Yarden Mazor

Longitudinal chirality, enhanced nonreciprocity, and nanoscale planar one-way plasmonic guiding

(Received 24 January 2012; revised manuscript received 26 June 2012; published 16 July 2012)When a linear chain of plasmonic nanoparticles is exposed to a transverse dc magnetic field, the chain modesare elliptically polarized in a single plane parallel to the chain axis; hence, a new chain mode of longitudinalplasmon rotation is created. If, in addition, the chain geometry possesses longitudinal rotation, e.g., by usingellipsoidal particles that rotate in the same plane as the plasmon rotation, strong nonreciprocity is created. Thestructure possesses a new kind of chirality—longitudinal chirality—and supports one-way guiding. Since allparticles rotate in the same plane, the geometry is planar and can be fabricated by printing leaflike patches on asingle plane. Furthermore, the magnetic field is significantly weaker than in previously reported one-way guidingstructures. These properties are examined for ideal (lossless) and lossy chains.DOI: 10.1103/PhysRevB.86.045120 PACS number(s): 41

Waves in almost periodic particle chains

Almost periodic particle chains exhibit peculiar propagation properties that are not observed in perfectly periodic ones. Furthermore, since they inherently support nonnegligible long-range interactions and radiation through the surrounding free space, nearest-neighbor approximations cannot be invoked. Hence the governing operator is fundamentally different from that used in traditional analysis of almost periodic structures, e.g., Harper’s model and almost Mathieu difference equations. We present a mathematical framework for the analysis of almost periodic particle chains, and study their electrodynamic properties. We show that they support guided modes that exhibit a complex interaction mechanism with the light cone. These modes possess a two-dimensional fractal-like structure in the frequency–wave number space, such that a modal phase velocity cannot be uniquely defined. However, a well-defined group velocity is revealed due to the fractal’s inner structure.

Planar one-way guiding in periodic particle arrays with asymmetric unit cell and general group-symmetry considerations

We develop a general theory for one-way optical guiding in magnetized periodic particle arrays. Necessary conditions for a non-even dispersion curves are derived and presented in the context of Frieze symmetry-groups. It is shown, for example, that one-way guiding can be supported in particle \emph{strips} consisting of geometrically isotropic particles arranged in transversely asymmetric arrays. Specific examples consist e.g.~two parallel isotropic particle chains with different periods. The previously studied one-way effect based on the two-type rotation principle is shown to be a special case. In the latter the exclusion of the appropriate Frieze-symmetries is achieved in a single linear chain by associating a geometric rotation to each particle, thus providing the narrowest possible one-way waveguides. It is also shown that nearly any randomly created period may result in uneven dispersion and one-way guiding.

Modal and excitation asymmetries in magnetodielectric particle chains

We study the properties of dipolar wave propagation in linear chains of isotropic particles with independent electric and magnetic response, embedded in vacuum. It is shown that the chain can support simultaneously right-handed modes (RHM) and left-handed modes (LHM) of transverse-polarization. The LHM are supported by the structure even if the chains particles possess positive polarizabilities and no Bi-isotropy; the needed structural Bi-isotropy is provided by the propagator instead of by the particles local properties. In contrast to the transverse modes in chains that consist of purely electric particles that are inherently RHM, the LHM dispersion lacks the light-line branch since their dipolar features are not aligned with the electric and magnetic fields of a right-handed plane-wave solution in free space. Furthermore, it is shown that the spatial width of the LHM is significantly smaller than that of the RHM. Excitation theory is developed, and it is shown that the chain possesses modal and excitation asymmetries that can be used to eliminate reflections from chains termination.

Left handedness and asymmetric excitation in linear arrays of isotropic electric-magnetic particles

We study the properties of wave propagation in linear chains of particles with both electric and magnetic response. In the case of transverse modes, and in contrast to the purely electric case, there are dispersion branches which lack light-line modes. Using Z-Transform the variety of modal properties are revealed and the inherent left-handedness and excitation asymmetry in the chain modes is demonstrated.

Breach of electromagnetic symmetries in particle arrays

We describe several basic schemes for magnetization-based strongly non-reciprocal plasmonic particle arrays. Examples of periodic arrangements are discussed and presented as special cases of a more general Frieze-group symmetry framework. Quasi-periodic particle arrays are discussed as well, and their support of non-reciprocity is explored. The manifestation of strong non-reciprocity in the fractal spectrum of quasi-periodic arrays is presented.

Enhanced non-reciprocity induced by synergy of dark-modes and Faraday rotation

Dark-mode of a small particle consists of two equally intense and mutually opposing dipolar excitations. Each of these two opposing dipoles may even resonate at or near the dark-mode frequency. Nevertheless, the net dipole moment of the system vanishes due to the destructive interference between the opposing dipoles, hence the dark-mode resonance cannot be observed externally. We show that under external magnetic bias the opposing dark-resonances of a plasmonic particle shift in opposite directions and create a region of extremely sensitive Faraday rotation. We show that the magnetized dark resonance in Ag particle may provide 50 degrees rotation under magnetic fields of the order of 1 Tesla.

Left handed modes in linear arrays of isotropic particles with electric and magnetic response

We study the properties of dipolar wave propagation in linear chains of isotropic particles with independent electric and magnetic response, embedded in vacuum. It is shown that transverse-polarization left-handed waves can be supported by the structure even if the chains particles possess positive polar-izabilities and no Bi-isotropy; the needed Bi-isotropy is provided by the propagator instead of by the particles local properties. In contrast to the transverse modes in chains that consist of purely electric particles, the left-handed modes dispersion lack the lightline branch since their dipolar features are not aligned with the electric and magnetic fields of a right-handed plane-wave solution in free space.

Synergetic interaction of dark-modes and Faraday rotation for enhanced non-reciprocity

Dark-mode of a small particle consists of two co-existing equal-intensity and mutually opposing dipolar excitations. Each of these two opposing dipoles may even resonate at or near the dark-mode frequency. Nevertheless, the net dipole moment of the system vanishes due to the destructive interference between the opposing dipoles, hence the dark-mode resonance cannot be observed externally. We show that under external magnetic bias the opposing dark-resonances of a plasmonic particle shift in opposite directions and create a region of extremely sensitive Faraday rotation. We show that the magnetized dark resonance in Ag particle may provide 50 degrees rotation under magnetic fields of the order of 1 Tesla.

Laterally asymmetric particle arrays for one-way guiding

A general theory for one-way optical guiding in periodic particle arrays is developed. Conditions on the asymmetry properties of the structures period that are necessary to obtain asymmetric dispersion are derived. The two-type rotation principle, presented and studied in previous works on one-way guiding in particle chains, is viewed as a special design that achieves the necessary violation of the periods symmetries. Specific examples of periodic strips that consist of circular particles and support one way guiding, are provided.