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Abstract We investigate the spectral properties of one-dimensional spatially modulated nonlinear phononic lattices, and their evolution as a function of amplitude. In the linear regime, the stiffness modulations define a family of periodic and quasiperiodic lattices whose bandgaps host topological edge states localized at the boundaries of finite domains. With cubic nonlinearities, we show that edge states whose eigenvalue branch remains within the gap as amplitude increases remain localized, and therefore appear to be robust with respect to amplitude. In contrast, edge states whose corresponding branch approaches the bulk bands experience de-localization transitions. These transitions are predicted through continuation studies on the linear eigenmodes as a function of amplitude, and are confirmed by direct time domain simulations on finite lattices. Through our predictions, we also observe a series of amplitude-induced localization transitions as the bulk modes detach from the nonlinear bulk bands and become discrete breathers that are localized in one or more regions of the domain. Remarkably, the predicted transitions are independent of the size of the finite lattice, and exist for both periodic and quasiperiodic lattices. These results highlight the co-existence of topological edge states and discrete breathers in nonlinear modulated lattices. Their interplay may be exploited for amplitude-induced eigenstate transitions, for the assessment of the robustness of localized states, and as a strategy to induce discrete breathers through amplitude tuning.
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Topological edge states of a long-range surface plasmon polariton at the telecommunication wavelength
Confining light by plasmonic waveguides is promising for miniaturizing optical components, while topological photonics has been explored for robust light localization. Here we propose combining the two approaches into a simple periodically perforated plasmonic waveguide (PPW) design exhibiting robust localization of long-range surface plasmon polaritons. We predict the existence of a topological edge state originating from a quantized topological invariant, and numerically demonstrate the viability of its excitation at telecommunication wavelength using near-field and waveguide-based approaches. Strong modification of the radiative lifetime of dipole emitters by the edge state, and its robustness to disorder, are demonstrated.
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- Award ID(s):
- 1719875
- PAR ID:
- 10370352
- Publisher / Repository:
- Optical Society of America
- Date Published:
- Journal Name:
- Optics Letters
- Volume:
- 47
- Issue:
- 17
- ISSN:
- 0146-9592; OPLEDP
- Format(s):
- Medium: X Size: Article No. 4532
- Size(s):
- Article No. 4532
- Sponsoring Org:
- National Science Foundation
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