose Bloch modes are strongly localized in the low index regions This happens due to the presence of a Bragg resonances between the defects. Most importantly, independently of the intensity of light, linear and nonlinear modes associated with this defect band can strongly be localized in the low index regions, and CMT between low index defect modes can be directly applied
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