Graphene and its relatives, such as bilayer and trilayer graphene, are promising plasmonic materials. Very recently, graphene has been demonstrated to be precisely folded (Chen et al 2019 Science
365 1036–40), thus folded graphene provides another appealing platform for plasmonics. In folded graphene nanodisks, we find fundamental dipole modes (DMs) will exhibit mode splitting, with one parallel and another perpendicular to the folding axis. The two DMs show differences in field patterns and folding angle dependence, but they both can be tuned by the size of structures and the Fermi level of graphene. Some interesting high order modes are introduced as well, which can be further engineered by folding. Our studies enrich the current research of graphene plasmonics, and pave the way for particular plasmonic device applications.
Bound states in the continuum (BICs) have emerged as a significant design principle for producing systems with high-quality (Q) factor states to enhance light-matter interactions. As a particular case, symmetry-protected BICs are flexible to be designed, commonly by utilizing two identical lossless dielectric elements. Herein, different from previous studies, we propose symmetry-protected BICs in a plasmonic structure of two contacting graphene nanoribbons (GNRs), in which two GNRs are not identical and lossy. We show that BICs are achieved when two GNRs are perpendicular to each other, and as the vertical GNR deviates from the vertical direction (inversion symmetry breaking), it will evolve into quasi-BICs, with a new resonance dip appearing in the transmission spectrum. The spectrum curve can be well described by the coupled-mode theory, from which the variation of two fundamental states is clearly seen. Since in the presence of internal loss, the Q-factor of quasi-BICs does not follow the linear formula that is generally valid for symmetry-protected BICs. Alternatively, an extended formula is derived, which predicts exactly the behavior of the Q-factor of quasi-BICs. Besides BICs, the structure can also support plasmonically induced transparency (PIT) like effects, through rotating the vertical GNR to a particular angle. Therefore, a mechanically tunable switch, from BIC to PIT, is achieved here. Our work demonstrates an alternative scheme for BICs, and a new degree of freedom for tuning plasmonic coupling related effects.
Most of the current graphene plasmonic researches are based on the substrates with isotropic dielectric constant such as silicon. In this work, we investigate optical properties of graphene nanoribbon arrays placed on a uniaxially anisotropic substrate, where the anisotropy provides an additional freedom to tune the behaviors of graphene plasmons, and its effect can be described by a simple effective formula. In practice, the substrates of semi-infinite and finite thickness are discussed by using both the formula and full wave simulations. Particularly, the dielectric constants ε
∥ and ε
⊥ approaching zero are intensively studied, which show different impacts on the transverse magnetic (TM) surface modes. In reality, the hexagonal boron nitride (hBN) can be chosen as the anisotropic substrate, which is also a hyperbolic material in nature.
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