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[INVITED] Self-assembled optical metamaterials
Optics & Laser Technology 82 (2016) 94–100
Contents lists available at ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Review
Self-assembled optical metamaterials Alexandre Baron a,b,c,n, Ashod Aradian a,b, Virginie Ponsinet a,b, Philippe Barois a,b a b c
CNRS, CRPP, UPR8641, F-33600 Pessac, France University of Bordeaux, CRPP, UPR8641, F-33600 Pessac, France Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA
art ic l e i nf o
a b s t r a c t
Article history: Received 5 February 2016 Accepted 29 February 2016
Self-assembled metamaterials constitute a promising platform to achieving bulk and homogenous optical materials that exhibit unusual effective medium properties. For many years now, the research community has contemplated lithographically fabricated metasurfaces, with extraordinary optical features. However, achieving large volumes at low cost is still a challenge by top-down fabrication. Bottomup fabrication, that relies both on nanochemistry and self-assembly, is capable of building such materials while greatly reducing the energy footprint in the formulation of the metamaterial. Self-assembled metamaterials have shown that they are capable of reaching unprecedented values of bulkiness and homogeneity figures of merit. This feat is achieved by synthesizing plasmonic nanoresonators (metaatoms in the sense of artificial polarizable units) and assembling them into a fully three-dimensional matrix through a variety of methods. Furthermore it has been shown that a wide range of material parameters can be tailored by controlling the geometry and composition of the meta-atoms as well as the volume fraction of the nano-objects in the metamaterial. Here we conduct a non-comprehensive review of some of the recent trends in self-assembled optical metamaterials and illustrate these trends with our recent work. & 2016 Elsevier Ltd. All rights reserved.
Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. From top-down to bottom-up approaches to metamaterial fabrication . 3. Exploring homogenization and bulkiness empirically . . . . . . . . . . . . . . . 4. Optical properties of self-assembled metamaterials . . . . . . . . . . . . . . . . 5. Future challenges for self-assembled metamaterials . . . . . . . . . . . . . . . . 6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction As metamaterials make their way into the applications realm [1–3], notably for RF applications, some members of the research and industrial communities have adopted a broad definition of metamaterials in terms of design [4]. The field of metamaterials may be viewed as a design approach that enables the production
n Corresponding author at: University of Bordeaux, CRPP, UPR8641, F-33600 Pessac, France. E-mail address: [email protected] (A. Baron).
http://dx.doi.org/10.1016/j.optlastec.2016.02.024 0030-3992/& 2016 Elsevier Ltd. All rights reserved.
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of artificial materials that exhibit electromagnetic properties on demand [5]. Undeniably, the concept of metamaterials has influenced how scientists think about device design and materials. This has led to elegant solutions to several electromagnetic problems. However some of the hurdles that have existed for several years in the field and have restricted the applications of metamaterials still exist today, notably as research and engineering move toward optical frequencies. Originally, metamaterials were thought of as artificial assemblies of subwavelength resonators with extraordinary effective medium properties. By extraordinary, the research community meant effective properties that cannot be
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Fig. 1. Electromagnetic properties of metamaterials and typical examples of metamaterials. The horizontal axis represents the real part of the dielectric permittivity ε. The vertical axis represents the real part of the magnetic permeability μ. Several applications are represented on the graph. The green line represents natural optical materials for which μ¼1, while the red line represents impedance-matched materials for which ε ¼μ. Building an electromagnetic cloak requires varying the index of refraction spatially over an interval between 0 and 1. A negative refractive index requires that ε and μ be simultaneously negative and enables the fabrication of a perfect lens. The blue dashed axis (ε∼0) represents materials that may serve as perfect electromagnetic couplers. The sketches in inset representing the invisibility cloak, the Perfect lens and the perfect coupler are adapted from Refs. [14,22,23]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
found in natural materials. Of course, this broad definition is applicable to many areas of material science and engineering: electromagnetic, acoustic, thermal materials [6–9], but we wish to focus on electromagnetic metamaterials and more specifically optical metamaterials. The electromagnetic properties of a material are characterized by the dielectric permittivity ε and the magnetic permeability μ. The graph represented on Fig. 1 illustrates the different classes of materials depending on the values that the real part of ε and μ take on. A historically famous example of extraordinary property was achieved in 2000 by Smith et al. [10]. They managed to build an artificial composite medium with simultaneously negative permeability and permittivity which is equivalent to a material with a negative refractive index. A few years prior to this demonstration, Pendry et al. had proposed a strategy to achieve negative values of these two parameters by combining electric dipoles made of metallic wires with magnetic dipoles made of metallic split rings [11]. The achieved material was exceptional in many respects. On the one hand, natural materials only have positive refractive indices. On the other hand, the electrodynamic consequences of such a material had been theoretically predicted by Veselago in the 1960s, stemming from the fact that group and phase velocities have opposite signs: reversal of the Doppler shift, reversal of the Cherenkov radiation, anomalous and negative refraction [12]. The first metamaterials were built by top-down fabrication, but now they are also immerging in bottom-up schemes. In this review, we shall briefly describe the transition from tow-down to bottom-up approaches to metamaterial fabrication (Section 2). Section 3 is devoted to explaining how self-assembled metamaterials constitute a convenient means to exploring empirically homogenization and bulkiness. Section 4 reviews some of our recent work highlighting some of the optical properties that can be achieved with self-assembled metamaterials. Some of the future challenges of self-assembled metamaterials are exposed in Section 5, before concluding (section6).
2. From top-down to bottom-up approaches to metamaterial fabrication Since the experimental demonstration by Smith et al. [10],
many experimental realizations have shown the validity of these predictions and further explored the large diversity of extraordinary properties that can be achieved using the metamaterials approach. Up until recently this approach consisted in carefully designing composite resonators that associate metals with dielectrics so as to fine-tune the electric and magnetic dipolar resonances, such that the material composed of a large volume of these resonators (or meta-atoms) would take on new values of ε and μ. This design approach has enabled the metamaterials community to realize a great number of applications and proofsof-concept. For instance, combined with the Transformation Optics approach developed by Pendry et al. [13], spatial variations of the index of refraction on the interval [0,1] enabled Smith and Pendry to design and realize the first electromagnetic cloak [14]. Another famous example is the ideal electromagnetic coupler that can be achieved by fabricating a so-called epsilon near-zero metamaterial, i.e. when ε∼0 [15,16] (see Fig. 1). Metamaterials have also enabled the realization of subwavelength imaging systems such as the hyper-lens [17] and ultraviolet flat lensing [18]. Historically, metamaterials have been built by lithographic approaches using microelectronics technology. This has enabled the fabrication of a very large number of electromagnectic metamaterials operating at frequencies ranging from microwaves all the way to the ultraviolet [18,19]. However this top-down approach, though extremely precise in making ordered structures is highly cost-intensive, such that almost all realized metamaterials are two dimensional, which renders the material highly anisotropic. Consequently, most metamaterials are actually metasurfaces. Achieving bulk three-dimensional metamaterials has remained a challenge in recent years. It requires that large assemblies of optical resonators be made in the three directions of space (bulkiness criterion) and that the dimensions of the resonator be much smaller that the optical wavelength (homogeneity criterion). In other words, the height h of a material needs to be very large compared to the typical length of a unit cell a of a nanoresonator, such that a figure of merit (FOM) for dimensionality (or bulkiness) may be defined as the ratio h/a and a homogeneity FOM may be defined as the ratio λ/a. These two FOMs may be viewed as two important quantities that need to be maximized to reach the realm of bulk optical metamaterials. To date, the best values of these FOMs obtained for metamaterials by top-down fabrication do not exceed 10 for h/a and 5 for λ/a (see Table 1).
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Table 1 Comparison of the bulkiness FOM h/a for several metamaterial realizations. Year
Reference
h/a
λ (nm)
Fabrication
2007 2008 2008 2008 2011 2013 2013 2013
[20] [21] [24] [25] [26] [18] [27] [28]
3 10 5 4 3 3 7 600
1500 1800 1600 3000 683 364 400 500
top-down top-down top-down top-down top-down top-down bottom-up bottom-up
Today, a radically different approach to metamaterials is available that combines nanochemistry and several self-assembly techniques inherited from colloidal chemistry that make it possible to build self-assembled artificial materials with extreme values of the bulkiness and homogeneity FOM (see last entry in Table 1). Applying these concepts to metamaterials presents us with a unique opportunity to build large volumes of artificial materials with unusual optical properties. We propose to review our recent work to illustrate some of the hot topics of self-assembled metamaterials.
3. Exploring homogenization and bulkiness empirically Reaching the homogenization limit means that the typical size of metamaterial resonators (meta-atoms) and the average distance that separates each meta-atom should be very small compared to the wavelength of the electromagnetic radiation. This is equivalent to stating that both the homogeneity and bulkiness FOM must be maximized. Though top-down approaches have been able to reach a high degree of precision at the nanometer range, achieving high values of these FOMs for visible frequencies is challenging. Making a bulk sample typically requires a tremendous number of metaatoms on the order of 1012 /mm3 [27]. Today a large variety of meta-atoms with varying complexity can be synthesized by nanochemistry. These may serve as interesting metamaterial building blocks if they present optical resonances. At visible wavelengths, plasmonic nanoresonators may be used as meta-atoms. They are usually hybrid in nature, with metal and dielectric subparts. The conduction electrons in the metal compound oscillate with the electromagnetic field to form localized surface plasmons in the nanoparticle and by carefully controlling the geometrical parameters of the nano-object, the amplitude and resonance wavelength of the meta-atom polarizability may be tuned. Fig. 2 illustrates the typical meta-atoms that exhibit plasmonic resonances in the visible and that can be synthesized in large amounts by nanochemistry. It is remarkable to notice how complex and anisotropic the geometries can be, such that some of these nanoparticles resemble theoretical proposals of extraordinary meta-atoms. Metallic nanorods or core-shell nanoparticles typically exhibit large electric dipole resonances [29,30], while metallic nanoclusters have both strong electric and magnetic dipole resonances [31]. Fig. 2(b) is a nanocup geometry that consists of a dielectric nanosphere embedded in a metallic cup. These nanoparticles serve as efficient directional scatterers [32]. Optical nanoparticles have typical sizes ranging from 30 nm to 100 nm in diameter, which corresponds to homogeneity FOMs λ/a ranging from 5 to 40 at visible frequencies. Polarization resolved light scattering is a powerful experimental tool that can be used to characterize the optical response of such meta-atoms in a solvent. This technique has been used recently to measure the scattering cross-sections of electric and magnetic dipoles [31,33]. Once the properties of a meta-atom with tailored optical
properties have been designed and the nanoparticle has been synthesized, there are several self-assembly techniques that physical-chemists have at their disposal to assemble fully three-dimensional metamaterials. Fig. 3 shows three examples of metamaterials assembled by three different techniques. Templating with block-copolymers enables the fabrication of lamellar films that alternate between a pure polymer layer and a polymer layer containing metallic nanoparticles, reminiscent of optical thin films [35]. Langmuir-Blodgett and Langmuir-Schaefer films produce layer-by-layer deposition of metamaterial resonators. Malassis et al. have produced a metamaterial consisting of seven layers of densely packed nanoparticles [27]. Microfluidic evaporation has recently proven to be a very effective path toward assembling very large amounts of meta-atoms [28,29]. Typical materials assembled with this method have volumes on the order of 0.01 mm3 and consist of optical nanoresonators as small as 30 nm in size, which correspond to homogeneity FOMs h/a of several hundreds. The density of resonators reaches here 0.7 1012 /mm3. Having large volumes of assembled material makes it very convenient to characterize the bulk optical properties of the metamaterials using classical optical characterization such as angleresolved reflectance measurements or angle-resolved spectroscopic ellipsometry. Ellipsometry enables one to retrieve the spectral variations of the complex-valued optical index N(λ) ¼ n(λ)þik(λ), where n is the index of refraction of the material and k is related to the absorption coefficient α of the material: α ¼ 4πk/λ. Ellipsometry measures the complex quantity ρ ¼ rp/rs, where rp (rs) is the complex-valued reflection coefficient when the material is illuminated with p-polarized (s-polarized) light. For any layer of size h of a metamaterial, N can be determined by fitting ρ, with classical ellipsometric models. When the material depth is very large compared to the meta-atom size (h/a 4 41) such that the optical wave coupled to the material is severely attenuated before reaching the end facet (h4 41/α), the metamaterial can be considered as semi-infinite for all experimental purposes and the optical index is directly retrieved from the following formula [28]:
⎛ 1 − ρ ⎞2 2 N = sin θ 1 + ⎜ ⎟ tan θ ⎝ 1 + ρ⎠ where θ is the angle of incidence of the impinging light. So the combination of microfluidic evaporation and spectroscopic ellipsometry is particularly well-suited to the fabrication and characterization of optical metamaterials. In the end, self-assembled metamaterials are an excellent platform to explore empirically amorphous homogenization regimes for which numerical simulations and theory are still a little behind.
4. Optical properties of self-assembled metamaterials Several groups have shown that interesting optical properties can be achieved with self-assembled metamaterials. Malassis et al. showed that by carefully assembling a plasmonic metamaterial made of several layers of silver/silica core-shells similar to the material shown in Fig. 3(b), it is possible to build a metamaterial that exhibits topological darkness [36]. Topological darkness corresponds to a perfect cancellation of the reflectance of the thin film and occurs for either p- or s-polarized light (see Fig. 4 (a)). This cancellation is obtained by letting the metamaterial reach an exact value of N in the complex plane in order to cancel the reflection coefficient provided by the Fresnel equations, which can be determined semi-analytically. To get to the correct value of N, a large dispersion of the effective optical properties of the metamaterial is required, which can be obtained thanks to the plasmonic resonance of the effective polarizability of the core-
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Fig. 2. Nanochemically synthesized meta-atoms. Tunneling Electron Microscopy images of meta-atoms fabricated by nanochemistry. Most meta-atoms are nanocomposites that combine dielectric and metallic materials so as to produce a surface plasmon resonance at optical frequencies. (a) Gold nanorods as described in [29]. (b) Nanocups made of a dielectric sphere embedded into a gold nanocup. These nanocups act as efficient unidirectional scatterers. (c) Metallic nanocluster made of a silica core and silver satellites that exhibits both electric and magnetic dipole resonances. The bottom sketch illustrates the electric current displacements corresponding to the effective magnetic dipole. (d) Core-shell nanoparticles made of a gold core and a silica shell. (e) Patchy particle. This figure was assembled by combing several TEM images. (b), (c), (d) and (e) were obtained from [30–32,34] respectively.
Fig. 3. Self-assembled optical metamaterials. Scanning Electron Microscopy images of several self-assembled metamaterials fabricated by different techniques. These images illustrate the diversity of three-dimensional materials that can be obtained and the different homogenization regimes that can be explored. (a) Template assembled lamellar metamaterial made of stacked alternating polymer layers:one layer is loaded with gold nanoparticles (dark areas on the image), while the other layer is undoped. (b) Langmuir-Schaefer films of silver/silica core shell nanoparticles. The image shows six assembled layers of densely packed nanoparticles. This configuration may be used to tune the optical properties of a metamaterial film so as to achieve specific reflectance and transmittances properties. (c) Large volume metamaterial obtained by microfluidic evaporation. The sample is typically 100 mm in width, 10 mm in depth and several millimeters long. (d) Close-up of a metamaterial fabricated by microfluidic evaporation that reveals the dense-packing of meta-atoms. This figure is adapted from SEM images taken from Refs. [27,28] for panels (b), (c) and (d).
shell meta-atom. This work is representative of the tuning of the optical index that is rendered possible by a design approach that involves engineering both at the single particle and at the material level (see Fig. 4(b)). The size and shape of the meta-atom, the type and amount of composite materials involved, the volume fraction in the assembly are all instrumental in the final value that the index of refraction may take and large ranges of variations of n can be explored in the visible and near-infrared [28]. Localized surface plasmons are extremely sensitive to small perturbations of the refractive index of the medium in which they are embedded. This is due to the large field enhancement that is reached near a plasmonic nanoparticle because of the sub-wavelength nature of the confinement. Using plasmonic nanoparticles, the plasmon-induced cancellation of reflectance of topological darkness can be tuned by leveraging the interplay between the plasmonic resonance in the particles and the optical interferences in a thin film. This effect can also occur in self-assembled lamellar metamaterials consisting of stacked block-copolymer layers alternating between sheets that are doped with gold nanoparticles and sheets that are not, such as those shown in Fig. 3(a) [37]. Under such conditions the quantity Δ, which is the angle of ρ in the complex plane abruptly jumps. This occurs when ρ ¼ 0, i.e. when
the reflectance of p-polarized light vanishes. The monitoring of this jump allows the detection of infinitesimally small perturbations of the surrounding optical properties. Fig. 4(c) shows how tiny energy shifts in the spectral features of the effective dielectric function of the metamaterial affect Δ. Cloaking is an important application of metamaterials, whereby an object may be completely hidden from an electromagnectic point of view by suitably varying the permittivity and permeability spatially. This approach takes advantage of transformation optics and was successfully implemented in several configurations through lithography [14,38]. However, when the meta-atom scatterer is small, the electromagnetic response may be treated as a quasi-static excitation and it is then sufficient to shield an object with a shell made of a plasmonic material to cancel the scattering cross section [39]. Using similar concepts, an experimentally realized self-assembled three-dimensional cloak in the visible was demonstrated by Mühlig et al. and able to hide free-standing subwavelength objects [40]. Circular dichroism is an interesting optical property that can be obtained by assembling plasmonic nanoparticles in a helical fashion by a chiral ligand such as DNA [41] or by grafting on a chiral template [42].
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Fig. 4. Optical properties of selected self-assembled metamaterials. (a) Topological darkness of Langmuir-Schaefer assembled thin-films made of silver/silica core-shells. The graphs and sketch are assembled from figures found in [36]. The top sketch illustrates the basic layout of the sample. The two bottom panels are the reflectance coefficients of p-polarized (s-polarized) light measured for three different angles of incidence as a function of wavelength. (b) Effective optical index of self-assembled metamaterials obtained by microfluidic evaporation. This panel is assembled from figures found in [28]. The top sketch is an SEM image of the bulk materials that were assembled. The top (bottom) graph represents the spectral variations of the real and imaginary parts of the refractive index of assembled silver nanocubes (silver/silica core-shells). (c) Ellipsometric angle Δ as a function of the energy of incident light of template assembled multilayer metamaterial. This panel is assembled from figures found in [37].
5. Future challenges for self-assembled metamaterials Self-assembled metamaterials is still a young field but holds great promises [43–45]. Now that the demonstration of an artificial magnetic response at visible frequencies of a meta-atom has been made [31], it is safe to say that it should be possible to build a self-assembled metamaterial exhibiting optical magnetism, i.e. with a value of the magnetic permeability different from 1: μ≠1. Furthermore, the exceptional properties of the effective medium that are reached in self-assembled metamaterials still greatly rely on strong resonances in the meta-atom polarizability. This means that metamaterials are very lossy. This is an important physical limitation and prevents a variety of applications. Incorporating a gain medium in or around the meta-atom of either fluorophores or quantum dots that can electromagnetically couple to the system could serve as a platform for loss-compensation in self-assembled metamaterials [46]. Pump-probe configurations would be a means by which the energy lost by resistive dissipation in the metal part of plasmonic nanoparticles is compensated by an energy transfer mediated by such emitters. Spaser-based nanolasers have already been demonstrated in the visible [30], which suggests that such metamaterials could become a reality. On top of being a technological challenge, gain-compensated metamaterials should be fabricated to explore the rich physics of these systems. Peculiar effects are predicted theoretically such as conjugate-
plasmons and plasmon-assisted cooperative emission of dyes near plasmonic nanoparticles [47,48]. Finally, self-assembled metamaterials may also hold the key to tackling some of the hurdles of nonlinear optics. Notably the fact that the nonlinear parameters of most natural materials are small, which means that nonlinear optical applications require large propagation distances such as in fibers or else large operating powers such as in laser technology. Recently, many top-down realizations showing how metamaterials can be useful to nonlinear optical applications have been demonstrated [49–53]. In principle, the effective nonlinear parameters can be greatly enhanced by appropriately leveraging the large field confinements that are reached in plasmonic meta-atoms. Theoretical predictions also show that optical bistability of devices that follow the design of experimentally realizable self-assembled metasurfaces should be observable at very low command powers [54,55]. Self-assembled metamaterials could also be used to explore the ultrafast optical properties of metals contained in certain plasmonic nanoparticles, the physics of which still requires some investigation [56,57]. 6. Conclusion We have presented a brief overview of recent trends in the field of self-assembled metamaterials. These artificial structures are
A. Baron et al. / Optics & Laser Technology 82 (2016) 94–100
usually obtained by assembling a very large amount of plasmonic meta-atoms that combine dielectric and metal compounds at the nanoscale. Several assembly techniques exist that are very complimentary and versatile as they enable one to produce one-dimensionally layered structures, three-dimensional isotropic materials or layer-by-layer deposited thin films. These materials can be assembled in very large quantities, though at the expense of being somewhat amorphous. The present review is non-comprehensive as the field is much larger than what is exposed here. However, the authors of this paper believe that self-assembled metamaterials hold great promises and face novel challenges in the future.
Acknowledgements The authors would like to thank Sivasankaran Prathap Chandran for providing the image used in Fig. 2(a) and Clémence Tallet for providing the image used in Fig. 3(a). This work was supported by the LabEx AMADEus (ANR-10LABX-42) in the framework of IdEx Bordeaux (ANR-10-IDEX-0302), France.
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Contents lists available at ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Review
Self-assembled optical metamaterials Alexandre Baron a,b,c,n, Ashod Aradian a,b, Virginie Ponsinet a,b, Philippe Barois a,b a b c
CNRS, CRPP, UPR8641, F-33600 Pessac, France University of Bordeaux, CRPP, UPR8641, F-33600 Pessac, France Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA
art ic l e i nf o
a b s t r a c t
Article history: Received 5 February 2016 Accepted 29 February 2016
Self-assembled metamaterials constitute a promising platform to achieving bulk and homogenous optical materials that exhibit unusual effective medium properties. For many years now, the research community has contemplated lithographically fabricated metasurfaces, with extraordinary optical features. However, achieving large volumes at low cost is still a challenge by top-down fabrication. Bottomup fabrication, that relies both on nanochemistry and self-assembly, is capable of building such materials while greatly reducing the energy footprint in the formulation of the metamaterial. Self-assembled metamaterials have shown that they are capable of reaching unprecedented values of bulkiness and homogeneity figures of merit. This feat is achieved by synthesizing plasmonic nanoresonators (metaatoms in the sense of artificial polarizable units) and assembling them into a fully three-dimensional matrix through a variety of methods. Furthermore it has been shown that a wide range of material parameters can be tailored by controlling the geometry and composition of the meta-atoms as well as the volume fraction of the nano-objects in the metamaterial. Here we conduct a non-comprehensive review of some of the recent trends in self-assembled optical metamaterials and illustrate these trends with our recent work. & 2016 Elsevier Ltd. All rights reserved.
Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. From top-down to bottom-up approaches to metamaterial fabrication . 3. Exploring homogenization and bulkiness empirically . . . . . . . . . . . . . . . 4. Optical properties of self-assembled metamaterials . . . . . . . . . . . . . . . . 5. Future challenges for self-assembled metamaterials . . . . . . . . . . . . . . . . 6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction As metamaterials make their way into the applications realm [1–3], notably for RF applications, some members of the research and industrial communities have adopted a broad definition of metamaterials in terms of design [4]. The field of metamaterials may be viewed as a design approach that enables the production
n Corresponding author at: University of Bordeaux, CRPP, UPR8641, F-33600 Pessac, France. E-mail address: [email protected] (A. Baron).
http://dx.doi.org/10.1016/j.optlastec.2016.02.024 0030-3992/& 2016 Elsevier Ltd. All rights reserved.
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of artificial materials that exhibit electromagnetic properties on demand [5]. Undeniably, the concept of metamaterials has influenced how scientists think about device design and materials. This has led to elegant solutions to several electromagnetic problems. However some of the hurdles that have existed for several years in the field and have restricted the applications of metamaterials still exist today, notably as research and engineering move toward optical frequencies. Originally, metamaterials were thought of as artificial assemblies of subwavelength resonators with extraordinary effective medium properties. By extraordinary, the research community meant effective properties that cannot be
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Fig. 1. Electromagnetic properties of metamaterials and typical examples of metamaterials. The horizontal axis represents the real part of the dielectric permittivity ε. The vertical axis represents the real part of the magnetic permeability μ. Several applications are represented on the graph. The green line represents natural optical materials for which μ¼1, while the red line represents impedance-matched materials for which ε ¼μ. Building an electromagnetic cloak requires varying the index of refraction spatially over an interval between 0 and 1. A negative refractive index requires that ε and μ be simultaneously negative and enables the fabrication of a perfect lens. The blue dashed axis (ε∼0) represents materials that may serve as perfect electromagnetic couplers. The sketches in inset representing the invisibility cloak, the Perfect lens and the perfect coupler are adapted from Refs. [14,22,23]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
found in natural materials. Of course, this broad definition is applicable to many areas of material science and engineering: electromagnetic, acoustic, thermal materials [6–9], but we wish to focus on electromagnetic metamaterials and more specifically optical metamaterials. The electromagnetic properties of a material are characterized by the dielectric permittivity ε and the magnetic permeability μ. The graph represented on Fig. 1 illustrates the different classes of materials depending on the values that the real part of ε and μ take on. A historically famous example of extraordinary property was achieved in 2000 by Smith et al. [10]. They managed to build an artificial composite medium with simultaneously negative permeability and permittivity which is equivalent to a material with a negative refractive index. A few years prior to this demonstration, Pendry et al. had proposed a strategy to achieve negative values of these two parameters by combining electric dipoles made of metallic wires with magnetic dipoles made of metallic split rings [11]. The achieved material was exceptional in many respects. On the one hand, natural materials only have positive refractive indices. On the other hand, the electrodynamic consequences of such a material had been theoretically predicted by Veselago in the 1960s, stemming from the fact that group and phase velocities have opposite signs: reversal of the Doppler shift, reversal of the Cherenkov radiation, anomalous and negative refraction [12]. The first metamaterials were built by top-down fabrication, but now they are also immerging in bottom-up schemes. In this review, we shall briefly describe the transition from tow-down to bottom-up approaches to metamaterial fabrication (Section 2). Section 3 is devoted to explaining how self-assembled metamaterials constitute a convenient means to exploring empirically homogenization and bulkiness. Section 4 reviews some of our recent work highlighting some of the optical properties that can be achieved with self-assembled metamaterials. Some of the future challenges of self-assembled metamaterials are exposed in Section 5, before concluding (section6).
2. From top-down to bottom-up approaches to metamaterial fabrication Since the experimental demonstration by Smith et al. [10],
many experimental realizations have shown the validity of these predictions and further explored the large diversity of extraordinary properties that can be achieved using the metamaterials approach. Up until recently this approach consisted in carefully designing composite resonators that associate metals with dielectrics so as to fine-tune the electric and magnetic dipolar resonances, such that the material composed of a large volume of these resonators (or meta-atoms) would take on new values of ε and μ. This design approach has enabled the metamaterials community to realize a great number of applications and proofsof-concept. For instance, combined with the Transformation Optics approach developed by Pendry et al. [13], spatial variations of the index of refraction on the interval [0,1] enabled Smith and Pendry to design and realize the first electromagnetic cloak [14]. Another famous example is the ideal electromagnetic coupler that can be achieved by fabricating a so-called epsilon near-zero metamaterial, i.e. when ε∼0 [15,16] (see Fig. 1). Metamaterials have also enabled the realization of subwavelength imaging systems such as the hyper-lens [17] and ultraviolet flat lensing [18]. Historically, metamaterials have been built by lithographic approaches using microelectronics technology. This has enabled the fabrication of a very large number of electromagnectic metamaterials operating at frequencies ranging from microwaves all the way to the ultraviolet [18,19]. However this top-down approach, though extremely precise in making ordered structures is highly cost-intensive, such that almost all realized metamaterials are two dimensional, which renders the material highly anisotropic. Consequently, most metamaterials are actually metasurfaces. Achieving bulk three-dimensional metamaterials has remained a challenge in recent years. It requires that large assemblies of optical resonators be made in the three directions of space (bulkiness criterion) and that the dimensions of the resonator be much smaller that the optical wavelength (homogeneity criterion). In other words, the height h of a material needs to be very large compared to the typical length of a unit cell a of a nanoresonator, such that a figure of merit (FOM) for dimensionality (or bulkiness) may be defined as the ratio h/a and a homogeneity FOM may be defined as the ratio λ/a. These two FOMs may be viewed as two important quantities that need to be maximized to reach the realm of bulk optical metamaterials. To date, the best values of these FOMs obtained for metamaterials by top-down fabrication do not exceed 10 for h/a and 5 for λ/a (see Table 1).
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Table 1 Comparison of the bulkiness FOM h/a for several metamaterial realizations. Year
Reference
h/a
λ (nm)
Fabrication
2007 2008 2008 2008 2011 2013 2013 2013
[20] [21] [24] [25] [26] [18] [27] [28]
3 10 5 4 3 3 7 600
1500 1800 1600 3000 683 364 400 500
top-down top-down top-down top-down top-down top-down bottom-up bottom-up
Today, a radically different approach to metamaterials is available that combines nanochemistry and several self-assembly techniques inherited from colloidal chemistry that make it possible to build self-assembled artificial materials with extreme values of the bulkiness and homogeneity FOM (see last entry in Table 1). Applying these concepts to metamaterials presents us with a unique opportunity to build large volumes of artificial materials with unusual optical properties. We propose to review our recent work to illustrate some of the hot topics of self-assembled metamaterials.
3. Exploring homogenization and bulkiness empirically Reaching the homogenization limit means that the typical size of metamaterial resonators (meta-atoms) and the average distance that separates each meta-atom should be very small compared to the wavelength of the electromagnetic radiation. This is equivalent to stating that both the homogeneity and bulkiness FOM must be maximized. Though top-down approaches have been able to reach a high degree of precision at the nanometer range, achieving high values of these FOMs for visible frequencies is challenging. Making a bulk sample typically requires a tremendous number of metaatoms on the order of 1012 /mm3 [27]. Today a large variety of meta-atoms with varying complexity can be synthesized by nanochemistry. These may serve as interesting metamaterial building blocks if they present optical resonances. At visible wavelengths, plasmonic nanoresonators may be used as meta-atoms. They are usually hybrid in nature, with metal and dielectric subparts. The conduction electrons in the metal compound oscillate with the electromagnetic field to form localized surface plasmons in the nanoparticle and by carefully controlling the geometrical parameters of the nano-object, the amplitude and resonance wavelength of the meta-atom polarizability may be tuned. Fig. 2 illustrates the typical meta-atoms that exhibit plasmonic resonances in the visible and that can be synthesized in large amounts by nanochemistry. It is remarkable to notice how complex and anisotropic the geometries can be, such that some of these nanoparticles resemble theoretical proposals of extraordinary meta-atoms. Metallic nanorods or core-shell nanoparticles typically exhibit large electric dipole resonances [29,30], while metallic nanoclusters have both strong electric and magnetic dipole resonances [31]. Fig. 2(b) is a nanocup geometry that consists of a dielectric nanosphere embedded in a metallic cup. These nanoparticles serve as efficient directional scatterers [32]. Optical nanoparticles have typical sizes ranging from 30 nm to 100 nm in diameter, which corresponds to homogeneity FOMs λ/a ranging from 5 to 40 at visible frequencies. Polarization resolved light scattering is a powerful experimental tool that can be used to characterize the optical response of such meta-atoms in a solvent. This technique has been used recently to measure the scattering cross-sections of electric and magnetic dipoles [31,33]. Once the properties of a meta-atom with tailored optical
properties have been designed and the nanoparticle has been synthesized, there are several self-assembly techniques that physical-chemists have at their disposal to assemble fully three-dimensional metamaterials. Fig. 3 shows three examples of metamaterials assembled by three different techniques. Templating with block-copolymers enables the fabrication of lamellar films that alternate between a pure polymer layer and a polymer layer containing metallic nanoparticles, reminiscent of optical thin films [35]. Langmuir-Blodgett and Langmuir-Schaefer films produce layer-by-layer deposition of metamaterial resonators. Malassis et al. have produced a metamaterial consisting of seven layers of densely packed nanoparticles [27]. Microfluidic evaporation has recently proven to be a very effective path toward assembling very large amounts of meta-atoms [28,29]. Typical materials assembled with this method have volumes on the order of 0.01 mm3 and consist of optical nanoresonators as small as 30 nm in size, which correspond to homogeneity FOMs h/a of several hundreds. The density of resonators reaches here 0.7 1012 /mm3. Having large volumes of assembled material makes it very convenient to characterize the bulk optical properties of the metamaterials using classical optical characterization such as angleresolved reflectance measurements or angle-resolved spectroscopic ellipsometry. Ellipsometry enables one to retrieve the spectral variations of the complex-valued optical index N(λ) ¼ n(λ)þik(λ), where n is the index of refraction of the material and k is related to the absorption coefficient α of the material: α ¼ 4πk/λ. Ellipsometry measures the complex quantity ρ ¼ rp/rs, where rp (rs) is the complex-valued reflection coefficient when the material is illuminated with p-polarized (s-polarized) light. For any layer of size h of a metamaterial, N can be determined by fitting ρ, with classical ellipsometric models. When the material depth is very large compared to the meta-atom size (h/a 4 41) such that the optical wave coupled to the material is severely attenuated before reaching the end facet (h4 41/α), the metamaterial can be considered as semi-infinite for all experimental purposes and the optical index is directly retrieved from the following formula [28]:
⎛ 1 − ρ ⎞2 2 N = sin θ 1 + ⎜ ⎟ tan θ ⎝ 1 + ρ⎠ where θ is the angle of incidence of the impinging light. So the combination of microfluidic evaporation and spectroscopic ellipsometry is particularly well-suited to the fabrication and characterization of optical metamaterials. In the end, self-assembled metamaterials are an excellent platform to explore empirically amorphous homogenization regimes for which numerical simulations and theory are still a little behind.
4. Optical properties of self-assembled metamaterials Several groups have shown that interesting optical properties can be achieved with self-assembled metamaterials. Malassis et al. showed that by carefully assembling a plasmonic metamaterial made of several layers of silver/silica core-shells similar to the material shown in Fig. 3(b), it is possible to build a metamaterial that exhibits topological darkness [36]. Topological darkness corresponds to a perfect cancellation of the reflectance of the thin film and occurs for either p- or s-polarized light (see Fig. 4 (a)). This cancellation is obtained by letting the metamaterial reach an exact value of N in the complex plane in order to cancel the reflection coefficient provided by the Fresnel equations, which can be determined semi-analytically. To get to the correct value of N, a large dispersion of the effective optical properties of the metamaterial is required, which can be obtained thanks to the plasmonic resonance of the effective polarizability of the core-
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Fig. 2. Nanochemically synthesized meta-atoms. Tunneling Electron Microscopy images of meta-atoms fabricated by nanochemistry. Most meta-atoms are nanocomposites that combine dielectric and metallic materials so as to produce a surface plasmon resonance at optical frequencies. (a) Gold nanorods as described in [29]. (b) Nanocups made of a dielectric sphere embedded into a gold nanocup. These nanocups act as efficient unidirectional scatterers. (c) Metallic nanocluster made of a silica core and silver satellites that exhibits both electric and magnetic dipole resonances. The bottom sketch illustrates the electric current displacements corresponding to the effective magnetic dipole. (d) Core-shell nanoparticles made of a gold core and a silica shell. (e) Patchy particle. This figure was assembled by combing several TEM images. (b), (c), (d) and (e) were obtained from [30–32,34] respectively.
Fig. 3. Self-assembled optical metamaterials. Scanning Electron Microscopy images of several self-assembled metamaterials fabricated by different techniques. These images illustrate the diversity of three-dimensional materials that can be obtained and the different homogenization regimes that can be explored. (a) Template assembled lamellar metamaterial made of stacked alternating polymer layers:one layer is loaded with gold nanoparticles (dark areas on the image), while the other layer is undoped. (b) Langmuir-Schaefer films of silver/silica core shell nanoparticles. The image shows six assembled layers of densely packed nanoparticles. This configuration may be used to tune the optical properties of a metamaterial film so as to achieve specific reflectance and transmittances properties. (c) Large volume metamaterial obtained by microfluidic evaporation. The sample is typically 100 mm in width, 10 mm in depth and several millimeters long. (d) Close-up of a metamaterial fabricated by microfluidic evaporation that reveals the dense-packing of meta-atoms. This figure is adapted from SEM images taken from Refs. [27,28] for panels (b), (c) and (d).
shell meta-atom. This work is representative of the tuning of the optical index that is rendered possible by a design approach that involves engineering both at the single particle and at the material level (see Fig. 4(b)). The size and shape of the meta-atom, the type and amount of composite materials involved, the volume fraction in the assembly are all instrumental in the final value that the index of refraction may take and large ranges of variations of n can be explored in the visible and near-infrared [28]. Localized surface plasmons are extremely sensitive to small perturbations of the refractive index of the medium in which they are embedded. This is due to the large field enhancement that is reached near a plasmonic nanoparticle because of the sub-wavelength nature of the confinement. Using plasmonic nanoparticles, the plasmon-induced cancellation of reflectance of topological darkness can be tuned by leveraging the interplay between the plasmonic resonance in the particles and the optical interferences in a thin film. This effect can also occur in self-assembled lamellar metamaterials consisting of stacked block-copolymer layers alternating between sheets that are doped with gold nanoparticles and sheets that are not, such as those shown in Fig. 3(a) [37]. Under such conditions the quantity Δ, which is the angle of ρ in the complex plane abruptly jumps. This occurs when ρ ¼ 0, i.e. when
the reflectance of p-polarized light vanishes. The monitoring of this jump allows the detection of infinitesimally small perturbations of the surrounding optical properties. Fig. 4(c) shows how tiny energy shifts in the spectral features of the effective dielectric function of the metamaterial affect Δ. Cloaking is an important application of metamaterials, whereby an object may be completely hidden from an electromagnectic point of view by suitably varying the permittivity and permeability spatially. This approach takes advantage of transformation optics and was successfully implemented in several configurations through lithography [14,38]. However, when the meta-atom scatterer is small, the electromagnetic response may be treated as a quasi-static excitation and it is then sufficient to shield an object with a shell made of a plasmonic material to cancel the scattering cross section [39]. Using similar concepts, an experimentally realized self-assembled three-dimensional cloak in the visible was demonstrated by Mühlig et al. and able to hide free-standing subwavelength objects [40]. Circular dichroism is an interesting optical property that can be obtained by assembling plasmonic nanoparticles in a helical fashion by a chiral ligand such as DNA [41] or by grafting on a chiral template [42].
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Fig. 4. Optical properties of selected self-assembled metamaterials. (a) Topological darkness of Langmuir-Schaefer assembled thin-films made of silver/silica core-shells. The graphs and sketch are assembled from figures found in [36]. The top sketch illustrates the basic layout of the sample. The two bottom panels are the reflectance coefficients of p-polarized (s-polarized) light measured for three different angles of incidence as a function of wavelength. (b) Effective optical index of self-assembled metamaterials obtained by microfluidic evaporation. This panel is assembled from figures found in [28]. The top sketch is an SEM image of the bulk materials that were assembled. The top (bottom) graph represents the spectral variations of the real and imaginary parts of the refractive index of assembled silver nanocubes (silver/silica core-shells). (c) Ellipsometric angle Δ as a function of the energy of incident light of template assembled multilayer metamaterial. This panel is assembled from figures found in [37].
5. Future challenges for self-assembled metamaterials Self-assembled metamaterials is still a young field but holds great promises [43–45]. Now that the demonstration of an artificial magnetic response at visible frequencies of a meta-atom has been made [31], it is safe to say that it should be possible to build a self-assembled metamaterial exhibiting optical magnetism, i.e. with a value of the magnetic permeability different from 1: μ≠1. Furthermore, the exceptional properties of the effective medium that are reached in self-assembled metamaterials still greatly rely on strong resonances in the meta-atom polarizability. This means that metamaterials are very lossy. This is an important physical limitation and prevents a variety of applications. Incorporating a gain medium in or around the meta-atom of either fluorophores or quantum dots that can electromagnetically couple to the system could serve as a platform for loss-compensation in self-assembled metamaterials [46]. Pump-probe configurations would be a means by which the energy lost by resistive dissipation in the metal part of plasmonic nanoparticles is compensated by an energy transfer mediated by such emitters. Spaser-based nanolasers have already been demonstrated in the visible [30], which suggests that such metamaterials could become a reality. On top of being a technological challenge, gain-compensated metamaterials should be fabricated to explore the rich physics of these systems. Peculiar effects are predicted theoretically such as conjugate-
plasmons and plasmon-assisted cooperative emission of dyes near plasmonic nanoparticles [47,48]. Finally, self-assembled metamaterials may also hold the key to tackling some of the hurdles of nonlinear optics. Notably the fact that the nonlinear parameters of most natural materials are small, which means that nonlinear optical applications require large propagation distances such as in fibers or else large operating powers such as in laser technology. Recently, many top-down realizations showing how metamaterials can be useful to nonlinear optical applications have been demonstrated [49–53]. In principle, the effective nonlinear parameters can be greatly enhanced by appropriately leveraging the large field confinements that are reached in plasmonic meta-atoms. Theoretical predictions also show that optical bistability of devices that follow the design of experimentally realizable self-assembled metasurfaces should be observable at very low command powers [54,55]. Self-assembled metamaterials could also be used to explore the ultrafast optical properties of metals contained in certain plasmonic nanoparticles, the physics of which still requires some investigation [56,57]. 6. Conclusion We have presented a brief overview of recent trends in the field of self-assembled metamaterials. These artificial structures are
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usually obtained by assembling a very large amount of plasmonic meta-atoms that combine dielectric and metal compounds at the nanoscale. Several assembly techniques exist that are very complimentary and versatile as they enable one to produce one-dimensionally layered structures, three-dimensional isotropic materials or layer-by-layer deposited thin films. These materials can be assembled in very large quantities, though at the expense of being somewhat amorphous. The present review is non-comprehensive as the field is much larger than what is exposed here. However, the authors of this paper believe that self-assembled metamaterials hold great promises and face novel challenges in the future.
Acknowledgements The authors would like to thank Sivasankaran Prathap Chandran for providing the image used in Fig. 2(a) and Clémence Tallet for providing the image used in Fig. 3(a). This work was supported by the LabEx AMADEus (ANR-10LABX-42) in the framework of IdEx Bordeaux (ANR-10-IDEX-0302), France.
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