Here we show that a continuous highly conducting metal film can be made transparent for wide-angle and polarization-insensitive incidence of near-infrared light by depositing periodic metal patches on top of the metal film. Based on the optimized computations, the whole system could suppress the reflection and enhance the transmission. This design of transparent metal film can be useful in applications, such as optoelectronic electrodes, solar cells, and micro-electronic displays, where both high electrical conductivity and high optical transmittance are desirable.
© 2014 Optical Society of America
Transparent conducting metals (TCMs) have drawn lots of attention recently [1–14], because of its potential applications in optoelectronic devices varying from solar cells to electronic paper, touch screens, and optical displays. TCMs possess the unique property of allowing a certain portion of the electromagnetic spectrum of interest to pass through a continuous metal film while its electrical connection is kept intact. However, it is well known that a high-conducting metal with a high electron density is generally opaque for light, since the metal’s permittivity is generally very negative at optical frequencies. Previous chemical approaches to construct TCMs were to decrease the electron density either directly in materials (e.g., using indium tin oxide (ITO)  or doped silicon ) or effectively in structures (e.g., making nano-meshes  or nano-wires ). But the (effective) conductivity of such TCMs was much smaller than that of a continuous metal film . Some physical approaches perforate the targeted noble metals (Ag, Au, etc.) in various shapes (holes, slits, etc.) to make them transparent within a certain frequency window [6,7]. Yet, perforation will decrease the mechanical stability and electric conductivity of a metallic layer, which is undesired in many practical applications. Moreover, surface plasmon polariton (SPP)-enhanced transmission  is sensitive to structuring, and the perforation approach based on Fabry-Perot (FP) interference  requires the thickness of samples comparable to wavelength. New routes were also investigated to make an opaque medium transparent in low-frequency regime (e.g., GHz) based on metamaterials (MTMs) , but a direct scaling of those MTMs to optical regime is generally difficult because of their saturation effect at high frequencies . In addition, some previous efforts have been devoted to making free-standing TCMs [8,10], but in many real applications such as solar cells, the TCMs should be deposited on a substrate [11,12]. Therefore, it is desirable to consider a realistic geometry of TCM on a substrate.
In this paper, we propose a new type of TCM to make a continuous (apertureless, seamless) metal film optically transparent on a substrate at near-infrared frequencies. Since our design does not require any perforations on the metal film, its full electric and mechanical properties can be preserved. Moreover, the transparency is robust against polarization and incidence angle. In terms of fabrication, our design requires only planar operation which does not involve complicated three-dimensional construction.
Our paper is organized as follows. We first numerically calculated transmission behavior of the proposed model system in Sec. 2. The interesting transparent metal film at near-infrared frequencies is verified based on full-wave simulations. In Sec. 3, we discussed the underlying physics behind this phenomenon. After presenting the properties of wide angle and polarization insensitivy of our proposed system in Sec. 4, we concluded our paper in the last section.
2. Numerical calculations on the designed system
As shown in Fig. 1, the proposed TCM consists of three thin layers. The first layer is an array of square sliver patches which are arranged periodically in square lattices; the second layer, called the spacer layer, is filled with one homogeneous thin dielectric medium (); the third layer is the target continuous silver film. The whole structure is assumed to be deposited on a substrate which is semi-infinite in simulation. The thicknesses of square silver patch, dielectric layer, and the continuous silver film are , , and respectively. This configuration is geometrically similar to a high-efficiency absorber [15,16]. Yet, the bottom metal film in the previous absorber is generally thick enough to prevent the light from transmitting. Here our aim is to transmit light efficiently through the metal film into the substrate. The metal film is set to be relatively thin in our design.
To illustrate how the idea works, numerical simulations and optimizations for high optical transmission were performed with the commercial software COMSOL Multiphysics based on finite element method. In simulations, the relative electric permittivity of is 11.6 (3.0625) , and that for silver is described by with and . All materials are assumed to be non-magnetic (). The system is illuminated with a linearly polarized plane wave propagating along the negative direction. In our calculations, the reference plane of transmission is located in the GaAs substrate, but it is very far away from the metal layer so as to get only the information of propagating waves. The dimensions of this TCM with central operating wavelength of 1.55 μm are optimized to be and , where and are the width and the period of square silver patches respectively. The solid line of Fig. 2 shows the simulated transmittance spectrum of our designed TCM with parameters optimized above. At the wavelength of 1.55 μm, ~73% energy of light can pass through the continuous silver film with the negative permittivity (~-118) and enter into the substrate. As a comparison, one can see that the transmittance curve of the bare continuous silver film with thickness of 20 nm is less than ~5% when the wavelength is longer than 1.2 μm. The presented TCM at 1.55 μm yields a ~24 times transmission enhancement compared to the bare continuous silver film case. Therefore, it is worth noting that by putting square silver patches on top of the continuous silver film, one can make an optically opaque metal film transparent. Since this design needs not structuring the metal film, the full DC conductivity of the metal film can be preserved. ITO is a good candidate for transparent conducting oxide and commonly used in many applications. However, its transmittance is only ~25% at the wavelength of  because of heavy doping and free-carrier absorption. The electrical resistance of a 20 nm thickness silver film is about 200 nΩ⋅m , although it cannot compare with the bulk resistivity of silver (15.9 nΩ⋅m), which is still significantly lower than the ones of the ITO (2000 nΩ⋅m) [1,19] and zinc-indium-oxide (4000 nΩ⋅m)  films. Therefore, compared to some previous works on TCMs, such as ITO and some transparent oxides, such a device not only has high optical transmittance at near-infrared frequencies, but is also a good in-plane electrical conductor due to the existence of the silver film, which is desirable in many optoelectronic applications.
Further numerical simulations were also performed to investigate the relationship between the transmission spectrum and the geometric dimension of the silver patches. Figure 3 shows the transmittance as a function of wavelength () and width () of silver patches with other geometric parameters , , , and fixed. By increasing the width of silver patches from 100 nm to 180 nm with a step of 5 nm while keeping the other parameters unchanged, the transparency wavelength gradually changes from 1.1 μm to 2.0 μm, demonstrating the flexibility of our approach.
3. Discussion on physics behind this phenomenon
Inspired by optical scattering from nanoparticles due to the interference between the electric and magnetic dipoles [22–25], we qualitatively identify that high transmission at the wavelength of could be attributed to the constructive interference between the electric and magnetic dipoles in the forward propagating direction. Especially, the results in  tell that the system with large aspect ratio will have a noticeable increase in the forward scattering. The aspect ratio of our designed structure is , which is consistent with the effect of high transmission. Herein, the electric dipole with charges accumulated at the sides of the silver patch is easily understood to be parallel to the electric field of incidence wave, and the magnetic dipole parallel to the magnetic field of incoming light originates from the circular displacement currents. A bare silver patch has only electric response to electromagnetic radiation. But when a silver film is added, near-field coupling between the silver patch and the silver film generates electric currents flowing oppositely on each of them, which then form a circulating current loop and lead to a magnetic resonance [26,27]. The corresponding magnetic field intensity () at the wavelength of 1.55 μm is illustrated in Fig. 4. We find that the magnetic field is strongly enhanced in the dielectric layer, as a characteristic feature of this phenomenon. We also plotted in Fig. 4 the distribution of electric displacement inside this structure at the wavelength of 1.55 μm. Clearly, the electric displacement vectors represented by the arrows in both the silver patches and the silver film are opposite to each other, which generate a significant magnetic response aided by strongly enhanced magnetic fields localized in the gaps between the silver patches and the silver film. In principle, the contributions of different modes in this system could be expected to be rigorously analyzed by multipole decomposition method in the future . Alternatively, this phenomenon can also be interpreted from the perspective of scattering cancellation mechanism [10,12] or interference-based principle [29,30]. By modeling the distributed array of square silver patches as a homogeneous impedance-tuned interface, the destructive and constructive interferences, respectively, due to the superpositions of the multiple reflections and transmissions, are responsible for the reduction of reflection and enhancement of transmission.
4. Polarization-insensitive and large tolerance of oblique incidence
In addition, for this newly designed TCM, this high transmission is robust against polarization and oblique incidence. Simulations were performed to verify these features with the same optimized dimensions in Fig. 2. The simulated transmittances as a function of frequencies () and incidence angles () are shown in Fig. 5(a) for transverse-electric (TE) polarization and Fig. 5(b) for transverse-magnetic (TM) polarization. Numerical results reveal that the transmittance is rather stable even for the incidence angles up to for TE waves and for TM waves.
To summarize, we have presented a new TCM based on the plasmonic nanostructure on a substrate at near-infrared wavelengths. Numerical results show that the high transmission is insensitive for the wide variation of incidence angles for both TE and TM polarizations, and can be tuned by adjusting the geometric dimension. Furthermore, the fabrication of this configuration can be straightforwardly fabricated by focused ion beam etching or electron beam lithography technique. This TCM design may find applications in photovoltaic cells, touch screens, and other display devices, where transparent electrodes are in significant demand.
This work was sponsored by Nanyang Technological University under Grants Nos. M4080806.110 and M4081153.110, and Singapore Ministry of Education under Grants No. M4011039.110 and No. MOE2011-T3-1-005.
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