A lens can bend or focus light beams by introducing different delays across its section. For example, a convex lens is thicker in the middle, and therefore light travels slower at the center than at the border of the lens. However, light can also be delayed by interacting with resonators, such as optical antennas. The advantage of using antennas is that the resulting device thickness can be as low as few nanometers, a million times thinner than glass lenses, opening the way to ultrathin optical devices that can be integrated with electronic chips and microprocessors.
Scanning electron microscope (SEM) image of a representative antenna array fabricated on a silicon wafer. The unit cell of the plasmonic interface (yellow) comprises eight gold V-antennas of width ∼220nm and thickness ∼50nm, and repeats with a periodicity of Γ=11μm in the x direction and 1.5μm in the y direction.1
To demonstrate the potential of such ultrathin optical devices, we fabricated an array of antennas (see Figure 1) that have a linearly increasing delay along a specific direction for mid-IR-wavelength beams.1 This array steers a plane wave by an arbitrary angle, much the same way a prism does. In a prism, the delay of light also increases linearly over the beam cross-section as a result of propagation through the material wedge. We exploit a very different kind of delay. We designed several different antennas, each with its own delay, and arranged them into an array, making a flat and ultrathin surface. Thus, the delay is designed on a point-by-point fashion, and is not due to propagation. The output beam is built according to the Huygens-Fresnel principle (Figure 2).
Finite difference time-domain simulations of the scattered electric field for the individual antennas composing the array in Figure 1
. The diagonal red line is the envelope of the projections of the spherical waves. On account of Huygens' principle, the anomalously refracted beam resulting from the superposition of these spherical waves is a tilted plane wave that satisfies a generalized Snell's law.1
: Electric field component along x. λ0
: Wavelength in air.
Because of the extremely thin material, this delay appears to an observer in the far field to be an effective discontinuity in the oscillation of the field. The exiting beam of this specific array, being excited by a plane wave, is also a plane wave, but it is steered toward the side of the more delayed antennas. Our antennas are like the continuous tracks of a turning bulldozer: if one of the tracks slows down, the bulldozer steers toward that side. Unlike the bulldozer, however, we have not just two, but many antennas perpendicular to the direction of motion. In fact, the surface of the device must be densely populated, with many antennas within a wavelength extension, to make sure it behaves as a ‘metasurface.’ Thus, we have to introduce many different delays within a wavelength, which must be mutually consistent: they must be linearly progressing, as they would be in a properly turning ‘fat bulldozer,’ one with many parallel continuous tracks.
Why did we use V-shaped fat bulldozer antennas? Linear antennas exhibit some fundamental properties, common to all harmonic oscillators. The relevant property is the largest attainable delay, which is only half of the period of the oscillating excitation. But our fat bulldozer needs to introduce all possible delays in its dense set of tracks. Because of this ‘lame range’ of available delays, it is not possible to build an arbitrary wavefront by scattering a plane wave with an array of linear antennas. V-antennas circumvent this limitation by introducing two uncoupled and nonparallel resonant dipole moments. It is then possible to combine these two oscillations to cover the whole range of delays over one full period of oscillation. The V-antennas work by exploiting a properly balanced excitation of both nonparallel moments, but the price paid is that the excitation beam must have a controlled polarization. For many applications this can be also viewed as an additional ability of our devices to provide polarization functionality.
In terms of the quantitative description of refraction, this metasurface introduces an additional term in the Snell's law, which is proportional to the delay gradient.1 The gradient can be out of the plane of incidence, giving rise to the 3D out-of-plane anomalous refraction.2 Since the working principle is based on the point-by-point construction of the scattered wave, it is then possible to move from the simpler constant gradient array to a general and arbitrary 2D delay map. We have shown the flexibility of our approach by generating optical vortices with ultrathin phase maps (see Figure 3).3
(A, B) Scanning electron microscopy images of a plasmonic interface that creates an optical vortex. (C, D) measured (C) and calculated (D) far-field intensity distributions of the generated optical vortex. (E–H) Measured (E, G) and calculated (F, H) interference images of the vortex.1
Arrays of V-antennas may provide a way to fabricate ultrathin and broadband optical devices with functionality of prisms, lenses, curved mirrors and polarizers, compatible with silicon planar technology. Since the working principle is based on material structuring rather than material properties, this approach not only has the advantage of being virtually disconnected from specific materials but is also scalable, and hence adaptable, to different regions of the electromagnetic spectrum, for example, to the near-IR.4 Our metasurfaces can also be used for creating highly confined cavity modes of potential interest in quantum optics. Our next steps will be to fabricate and test focusing metasurfaces (flat lenses), as well as polarizing devices such as flat counterparts of wave plates. We also plan to exploit the near-field properties of V-shaped individual antennas, for example, toward applications for plasmonic sensors.
University of Trento
1. Nanfang Yu, Patrice Genevet, Mikhail A. Kats, Francesco Aieta, Jean-Philippe Tetienne, Federico Capasso, Zeno Gaburro, Light propagation with phase discontinuities: generalized laws of reflection and refraction, Science 334, p. 333, 2011.
2. Francesco Aieta, Patrice Genevet, Nanfang Yu, Mikhail A. Kats, Zeno Gaburro, Federico Capasso, Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities, Nano Lett. 12, p. 1702, 2012.
3. Patrice Genevet, Nanfang Yu, Francesco Aieta, Jiao Lin, Mikhail A. Kats, Romain Blanchard, Marlan O. Scully, Zeno Gaburro, Federico Capasso, Ultra-thin plasmonic optical vortex plate based on phase discontinuities, Appl. Phys. Lett. 100, p. 13101, 2012.
4. Xingjie Ni, Naresh K. Emani, Alexander V. Kildishev, Alexandra Boltasseva, Vladimir M. Shalaev, Broadband light bending with plasmonic nanoantennas, Science 335, p. 427, 2012.