Metamaterial Shrinks Integrated-Photonics Devices

Rajesh Menon

Author: Rajesh Menon

Affiliation: Department of Electrical & Computer Engineering, University of Utah, USA.

Integrated electronics is the driving force behind the information revolution of the last 6 decades. A similar revolution is happening in photonics, where devices that manipulate the flow of light (or photons) are being miniaturized and integrated. The main challenge for integrated photonics is that the wavelength of light is far larger than the equivalent wavelength of electrons. This is the main reason that devices fundamental to integrated electronics are significantly smaller than those used in integrated photonics. Furthermore, no one had come up with a way to design devices close to this limit for integrated photonics.

We recently solved this problem by first coming up with a new design algorithm and then experimentally verifying that our devices work as intended [1-3]. One crucial advantage of our method is that our fabrication process is completely compatible with the very mature processes already developed for silicon electronics. This means that we can exploit the vast existing manufacturing infrastructure to enable integrated photonics.

In our recent publication, we demonstrated the smallest polarization beam-splitter to date [1]. This device (shown in the figure below) has 1 input and 2 outputs. The 2 outputs correspond to the 2 linear polarization states of light. The device is designed to take either polarization of light (or both) as the input and separate the 2 polarizations into the 2 outputs. We input light into our device one polarization at a time and measured the transmission efficiency into the correct output. This allowed us to verify that the device performs as designed. This is analogous to separating two channels of communication (for example, a video stream from PBS and another from Netflix). Previously such separation would have required time and power-consuming electronics or if photonics devices were used, they would have been much larger (so much harder to integrate onto a chip).

Figure 1: (a) Scanning-electron micrograph of fabricated polarization beamsplitter. Simulated intensity distribution at (b) TE polarization and (c) TM polarization showing the separation of the beams.

In the big picture, our research has the potential to maintain Moore's law for photonics. By enabling integrated photonics devices to be much smaller (in fact, close to their theoretical limits), we allow the integration of more devices in the same area (which increases functionality) and also enable the devices to communicate faster (since they are closer together; light has to travel shorter distances). Finally, by packing more devices into the same chip, one also exploits economies of scale to reduce the cost per chip (similar to what has happened in electronics). The practical impact for customers is that one can expect to drastically reduce power consumption and enable faster communications and computing. Data centers today consume over 2% of the total global electricity. Reducing power consumption in data centers and other electronics can go a long way to reduce our CO2 emissions and stem global climate change.

Our vision is to create a library of ultra-compact devices (including beamsplitters, but also other devices) that can then be all connected together in a variety of different ways to enable both optical computing and communications. The first devices were fabricated at a University. Next, we need to fabricate these in a standard process at a company, and then provide this library of devices to designers and hopefully, unleash their creativity. We believe that these devices will usher in unpredictable, but unbelievably exciting applications.

References :
[1] Bing Shen, Peng Wang, Randy Polson, Rajesh Menon, “An integrated-nanophotonic polarization beamsplitter with 2.4 × 2.4 μm² footprint”, Nature Photonics, 9, 378-382 (2015). Abstract.
[2] Bing Shen, Peng Wang, Randy Polson, Rajesh Menon, “Integrated metamaterials for efficient, compact free-space-to-waveguide coupling”, Optics Express, 22, 27175-27182 (2014). Abstract.
[3] Bing Shen, Randy Polson, Rajesh Menon, “Integrated digital metamaterials enables ultra-compact optical diodes”, Optics Express, 23, 10847-10855 (2015). Abstract.

Novel Electromagnetic Cavities: Bound States in the Continuum

Thomas Lepetit (left) and Boubacar Kanté (right)

Authors: Thomas Lepetit and Boubacar Kanté 

Affiliation: Department of Electrical and Computer Engineering, University of California San Diego, USA. 

In the last 10 years, an intense research effort has been devoted to bringing all-optical signal generation and processing on chip to realize true photonic integrated circuits (PICs). PICs are at their core made of waveguides, which transfer signals to different devices on the circuit, and cavities, which process signals for different functionalities [1]. First, linear devices such as couplers, splitters, and add-drop filters were developed and, more recently, nonlinear devices such as frequency combs, nanolasers, and optical rams have been demonstrated [2-4]. Overall, progress has resulted in devices with increased functionalities that work at lower power and are more compact.

Cavities are an essential building block of PICs because they provide enhanced light-matter interaction. Currently, the most mature technology is based on a silicon on insulator platform and ring resonators. Typically, these dielectric resonators are several microns in diameter [5]. However, due to the difficulty of integration with much smaller electronic components, other technologies such as plasmonics have started to be investigated. One of the main advantages of plasmonic devices, which are made of noble metals such as gold and silver, is that their size is not limited by the wavelength. For example, plasmonic ring resonators of only several hundred nanometers in diameter have been demonstrated [6]. Generally, cavities are characterized by their quality factor Q, which is a measure of their capacity to store signals for a long time. At present, dielectric cavities have reached quality factors of 10⁶, which are only limited by radiation losses coming from sidewall roughness, but typically have a footprint of 80 μm². In contrast, plasmonic cavities can have a footprint as low as 1.25 μm² but their quality factors are usually below 10², being limited by thermal losses coming from conduction electrons. Therefore, there is a need for novel cavity designs that can simultaneously achieve high quality factors and low footprints.

Figure 1: Cross-section of the electric field magnitude for the coupled resonators system (Half of it). Resonator 1, whose inner radius is zero, is on top and resonator 2, with a non-zero inner radius, is at the bottom. The symmetry plane on the right of each plot denotes the symmetry plane of interest. Odd modes are mostly confined in resonator 1 and even modes mostly in resonator 2.

Recently, we have demonstrated the possibility of making electromagnetic cavities using a different concept, namely bound states in the continuum (BICs) [7]. BICs were first proposed in 1929 in the context of quantum mechanics by Von Neumann and Wigner [8]. They surprisingly showed that bound states can exist above the continuum threshold, i.e., there are states that do not decay even in the presence of open decay channels. However, due to the theoretical nature of the first proposal, BICs did not become fully appreciated until 1985 when Friedrich and Wintgen showed that they could be interpreted as resulting from the interference of two distinct resonances [9]. In this picture, one resonance traps the other and thus one quality factor decreases while the other one tends to infinity. Since BICs are essentially a wave phenomenon they also appear in electromagnetics where they translate for lossless dielectrics into an infinite quality factor. As a proof of concept, we have designed and measured a BIC in the microwave range using a periodic metasurface [10-11].

BICs are intrinsically sensitive to perturbations as they only exist at a single point in phase space. This is very useful for sensing applications but detrimental for most others. To obtain an extended BIC, we designed a system with two quasi-degenerate BICs. We achieved this by considering a unit cell with two resonators, a disk and a ring (see Figure 1). Odd modes of the disk resonator interfere and lead to one BIC and even modes of the ring resonator interfere and lead to another BIC. We use ceramic resonators of high-permittivity (ε_r=43±0.75) and they are thus only slightly coupled. Experimentally, to limit the fabrication dispersion inherent to a large array, we made the measurements in a rectangular metallic waveguide (X-band, 8.2-12.4 GHz). It is possible because such a guided setup is equivalent to an infinite array at oblique incidence as shown by image theory.

Figure 2: Modes of two dielectric resonators (ε_r=43) in a rectangular metallic waveguide (X-band). Both resonators are cylindrical (r=3.5 mm, h₁=2.25 mm, h₂=3.0 mm) and the second has a non-zero inner radius. a) Resonance frequencies vs. inner radius for even and odd modes. b) Quality factor vs. inner radius for even and odd modes for lossless and lossy resonators.

We explored phase space along a line, by varying the inner radius of the ring resonator, and showed the presence of two avoided resonance crossings (see Figure 2a), which are typical of BICs [12]. As a result, there is an extended region of phase space where the quality factor tends to infinity (see Figure 2b). BICs only serve to cancel radiation losses and in the presence of thermal losses these are the limiting factor. At present, this scheme is therefore practical only for dielectrics but it could be extended to plasmonics by introducing gain materials to achieve loss-compensation.

Beyond the fundamental interest on the limit of quality-factors given a certain volume, there is a sustained interest in reducing the footprint of many cavity-based devices for future PICs. Tailoring the optical potential further, for example by moving away from perfectly periodic structures [13], opens the possibility improving the field confinement and thus shrink devices. Our work is a first step in this promising direction.

References:
[1] L. A. Coldren, S. W. Corzine, and M. Mašanović, “Diode Lasers and Photonic Integrated Circuits”, 2nd edition, Wiley (2012).
[2] Fahmida Ferdous, Houxun Miao, Daniel E. Leaird, Kartik Srinivasan, Jian Wang, Lei Chen, Leo Tom Varghese, Andrew M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs”, Nature Photonics, 5, 770 (2011). Abstract.
[3] M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, Y. Fainman, “Thresholdless nanoscale coaxial lasers”, Nature 482, 204 (2012). Abstract.
[4] Eiichi Kuramochi, Kengo Nozaki, Akihiko Shinya, Koji Takeda, Tomonari Sato, Shinji Matsuo, Hideaki Taniyama, Hisashi Sumikura, Masaya Notomi, “Large-scale integration of wavelength-addressable all-optical memories on a photonic crystal chip”, Nature Photonics 8, 474 (2014). Abstract.
[5] W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, R. Baets, “Silicon microring resonators”, Laser Photonics Review 6, 47 (2012). Abstract.
[6] Hong-Son Chu, Yuriy Akimov, Ping Bai, Er-Ping Li, “Submicrometer radius and highly confined plasmonic ring resonator filters nased on hybrid metal-oxide-semiconductor waveguide”, Optics Letters, 37, 4564 (2012). Abstract.
[7] Thomas Lepetit, Boubacar Kanté, “Controlling multipolar radiation with symmetries for electromagnetic bound states in the continuum”, Physical Review B Rapid Communications, 90, 241103 (2014). Abstract.
[8] J. von Neumann and E. Wigner, “On unusual discrete eigenvalues”, Zeitschrift für Physik 30, 465 (1929).
[9] H. Friedrich and D. Wintgen, “Interfering resonances and bound states in the continuum”, Physical Review A, 32, 3231 (1985). Abstract.
[10] Boubacar Kanté, Jean-Michel Lourtioz, André de Lustrac, “Infrared metafilms on a dielectric substrate”, Physical Review B, 80, 205120 (2009). Abstract.
[11] Boubacar Kanté, André de Lustrac, Jean Michel Lourtioz, “In-plane coupling and field enhancement in infrared metamaterial surfaces”, Physical Review B, 80, 035108 (2009). Abstract.
[12] Chia Wei Hsu, Bo Zhen, Jeongwon Lee, Song-Liang Chua, Steven G. Johnson, John D. Joannopoulos, Marin Soljačić, “Observation of trapped light within the radiation continuum”, Nature, 499, 188 (2013). Abstract.
[13] Yi Yang, Chao Peng, Yong Liang, Zhengbin Li, Susumu Noda, “Analytical perspective for Bound States in the Continuum in Photonic Crystal Slabs”, Physical Review Letters, 113, 037401 (2014). Abstract.

Reconfigurable Acoustic Metamaterials: From Random To Periodic In A Split Second

Mihai Caleap (left) and Bruce Drinkwater (right)

Authors: Mihai Caleap and Bruce Drinkwater

Affiliation:
Faculty of Engineering, University of Bristol, United Kingdom.

Using an acoustic metadevice that can influence the acoustic space and can control any of the ways in which waves travel, we have demonstrated, for the first time, that it is possible to dynamically alter the geometry of a three-dimensional colloidal crystal in real time [1].

The colloidal crystals designed in our study, called metamaterials, are artificially structured materials that extend the properties of existing naturally occurring materials and compounds.

The reconfigurable metamaterial is assembled from microspheres in aqueous solution, trapped with acoustic radiation forces. The acoustic radiation force is governed by an energy landscape, determined by an applied high amplitude acoustic standing wave field, in which particles move swiftly to energy minima. This creates a colloidal crystal of several millilitres in volume with spheres arranged in an orthorhombic lattice in which the acoustic wavelength is used to control the lattice spacing.

Dynamically reconfigurable metamaterials based devices with optical or acoustic wavelengths from tens of microns to tens of centimetres could have a wide range of applications. In optics it could lead to new beam deflectors or filters for terahertz imaging and in acoustics it might be possible to create acoustic barriers that can be optimised depending on the changing nature of the incident sound. Further applications in reconfigurable cloaks and lenses are also now conceivable. The reconfigurable acoustic assembly method developed in this study is an important step as it has clear advantages over other possible approaches, for example optical trapping and self-assembly. In particular, acoustic assembly is scalable with wavelength from microns to metres. The method will work on a vast range of materials, such as nearly all solid-fluid combinations, it will also enable almost any geometry to be assembled and it is cheap and easy to integrate with other systems.

Figure 1: Acoustic metadevice capable of manipulating the acoustic space and controlling the propagation of waves (Image credit: Mihai Caleap, University of Bristol, copyright © 2014)

This first realization of an acoustic metamaterial that is reconfigurable in real-time represents a new and versatile means by which wave propagation phenomena can be controlled. The approach will allow the design and synthesis of a wide range of new colloidal crystals based on micrometre-sized particles arranged in crystal lattices. Using our acoustic assembly technique, low-density acoustic colloids could be conceived to form quasi-crystalline structures [2], which would otherwise be difficult by the self-assembly technique. The range of structures that can be constructed is limited only by the ability to produce the appropriate acoustic potential energy landscape. The technique can also provide a platform for performing bio-assays and cell-assays in a non-contact way using acoustic or magnetic standing waves.

References:
[1] Mihai Caleap and Bruce W. Drinkwater, "Acoustically trapped colloidal crystals that are reconfigurable in real time". Proceedings of the National Academy of Sciences of USA, 111 (17), 6226–6230 (2014). Full Article.
[2] Jules Mikhael, Johannes Roth, Laurent Helden, Clemens Bechinger Mikhael, "Archimedean-like tiling on decagonal quasicrystalline surfaces". Nature, 454, 501–504 (2008). Abstract.

“True” Stopping of Light – A New Regime for Nanophotonics

Kosmas L Tsakmakidis (left), Ortwin Hess (right)

Authors: Kosmas L Tsakmakidis¹, Ortwin Hess²

Affiliation:
¹NSF Nano-scale Science and Engineering Center (NSEC), University of California -- Berkeley, USA, 
²Blackett Laboratory, Department of Physics, Imperial College, London, UK.

1. Introduction

The enormous speed of light allows us to observe distant galaxies and to communicate in real time at remote points on the surface of the earth. At smaller frequencies, light passes through macroscopic solid objects almost completely unhindered, interacting weakly with matter. Reducing its velocity down to zero is of fundamental scientific interest [1-3] that could usher in a host of important photonic applications, some of which are hitherto fundamentally inaccessible. These include cavity-free, low-threshold nanolasers [4,5], novel solar-cell designs for efficient harvesting of light [6,7], nanoscale quantum information processing [8], as well as enhanced biomolecular sensing [9].

Until now complete stopping of light pulses, leading to their localisation in a specific region of space, in solid structures and at ambient conditions, has been hampered by fundamental difficulties. Ultraslow light requires strong group-index (n_g) resonances but the increased (compared with gases) damping at normal conditions invariably broadens and weakens such resonances. Certain resourceful schemes, such as electromagnetically induced transparency (EIT) [10], can exploit very narrow absorption dips arising from quantum interference effects to drastically slow-down light in ultracold atoms (where damping is minimised) but their solid-state implementations [11,12] usually decelerate light by up to a factor of a few hundreds. Furthermore, at the zero-group-velocity (zero-υ_g) point of an EIT scheme a light pulse usually relinquishes its photonic character by coherently mapping its optical quantum states to stationary electronic (spin) excitations [13].

Light is 'stored' in this way [14] but our ultimate goal of observing and harnessing photons at a zero-υ_g point is not satisfied ‒ even under extreme conditions entailing vacuum operation and ultralow temperatures. Periodic nanophotonic structures offer another route for slowing-down light, essentially via periodic back-reflections by a lattice of scatterers having sizes comparable to the wavelength [15]. Here, it is structural disorder that fundamentally limits the attainment of light stopping. Tiny nanometer-scale fluctuations destroy the (theoretically assumed) 'perfect' periodicity, leading to a 'smearing out' effect in the attained group indices at the band edges [16,17]. Practically this results in slowing-down factors that normally do not exceed a few hundreds.

Here we report on a solid-state configuration leveraging media with negative electromagnetic parameters [18,19] whereby an arbitrary number of light pulses can be stopped, remaining well localised ‒ without diffusing ‒ at predefined spatial locations despite the absence of any barriers in front or behind the pulses. Our work addresses two fundamental problems: First, how the detrimental role of decoherence mechanisms (losses and surface roughness) in the light-stopping ability of a solid-state nanophotonic structure can be overcome; and, second, how light stopping can be accomplished without overshooting the optical losses at the zero-υ_g point. The lifetime of the stopped light pulses in our nanoplasmonic structure (Fig.1) decreases only moderately (by a factor of ~ 1.5) compared with the normal (n_g ≤ 10) nanoplasmonic light regime, allowing for a broad range of applications in this field. Further, we present a realistic design and computational demonstration of a negative-refractive-index optical metamaterial in the fabric of which we insert a (four-level) gain medium (laser dyes), such that the metamaterial enters the full lasing regime. We, thus, demonstrate an ultra-thin, ultra-fast nanolaser, operating at visible wavelengths (710 nm) and with modulation bandwidth close to 1 THz ‒ orders of magnitude faster than typical modulation speeds of conventional lasers.

2. Stopping and localisation of light pulses in nanoplasmonic metamaterials

We have identified two light-stopping structures: The first is made of a negative-refractive-index core layer surrounded by air (illustrated schematically in Fig. 1), while the second is made of a Si layer sandwiched by two (plasmonic) ITO layers (see Fig. 1) [20]. While the negative-index structure clearly showed how we may access the zero group-velocity (zero-υ_g) points, it was still found to be incomplete in the following respects: First, the (negative) effective refractive index of the metamaterial slab may exhibit fluctuations, even at microwave frequencies where homogenization works best. Second, the group-velocity dispersion at the zero-υ_g point should be minimised to avoid late-time broadening (diffusion) of the stopped pulses. Third, the configuration should also be immune to the presence of surface roughness.

Figure 1: Schematic illustration of the two configurations used for obtaining complex-ω stopping of light. The first is an air/metamaterial/air slab heterostructure, with the middle metamaterial layer (yellow) having a negative refractive index at microwave wavelengths. An upper prism (not shown here) is used to in-couple spatially separated incident light beams (white) into the middle layer, exciting the complex-ω mode at its zero-υ_g point at different spatial locations along the waveguide. Rather than being guided along the structure, the excited pulses (in colors) remain stopped, decaying with time at their injection points. The second structure, operating at telecommunication wavelengths, is made of a Si slab bounded by two ITO layers, with the upper one (right) having a finite thickness. Here, the complex-ω mode is weakly leaky at its zero-υ_g point and, hence, there is no need to use a prism. The complex-ω pulses in this structure remain stopped and strongly localised, without diffusing and broadening at late times.

A structure that manages to comply with the above requirements, exhibiting complete and dispersion-free stopping of light pulses, is reported in Fig. 1 (schematically) and Figs. 2(b)-(d). We used a silicon slab of thickness 290 nm, bounded by a low-loss plasmonic material (indium tin oxide, ITO). The upper ITO cladding layer, through which the injection of the light pulses into the middle Si layer was performed, had a finite thickness of 500 nm. At near-infrared wavelengths (1.55 µm) and for p-polarized light the (real part of the) permittivity ε of the ITO layers is negative [21], thereby providing the required light-deceleration and stopping mechanism ‒ similarly to the negative-index structure [22]. We expect that in the β = 0 (quasistatic) region the bands of the supported modes become flat (υ_g = 0) [23]; therefore, to minimise group-velocity dispersion and to make the desired band as flat as possible at a finite-β zero-υ_g point, this point must be brought as close as possible to the β = 0 region. Indeed, we have designed the above ITO/Si/ITO heterostructure such that it accomplishes this goal, supporting a bulk complex-ω mode [20,24] with a zero-υ_g point on the right-hand side of the air light-line. In addition to low group-velocity dispersion and preservation of the light-stopping point (in the presence of losses), this weakly leaky mode features two further favourable characteristics: First, since β was designed to be finite but small at the zero-υ_g point, the effective index n_eff = β/k₀ of the mode therein turns out to be smaller than unity: n_eff = 0.39 < 1. Consequently, the wavelength λ_eff inside the structure became larger than the free-space one (λ₀ = 1.55 µm), which further diminished the effect of nm-scale surface roughness. Second, since the mode at the zero-υ_g point is (weakly) leaky there was no need to use a prism to excite it from air, thereby considerably alleviating the realisation of the scheme.

Figure 2(b) illustrates the time-evolution of four light pulses evanescently coupled into the above plasmonic heterostructure. The incident free-space wavelength was λ₀ = 1.55 µm (ω ≈ 1.2 PHz) and the angle of incidence was θ = 72.5_o, both selected such that precisely the zero-υ_g point was hit. We see from Fig. 2(b) that the four light pulses are stopped and strongly localised, decaying with time, without propagating and broadening. The e^-1-lifetime of each pulse, calculated by analytically solving the pertinent dispersion transcendental equation, was found to be 28.4 fs, while the time taken until the pulses are completely absorbed was approximately 131 fs, in agreement with the FDTD calculations of Fig. 2(b). When the angle of incidence of an exciting pulse is such that a non-zero-υ_g point is hit, a pulse injected into the heterostructure propagates away from its starting point, decaying but also dispersing (broadening) with time (Fig. 2(c)), as expected. Importantly, while the deceleration factor (group index) from the non-zero-υ_g point (n_g^B ≈ 6.6) to the zero-υ_g one (n_g^A → ∞) increases dramatically, the temporal losses increase by no more than a factor of two (from 2.4×10¹³ s^-1 to 3.7×10¹³ s^-1). This crucial aspect, together with the fact that the lifetimes at the stopping point (28.4 fs and 131 fs) are typical nanoplasmonic ones, suggests that a wealth of applications within this field should also be possible in the stopped-light regime. Note further from Fig. 2(b) that, since the herein observed localisation is not a cavity- or disorder-aided one, the optical pulses can be injected and stopped at any point along the structure, as well as be brought tighter together ‒ up to the diffraction limit.

Figure 2: (To view higher resolution click on the image) Full-wave FDTD calculations of the time-evolution of one or more pulses injected inside the light-stopping configurations of Fig. 1. In all cases the results are recorded on the vertical yz plane (translucent) cutting through the middle layer. (a) Shown are eight pulses in-coupled into the negative-index heterostructure at its zero-υ_g point. All pulses remain stopped for more than 6 ns, decaying with time at their initial positions. (b) Shown here are four pulses in-coupled into the plasmonic heterostructure at its zero-υ_g point. The pulses remain stopped and localized, without broadening, for more than 130 fs. (c) When a zero-υ_g point is hit, the pulse in-coupled into the plasmonic structure moves away from its initial point, both decaying and broadening with time. (d) The pulses in 'b' can also be brought closer together ‒ up to the diffraction limit ‒ since the structure is completely uniform, and the localization is not aided by disorder or a cavity-like action.

Finally, we have examined the effect of realistic levels of surface roughness on the light-stopping ability of the plasmonic heterostructure. To this end, we introduced random variations in the permittivities within a thin layer of ±1 nm around the two Si/ITO interfaces. We then recorded the time evolution of the centre of energy and full-width at half-maximum (FWHM) of a pulse in-coupled close to the complex-ω zero-υ_g point.

We have found [20] that the presence of roughness does not destroy the localisation (stopping and absence of broadening), since both the centre of energy and the FWHM (perturbed by the random surface landscape) oscillate ‒ with a very small amplitude ‒ around the values they had in the absence of roughness. From these results, we measured a group index of ~ 1.5×10⁷! Hence, although the pulses experience dissipative losses (from ITO), radiative losses (being weakly leaky) and surface roughness at the two Si/ITO interfaces, they remain robustly stopped and localised, with a movement of their center-of-energy being almost indiscernible. This robustness to nm-scale surface roughness arises from the fact that, unlike periodic structures, here the wavelength inside the structure at the zero-υg point is λ_eff = λ₀/n_eff = 3974 nm ‒ thousands of times larger than the surface-roughness amplitude, and therefore essentially insensitive to it.

The simplicity of the final design, together with the gigantic enhancement of the group refractive index and the minor increase of optical losses, make the structure appealing for a host of nanoplasmonic applications. Particularly, the enhancement of the density-of-states in the region around a flat band is a key parameter for enabling high-efficiency solar cells [25], as well as for giving rise to strong interactions between quantum emitters and plasmonic nanostructures [8] ‒ the cornerstone of strong optical nonlinearity. We anticipate that this might be extendable potentially even at the single-photon level, allowing for nonlinear quantum-optical logic operations on nanoscopic scales.

3. Ultrafast nanolasing in active nanoplasmonic metamaterials

Since the lifetime of our stopped-light excitations are of the order of 0.1 ps (owing to the presence of dissipative losses), we may use an optical gain medium to compensate for the losses. In general, the tight light localisation on truly nanoscopic dimensions ‒ well below the diffraction limit for visible light ‒ that nanoplasmonic metamaterials offer enhances the interaction of light with mater, paving the way for a multitude of classical and quantum nano-optics applications. However, metal optics suffers from inherent dissipative losses, which have persistently hampered many of the envisaged applications. We have recently shown that gain-enhanced nanoplasmonic metamaterials can overcome these hindrances and lead to novel nanophotonic components and devices.

Dissipative losses in nanoplasmonics arise from the interaction of the incident photons with the quasi-free conduction electrons of the metals, thereby constituting a rather inherent feature of the responses of metal-based nano-devices. For truly subwavelength plasmonic structures these losses follow universal laws, i.e. they do not depend on the particular geometric configuration but only on the deployed (usually noble) metal. Typical damping rates are thus of the order of Γ ~ 100 ps^-1, requiring gain coefficients Γ/c ~ 10³ - 10⁴ s^-1 to compensate for the losses. Meanwhile, the extreme control of light in optical metamaterials paves the way towards nano-enabled functionalities right at the materials level. But these need to be controlled dynamically, on-demand and in real time. Both of the aforementioned challenges can be met by enhancing metamaterials with gain, incorporated right into their fabric.

In the following, we briefly illustrate – on the basis of full-wave simulations – that high gain densities in a realistic nanoplasmonic metamaterial result in the compensation of, both, dissipative and radiative losses leading into the full lasing regime, where bright and dark lasing states dynamically compete giving rise to ultrafast nonlinear responses.

Figure 3: Electric-field amplitude profiles and charge distributions on the metal films inside the double-fishnet unit cell for (a) the bright mode at λ_bright =717.25 nm and (b) the dark mode at λ_dark = 731.8 nm. The direction of the electric field in the x-z plane is indicated by the white arrows. (c) Total average energy density (black area) and frequency-filtered contributions at λ_pump = 680 nm (green dashed line), λ_bright (white full line) and λ_dark (yellow dash-dotted line).

Figures 3(a) & (b) depict an example of an active (gain-enhanced) nanoplasmonic metamaterial comprised of two thin silver nanofilms, periodically perforated with holes, and laser dyes inserted between the films [4, 5]. The structure has been designed such that there is an optimum coupling of the plasmonic excitations to the gain molecules, ensuring efficient harnessing of the gain. An intense pump pulse of 2 ps duration (λpump = 680 nm) inverts the gain medium and dynamically creates a 3D occupation inversion profile closely matching the spatial distribution of the electric field at the probe wavelength (λprobe = 710 nm). After 7 ps, a weak broadband pulse of duration 12 fs probes the active structure, and its far-field spectrum is recorded at the two sides of the planar metamaterial. Detailed calculations have shown that in the regime of full loss compensation the real part of the effective refractive index of the nanostructure becomes more negative compared to the passive case. By prolonging the duration of the probe pulse such that the energy inside the nano-fishnet became constant with time, we have also ascertained that there can be net outflux of optical energy through a volume encompasing the metamaterial, i.e. there is more energy radiated away from the volume than energy incident on the volume. Hence, our quantum plasmonic amplifier can operate not only transiently but also in a steady-state mode.

Such active nanostructures can function as powerful light sources, either coherent (nanolasers) or incoherent (diodes), delivering intense optical power within ultrasmall volumes or ultrathin flat surfaces. We have shown that when the gain supplied by the active medium embedded within a quasi-2D active metamaterial is sufficient to overcome dissipative and radiative losses, the structure can indeed function as a coherent emitter of surface plasmons over the whole ultrathin 2D area, well below the diffraction limit for visible light. Both, bright and dark plasmonic lasing states can be generated, coupling either strongly or weakly to the continuum. Which one eventually dominates can be controlled by the design of the metametaterial. The dynamic, nonlinear competition between such lasing states is illustrated in Figure 3(c) where one may discern the initial build-up of the bright-mode energy (external and internal; red), followed by the damped-amplitude, ps-period relaxation oscillations, and then steady-state emission that is interrupted (at around 50 ps) by the instability of the dark mode (only internal; yellow) until again steady-state emission is reached.

Stopped-light plasmonic nanostructures, together with gain-enhanced optical metamaterials, constitute an exciting new frontier in nano-photonics and nano-science, and are precursors towards active, integrated quantum nano-optics. Reaching the full-light-stopping regime and bringing gain at the nanoscale is anticipated to improve the performance of a host of active nano-components, such as electro-optic modulators and light sources, but also passive ones, such as plasmonic waveguides or sensors featuring intensified plasmonic hotspots for single-emitter spectroscopy.

References:
[1] Robert W. Boyd, Daniel J. Gauthier, "Slow and fast light". Progress in Optics, 43, 497–530 (2002). Abstract.
[2]  Léon Brillouin, "Wave Propagation and Group Velocity" (Academic, 1960).
[3] P. W. Milonni, "Fast Light, Slow Light, and Left-Handed Light" (Institute of Physics, 2005).
[4] O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, K. L. Tsakmakidis, "Active nanoplasmonic metamaterials". Nature Materials, 11, 573–584 (2012). Abstract.
[5] Sebastian Wuestner, Joachim M. Hamm, Andreas Pusch, Fabian Renn, Kosmas L. Tsakmakidis, Ortwin Hess, "Control and dynamic competition of bright and dark lasing states in active nanoplasmonic metamaterials". Physical Review, B 85, 201406 (R) (2012). Abstract.
[6] Alexandre Aubry, Dang Yuan Lei, Antonio I. Fernández-Domínguez, Yannick Sonnefraud, Stefan A. Maier, J. B. Pendry, "Plasmonic light-harvesting devices over the whole visible spectrum". Nano Letters, 10, 2574–2579 (2010). Abstract.
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[13] M. D. Lukin, A. Imamoğlu, "Controlling photons using electromagnetically induced transparency". Nature, 413, 273–276 (2001). Abstract.
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Acoustically Invisible Walls

(left) Oliver Wright
(right) Sam Lee

Authors: Oliver B. Wright¹ and Sam Hyeon Lee²

Affiliation:
¹Division of Applied Physics, Faculty of Engineering, Hokkaido University, Sapporo, Japan
²Institute of Physics and Applied Physics, Yonsei University, Seoul, South Korea

Physicists in a Korea-Japan collaboration have devised a way to make hard walls transmit sound almost perfectly[1], which could prove useful for developing new types of windows or acoustic concentrators. Based on solid walls of metal or plastic perforated by small holes containing stretched membranes made of humble kitchen cling film, the collaboration have imaged sound travelling unimpeded through them. Sound in such structures, known as metamaterials, resonates strongly with the structure at certain frequencies, allowing counterintuitive effects such as zero sonic reflection. This is an example of a phenomenon known as extraordinary transmission, first demonstrated in the field of optics, whereby light waves are squeezed through sub-wavelength holes more efficiently than expected [2,3].

In the design presented, a tiny force from the sound wave is sufficient to launch a large motion of the membranes, a situation that mimics the air in the hole moving as if with zero mass. Sam Lee of Yonsei University, Kong-ju Bok Lee of Ehwa Women’s University and Oliver Wright of Hokkaido University speculate that this sonic invisible wall could be used for security glass, for example in banks or taxis, that allows you to talk across it, but protects you from any mechanical intrusion.

Figure 1: (left) Single hole with membrane in a cylindrical duct; (right) metamaterial wall consisting of an array of holes containing membranes.

In the first experiments done, sound was incident in a cylindrical tube of diameter 100 mm on a wall blocking the tube containing a single hole of diameter 17 mm mounted with a tight membrane, as shown in Figure 1. It was found that 90% of the acoustic amplitude was transmitted at the audio frequency of 1.2 kHz, in spite of only 3% of the area of the wall being open.

The team also demonstrated a giant concentration up to a factor of 5700 with smaller holes, and that the acoustic energy is effectively transmitted for any angle of incidence, as shown in the example of Figure 2. Figure 1 also shows an example of how a wall of membrane-covered holes could be constructed, effectively constituting a metamaterial wall that transmits sound effectively. This “extraordinary-transmission” phenomenon can be used over a wide range of frequencies. So the method would work equally well for ultrasound, for which preliminary experiments have been reported at lower efficiencies using resonances in bare holes [4]; this could be exploited to concentrate ultrasonic energy through tiny holes, forming novel lenses useful for high resolution ultrasonic imaging.

Figure 2: (Bottom image) Pressure map obtained in the audio-frequency extraordinary-acoustic transmission experiment at 1.2 kHz on an acoustic metamaterial consisting of tight membranes in 4 tiny holes, showing a giant acoustic concentration of 5700 in intensity with an areal coverage ratio of only 0.03. (Top image) Image for holes with no membranes.

References:
[1] Jong Jin Park, K. J. B. Lee, Oliver B. Wright, Myoung Ki Jung, and Sam H. Lee, "Giant Acoustic Concentration by Extraordinary Transmission in Zero-Mass Metamaterials", Physical Review Letters, 110, 244302 (2013). Abstract.
[2] R. Ulrich, in Optical and Acoustical Microelectronics, edited by J. Fox, page 359 (Polytechnic, New York, 1974).
[3] T.W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays", Nature, 391, 667 (1998). Abstract.
[4] Bo Hou, Jun Mei, Manzhu Ke, Weijia Wen, Zhengyou Liu, Jing Shi, and Ping Sheng, "Tuning Fabry-Perot resonances via diffraction evanescent waves", Physical Review B, 76, 054303 (2007). Abstract.

Inspiration from Nature: Ultralight Fractal Designs for High Mechanical Efficiency

[From Left to Right] Daniel Rayneau-Kirkhope, Robert Farr, Yong Mao



Authors: Daniel Rayneau-Kirkhope¹, Robert Farr^2,3, Yong Mao⁴

Affiliation:
¹Open Innovation House, School of Science, Aalto University, Finland,
²Unilever R&D, Colworth House, Sharnbrook, Bedford, UK
³London Institute for Mathematical Sciences, Mayfair, London, UK
⁴School of Physics and Astronomy, University of Nottingham, UK

Hierarchical design is ubiquitous in nature [1]. Material properties can be tailored by having structural features on many length scales. The gecko, a lizard ranging from 2 to 60 cm in length, has a remarkable ability to walk on vertical walls and even upside-down on ceilings. This ability is brought about through the repeated splitting of the keratinous fibres on the bottom of the gecko’s foot, which increases the contact area so effectively that even the very weak van der Waals interactions can support the entire weight of the gecko [2].

A more specific form of hierarchical design is self-similar design, where one structural feature is found to be repeated on a number of different length scales. A natural example is the trabecular or spongy bone found around the joints in animals [3]. Here, a series of small beams are arranged in such a way that the stiffness and strength requirements are met while using minimal material. Regardless of the level of magnification, the same patterns are found in the structure. Interestingly, the exact configuration of the constituent beams in the trabecular bone is constantly changing: it is the result of a continuous opitimisation process that goes on throughout the lifetime of the bone and responds to change in stress levels [4]. It is found that when the animal’s bones support only small loads, many very slender pillars are present, and when the loading increases, fewer but stouter pillars are employed [5].

In our recently published work [6], we demonstrate that through the use of hierarchical, self-similar design principles, advantageous structural properties can be obtained. We show that the scaling of the amount of material required for stability against the loading can be altered in a systematic manner. A particular structure is fabricated through rapid prototyping, and we obtain the optimal generation number (for our specific structure) for any given value of loading.

Scaling

The volume of material required for stability can be related to the loading through a simple power law relationship. That is, the volume required is given by a dimensionless loading parameter raised to some power with a pre-factor (that is dependent only on material properties and specifics of the geometry). When the loading is small, it is the scaling (power) of the loading that dominates the relationship. Under tension, this power is one and a structure requires an amount of material that is proportional to the loading it must withstand; for a solid beam under compression, due to elastic buckling, the power is one-half. Given, for all realistic applications, the non-dimensional loading parameter is much less than 1, this means more material is required to support compressive than tensional loads. This one-half power law has direct consequences when one considers optimal structure: if a beam is bearing a compressive load, it is more efficient to use one beam rather than two, whereas in the case of tension, due to the linear relationship, splitting a tension member into more than one piece has no effect on the volume required for stability.

Fractal design

Our work centers on a very simple, iterative procedure that can be used to create designs of great complexity. The “generation” of a structure describes the number of iterations used to create the geometry. The simplest compression bearing structure is a solid slender beam. When loaded with a gradually increasing force, the beam will eventually buckle into a sinusoidal shape known as an “Euler buckling mode”. We can suppress this by using a hollow tube, but we introduce a second mode of a local failure of the tube wall – Koiter buckling. After optimizing for tube diameter and thickness, it is found that the scaling power increases to two-thirds, and the volume of material required for stability is reduced.

Figure 1: Showing the iterative process from low generation numbers to higher for structures bearing compression along their longest axis. At each step, all beams that are compressively loaded are replaced by a (scaled) generation-1 frame.

The next step is to replace the hollow beam with a space frame of hollow beams. The space frame used here is made up of n octahedra and two end tetrahedra. Optimising the number of octahedra, the radius and the wall thickness of the component beams (which are all assumed be identical) we find a new power law, and again, an improvement over the hollow beam design.

Continuing this procedure of replacing all beams under compressive load with (scaled) space frames constructed from hollow beams (figure 1), we find that the scaling law is always improved by the increased level of hierarchy. In general, the scaling is described by a (G+2)/(G+3) power-law relating non-dimensional volume to non-dimensional loading. Thus, as the generation number tends to infinity, the scaling relating material required for stability to loading approaches that of the tension member.

3D Printing

Working with Joel Segal, of the University of Nottingham, we fabricated an example of a generation-2 structure with solid beams, shown in figure 2. This was done through rapid prototyping technologies: micrometer-layer-by-micrometer-layer the structure was printed in a photosensitive polymer with each beam a fraction of a millimeter in radius. This structure shows the plausibility of the design and the extent to which modern manufacturing techniques allow for an increased creativity in design geometry. Through a process of 3-d printing and electro less deposition, it is believed that a metallic, hollow tubed structure could be created.

Figure 2: Showing a structure fabricated through rapid prototyping techniques. The inset shows the layering effect of the 3D printing technique. The structure shown in constructed in RC25 (Nanocure) material from envisionTEC on an envisionTEC perfactory machine.

Optimal generations

Although the scaling is always improved by increasing the generation number of the structure, the prefactor isn’t. The optimal structure is then obtained by balancing the scaling relationship with the prefactor in the expression. Generally, as the loading decreases (or the size of the structure increases), the scaling becomes more important and the optimal generation number increases. For large loads (or small structures) it can even be the case a simple, solid, beam is optimal.

Our work also formalises this relationship, for a long time engineers have created chair legs from hollow tubes or cranes out of space frames, Gustave Eiffel used three levels of structural hierarchy in designing the Eiffel tower. We show formally, that the optimal generation number has a set dependence on the loading conditions and allow future structures to be designed with this in mind. A further consequence of the alteration of the scaling law is that the higher the generations, the less difference it makes as to whether you have one structure holding a given load or two structures holding half the load each.

Reference:
[1] Robert Lakes, "Materials with structural hierarchy", Nature, 361, 511 (1993). Abstract.
[2] Haimin Yao, Huajian Gao, "Mechanics of robust and releasable adhesion in biology: Bottom–up designed hierarchical structures of gecko", Journal of the Mechanics and Physics of Solids, 54,1120 (2006). Abstract.
[3] Rachid Jennanea, Rachid Harbaa, Gérald Lemineura, Stéphanie Bretteila, Anne Estradeb, Claude Laurent Benhamouc, "Estimation of the 3D self-similarity parameter of trabecular bone from its 2D projection", Medical Image Analysis, 11, 91 (2007). Abstract.
[4] Rik Huiskes, Ronald Ruimerman, G. Harry van Lenthe, Jan D. Janssen, "Effects of mechanical forces on maintenance and adaptation of form in trabecular bone", Nature, 405, 704 (2000). Abstract.
[5] Michael Doube, Michał M. Kłosowski, Alexis M. Wiktorowicz-Conroy, John R. Hutchinson, Sandra J. Shefelbine, "Trabecular bone scales allometrically in mammals and birds", Proceedings of the Royal Society B, 278, 3067 (2011). Abstract.
[6] Daniel Rayneau-Kirkhope, Yong Mao, Robert Farr, "Ultralight Fractal Structures from Hollow Tubes", Physical Review Letters, 109, 204301 (2012). Abstract.

Graphene Can Be Used for Terahertz Hyperlens

From left to right: Andrei Andryieuski, Dmitry Chigrin, Andrei Lavrinenko








Author: Andrei Andryieuski
Affiliation: DTU Fotonik, Technical University of Denmark, Denmark

Andrei Andryieuski and Andrei Lavrinenko, the researchers from the Metamaterials group at Technical University of Denmark (DTU) -- in collaboration with Dmitry Chigrin from the University of Wuppertal (BUW) -- made the first theoretical description of graphene hyperlens, able to work in the terahertz range.

Terahertz radiation, which occupies the spectral range between infrared and microwaves, is harmless to humans and animals and passes easily through many dielectric materials. Terahertz waves, which are able to detect drugs even in sealed vessels, to reveal hidden weapon and to detect cancer tumors, may revolutionize spectroscopy, defense and medical analysis.

 Fig. 1. Artistic view of the graphene hyperlens in action. Multiple structured graphene layers resolve and magnify two subwavelength sources.

The wavelength of terahertz radiation is, however, relatively large (300 µm at 1 THz) so the image-quality is seriously limited by the natural diffraction limit. To overcome this limit, artificially structured metamaterial lenses or metallic funnels can be employed. The very fine details hindered in the evanescent waves, which rapidly decay from the radiating object, can be captured by negative index superlens or indefinite medium (hyperbolic dispersion) hyperlens. While negative index metamaterials are still very lossy and far from being employed for practical purposes, the hyperlens present a realistic approach to imaging.

To make the hyperlens a very special material is required. It should behave as a metal in one direction and as an insulator in another. To obtain such properties, thin multiple metal-dielectric layers are normally used in optics. The theoretical concept -- proposed by Evgenii Narimanov’s group from Princeton University (USA) in 2006 [1] -- was checked experimentally by Xiang Zhang’s group from UC Berkeley (USA) in 2007 [2]. To realize the hyperlens the researchers deposited many ultrathin (35 nm) layers of silver and alumina. Even though the metal based hyperlens shows a subwavelength resolution, it is prohibited in tunability; basically, once being fabricated, its properties cannot be changed.

Contrary to metals, graphene, an atomically thin layer of carbon atoms, easily changes its properties under the influence of electrostatic field, magnetic field or chemical doping. This is why the researchers from DTU and BUW decided to employ it for the hyperlens. They propose to construct the hyperlens from narrow (starting from 40 nm) tapered graphene wires embedded into polymer.

Fig. 2. The building block of the hyperlens is the narrow graphene wire embedded into polymer. Arranging such tapered wires radially gives the required material properties for the hyperlens, namely, negative dielectric permittivity in radial direction and positive in azimuthal direction.

Such structured graphene arranged into multiple layers has the very properties needed for hyperbolic dispersion: the wave feels it as metal along the wires and as dielectric perpendicular to the wires. The hyperlens showed subwavelength resolution at the wavelength 50 µm of two sources separated with 10 µm, thus giving the possibility to image the points as close as 1/5 of the wavelength. The resolution of the hyperlens depends on its radii, so with proper selection of geometrical parameter it is possible to separate the images far enough to be captured by the conventional terahertz camera. The hyperlens can be tuned by applying voltage to various graphene layers. It works reciprocally, thus being able not only to image, but also to concentrate terahertz radiation in small volumes.

Fig. 3. Electromagnetic waves emitted by two line sources are captured by the hyperlens and magnified to such extent that they can be resolved with a conventional imaging device.

DTU’s researchers are looking forward to realize and test the graphene hyperlens experimentally.

The paper presenting the above work was published last week in Physical Review B Rapid Communications [3].

References:
[1] Zubin Jacob, Leonid V. Alekseyev, and Evgenii Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit”, Optics Express, 14, 8247 (2006). Abstract.
[2] Zhaowei Liu, Hyesog Lee, Yi Xiong, Cheng Sun and Xiang Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects”, Science, 315,  1686 (2007). Abstract.
[3] Andrei Andryieuski, Andrei V. Lavrinenko, Dmitry N. Chigrin, "Graphene hyperlens for terahertz radiation", Physical Review B, 86, 121108(R) (2012). Abstract. Also available at: arXiv:1209.3951.

A Newtonian Approach to Negative Index Metamaterials

Hosang Yoon (left) and Donhee Ham (right)














Authors: Hosang Yoon and Donhee Ham 
Affiliation:
School of Engineering and Applied Sciences, Harvard University, USA

Link to Donhee Ham Research Group >>

Negative index metamaterials have been celebrated due to their unusual ability to manipulate electromagnetic waves, such as bending light in the ‘wrong’ direction [1] and focusing light below the diffraction limit [2], which may prove technologically useful. To achieve negative refraction, a variety of material systems with engineered electric and/or magnetic properties have been developed. Reporting in Nature [3], we have demonstrated a ‘kinetic’ route to negative refraction, where exploitation of acceleration of electrons in a two-dimensional (2D) conductor leads to extraordinarily strong negative refraction with refractive index as large as -700.

Electrons in a conductor subjected to an electric field collectively accelerate according to Newton’s 2nd law of motion, creating a current that lags the electric field by 90°, as in a magnetic inductor. The conductor may then be considered as an inductor, but with its inductance being of kinetic origin [4]. This kinetic inductance is usually not much appreciable in ordinary three-dimensional conductors, but in a 2D conductor, it is orders-of-magnitude larger than magnetic inductance, which is what we exploit to create the dramatically strong negative refraction.

The acceleration of electrons is continually interrupted by their collisions with vibrations, impurities, or defects of the crystal lattice. Imagine a time-varying sinusoidal electric field at a given frequency, which accelerates/decelerates electrons into an oscillation motion. If the mean scattering rate is too high to accommodate an appreciable fraction of an oscillation period, the acceleration effect is hard to observe, and the conductor acts as an Ohmic resistor. This can be avoided in two ways: one is to cool the conductor to lower the scattering rate as in our work [3]; the other is to increase the frequency at room temperature, as currently pursued in our lab.

Figure 1. Optical micrograph (left) and schematic (right) of the metamaterial. The 2DEG strip array is connected to electromagnetic waveguides to the left and right. (Image reproduced from the paper published in Nature [3])

We employ a GaAs/AlGaAs 2D electron gas (2DEG) as a demonstrational 2D conductor. Our metamaterial designed in the GHz frequency range is an array of 2DEG strips (Fig. 1). Signal (S) lines flanked by ground (G) lines on the left and right of the strip array are coplanar waveguides (CPWs) that guide electromagnetic waves to and from the metamaterial. As an electromagnetic wave arrives from the left CPW, its electric field between the S and G lines accelerates electrons in/along the leftmost few strips. This inductive movement of electrons is capacitively coupled to the strip on the right, accelerating electrons there. This dynamics repeats to propagate an ‘electro-kinetic’ wave from left to right, perpendicular to the strips acting as kinetic inductors. It is this electro-kinetic wave that is negatively refracting. The negative refractive index is large due to the large kinetic inductance of the GaAs/AlGaAs 2DEG strip.

Figure 2. (Click on the image to see high resolution version) Dispersion relation (left) and refractive index (middle) of a 13-strip metamaterial with strip length 112 μm and periodicity 1.25 μm measured at different cryogenic temperatures. (right) Refractive index measured for metamaterials with various strip length (l) and periodicity (a). (Image reproduced from the paper published in Nature[3]) 

Microwave scattering experiments over 1~50 GHz confirms negative refraction; the measured dispersion of the electro-kinetic wave (Fig. 2, left) shows opposite signs for the phase and group velocities above a cutoff frequency. The corresponding negative refractive index is hundreds in magnitude, two orders of magnitude larger than typical negative refractive indices (Fig. 2, middle). With varying geometric parameters, an index as large as -700 is obtained (Fig. 2, right).

The very large negative index brings the science of negative refraction into drastically miniaturized scale, enabling ultra-subwavelength manipulation of electromagnetic waves. We expect to see the similar result at room temperatures by increasing the frequency towards the THz range, which is the direction our lab is now taking.

References:
[1] V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Soviet Physics Uspekhi, 10, 509–514 (1968). Abstract.
[2] J. B. Pendry, "Negative refraction makes a perfect lens," Physical Review Letters, 85, 3966–3969 (2000). Abstract.
[3] H. Yoon, K. Y. M. Yeung, V. Umansky, and D. Ham, "A Newtonian approach to extraordinarily strong negative refraction," Nature, 488, 65–69 (2012). Abstract.
[4] R. Meservey, "Measurements of the kinetic inductance of superconducting linear structures," Journal of Applied Physics, 40, 2028–2034 (1969). Abstract.

First Material with Longitudinal Negative Compressibility

Adilson E. Motter (Left) and Zachary G. Nicolaou (Right)
















Authors: Zachary G. Nicolaou^1,2 and Adilson E. Motter¹
Affiliation:
¹Department of Physics and Astronomy, Northwestern University, USA
²Department of Physics, California Institute of Technology, USA

Conventional materials deform along the direction of the applied force in such a way that they expand when the force is tensional and contract when it is compressive. But our new paper [1] published this month in Nature Materials demonstrates that not all materials have to be that way. We explored network concepts to design metamaterials exhibiting negative compressibility transitions, during which a material undergoes contraction when tensioned (or expansion when pressured). This effect is achieved through destabilizations of metastable equilibria of the constituents of the material. These destabilizations give rise to a stress-induced phase transition associated with a twisted hysteresis curve for the stress-strain relationship. The proposed materials are the first to exhibit longitudinal negative compressibility at zero frequency.

Negative compressibility surface. When pressured, the surface expands instead of contracting [Image copyright: Adilson E Motter]

.
The motivation for this work comes from our previous research on networks. It has been known that some networks respond in a surprising way to various types of perturbations. For example, in previous research our group has shown that the removal of a gene from the metabolic network of a living cell can often be compensated by the removal (not addition) of other genes [2]. Our hypothesis was that, with the right design, similarly counter-intuitive responses could occur in materials as well, which are essentially networks of interacting particles. The idea of using network concepts to design a material that could contract longitudinally when tensioned was particularly attractive because no existing material (natural or engineered) had been found to exhibit that property.

Negative compressibility cube. When tensioned, the cube contracts instead of expanding [Image copyright: Adilson E Motter]. 

.
There are numerous potential applications for materials with negative compressibility transitions. They include the development of new actuators, microelectromechanical systems, and protective devices---from ordinary ones, such as seat belts, to devices that reduce the consequences of equipment failure. These materials may also lead to force amplification devices, which could be used to sense minute forces and transform them into large ones. Indeed, the strain-driven counterpart of negative compressibility transitions is a force amplification phenomenon, where an increase in deformation induces a discontinuous increase in response force. Other potential applications would be to improve the durability of existing materials, such as in crack closure of fractured materials. In fact, we expect other researchers to come up with yet different applications that we have not even thought about.

Negative compressibility material. The material at the center of the image expands vertically as it is squeezed [Image copyright: Adilson E Motter].

.
The most surprising aspect of this research is the very finding that you can create a material that contracts when it would be expected to expand and expands when it would be expected to contract. Think of a piece of rod that you tension by pulling its ends with your fingers. It would normally get longer, but for these materials it can get shorter. This has been generally assumed not to be possible for the excellent reason that no known material behaves that way. Moreover, it is easy to show that this is indeed impossible if we assume that the material will respond continuously to the applied force. Our work shows, however, that this unfamiliar form of compressibility can occur by means of an abrupt change---a phase transition. A posteriori, perhaps another surprising aspect of our research was the simplicity of the system once we understood how it works, and this can have practical implications for the fabrication of the material.

This work illustrates rather dramatically how deceiving it is to assume that a material’s property will be limited by those of existing ones, the reason being that existing materials explore only a tiny fraction of the space of all possibilities. Previous research has pushed the boundaries of electromagnetic properties and led, for example, to materials with negative refractive index [3]. Our research shows that even mechanical properties that have no immediate analogs in electromagnetic metamaterials can be tailored and even inverted. At the end, the material’s properties are only limited by how different interacting parts can be assembled together. For a related discussion in the context of networks, see Ref. [4].

References:
[1] Z. G. Nicolaou and A. E. Motter, Mechanical metamaterials with negative compressibility transitions, Nature Materials 11, 608-613 (2012). Abstract.
[2] A. E. Motter, "Improved network performance via antagonism: From synthetic rescues to multi-drug combinations", BioEssays 32, 236-245 (2010). Full Article.
[3] R. A. Shelby, D. R. Smith and S. Schultz, "Experimental verification of a negative index of refraction", Science 292(5514), 77-79 (2001). Abstract.
[4] A. E. Motter and R. Albert, "Networks in motion", Physics Today 65(4), 43-48 (2012). Abstract.