There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Graphene, the single-atom-thick form of carbon, holds promise for many applications, notably in electronics where it can complement or be integrated with silicon-based devices. Intense efforts have been devoted to develop a key enabling device, a broadband, fast optical modulator with a small device footprint. Now Liu et al. demonstrate an exciting new possibility for graphene in the area of on-chip optical communication: a graphene-based optical modulator integrated with a silicon chip. This new device relies on the electrical tuning of the Fermi level of the graphene sheet, and achieves modulation of guided light at frequencies over 1 gigahertz, together with a broad operating spectrum. At just 25 square micrometres in area, it is one of the smallest of its type. Integrated optical modulators with high modulation speed, small footprint and large optical bandwidth are poised to be the enabling devices for on-chip optical interconnects1,2. Semiconductor modulators have therefore been heavily researched over the past few years. However, the device footprint of silicon-based modulators is of the order of millimetres, owing to its weak electro-optical properties3. Germanium and compound semiconductors, on the other hand, face the major challenge of integration with existing silicon electronics and photonics platforms4,5,6. Integrating silicon modulators with high-quality-factor optical resonators increases the modulation strength, but these devices suffer from intrinsic narrow bandwidth and require sophisticated optical design; they also have stringent fabrication requirements and limited temperature tolerances7. Finding a complementary metal-oxide-semiconductor (CMOS)-compatible material with adequate modulation speed and strength has therefore become a task of not only scientific interest, but also industrial importance. Here we experimentally demonstrate a broadband, high-speed, waveguide-integrated electroabsorption modulator based on monolayer graphene. By electrically tuning the Fermi level of the graphene sheet, we demonstrate modulation of the guided light at frequencies over 1 GHz, together with a broad operation spectrum that ranges from 1.35 to 1.6 µm under ambient conditions. The high modulation efficiency of graphene results in an active device area of merely 25 µm2, which is among the smallest to date. This graphene-based optical modulation mechanism, with combined advantages of compact footprint, low operation voltage and ultrafast modulation speed across a broad range of wavelengths, can enable novel architectures for on-chip optical communications.

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A graphene-based broadband optical modulator

We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

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Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

Modern nanotechnology allows one to scale down various important devices (sensors, chips, fibers, etc.) and thus opens up new horizons for their applications. The efficiency of most of them is based on fundamental physical phenomena, such as transport of wave excitations and resonances. Short propagation distances make phase-coherent processes of waves important. Often the scattering of waves involves propagation along different paths and, as a consequence, results in interference phenomena, where constructive interference corresponds to resonant enhancement and destructive interference to resonant suppression of the transmission. Recently, a variety of experimental and theoretical work has revealed such patterns in different physical settings. The purpose of this review is to relate resonant scattering to Fano resonances, known from atomic physics. One of the main features of the Fano resonance is its asymmetric line profile. The asymmetry originates from a close coexistence of resonant transmission and resonant reflection and can be reduced to the interaction of a discrete (localized) state with a continuum of propagation modes. The basic concepts of Fano resonances are introduced, their geometrical and/or dynamical origin are explained, and theoretical and experimental studies of light propagation in photonic devices, charge transport through quantum dots, plasmon scattering in Josephson-junction networks, and matter-wave scattering in ultracold atom systems, among others are reviewed.

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Fano resonances in nanoscale structures

Metal interconnections are expected to become the limiting factor for the performance of electronic systems as transistors continue to shrink in size. Replacing them by optical interconnections, at different levels ranging from rack-to-rack down to chip-to-chip and intra-chip interconnections, could provide the low power dissipation, low latencies and high bandwidths that are needed. The implementation of optical interconnections relies on the development of micro-optical devices that are integrated with the microelectronics on chips. Recent demonstrations of silicon low-loss waveguides, light emitters, amplifiers and lasers approach this goal, but a small silicon electro-optic modulator with a size small enough for chip-scale integration has not yet been demonstrated. Here we experimentally demonstrate a high-speed electro-optical modulator in compact silicon structures. The modulator is based on a resonant light-confining structure that enhances the sensitivity of light to small changes in refractive index of the silicon and also enables high-speed operation. The modulator is 12 micrometres in diameter, three orders of magnitude smaller than previously demonstrated. Electro-optic modulators are one of the most critical components in optoelectronic integration, and decreasing their size may enable novel chip architectures.

Micrometre-scale silicon electro-optic modulator

We present a novel waveguide geometry for enhancing and confining light in a nanometer-wide low-index material. Light enhancement and confinement is caused by large discontinuity of the electric field at highindex-contrast interfaces. We show that by use of such a structure the field can be confined in a 50-nm-wide low-index region with a normalized intensity of 20 mm 22 . This intensity is approximately 20 times higher than what can be achieved in SiO2 with conventional rectangular waveguides. © 2004 Optical Society of America OCIS codes: 030.4070, 130.0130, 130.2790, 230.7370, 230.7380, 230.7390, 230.7400. Recent results in integrated optics have shown the ability to guide, bend, split, and f ilter light on chips by use of optical devices based on high-index-contrast waveguides. 1–5 In all these devices the guiding mechanism is based on total internal ref lection (TIR) in a highindex material (core) surrounded by a low-indexmaterial (cladding); the TIR mechanism can strongly confine light in the high-index material. In recent years a number of structures have been proposed to guide or enhance light in low-index materials, 6–1 1 relying on external ref lections provided by interference effects. Unlike TIR, the external ref lection cannot be perfectly unity; therefore the modes in these structures are inherently leaky modes. In addition, since interference is involved, these structures are strongly wavelength dependent. Here we show that the optical field can be enhanced and conf ined in the low-index material even when light is guided by TIR. For a high-index-contrast interface, Maxwell’s equations state that, to satisfy the continuity of the normal component of electric f lux density D, the corresponding electric field (E-field) must undergo a large discontinuity with much higher amplitude in the low-index side. We show that this discontinuity can be used to strongly enhance and confine light in a nanometer-wide region of low-index material. The proposed structure presents an eigenmode, and it is compatible with highly integrated photonics technology. The principle of operation of the novel structure can be illustrated by analysis of the slab-based structure shown in Fig. 1(a), where a low-index slot is embedded between two high-index slabs (shaded regions). The novel structure is hereafter referred to as a slot waveguide. The slot waveguide eigenmode can be seen as being formed by the interaction between the fundamental eigenmodes of the individual slab waveguides. Rigorously, the analytical solution for the transverse E-field profile Ex of the fundamental TM eigenmode of the slab-based slot waveguide is

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Guiding and confining light in void nanostructure.

We show a scheme for achieving high-speed operation for carrier-injection based silicon electro-optical modulator, which is optimized for small size and high modulation depth. The performance of the device is analyzed theoretically and a 12.5-Gbit/s modulation with high extinction ratio >9dB is demonstrated experimentally using a silicon micro-ring modulator.

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12.5 Gbit/s carrier-injection-based silicon micro-ring silicon modulators

We experimentally demonstrate a novel silicon waveguide structure for guiding and confining light in nanometer-wide low-refractive-index material. The optical field in the low-index material is enhanced because of the discontinuity of the electric field at high-index-contrast interfaces. We measure a 30% reduction of the effective index of light propagating in the novel structure due to the presence of the nanometer-wide low-index region, evidencing the guiding and confinement of light in the low-index material. We fabricate ring resonators based on the structure and show that the structure can be implemented in highly integrated photonics.

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Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material.

We provide the first experimental observation of structure tuning of the electromagnetically induced transparencylike spectrum in integrated on-chip optical resonator systems. The system consists of coupled silicon ring resonators with $10\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ diameter on silicon, where the coherent interference between the two coupled resonators is tuned. We measured a transparency-resonance mode with a quality factor of 11 800.

Qianfan Xu

Papers

Micrometre-scale silicon electro-optic modulator

Guiding and confining light in void nanostructure.

12.5 Gbit/s carrier-injection-based silicon micro-ring silicon modulators

Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material.

Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency