Electrical 2π phase control of infrared light in a 350-nm footprint using graphene plasmons

Abstract

Modulating the amplitude and phase of light is at the heart of many applications such as wavefront shaping, 1 transformation optics, 2,3 phased arrays, 4 modulators 5 and sensors. 6 Performing this task with high efficiency and small footprint is a formidable challenge. 7,8 Metasurfaces 5,9 and plasmonics 10 are promising , but metals exhibit weak electro-optic effects. Two-dimensional materials, such as graphene, have shown great performance as modulators with small drive voltages. 11,12 Here we show a graphene plasmonic phase modulator which is capable of tuning the phase between 0 and 2π in situ. With a footprint of 350 nm it is more than 30 times smaller than the 10.6 µm free space wavelength. The modulation is achieved by spatially controlling the plasmon phase velocity in a device where the spatial carrier density profile is tunable. We provide a scattering theory for plasmons propagating through spatial density profiles. This work constitutes a first step towards twodimensional transformation optics 3 for ultra-compact modulators 7 and biosensing. 13 Graphene plasmons are a versatile tool for integrated photonics and nano-optoelectronics as they provide extreme sub-wavelength confinement of light 14-16 while still offering a long lifetime approaching 1 ps. 16 The graphene plasmon phase velocity (and thus wavelength) is in situ tunable, and can be varied spatially, making it a unique platform for for transformation optics in two dimensions. 3,17 The full spatial and dynamic control of the plasmon velocity profile makes completely new device concepts possible. This includes on-chip interferometers and tunable metamaterials such as phased arrays for a full dynamical beam manipulation. 4 This full control has thus far remained a great challenge and the plasmon propagation was mainly controlled by physical features in the graphene. [18][19][20] Here, we manipulate for the first time the spatial profile of the plasmon phase velocity actively employing local metal gates, achieving in situ control of the plasmon wavelength, as sketched in Fig. 1. A plasmon (launched by scattering light on a gold edge) that propagates trough the tunable spatial carrier density profile picks up a phase, that is transferred to the photon after scatter-10.6 μm Mirror B S λ 0 /2 λ pl /2 Launching contact 150 nm 100 nm 100 nm 27 nm 5 nm V PS h-BN V 0 = -10 V Figure 1 | Device sketch and measurement principle.The three local gates are used to independently tune the carrier concentration in the different graphene regions. The phase shifter voltage V PS is tuned and during all experiments V0 = −10 V is kept constant. The gate thickness is 15 nm. The plasmons propagate from the launching contact over the phase shifter region and are ultimately scattered into far-field light using a metallized AFM tip, and subsequently interfered with the incoming light.ing of a metallized atomic force microscopy probe tip. In this way, we are able to continuously tune the phase shift of the plasmon and the outcoming photons from 0 to 2π, and experimentally ...

Functional Mid‐Infrared Polaritonics in van der Waals Crystals

“…Their atomically thin geometry, meanwhile, is ideal for creating structures that can be electrostatically gated. These two properties make vdW materials an effective and compact platform for active modulation of both guided waves and free space light at mid‐infrared frequencies. The extremely confined nature of vdW plasmons, however, makes them difficult to couple strongly to the free waves and thus hinders their efficiency in optoelectronic devices .…”

“…In particular, the tunable and ultrahigh‐confined properties of graphene plasmons discussed in Section allow dynamic manipulation of electromagnetic waves at deep‐subwavelength scale. For example, an in situ electrical 2π phase shift has been experimentally demonstrated in graphene . As shown in Figure a, propagating plasmons along encapsulated graphene were launched by a top metal contact, and their phase velocity, or the dispersion, was actively controlled by local gating.…”

“…Surprisingly, the optical path length of the graphene plasmons was observed to be tuned in the order of micrometers within a couple of hundreds nanometer length scale due to the ultrahigh confinement factor ( n eff ≈ 100). As a result of the modulated optical path lengths of the graphene plasmons, a dynamic 2π phase shift was achieved within a λ 0 /30 length scale, which corresponds to 350 nm …”

“…(Bottom) Measured phase shift (orange circles) and calculated phase shift (orange curve). Adapted with permission . Copyright 2017, Springer Nature.…”

Lippmann-Schwinger theory for two-dimensional plasmon scattering

“…given by (23) and effective interaction given by (24). Note that T is a function of a reciprocal vector q, of an angle θ giving the direction of the incoming wave, and of the frequency ω.…”