Isotropic Bulk Negative Index Metamaterials
Abstract: The simultaneously negative effective magnetic permeability and electric permittivity of metamaterials gives rise to exotic electromagnetic phenomena not known to exist naturally. These materials can enable, for example, ultrahigh-resolution imaging and lithography systems. Bulk isotropic three-dimensional (3D) negative index metamaterial (NIM) designs with low absorption and high transmission that operate at terahertz and optical frequencies are needed to explore all the potential applications of NIMs. Direct laser writing is a promising technique for the fabrication of truly 3D large-scale photonic metamaterials. In this project we develop feasible NIM designs for DLW processes.
Keywords: Metamaterials
Collaborators: Costas Soukoulis (Ames Laboratory), Thomas Koschny (Ames Laboratory), Martin Wegener (University of Karlsruhe, Germany), Eric Mazur (Harvard University), Maria Kafesaki (University of Crete, Grece)
Support: NSF, ONR (current); DOE, USAFOSR, DARPA, ONR, FET (past)
The simultaneously negative effective magnetic permeability and electric permittivity of metamaterials gives rise to exotic electromagnetic phenomena [1,2] not known to exist naturally. These materials can enable, for example, ultrahigh-resolution imaging and lithography systems.
All photonic metamaterials at terahertz frequencies have been fabricated by well-established two-dimensional (2D) fabrication technologies, such as electron-beam lithography and evaporation of metal films, but they are one-dimensional (1D) designs with few functional layers [3,4]. A few efforts have been made to fabricate three to five layers [5,6], but this is also a 1D design.
3D Isotropy is a necessary ingredient to fully harvest the potential applications of negative index metamaterials, such as Pendry's perfect lens [7]. Since no isotropic magnetic material exists in nature, which possesses negative permeability at THz frequencies, such single-negative metamaterials would be of interest by itself for imaging, magnetic shielding, and other practical applications. In 2002, Gay-Balmaz and Martin [8] experimentally demonstrated the first 2D isotropic magnetic metamaterial formed by two crossed split-ring-resonators (SRRs). In 2007, Padilla [9] and Baena et al. [10] independently proposed fully isotropic bulk magnetic metamaterial designs, based on SRRs arranged in a cubic lattice by employing the spatial symmetries.
On the other hand, some designs of 3D isotropic NIMs exist, but fabricating them has remained a challenging task and virtually impossible at optical frequencies. In 2005, our colleagues [6] for example, designed an early example of an isotropic NIM. However, high-constant dielectric assumed across the gaps of the SRRs render the experimental realization impractical. Alternative approaches have also been investigated including transmission lines [11,12], chiral resonators [13], and high refractive index spheres [14]; but, no practical feasible designs have yet occurred, operating at frequencies beyond the microwave ranges. It is an open question, whether there is any 3D isotropic metamaterial design working for optical frequencies still feasible to fabricate.
Direct Laser Writing
Figure 1 Electron micrographs of photonic metamaterial structures using direct laser writing.
Bulk isotropic three-dimensional (3D) NIM designs with low absorption and high transmission that operate at terahertz and optical frequencies are needed to explore all potential applications of NIMs. Direct laser writing (DLW) with chemical vapor deposition appears to be a more promising route toward the fabrication of three-dimensionally (3D) isotropic bulk optical metamaterials [5]. Rill et al. [5] recently demonstrated the feasibility of this technique at near-IR frequencies assisted with silver chemical vapor deposition (CVD).
The DLW processes, assisted by chemical vapor deposition (CVD), offer a viable means to fabricate metamaterial structures at THz and optical regions by enabling computer-controlled formation of almost arbitrary three-dimensional patterns. These are not possible to fabricate with traditional photolithographic processes [5]. Structural length scales of generated individual 3D materials can span six orders of magnitude, from tens of nanometers to millimeters [5,15-17]. DLW produces a binary structure defined by the path exposed to the laser focus (which polymerizes and remains standing) within the homogeneous background of unexposed photoresist (which dissolves). After the unexposed photoresist has been removed during development, the remaining structure can be metalized by CVD or entirely replaced by metal. In contrast to lithography, directed self-assembly or other patterning approaches, DLW does not require masks or pre-existing patterns. Therefore, it can be also considered as a 'rapid prototyping' tool.
Laser sources for DLW ranges from ultrafast femtosecond-pulsed lasers to continuous wave lasers such as solid-state, gas, fiber, or semiconductor lasers. For example, a diode laser, which induces a phase transition between crystalline and amorphous material (i.e., DLW modification), is used to rewrite a compact disc. [15]
In the manufacturing of electronic and optoelectronic devices such as cell phones, digital cameras, and laptop computers, DLW is an established technology, especially for laser drilling of via holes for stacked or built-up printed circuit boards. DLW can also be used to trim or pattern thin metal films on the microelectromechanical structures, which is otherwise difficult to process by conventional techniques due to extreme topography and/or fragility. DLW with multibeam parallel processing can be employed to achieve high throughput in mass production. [16]
Figure 1 shows electron micrographs of the structures made by using these methods. The samples go through 10 chemical vapor deposition cycles, resulting in an estimated silver thickness of approximately 50 nm. The coating is uniform around the structures, even in 3D; this is in sharp contrast to the usual 2D evaporation process. Our collaborators used retrieval methods to determine the electromagnetic properties of the metamaterials grown by DLW. The magnetic permeability exhibits the anticipated negative values around the 100 THz frequency range. This clearly shows that the fabrication of a magnetic metamaterial using DLW and silver CVD is possible. However, the influence of bi-anisotropy of the fabricated structure results in a positive index of refraction. Therefore, there is a clear need to come up with a better design that is suitable for DLW. [18]
To fabricate large-scale bulk metamaterial structures, interconnected unit cells are desired. This helps avoid the collapse of otherwise disconnected and unsupported metallic unit cell components, left free-standing after the unexposed photoresist has been removed. Moreover, connectivity, in general, provides an advantage for rapid prototyping of arbitrary 3D metallic structures using DLW and CVD.
From the design perspective, it is a very difficult task to determine a connected structure amenable to fabrication and simultaneously exhibiting acceptable metamaterial properties, particularly at optical frequencies. The fabrication of a fully isotropic photonic NIM structures is a great challenge. The magnetic and electric constitutes of the intra-connected metamaterial structure can be thought of as forming an integrated nanocircuitry, which needs a careful design to prevent any unwanted short circuits. Most common NIM geometries, SRRs or fishnet structures [19] with their current design features cannot be assembled into spatially isotropic metamaterials for fabrication at THz frequencies and yet maintain the desired optical properties unless their constitutes are cleverly interconnected.
Recent Results
As a part of this project, we designed the first truly bulk 1D and 2D isotropic photonic NIMs, which can potentially be fabricated with DLW around telecom wavelengths with about 20THz bandwidth [20]. Given state-of-the-art 2D fabrication technologies, manufacturability is still a concern to realize any practical optical devices based on metamaterials. Therefore, alternative technologies, such as DLW with compatible designs, are essential. Our design, owing to its inherently connected nature with the next-unit-cell neighbors, presents the first truly bulk photonic metamaterials feasible to fabricate with DLW and CVD. This is important step to fabricate large-scale 3D metamaterials operating at optical frequencies.
We also showed the first, fully intra-connected and isotropic metamaterial design, principally amenable to fabrication by DLW and CVD [21]. Using rotation symmetries of the cube, our metamaterial allows left-handed behavior for any orthogonal direction of propagation and any polarization of light. Although the size requirements make the designed structure unfeasible to fabricate with the state-of-the-art DLW processes, the idea of proper connectivity, which is behind our proof-of-principle design, can enable the fabrication of metallic metamaterial structures in the optical region and open a new avenue in the design and fabrication of functional metamaterial devices to allow the unprecedented manipulation of light.
2D Isotropic Meandering Wire Design
Figure 2 Unit cell and incident field configuration for the 2D NIM consisting of two pairs of meandering wires and corresponding retrieved effective parameters using the HEM approximation. The solid curves indicate the real parts, and the dashed curves indicate the imaginary parts.
The unit cell for our designed 2D photonic NIM is illustrated in Fig. 2. The structure has C4 symmetry, consisting of one pair of meandering wires (radius 37 nm) embedded in a polyimide substrate, with inversion symmetries in both x and z directions. The negative index of refraction is achieved for two orthogonal propagation directions.
Figure 3 Illustration of our blueprint design for DLW and CVD.
Our meandering wire designs were also featured in the November 2008 issue of Optics and Photonics News (see Ref. 18). Currently we collaborate with Martin Wegener's group in Karlsruhe, Germany to fabricate our blueprint designs (see Figure 3).
3D Isotropic Intra-connected Design
Figure 4 Unit cell and the 3 x 3 x 3 bulk illustration of the designed intra-connected isotropic NIM structure. Full connectivity is achieved by diagonal connectors and square frames.
We also showed the design of a fully isotropic 3D photonic NIM structure [21]. The cubic unit cell of our structure is illustrated in the left panel of Fig. 4. It is arranged into a cubic lattice to form the actual bulk metamaterial shown in the right panel.The bulk structure is fully intra-connected and is spatially isotropic for all principal directions of propagation and any polarization of light. It is able to provide 3D isotropic left-handed behavior.
Figure 5 Retrieved effective parameters for a different number of unit cells up to four, using the homogeneous effective medium approximation. Black, red, green, and blue correspond to 1-4 unit cells, respectively.
Fig. 5 shows the retrieved effective parameters for our structure, which has about a five times smaller unit cell size than the relevant vacuum wavelength. The structure homogenizes well after a few unit cells evident from the converging effective parameters. For the 4-unit cell structure, effective permittivity and permeability are simultaneously negative over a 4THz bandwidth with a center frequency of 148THz.
Acknowledgments
We collaborate with Costas Soukoulis (Ames Laboratory), Thomas Koschny (Ames Laboratory), Martin Wegener (University of Karlsruhe, Germany), Johannes Kaschke (University of Karlsruhe, Germany), Eric Mazur (Harvard University), and Maria Kafesaki (University of Crete, Grece). Our past collaborators include Michael Rill (University of Karlsruhe, Germany), and Michael Thiel (University of Karlsruhe, Germany).
This project is currently funded at Michigan Tech by the National Science Foundation (NSF) under grant ECCS-1202443 and Office of Naval Research (ONR) (award N00014-15-1-2684). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the NSF or ONR. Previously, the project was in part supported at Ames Laboratory by the Department of Energy (DOE) (Basic Energy Sciences). It was also partially supported by the United States Air Force Office of Scientific Research (USAFOSR), by Defense Advanced Research Agency (DARPA), ONR, and European Community Future and Emerging Technologies (FET) project Photonic Metamaterials (PHOME).
References
[1] C. M. Soukoulis, S. Linden, and M. Wegener, Negative refractive index at optical wavelengths, Science 315, 47 (2007).
[2] V. M. Shalaev, Optical negative-index metamaterials, Nat. Photonics 1, 41 (2007).
[3] G. Dolling, M. Wegener, and S. Linden, Realization of a three-functional-layer negative-index photonic metamaterial, Opt. Lett. 32, 551 (2007).
[4] N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, Three-dimensional photonic metamaterials at optical frequencies, Nature Mater. 7, 31 (2008).
[5] M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, Photonic metamaterials by direct laser writing and silver chemical vapour deposition, Nature Mater. 7, 543 (2008).
[6] Th. Koschny, L. Zhang, and C. M. Soukoulis, Isotropic three-dimensional left-handed metamaterials, Phys. Rev. B 71, 121103 (2005).
[7] J. B. Pendry, Negative refraction makes a perfect lens, Phys. Rev. Lett. 85, 3966 (2000).
[8] P. Gay-Balmaz and O. J. F. Martin, Efficient isotropic magnetic resonators, Appl. Phys. Lett. 81, 939 (2002).
[9] J. D. Baena, L. Jelinek, and R. Marques, Towards a systematic design of isotropic bulk magnetic metamaterials using the cubic point groups of symmetry, Phys. Rev. B 76, 245115 (2007).
[10] W. J. Padilla, Group theoretical description of artificial electromagnetic metamaterials, Opt. Express 15, 1639 (2007).
[11] A. Grbic and G. V. Eleftheriades, An isotropic three-dimensional negative-refractive-index transmission-line metamaterial, J. App. Phys. 98, 043106 (2005).
[12] P. Alitalo, S. Maslovski, and S. Tretyakov, Experimental verification of the key properties of a three-dimensional isotropic transmission-line superlens, J. Appl. Phys. 99, 124910 (2006).
[13] R. Marques, L. Jelinek, and F. Mesa, Negative refraction from balanced quasi-planar chiral inclusions, Microwave Opt. Technol. Lett. 49, 2606 (2007).
[14] I. Vendik, O. Vendik, I. Kolmakov, and M. Odit, Modelling of isotropic double negative media for microwave applications, Opto-Electron. Rev. 14, 179 (2006).
[15] C. B. Arnold and A. Pique, Laser direct-write processing, MRS Bulletin 32, 9 (2007).
[16] K. Sugioka, B. Gu, and A. Holmes, The state of the art and future prospects for laser direct-write for industrial and commercial applications, MRS Bulletin 32, 47 (2007).
[17] G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, Three-dimensional photonic nanostructures for photonics, Adv. Funct. Mater. 20, 1038 (2010).
[18] E. Ozbay, The magical world of photonic metamaterials, Optics Photonics News 19, 22 (2008).
[19] G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, Low-loss negative-index metamaterial at telecommunication wavelengths, Opt. Lett. 31, 1800 (2006).
[20] D. O. Guney, Th. Koschny, M. Kafesaki, and C. M. Soukoulis, Connected bulk negative index photonic metamaterials, Opt. Lett. 34, 506 (2009).
[21] D. O. Guney, Th. Koschny, and C. M. Soukoulis, Intra-connected three-dimensionally isotropic bulk negative index photonic metamaterial, Opt. Express 18, 12348 (2010).