Abstract
Optical metamaterials with an artificial subwavelength structure offer new approaches to implement advanced optical devices. However, some of the biggest challenges associated with the development of metamaterials in the visible spectrum are the high costs and slow production speeds of the nanofabrication processes. Here, we demonstrate a macroscale (>35 mm) transformationoptics wave bender (293 mm^{2}) and Luneburg lens (855 mm^{2}) in the broadband whitelight visible wavelength range using the concept of elastooptic metamaterials that combines optics and solid mechanics. Our metamaterials consist of mesoscopically homogeneous chunks of bulk aerogels with superior, broadband optical transparency across the visible spectrum and an adjustable, stresstuneable refractive index ranging from 1.43 down to nearly the free space index (∼1.074). The experimental results show that broadband light can be controlled and redirected in a volume of >10^{5}λ × 10^{5}λ × 10^{3}λ, which enables natural light to be processed directly by metamaterialbased optical devices without any additional coupling components.
Introduction
Controlling the propagation of natural visiblespectrum light through macroscopically thick optical components without significant attenuation is a requirement for many advanced optical applications. By introducing a specifically graded refractive index, inhomogeneous photonic materials offer an opportunity for lenses and other broadband optical elements. By designing the artificial subwavelength details of a structure, metamaterials are able to exhibit properties difficult to observe in nature, such as negative or gradient refractive index properties enabling superlenses, optical cloaking or optical elements with gradient indices^{1,2,3,4,5,6,7}. Because commonly used nanofabrication techniques, such as electronbeam lithography or focused ion beam patterning, are expensive and timeconsuming, optical metamaterials have been demonstrated almost exclusively on microscopic scales, for functions such as light redirection in confined modes of thin planar waveguides or in surface waves^{8}. Thus, the typical lightcontrolling volume (that is, the volume of the region where we can control the fields and distinguishably redirect light rays) has been limited to approximately one thousand cubic wavelengths, or <10λ × 10λ × 10λ. For light to interact with optical devices of volume in the order of wavelength, artificial light couplers are required, such as fibre couplers or grating couplers^{9,10}. Furthermore, microscopic light manipulation devices typically rely on diffractive phenomena and, thus, are bandwidthlimited. Although ray optics enables devices with multipleoctave bandwidths, it requires much larger volumes of optical components. Macroscopically large, yet massproducible at a consumeraffordable price, optical metamaterials would therefore provide new opportunities in the photonics markets.
Here, we demonstrate a macroscale (>35 mm) transformationoptics wave bender and a Luneburg lens for naturallight coupling. To combine optics and solid mechanics, we introduce an elastooptic metamaterial^{11,12,13,14}, specifically, a mesoscopically homogeneous aerogel with a nanoporous (∼60 nm) microstructure. Through elastic deformations, we establish and control ondemand gradedindex distributions at the mesotomacro range of scales in a large area or volume. These metamaterials are based on compressible transparent homogeneous aerogels with an ultralow refractive index of 1.074 and a Poisson’s ratio of 0.12. The areas of our two proofofconcept demonstrators, a wave bender and a Luneburg lens, are 293 and 855 mm^{2}, respectively. The vertical thickness of the working devices (∼1 mm) is determined by the maximally compressed region. This shows that widespectrum naturallight propagation can be controlled in the metamaterial volume of >10^{5}λ × 10^{5}λ × 10^{3}λ without any extra coupling components.
Results
Theory of elastooptic metamaterials
To understand the concept of elastooptic, mechanically tuneable metamaterials, consider a deformable homogeneous effective medium^{15}, such as a binary composite of a stiff dielectric and an airfilled void. There have been some studies that controlled the elastic wave phenomena by use of the solid mechanics concept^{16,17,18}. For simplicity, consider a composite with a periodic arrangement of identical unit cells. An elastic deformation of such a medium changes the refractive index and simultaneously the volume of a representative unit cell, as shown in Fig. 1a,b. Upon deformation, stress and strain fields propagate through the lattice of such cells, and a new mechanical equilibrium is established. Using conventional continuum mechanics, we describe these deformations using a displacement vector field with components (u_{1}, u_{2}, u_{3}), which relates the displacement of a point (X_{1}, X_{2}, X_{3}) to its new position (x′_{1}, x′_{2}, x′_{3}), according to the relationship X+u=x′^{19}. We use the deformation gradient tensor , and express the compression (or expansion) ratio (J) through its Jacobian, . After the deformation, the volume fraction (f) of the stiff dielectric component changes from f=V_{d}/V_{t} to f′=V_{d}/V′_{t}, resulting in f′=(V_{d}/V_{t})/(V′_{t}/V_{t})=f/J, where the volume of the dielectric is V_{d}, and the volume of the total unit cell is V_{t}. By changing the compression ratio (J) or volume fraction (f), we are able to obtain a wide range of effective refractive indices (n_{eff}(J)) that are predicted in numerical simulations using a retrieval method^{20,21,22}.
Previous demonstrations of metamaterialbased Luneburg lenses were based on periodic or quasiperiodic lattices of fixedsize, variableholegeometry metamaterials, as shown in Fig. 1c. Such an approach, while feasible for microwave and even millimetrewave devices, becomes prohibitively expensive for optical applications. Here, by employing the elastooptic metamaterial concept, we achieve the required gradedindex profiles through a compression ratio distribution. The Luneburg lens can be achieved with a simple elastic deformation process of a homogeneous nanoporous material, as shown in Fig. 1d. On the basis of continuum mechanics, stress and strain are continuously distributed in a deformed network medium, leading to a controllable effective index distribution in elastooptic metamaterials.
Aerogels for elastooptic metamaterials
To verify the macroscale elastooptic concept, differing from conventional rigid and undeformable aerogels, we employ a compressible, transparent aerogel with a nanoporous structure, as presented in Fig. 2a. In our samples, the precursor methyltrimethoxysilane (MTMS) enables us to compress the aerogel in the same manner as a sponge. To reduce the size of granules, we efficiently spread MTMS in the solution using a surfactant, that is, nonionic surfactant poly(ethylene oxide)blockpoly(propylene oxide)blockpoly(ethylene oxide) triblock copolymer (F127, EO_{108}PO_{70}EO_{108}). Ultrafine nanogranules of ∼20 nm allow us to produce an aerogel that is transparent in the optical regime. The SEM image shows that silicacomposite nanogranules form a network structure with ∼60 nm nanopores (Supplementary Fig. 1). The experimentally measured transmittance and reflectance of a 3mmthick aerogel show good broadband transparency (Fig. 2b). We measured the attenuation coefficients of aerogels as 0.039, 0.055, 0.080, 0.109 and 0.069 mm^{−1} at 633, 589, 523, 473 and 400∼700 nm, respectively (Fig. 2c), (Supplementary Fig. 2 and Supplementary Table 1). Figure 2d shows the propagation of white light through the aerogel. The aerogel is also compressible by its own springback mechanical property with a Poisson’s ratio of 0.12 (Fig. 2e); the deformation process is shown in Supplementary Movie 1. The aerogel can compress from an initial porosity of 84% to nearly zero at the maximum^{23}. Finally, we can use the aerogel bulk as an elastooptic metamaterial in the visible spectrum.
Optical properties versus compression of aerogels
We experimentally measured the refractive index of our aerogel as n_{0}=1.078 using Snell’s law^{24} (Supplementary Fig. 3). This ultralow index is close to the index of air because of its high porosity, whereas it can reach as high as n∼1.43 when maximally compressed, resulting in a broad tuneable range of Δn∼0.35. The airlike ultralow index of aerogel also minimizes the indexmismatching loss with air at the interfaces. On the basis of the metamaterial retrieval method implemented with a Finite element method (FEM) solver COMSOL, we numerically calculated the effective index (n_{eff}(J)) of the mechanically deformed aerogel versus the compression ratio (J)^{20,21,22}. The unit cell comprises a silica cubic shell structure around an air void with a side length of 60 nm (Fig. 2f). The unit cells are elastically deformed in the zdirection with a Poisson’s ratio of 0.12, and the light propagates in the ydirection with TE or TM polarizations. In a previous study, anisotropic elastic deformation caused negligible birefringence while compressing the aerogels^{25}, which is consistent with our simulation results. We approximately simulate the mesoscopically homogeneous aerogels using the ClausiusMossotti relation, (n^{2}−1)/(n^{2}+2)=Nα/3, where N is the number density of molecules, and α is the molecular polarizability. Using N=N_{0}/J, after mechanical compression, we can obtain n_{eff}(J) from , which precisely agrees with the retrieval method. We also experimentally measured the effective indices of our aerogel chunks as a function of the compression ratios; the measurements show good agreement with the approximate model. The measured indices versus various wavelengths are also given in Supplementary Fig. 4 and Supplementary Table 2.
Design of macroscale elastooptic metamaterial devices
Next, we produced macroscale naturallightcontrolling twodimensional (2D) metamaterial devices in the xyplane by compressing the aerogel in the outofplane zdirection. The two examples of gradedindex devices selected were: a transformationoptics (TO) wave bender and a Luneburg lens. In the TO wave bender, incident light can propagate in an arbitrary path defined by the shape of the bender while maintaining its initial phase information^{26,27,28}, somewhat similar to wave propagation through an optical fibre. The Luneburg lens has a gradedindex distribution such that it focuses plane waves from all directions to a focal point without aberrations^{29,30}. To date, there have been only microscale demonstrations of optical Luneburg lenses because of the limitations of current nanofabrication technology^{31,32,33,34}. Here, an arcshaped TO wave bender and a Luneburg lens are designed as n_{eff}=R_{0}/r and , respectively^{26,29}, where R_{0} is the outer radius, and r is the distance from the origin (Fig. 3a,b). From the desired graded indices of the target objects, we obtain the 2D compression ratio (J) distribution for the aerogel using the inverse function of n_{eff}(J), calculated in Fig. 2f. To obtain the designed compression ratio on the xyplane, we calculate the crosssectional shape resulting from a deformation in the zdirection using the solid mechanics module in COMSOL Multiphysics (Fig. 3c,d, Supplementary Fig. 5). As we deform homogeneous rectangular aerogel chunks (dashed lines) into solid line shapes by compressing the moulds, we obtain the desired index distribution on the top surface region. These devices are operating as described for light propagating within the crosssectional thickness (t) determined by the maximally compressed region, where the distributions of compression ratio (J) are almost constant along the zdirection. By rotating the crosssections, we designed the threedimensional (3D) pressing moulds and fabricated with a 3D printer (3Dwox, Sindoh) (Fig. 3e,f). The initial undeformed homogeneous aerogels are presented as green structures. For the Luneburg lens, we use an aerogel plate with a hole to reduce the resistive force for compression in the centre region. After we deform the aerogels by pressing the moulds, we obtain the required compression ratio distributions for the wave bender and the Luneburg lens (Fig. 3g,h).
Demonstrations of macroscopic optical devices
To demonstrate the practical feasibility of our approach, we prepared the described macroscale optical devices by mechanically deforming homogeneous aerogels. We fabricated a homogeneous arcshaped aerogel bulk for the wave bender with a 45° bend (outer radius R_{0}=46 mm, inner radius r_{0}=37 mm, thickness t_{0}=5 mm) and an aerogel plate with a central hole for the Luneburg lens (outer radius R_{0}=16.5 mm, inner radius r_{0}=2.5 mm, thickness t_{0}=5 mm). After sandwiching the homogeneous aerogel bulk with 3D printed pressing moulds and acryl top windows, we elastically compressed the aerogel on an aluminium plate into the designed shapes of Fig. 3g,h, leading to the index distributions of the target devices within the 1mmthick top surface region. Figure 4a presents a TO wave bender realized by elastooptic metamaterials after mechanical compression. To investigate the TO waveguiding characteristics, as references, we also prepared a 45°bend aerogel chunk and a straight homogeneous aerogel chunk without mechanical deformation. When a collimated whitelight beam from a solar simulator (YCSS50, Yamashita Denso) is incident on spot A from the right side, the broadband light propagates along the curved path, as designed by the TO (Fig. 4b). Figure 4c,d describe the straight light propagations in homogeneous aerogel chunks. At the output surfaces of samples (red edges in Fig. 4b–d), the crosssectional images (Fig. 4e) and intensity profiles (Fig. 4f) of the light beams clearly show the TO wavebending characteristics of the mechanically compressed elastooptic metamaterial. The light intensity decays because nanopores in the aerogel scatter the propagating light; the average attenuation coefficient for a broad range of wavelengths from 400 to 700 nm is 0.069 mm^{−1}. The attenuation constants at various wavelengths are also given in Supplementary Table 1. In the TO wave bender, laser beams also propagate along the same curved path at various wavelengths of 633, 589, 523 and 473 nm (Fig. 4g). We used lowpower cw laser sources to eliminate any nonlinear effects, such as thermal lensing^{35}.
Figure 5a shows a macroscale visible Luneburg lens of 3.3 cm in diameter made by a deformed aerogel. When whitelight beams are incident in the ydirection, as we change the xpositions for incidence, the Luneburg lens has a clear tendency to redirect the broadband light into a broad focal position at the output surface (Fig. 5b). Because the focusing performance is limited by the shear modulus properties of aerogels, further research is required to realize an ideal Luneburg lens. The lens shows similar focusing behaviour for laser beams at the wavelengths of 633, 589, 523 and 473 nm (Fig. 5c–f). For a larger Luneburg lens of 5 cm in diameter, the same lightredirecting tendency was demonstrated (Supplementary Fig. 6).
Discussion
These results demonstrate the feasibility of largearea broadband naturallight optical devices based on elastooptic metamaterials. The desired gradientindex profiles are achieved without nanofabrication by virtue of stressing our reversibly compressible transparent homogeneous aerogels. In the Luneburg lens demonstration, the total optical path that can be controlled within the device can be as long as ∼50 mm, that is ∼10^{5}λ. The crosssectional areas of the wave bender and the Luneburg lens are 293 and 855 mm^{2}, respectively, with the thickness of the functional layer being approximately 1 mm.
Elastooptic metamaterials enable the development of optical devices with a very large lateral area, transverse thickness and volume that exceed previous optical metamaterial device dimensions by many orders of magnitude. This technique enables precise control over broadband light propagation in volumes as large as 10^{13}λ^{3} (for example, 10^{5}λ × 10^{5}λ × 10^{3}λ). This allows natural light to interact directly with metamaterial devices without any additional coupling components, opening the door to industrial applications of optical metamaterials in general, and transformation optics in particular, for example, adaptive lenses for advanced miniaturized cameras, machine vision, lidarbased technologies and energy harvesting.
Methods
Deformation gradient tensor in solid mechanics
If we consider an elastic deformation process, there are two explicit coordinates, that is, the original flat space X and the mechanically deformed space x′=X+u, where the vector field is the displacement field u, as described in Supplementary Fig. 7. To quantify the change in the shape of a deformed solid body, the concept of the deformation gradient tensor is introduced as . The Jacobian (J) of the deformation gradient is defined as and represents the ratio of the deformed volume over the initial volume according to the relationship . For an incompressible solid, J=1. If J>1 (J<1), the solid expands (is compressed).
Fabrication of the aerogel
For the fabrication of the aerogel, we prepared the sol by mixing solutions of 10 mM aqueous acetic acid, MTMS, urea and the surfactant (F127) with the mass ratios of 7:4.76:0.5:1.1 and then thermally heated the sol for gelation in an oven at 60 °C for 4 days. Next, we soaked the obtained wetgel in 2propanol at 60 °C for 3 days with two solvent exchanges. Finally, we dried the wetgel using a supercritical drying process. The completely dried nanoporous aerogel consists of 16% polymethylsilsesquioxane (PMSQ) network and 84% voids^{36}.
Measurement of the compressed aerogel refractive index using Snell’s law
Following the method from ref. 24, we experimentally measured the refractive index of a compressed aerogel as shown in Supplementary Fig. 3. If an incident beam entered a rectangular aerogel at an oblique angle (45°, 50°, 55°, 60° in our setup), the two refractions at the input and output surfaces of the aerogel exhibit a large lateral shift, δ_{y}, for the laser beam propagation. By measuring the values of δ_{x}, δ_{y}, θ_{1} and β in the experiment, we obtain θ_{2}, θ_{3}, and the refractive index of aerogels using Snell’s law. To characterize the effective index of a compressed aerogel, we experimentally measured the effective indices of an aerogel chunk at different compression ratios. Supplementary Fig. 4 presents the effective refractive indices of a compressed aerogel measured by laser beams of different wavelengths (633, 589, 523 and 473 nm) for the compression ratios of 0.28, 0.32, 0.45, 0.64, 0.83 and 1. The measured values for 633 nm are presented with the theoretical results in Fig. 2f of the manuscript. The experimental results are summarized in Supplementary Table 2.
Optical measurement of transmittance and reflectance of the aerogels
To measure the transmittance and reflectance of the aerogels in the wavelength range of 300–1,000 nm, we used a ultraviolet–visble–NIR spectrometer (UV3600, Shimadzu Scientific Instruments) with a 60mmdiameter integrating sphere (MPC3100) by scanning a monochromator coupled to a halogen lamp. The transmitted and reflected light from the aerogels was scattered and collected in an integrating sphere and then detected with a photomultiplier tube. Using an integrating sphere, we can thoroughly measure the total reflectance R(λ) (transmittance (T(λ)) spectra of aerogels with scattering from ∼60 nm nanopores, including both diffuse and specular reflections (transmissions). For the measurement of the reflection/transmission spectra, we mounted the samples at an oblique incidence angle (8°) with respect to the normal at the rear/front of an integrating sphere.
Measurement of the attenuation coefficient of the aerogels
To characterize the attenuation coefficient of the aerogels, we measured the total spectral transmittance of aerogels with various thicknesses as described in Supplementary Fig. 2. We used a ultraviolet–visble–NIR spectrometer (UV3600, Shimadzu Scientific Instruments) with a 60mmdiameter integrating sphere (MPC3100). Supplementary Fig. 2a presents the transmittance of the aerogels in the wavelength range of 400–850 nm with thicknesses of 2.4, 3.0, 4.2, 4.8, 5.9, 6.9, 7.2 and 7.6 mm. The transmittance reduction during light propagation is lower at longer wavelengths. This results in a smaller attenuation coefficient at longer wavelengths; consequently, red light can propagate for longer distances in the aerogels compared with light at shorter wavelengths (Supplementary Fig. 2b). Figure 2c shows the attenuation in the aerogels as a function of the propagation length (the thickness of aerogels) on a semilogarithmic scale at wavelengths of 633, 589, 523 and 473 nm. The attenuation for an averaged transmittance in the visible spectrum from 400 to 700 nm is also plotted. The slope of the fit gives an estimate of the attenuation coefficient (in mm^{−1}) of each wavelength; the results are summarized in Supplementary Table 1.
Calculation of the optical properties versus the compression of aerogels
To calculate the optical properties as the aerogels are mechanically compressed, it is necessary to find the parameter relating the elasticity and the optical properties in the same material. Using the solid mechanics and optics modules of COMSOL simulation, we find the relationship between the strain tensor (induced by elastic deformation) and the permittivity and permeability tensors. Because the optical birefringence generated by anisotropic elastic compression is reported to be negligibly small^{25}, the permeability and permittivity tensors can be represented with the isotropic refractive index. The strain tensor can also be quantified using the volume compression ratio (J). We modelled a unit cell of the elastooptic metamaterial with a single pore surrounded by a dielectric shell. As the unit cell is mechanically compressed, we can obtain the refractive index versus the compression ratio (J) using the metamaterial retrieval method^{20,21,22}. The results are shown in Fig. 2f.
Data availability
The authors declare that the data supporting the findings of this study are available within the paper and its Supplementary Information files.
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How to cite this article: Shin, D. et al. Scalable variableindex elastooptic metamaterials for macroscopic optical components and devices. Nat. Commun. 8, 16090 doi: 10.1038/ncomms16090 (2017).
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Acknowledgements
This research was supported by the Global Research Lab (GRL) Program, the Pioneer Research Centre Program, a grant of the National Research Foundation (NRF) of Korea funded by the Ministry of Science, ICT and Future Planning (NRF2016K1A1A2912758, NRF2013M3C1A3065045, NRF2015R1A2A2A11001112), the Centre for Advanced MetaMaterials (CAMM2014M3A6B3063712) funded by the Ministry of Science, ICT and Future Planning as Global Frontier Project, the Low Observable Technology Research Centre Program of the Defense Acquisition Program Administration and Agency for Defense Development, and the Asian Office of Aerospace R&D grant, FA23861514024 (15IOA024).
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K.K. and D.S. conceived the idea of this study. D.S. performed the numerical simulations. J.K. and C.K. fabricated the aerogel samples. J.K. and K.B. performed the optical characterizations and analysed the aerogel. D.S., S.B. and G.K. developed the fabrication process of the macroscale optical device using deformed aerogel. D.S., Y.U. and D.R.S. performed the theoretical analysis. K.K. supervized the project.
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Correspondence to Kyoungsik Kim.
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Shin, D., Kim, J., Kim, C. et al. Scalable variableindex elastooptic metamaterials for macroscopic optical components and devices. Nat Commun 8, 16090 (2017) doi:10.1038/ncomms16090
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