Metamaterials

# Steering surface plasmon wakes

### Subjects

The propagation direction of surface plasmon wakes can be controlled by exciting a series of dipoles with different phases along a one-dimensional metamaterial.

A boat that moves across a rippled water surface with a speed greater than the speed of the water waves produces a wake pattern behind it. These wakes are water shock waves generated by a constructive interference of the water waves created by the motion of the boat. Analogously, when a charged particle travels faster than the speed of light in a medium, a photonic shock wave called Cherenkov radiation is emitted. Although the principle behind these two phenomena is the same, there is one significant difference: the electromagnetic shock wave is emitted as a cone in the three spatial dimensions, whereas the water shock wave is a two-dimensional, surface wave phenomenon. Writing in Nature Nanotechnology, Patrice Genevet, Federico Capasso and colleagues now show that the Cherenkov radiation1 emitted as an electron propagates at the dielectric/metal interface can be confined in two dimensions using a specific metamaterial design. By doing so, they can control the propagation direction of the Cherenkov radiation.

The energy and the angle of emission of Cherenkov radiation depend on the speed of the charged particles travelling across the medium. In the field of high-energy physics, this principle has served well for the discovery of new particles, most notably antiprotons2 and J particles3. In the last decades, however, scientists working on metamaterials — artificial materials with unusual electromagnetic properties that cannot be found in nature — have found ways to go beyond mere detection of Cherenkov radiation and have demonstrated ways in which the direction of the emission could be modified. Using metamaterials with a negative refractive index, for example, Cherenkov wakes can be directed backwards4. Genevet and colleagues, who are based at the Singapore Institute of Manufacturing Technology, Harvard University, the University of Naples in Italy and EOS Photonics, have managed to connect the physics of Cherenkov radiation with that of surface plasmon polaritons (SPP) demonstrating that the emission can be steered in specific directions.

The researchers use a one-dimensional metallic metasurface composed of an array of identical nanoslits etched at a different angle. When a beam of light hits the surface at an angle θ, a series of dipoles with different phases is induced along the metasurface. These dipoles interact with the local distribution of free electrons on the metal surface and radiate SPP waves along the metal–dielectric surface. This dipole array is equivalent to a charged particle moving at a speed c/sinθ, where c is the speed of light. This speed is always larger than the SPP phase velocity (cSPP). The system, therefore, generates SPP Cherenkov wakes (Fig. 1).

The key advantage of the design of Genevet and colleagues is the ability to steer these SPP wakes. The different orientations of the nanoslits introduce an additional local phase shift along the one-dimensional metamaterial. Thus, when circularly polarized light hits the surface, the emission angle of the SPP wakes depends on both the local phase shift of the nanoslits array and the phase shift associated with the incident angle of the light beam. As a result, the direction of propagation of the SPP wakes can be controlled all the way from the forward (Fig. 1b) to the backward directions (Fig. 1c).

The physics behind this experiment is the phase matching condition, which states that the phase velocity of the excited SPPs along the particle's movement direction must be equal to the velocity of the particle. This situation is analogous to the refraction of SPP waves incident at the grazing angle (90°) from a lower-refractive-index medium (the array of nanoslits that corresponds to a medium with an effective refractive index of n1 = sinθ) to a higher-refractive-index medium (the metal/dielectric interface that corresponds to a medium with an effective refractive index of nSPP = c/cSPP). The geometric rotation of the slits produces an additional phase shift at the interface, so that applying the phase matching condition allows for steering of the refracted wave.

The ability to manipulate the Cherenkov surface plasmon wakes can, in principle, be useful in applications that require real-time control of the SPPs by incident light, such as plasmonic phase modulators, plasmonic holograms and beam-steering devices. However, for some applications the design of Genevet and colleagues may be limited by the fact that the excitation of the SPP wakes requires coherent incident light with either circular or elliptical polarization. Furthermore, the coupling efficiency of the incident light with the SPP wakes remains low. Nevertheless, this work is a significant conceptual step towards the complete control of Cherenkov wakes, which offers the potential to manipulate SPPs in plasmonic devices.

## References

1. 1

Genevet, P. et al. Nature Nanotech. 10, 804–809 (2015).

2. 2

Chamberlain, O., Segre, E., Wiegand, C. & Ypsilantis, T. Phys. Rev. 100, 947–950 (1955).

3. 3

Aubert, J. J. et al. Phys. Rev. Lett. 33, 1404–1406 (1974).

4. 4

Xi, S. et al. Phys. Rev. Lett. 103, 194801 (2009).

## Author information

Authors

### Corresponding authors

Correspondence to Hongsheng Chen or Zhaoyun Duan or Min Chen.

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Chen, H., Duan, Z. & Chen, M. Steering surface plasmon wakes. Nature Nanotech 10, 736–737 (2015). https://doi.org/10.1038/nnano.2015.138

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