Abstract
In this article, properties of solitons in a parity-time periodical lattices with a single-sited defect are investigated. Both of the negative and positive defects are considered. Linear stability analyses show that, when the defect is positive, in the semi-infinite gap, the solitons are always stable, while in the first gap, the solitons are unstable in most of their existence region except for those near the edge of the second band; when the defect is negative, in the semi-infinite gap, other than those near the edge of the first band, most solitons are stable, but in the first gap, all solitons are unstable. Such stability analyses are corroborated by numerical simulations.
Highlights
In quantum mechanics, physical observables require the corresponding operators must be Hermitian, i.e. the operator shows a real spectrum
In the PT symmetric potentials, there exists a critical threshold above which the system undergoes a sudden phase transition, i.e., the spectrum is no longer real but instead becomes a complex one [1, 6,7,8]
PT symmetric potentials can be constructed by introducing a complex refractive-index distribution into the wave-guided system: n(x) = nr(x) + ini(x), where nr(x) = nr(−x), ni(x) = −ni(−x), and x is the normalized transverse coordinate
Summary
Physical observables require the corresponding operators must be Hermitian, i.e. the operator shows a real spectrum. The real part of a PT complex potentials must be an even function of position whereas the imaginary component is odd. In the PT symmetric potentials, there exists a critical threshold above which the system undergoes a sudden phase transition, i.e., the spectrum is no longer real but instead becomes a complex one [1, 6,7,8]. When light propagates in periodic optical lattice with a local defect, both linear and nonlinear defect modes can be formed due to the bandgap guidance [10, 11]. Very recently, existing properties of linear defect modes in a PT periodic potential were studied [24]. Nonlinear defect modes (defect solitons) in PT periodic lattices with a single-sited defect are studied, and their stability properties are analyzed
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