Selection rules for plasmonics
© 2014 EPFL
We describe a general theoretical framework based on the Bergman spectral representation to study how a nanostructure interacts with an external electromagnetic field. The selection rules for localized surface plasmon resonances (LSPRs) are obtained by implementing the group theory upon the electric vector field. The influence of symmetry breaking on the splitting of degenerated modes and the switching of dark modes by specific illuminations are discussed. These results emphasize the fact that the selection rules for a vector field are different from the case of a scalar field and essentially induced by the geometry of the structure. Finally, this work not only points out that measurements of LSPRs may result in very different results with different external fields, but also provides a strategy to selectively excite specific LSPRs of plasmonic structures.
Plasmonic nanostructures can usually support numerous different modes. Some of these modes are so-called bright, i.e. they can couple to the far-field; other modes are dark, i.e. do not couple into the far-field. The former modes have a dipole moment, while the latter do not. Bright and dark modes can however couple together, leading to Fano resonances. Furthermore, in a given nanostructure, existing dark mode can become bright when the geometry of the particle is slightly modified, or the exitation is changed. Understanding these phenomena is or paramount importance for engineering efficient plasmonic nanostructures.
In a recent publication, we describe a general theoretical framework based on the Bergman spectral representation to study how a nanostructure interacts with an external electromagnetic field. The selection rules for localized surface plasmon resonances (LSPRs) are obtained by implementing the group theory upon the electric vector field. The influence of symmetry breaking on the splitting of degenerated modes and the switching of dark modes by specific illuminations are discussed. These results emphasize the fact that the selection rules for a vector field are different from the case of a scalar field and essentially induced by the geometry of the structure. Finally, this work not only points out that measurements of LSPRs may result in very different results with different external fields, but also provides a strategy to selectively excite specific LSPRs of plasmonic structures.
The figure on the left shows the dipole moments of the LSPR modes as a function of the permittivity (corresponding to the eigenvalues) for a 2.5 nm thick square flake with dimensions 20x20 nm2. At the top, the structure is symetrical and two bright modes are degenerated (modes 1 and 2). This degenerancy disappears when a corner of the particl is removed (middle of the figure). A similar behavior is observed when the particle has a shorter side (bottom of the figure). The electric field distributions of the dominant modes appearing in the spectra are shown in the corresponding insets; the direction and intensity of the electric fields are denoted by the orientation and length of the arrows.
Another important issue in this work is the implementation of the group theory upon the electric vector field E, leading to selection rules of LSPRs under different illumination conditions. These results emphasize the fact that the selection rules for a vector field are different from the case of a scalar field, because a symmetry operator acts on both the position vector and the field vector. All the selection rules are essentially induced by the geometry of the structure. Finally, this work not only points out that measurements of LSPRs may result in very different results with different external fields, but also provides a strategy to selectively excite specific LSPRs of plasmonic structures.
Further information is available in the corresponding publication:
Symmetry and selection rules for localized surface plasmon resonances in nanostructures
Check the corresponding publication: PDF External link: doi: 10.1103/PhysRevB.81.2334073