Do truly unidirectional surface plasmon-polaritons exist?

Abstract

In this work, we revisit the topic of surface waves on nonreciprocal plasmonic structures, and clarify whether strictly unidirectional surface plasmon-polaritons are allowed to exist in this material platform. By investigating different three-dimensional configurations and frequency regimes, we theoretically show that, while conventional surface magneto-plasmons are not strictly unidirectional due to nonlocal effects, consistent with recent predictions made in the literature, another important class of one-way surface plasmon-polaritons, existing at an interface with an opaque isotropic material, robustly preserve their unidirectionality even in the presence of nonlocality, and for arbitrarily-small levels of dissipation. We also investigate the extreme behavior of terminated unidirectional waveguiding structures, for both classes of surface waves, and discuss their counter-intuitive implications.

Photonic Weyl points due to broken time-reversal symmetry in magnetized semiconductor

“…The small deviation between measurements and theory may arise from the nonlocal effect, i.e. spatial dispersion, of the material42,43 . It should be noted that due to the presence of loss, the Weyl point transforms into exceptional ring19 , which possesses the same topological charge as a Weyl point.…”

Nonreciprocal and Topological Plasmonics

“…Although this unidirectional mode has been known for nearly five decades [3], its topological origin was discovered only recently [45,65,66]. Importantly, unlike the topologically trivial SPP modes described above (Figures 4 and 5), these topological surface modes are robust to non-local effects and do not lose their strict unidirectionality even if strong nonlocalities are taken into account [52,57]. This can also be explained by recognizing that their unidirectional nature depends on their dispersion behavior for small wavevectors (asymmetry in lower-frequency cut-offs, as seen in Figure 7b), and not on their behavior for large wavevectors (asymmetry in flat dispersion asymptotes) which is much more affected by the presence of nonlocal effects that depend on k. Thanks to their topological robustness, even the presence of large sharp defects and discontinuities does not lead to the backscattering of these unidirectional surface modes.…”

“…However, in practice, material losses affect modes with larger wavevectors more strongly, which may lead to a situation in which the SPP mode propagating in one direction is underdamped, whereas the nonlocality-induced counterpropagating mode is overdamped, as shown in Figure 4d. This may result in SPP propagation that can be considered, for all practical purposes, unidirectional in a small frequency range [52,57]. We stress, however, that the central conclusion of recent works in this area is that the unidirectional properties of these surface modes depend on the relative strength of dissipative and nonlocal effects in a given plasmonic material, and more realistic material models are necessary to make accurate predictions [57].…”

“…The existence of the unidirectional frequency window in Figure 4b crucially depends on the group velocity of the counterpropagating mode asymptotically tending to zero for large wavevectors. This behavior is however unphysical [46,52], as mentioned in the previous section for bulk modes, and it can be regularized by modifying the simplistic Drude model that was used to derive the permittivity in Equation (3) to include the convective and diffusive transport effects of an electron gas [46,[52][53][54][55][56]. For example, using the popular hydrodynamic model of a free-electron gas and neglecting diffusion effects, the induced free-electron current J is governed by the following equation, in the presence of an external magnetic bias in the z direction,…”

“…Other considerations: One crucial difference between periodic systems and continuum systems such as magnetized plasmas is that the wavevector (momentum) of the eigenmodes of a periodic system is bounded due to a finite Brillouin zone (hence, momentum space is compact), which has relevant implications for the calculation of topological invariants, as discussed in Section 2.1, and for the bulk-edge correspondence principle Although a proof of this principle for continuum systems has been provided in [20], edge/surface modes may be located in the asymptotic part of the spatial spectrum [48,70], as in the plasma-PMC case mentioned above, which also need to be properly accounted for when applying the principle. Some methods to accurately count surface modes have been proposed such as by assuming a thin vacuum layer between the two materials [19,52], which brings the "missing" surface mode back to finite values of wavenumber. Other methods are based on the scattering matrix describing the system, as discussed in [70].…”