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Negative Refraction
| Metamaterials exhibit many interesting optical properties and bring about new exciting applications that cannot be obtained from nature materials, such as terahertz and optical magnetism, negative refraction, superlensing and cloaking. Recent shift of the focus from microwave to optical frequencies has resulted in considerable progress in optical metamaterials. However, major challenges still lay in the way to practical applications of metamaterials in the optical frequencies, namely, fabrication and loss. To tackle these issues, our group is vigorously working on novel design, fabrication and characterization techniques to develop low loss, bulk metamaterials that can be used for real device applications. At optical frequencies, the plasmonic effect starts to kick in; therefore, a deep understanding of the localized surface plasmon polaritons (LSPP) is key to the design of the optical metamaterials. In our group, much effort has been put into the investigation of the interactions among the plasmonic particles, as well as the new functionalization introduced by these interactions in the optical metamaterials. We are also interested in the nonlinear processes in optical plasmonic metamaterials, such as second harmonic generation and four-wave mixing. |
Negative Refraction in Indefinite Materials
We observed negative refraction in bulk metamaterials composed of silver nanowires embedded in alumina at optical frequencies (Fig. 1A). A porous alumina template was prepared by electrochemical anodization, into which silver nanowires were electrochemically deposited. A 1µm wide slit, etched through a 250nm-thick silver film coated on the metamaterials, was illuminated by a collimated diode laser beam at different incident angles (see left panel of Fig 1A). The transmitted light was mapped by scanning a tapered optical fiber at the bottom surface of the metamaterial. The results are shown in Fig. 2 for incident light at a wavelength of 660nm and 780nm, respectively. |
When the incident angle is 30°, the transmitted beam is shifted to the left for TM-polarized light, which corresponds to the negative refraction. The subwavelength composite forms an effective medium with opposite signs of electrical permittivities along and perpendicular to the wires . The hypobolic dispersion enables negative light refraction even though the phase velocity remains positive. Conversely, the TE-polarized light undergoes positive refraction. Fig. 1D shows the dependence of refraction angles on a range of incident angles at 780nm. The group refractive indices of the metamaterial are shown to be -4.0 and 2.2 for TM and TE light, respectively. The phase refractive index of the metamaterial remains positive, in contrast to left-handed metamaterials. For normal incidence, the light intensity only decays ~0.43/μm in the medium at 780nm wavelength, showing loss a few order of magnitude lower than that of single layer metamaterials reported at the same wavelength . Further calculations show that the negative refraction in this nanowire composite exists for longer wavelengths and also does not depend on the orientation of the nanowire lattice. |
Fig. 1, (Upper)
Schematic of negative refraction from air into the silver nanowire metamaterials.
(Lower) Nanowires embedded in an alumina matrix, as well as scanning electron
microscopy images showing the top and side view of the nanowires (60-nm wire
diameter and 110-nmcenter-to-center distance). |
As the dielectric response in this metamaterial does not require any resonance, the negative refraction has low loss and occurs in a broad spectral range, for all incident angles. Moreover, such bulk metamaterials have the potential of supporting propagation of large wave vectors which are evanescent in air or dielectrics, enabling manipulation of visible light at subwavelength scale. This can significantly impact applications such as waveguiding, imaging and optical communication.
Fig. 2, (Left and center) Measured beam intensity at the existing surface of the metamaterial slab at the
wavelength of 660 nm and 780 nm. The lateral displacement of TM
polarized light shows the negative refraction in the metamaterial at both
wavelengths, whereas TE light undergoes positive refraction. (Right) The dependence of
refraction angles on incident angles and polarizations at 780-nm wavelength.
The negative refraction occurs for broad incident angles. The experiment data
agree well with calculations (solid curves) using the effective medium theory.
Jie Yao, Zhaowei Liu, Yongmin Liu, Yuan Wang, Cheng Sun, Guy Bartal, Angelica Stacy and Xiang Zhang, "Optical Negative Refraction in Bulk Metamaterials", Science, Vol.321, 930, 2008 view pdf |
Negative Refraction Index at Optical Frequency
Background
In the past several years great progress has been made in developing optical metamaterials with a negative refractive index. However, current designs consist of thin materials, which are analogous to a monolayer of atoms. These thin metamaterials suffer from high loss due to their resonant nature. The thin thickness of the material also prohibits device applications. Therefore, it has been of great interest to have the ability to create thick, or three dimensional (3D), metamaterials exhibiting a low amount of loss. Our lab has created such a metamaterial by employing a fishnet design fabricated on 21 alternating layers of Ag (30 nm) and MgF2 (50 nm) resulting in a metamaterial 830 nm thick (figure 1a,b). To measure the index of refraction, a 3D prism was created out of the metamaterial (figure 1c) and a simple measurement employing “Snell’s Law” was used to measure the index of refraction.
Figure 1. (a) Schematic of the 3D fishnet metamaterial. (b) SEM image of the fabricated fishnet metamaterial with the inset showing the 21 alternating layers. (c) SEM image of the 3D prism made of the fishnet metamaterial.
Results
The index of refraction was determined by measuring the Fourier plane images of the 3D prism as well as a reference window as seen in figure 2a. The Fourier plane images at various wavelengths can be seen in Figure 2b and the calculated index of refraction vs. wavelength can be seen in figure 2c. The refractive index varies from n = 0.63 ± 0.05 at 1200 nm to n = -1.23 ± 0.34 at 1775 nm. The experimental results are found to be in good agreement with the theoretical predictions (black line in Fig. 2c) based on rigorous coupled wave analysis (RCWA). The measured negative refraction angle is a direct result of negative phase evolution for light propagating inside the sample caused by a negative refractive index.
Figure 2. (a) Experimental setup of the Fourier plane measurement. (b) Fourier plane images of both a reference window and the 3D metamaterial prism. (c) Theoretical and experimental refractive index of the fishnet metamaterial.
Transmission and reflection measurements were also performed on the 21 layer thick sample and the figure of merit (FOM) was calculated as Re(n)/Im(n). The theoretical and experimental FOM are shown in figure 3a. The theoretical FOM reaches 18 while the experimentally FOM reaches 3.5. The lower experimental FOM is due to fabrication imperfections and can be improved with future work. However, a FOM of 3.5 is still one of the highest values reported at optical wavelengths. Furthermore, it is shown in figure 3b that after stacking 3 functional layers (MgF2/Ag) the index of refraction has converged, demonstrating that the index of refraction is indeed a bulk property of the material. 
Figure 3. (a) Theoretical and experimental figure of merit [Re(n)/Im(n)]. (b) Index of refraction versus number of functional layers. After 3 functional layers the index of refraction has converged. The fabricated fishnet metamaterial has 10 functional layers.
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Jason Valentine, Shuang Zhang, Thomas Zentgraf, Erick Ulin-Avila, Dentcho A Genov, Guy Bartal and Xiang Zhang, "Three Dimensional Optical Metamaterial Exhibiting Negative Refractive Index", Nature, Vol.455, 376, 2008. view pdf
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