Negative index metamaterial combining
magnetic resonators with metal films
Uday K. Chettiar, Alexander V. Kildishev, Thomas A. Klar†, and Vladimir M. Shalaev Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907, USA洋节
†on leave from Ludwig-Maximilians-Universität, München, 80799, Germany
shalaev@purdue.edu
指鹿为马的反义词Abstract: We prent simulation results of a design for negative index
materials that us magnetic resonators to provide negative permeability and
metal film for negative permittivity. We also discuss the possibility of using
micontinuous metal films to achieve better manufacturability and
enhanced impedance matching.
References and links
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润肺的中药
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1. Introduction
The refractive index is a key parameter describing the interaction of light with matter. The real part of a refractive index is usually considered to be positive, which is in fact true for all
naturally existing materials. However, a refractive index with a negative real part does not violate any physical laws; indeed such materials will have some very interesting properties making them good candidates for a plethora of valuable applications. Since such materials do not exist in nature they have to be artificially fabricated. In a material characterized by a permittivity i εεε′′′=+ and permeability i μμμ′′′=+, the condition 0ε′< and 0μ′< is sufficient for negative refractive index [1]. But the condition 0εμμε′′′′′′+< reprents the necessary condition for a negative refractive index in a passive medium [2], where for example, a material with a large loss can have a negative refractive index even if the real parts of both permeability and permittivity are not negative simultaneously. Such a material will undoubtedly have a large loss preventing any uful application.
The first experimental demonstration of a negative index material (NIM) was given in the microwave frequency range using an array of metal lines and split ring resonators [3]. Negative index of refractio
n was demonstrated in optical frequencies using an array of paired nanorods [4], an array of elliptic voids in a multilayered structure [5] and a fishnet structure [6]. In this paper we prent a simpler and intuitive 2D geometry which shows a pronounced negative refractive index.
2. Magnetic resonator bad on a pair of metal nanostrips
It was predicted that a pair of metal rods parated by a dielectric can give ri to artificial permeability due to a localized plasmonic resonance [7-9]. In fact a pair of nanorods can have two kinds of resonance: a symmetric resonance, which results in an artificial permittivity and an asymmetric resonance, which gives ri to an artificial permeability; the two resonances make it possible to have a negative refractive index as was first predicted in [8]. In general, the two resonances occur at different wavelengths. We u a simplified 2D version of a nanorod pair as a magnetic resonator. This structure consists of two nanostrips parated by a dielectric as shown in Fig. 1(a). The strips are infinite in the direction perpendicular to the plane of the page (y -direction). The sample consists of an array of nanostrip pairs distributed periodically along the x direction. The incoming field is oriented in TM polarization as shown in Fig. 1(a). Similar to the nanorod pair, the nanostrip pair has two different principal resonances (the magnetic and electric resonance respectively). However, we are interested in using this structure exclusively as a magnetic resonator.
The metal nanostrips are assumed to be made of silver becau of its low loss. The dielectric spacer between the nanostrips is taken to be alumina becau the relatively large refractive index of alumina is of assistance to confining the field between the nanostrips. The space between adjacent pairs of nanostrips is filled with silica to provide mechanical support for further lamellar stacking of this structure.
The complex transmission and reflection coefficients of this structure were calculated using a spatial harmonic analysis bad code and verified with a commercial FEM solver. The permittivity of silver was taken from tabulated experimental values [10]. The transmission and reflection coefficients were then ud to retrieve the effective refractive index and impedance for the nanostrip composite [11, 12]. Fig. 1(c) and (d) show the effective permeability and permittivity for the following design parameters, t 30 nm, d 40 nm, w 300 nm, p = 600 nm (refer Fig. 1(a) for the key to the symbols). We note that there are two distinct resonances: a magnetic resonance around 1700 nm and an electric resonance around 900 nm. We also note the prence of an electric and a magnetic anti-resonance at 1700 nm and 900 nm, respectively. This is the result of the periodicity in the structure and has been studied extensively [13]. Becau of the prence of the anti-resonances it is hard to overlap the magnetic and electric resonances, since as the electric and magnetic resonances get clo
r to each other the anti-resonances increa in strength, nullifying the resonance for one of the two quantities (permittivity or permeability).
The transmittance and reflectance characteristic is shown in Fig. 1(b). We can clearly e the relations between the Fig. 1(b) and Fig. 1(c,d). The real and imaginary parts of the permeability around 1700 nm show good correspondence with the transmittance and absorbance as expected. On the other hand the real part of the permittivity around 900 nm
shows good correspondence with the transmittance, but there is no absorption corresponding to the electric resonance. There is an absorption band below 860 nm, but that corresponds to the radiation loss since the structure starts diffracting light in the forward direction below 860 nm. Hence the electric resonance does not result in any appreciable absorbance. 3. NIM using a magnetic resonator and continuous metallic films
In the previous ction we saw that a pair of nanostrips can generate a strong magnetic resonance resulting in a negative permeability. Now all we need for creating a negative index material is a negative permittivity. This is easy to achieve since noble metals like gold and silver have negative permittivity at optical frequencies below the plasma frequency. Hence just adding a metal film above 车胎气压多少合适
and below the magnetic resonator as shown in Fig. 2(a) should be sufficient to provide a negative permittivity. We note that an alternative way to provide negative permittivity is to u continuous wires [14]. In our design the films are brought in contact with the strips to avoid additional resonances due to the interaction between the strips and the films. Our simulations have shown that such additional resonances are detrimental to the magnetic properties of the nanostrip pair. The additional layer of silica on the top functions as a al preventing the silver from being oxidized or sulfurized due to exposure to air. Intuitively, only one metal film should suffice since we can u a single thick film instead of two thin films to provide similar permittivity. There are two reasons for using two films instead of one. Using two films ensures that the structure is symmetric and justifies the u of the retrieval formula to extract the effective optical parameters of the structure. The retrieval procedure assumes that the structure is symmetric. Using a single film would also generate additional resonances due to the interaction between the isolated strip and the film. This interaction is suppresd through the u of two films.
Fig. 1. (a) Unit cell for the array of nanostrip pairs; (b) Transmittance (T), reflectance (R) and absorbance (A) for the nanostrip pair array; (c) Effective permeability; (d) Effective permittivity
0.8
1.0
1.2 1.4 1.6 1.8
-10-50510
15Wavelength (μm)
Re(μ)Im(μ)
0.8
1.0
1.2 1.4 1.6
1.8
00.20.40.60.81Wavelength (μm)
0.8
1.0
1.2 1.4 1.6 1.8
-20-10
010203040Wavelength (μm)
Re(ε)Im(ε)
(c)
(d)
6 nm, 10 nm and 20 nm silver films. The structure was coated with a 20 nm thick silica layer. The effective refractive index, permeability and permittivity are shown in Fig. 2. Here the refractive index goes negative for all cas, but the permeability goes negative only when the metal film is 6 nm or 10 nm thick. Also the imaginary part of the refractive index is much lower when the real part of the permeability is negative. The sample with 6 nm thick films has a maximum transmittance of 27% with a negative real part of the refractive index at a wavelength of 1520 nm. The refractive index at this wavelength is −2.38+0.84i. However it should be remembered that it is almost impossible to fabricate a 6 nm thick continuous silver film. The silver film would be esntially mi-continuous at this thickness. Typically, the film thickness should be at least 20 nm to ensure that the silver is continuous, but as it is clear from Fig. 2, the properties are significantly wor with a 20 nm thick film. For example the minimum of Im()n is about 2.5 times as large for the 20 nm thick silver films as compared to the 6 nm thick films (Fig. 2(b)). This is a direct conquence of Re()0
μ> (Fig. 2(c)).
We also notice that the magnetic resonance is at shorter wavelengths for the thicker films. The addition of the metal films caus the currents in the nanostrip to leak into the metal films, especially towards the ends of the nanostrips. This reduces the effective width (w) of the nanostrips which resul
如何发财致富ts in a shorter resonance wavelength. This leakage of current also has the effect of diminishing the resonance in permeability.
4. NIM using a magnetic resonator and micontinuous metallic films
So far, our simulations have shown that combining continuous metal film with nanostrip
magnetic resonators could easily yield a negative index material. Unfortunately, that requires
变色的房子unrealistically thin metal films. The problem aris becau silver has a highly negative real part for it’s permittivity around 1.5 µm, but the magnetic resonator can not provide a comparable value of negative permeability. This results in a huge impedance mismatch and subquent large reflection which degrades the magnetism of the entire structure. Another way to look at the problem is to consider the electromagnetic shielding provided by the metal film. A thick film would shield the incoming field more efficiently, thus suppressing the performance of the magnetic resonator. An obvious way to circumvent this problem is to u a thinner metal film, except the minimum thickness is limited by the material properties and fabrication tolerances.
Instead of bulk metal, the film can be formed with a mixture of silica and metal (micontinuous meta如果我是男人
l films, SMF). Such films can be fabricated using very basic techniques like sub-monolayer evaporation. The permittivity of a SMF can be well described by the effective medium theory (EMT) [15]. According to EMT, the effective permittivity (e ε) of a d -dimensional metal-dielectric composite consisting of a metal with permittivity m εand a filling fraction of f , and a dielectric with permittivity d ε and filling fraction of 1f − is given by Eq. (1). This is a quadratic equation which has two solutions for e ε. We lect the solution that has a positive imaginary part (Im()0e ε≥).
()()()1011m e d e
m e d e
f
f d d εεεεεεεε−−+−=+−+− (1)
The performance of EMT has been tested against exact solution using numerical methods [16] and it has been confirmed that EMT provides good agreement with the numerical method
Fig. 3. Effective parameters and spectrum for the structure with micontinuous silver film (metal filling fraction = 65%, thickness = 20 nm). (a) Effective refractive index, (b) Transmittance, reflectanc
e and absorbance spectra, (c) Effective permeability, (d) Effective permittivity.
