Junctions between two-dimensional plasmonic waveguides in the presence of retardation

Abstract

Plasmons in two-dimensional waveguides are traditionally analysed within the electrostatic approximation, which assumes that the plasmon phase velocity is much smaller than the velocity of light. However, novel effects have recently been demonstrated for plasmons whose velocity is comparable to the velocity of light. In this retardation regime, electrostatic models are inaccurate. For a junction between two plasmonic waveguides, we present an analytical and a numerical model both valid in the retardation regime and compare them to an electrostatic model. We quantify the reflected and transmitted powers and the radiation loss in several scenarios. We found that power is radiated from a junction at the expense of the power of the reflected plasmon, but retardation has little effect on the phases of the reflected and transmitted plasmons. The radiation loss is typically below several percent when the plasmon velocities are five or more times below the light velocity. However, radiation still persists for slower plasmon velocities for a junction between a twodimensional waveguide and a perfectly conducting sheet. As a result, retardation is expected to degrade the quality factors of plasmonic resonators without affecting their eigenfrequencies.

Scattering-induced amplification of two-dimensional plasmons: Electromagnetic modeling

“…In a previous study 25 , we adopted this variational method to the problem of Fig. 1 but in the absence of dc current.…”

“…and − denotes the Cauchy principal value. The plasmon reflection coefficient in the absence of drift R (0) can also be found using the variational method 25 ; analytical expressions are also available that are applicable in the absence of retardation 19 .…”

“…Following Refs. [29] and [25], we choose the basis functions as the Laguerre polynomials L n (x) weighted by an exponential, so that…”

“…The field amplitudes at the ends of regions 1 and 4 were negligible, and these regions could be terminated with perfectly conducting boundaries. Since plasmon fields decay exponentially away from the 2D channels, radiation at the interface can be expected to be negligible 25 . The top and bottom of the computation domain could then be also terminated by perfectly conducting boundaries placed each 100 µm away from the 2D channels.…”

“…Initial theoretical studies have concentrated on dispersion relations and resonance frequencies of gated and ungated two-dimensional (2D) plasmons [12][13][14] , magnetoplasmons 15 , and edge (magneto-)plasmons 16,17 . There has recently been an upsurge of interest in plasmon scattering at discontinuities, such as those formed by interfaces between 2D systems with two different carrier densities [18][19][20] , between a gated and an ungated system [21][22][23] , or by edges 18,24 and electric contacts 25 . Plasmon scattering has been studied by adopting methods developed previously for the traditional metallic and dielectric waveguides, such as the mode-matching 26,27 and the variational methods 28,29 , transmission-line models 28 , and the Wiener-Hopf technique 26 .…”