Broadband nanowire-grid polarizers were designed and numerically simulated using the finite difference time domain (FDTD) method. Using a broadband stimulation source, optical properties of the polarizers were analyzed in the ultraviolet (UV)-visible-near infrared (NIR) regions. Specifically, the extinction ratios and optical transmittances of transverse magnetic (TM) and transverse electric (TE) modes were characterized for different metal materials and geometrical parameters including wire-grid periods, metal-wire fill ratios, and spacing between wire-grid layers. Based on the simulation results, an extra broadband polarizer with an average extinction ratio higher than 70 dB and transmission efficiency over 64% in the range of 0.3 to 5 µm was proposed.
©2007 Optical Society of America
Polarizers are important devices for optical systems such as free-space optical switching networks, fiber-optic networks, read-write magneto-optic data storage systems, and polarization-based imaging systems [1–4]. Conventional polarizers have large sizes that limit their applications. Subwavelength metal wire grids are a potential candidate for making a high-quality integration-capable thin-film-type polarizer, since the structures are compact and planar and have high performance of high extinction ratio, transmittance, and reflectance with a wide incident angle and wavelength range . Subwavelength metal wire-grid polarizers are widely used in the radio, microwave, and IR spectral regions . With the development of nanolithographic technology, it is possible to apply this type of polarizers into the near infrared (NIR), visible, and UV regions [5, 7–10]. In 2005, Wang  and Zhou  fabricated nanowire-grid polarizers using UV nanoimprint lithography and e-beam lithography independently. The grid period was about 200 nm, suitable for working in NIR. In 2006, Ekinci  and Wang  succeeded in fabricating nanowire-grid polarizers with about 100 nm periods using extreme ultraviolet (EUV) interference lithography. The devices can work in the region from 300 to 900 nm. However, up to now, a broadband polarizer which can work in the region from 0.3 to 5 µm has not been proposed and studied.
In this study, the FDTD method was used to design the nanowire-grid polarizers in the UV-Visible-NIR regions. Several metal materials, including gold (Au), silver (Ag), chromium (Cr), and Al, were studied. It is found that Al has preferred optical performances in the region from 0.3 to 5µ m. Al wire-grid polarizers with a wide variety of geometrical parameters were simulated. Based on the analysis, a broadband Al nanowire-grid polarizer was proposed. The simulation results indicated that an average extinction ratio over 70 dB and a transmission efficiency over 64% could be achieved.
2. Simulation models
The optical properties of nanowire-grid polarizers with different metal materials and structures were analyzed using the FDTD method. Figure 1 shows a schematic diagram of a structure used in the simulation. Metal wire-grids are embedded in a silica substrate. The refractive index of the silica substrate is 1.46 and frequency independent. It is assumed that all the metal wire-grids are sufficiently long along the Y direction so that a two dimensional FDTD method can be used to simplify the simulation. A plane wave illuminated the nanowire-grid polarizer along the positive Z direction for TM (magnetic field parallel to the Y direction) and TE (electric field parallel to the Y direction) modes. In the calculation, the plane wave is a broadband Gaussian-modulated pulsed light source which can be expressed as:
where toff is the offset time, tw the half width of the pulse, and ω the central frequency of the source. Using this broadband excitation source, information about all the frequencies can be obtained in a single calculation. For the study of UV-Visible regions, the following parameters were used: ω=0.6×1015Hz, toff=1×10-14 s, and tw=1×10-15 s; for NIR region: ω=0.12×1015Hz, toff=1×10-14 s, and tw=0.8×10-15 s. Figures 2(a) and 2(b) show the UV-visible excitation source both in time and frequency domains, respectively. Four metals, Au, Ag, Cr, and Al, whose dielectric functions were described by the Lorentz-Drude model , were used in the calculations. The perfectly matched layers (PML)  were along the Z direction. The boundaries along the X direction were confined with the periodic boundary conditions (PBC)  due to the periodicity of the wire-grids. This simplification greatly reduced the computation time. To make the calculations more stable, the space and time steps were set to be 0.5 nm and 1×10-3 fs, respectively. Figures 3 and 4 show the TM and TE polarized sources passing through an Al nanowire-grid polarizer. w: Wire width p: Grid period Silica Metal wire
3. Simulation results and analyses
3.1 Nanowire grids with different metals
Nanowire-grid polarizers with different metals, Au, Ag, Cr, and Al, were simulated. The cross-section of the simulation structure is shown in Fig. 5. The polarizers consisted of one layer of metal wire-grid. The thickness and width of the metal wires were both 40 nm. The period was 80 nm. The optical transmittances of TM and TE modes and the extinction ratios of Au, Ag, Cr, and Al are shown in Figs. 6(a), 6(b), 6(c), and 6(d), respectively. From Fig. 6, it is found that the Al wire-grid polarizers have the best optical performance in the range from 0.3 to 5 µm. Especially in UV-Visible regions, the average transmission efficiency and extinction ratio of the Al nanowire-grid polarizer were 74% and 19.4. Those of Au, Ag, and Cr, however, were (41%, 1.09), (39%, 0.88), and (54%, 6.17), respectively. The difference between the optical performances of Al and other metals could be explained by the following equation:
where R is the reflectivity between the metal and the air, n and κ are the refractive index and the extinction coefficient of the metal material, respectively. Al has the largest extinction coefficient and relatively small refractive index in the UV-visible-NIR regions . Therefore, Al wire-grids have a higher reflection for the TE mode light in the regions than that of other metal materials. In the following simulations, Al was used as the metal material for the nanowire-grids.
3.2 Dependence on grid periods
With the development of nanolithography technology, the available feature size of patterns is becoming smaller and smaller. Fabrication of grids with about 100 nm periods has been realized by the EUV interference lithography [12, 13]. This capability provides more flexibility for designing wire-grid polarizers in the UV-visible-NIR regions.
Structures with different periods (from 20 to 200 nm) were calculated, in which the wire thickness, and fill ratio were kept at 40 nm and 50%. The optical transmittances of TM and TE modes and extinction ratios are shown in Fig. 7. It could be seen that the smaller the period is, the higher the optical performance a polarizer has. When the period is larger than 120 nm, fluctuation in the transmission efficiency and the extinction ratio occurs. The reason is that when the period reaches the order of the light wavelength, the scattering loss becomes significant. However, smaller periods impose difficulty in fabrication processes. Therefore, a proper selection of periods for the polarizers is important. According to the present lithography capability, a 80 nm period is suitable for the extra broadband wire-grid polarizer. Furthermore, the optical performance of the polarizers could be improved by other methods including increasing the number of layers, which will be addressed later.
3.3 Influence of different fill ratios
Al wire-grid polarizers with different fill ratios (25%, 50%, 62.5%, and 87.5%) were simulated. The wire-grid thickness and period were kept at 40 and 80 nm. The transmittances of TM, TE modes and extinction ratios are shown in Fig. 8. With the increase in the fill ratio, the extinction ratios are increased while the transmission efficiencies are decreased. To obtain a high extinction ratio and proper transmission efficiency, polarizers with fill ratios between 50% and 62.5% are desirable.
3.4 Polarizers with F-P like dual-layer wire-grids
In general, nanowire-grid polarizers with a single layer cannot reach high optical performances. Therefore, other methods should be applied to improve their performance, such as increasing the number of layers. In 2000, Chou  realized a planar polarizer with a subwavelength dual-layer metal grating experimentally. Figure 9 shows a schematic diagram of the F-P (Fabry-Perot) like dual-layer wire-grid polarizers. In order to study the optical response of light propagating in the dual-layer wire-grid polarizers, calculations with different spacing between the layers were conducted. In the calculations, the thickness of the Al wires was set to be 40 nm with a fill ratio of 50% and a grid period of 80 nm. The simulation results are shown in Fig. 10. The extinctions of the dual-layer polarizers were much better than those of the single-layer polarizers. Furthermore, it is found that the transmittances of both TM and TE modes are dominated by strong oscillations that are similar to an F-P interferometer. This phenomenon can be explained by fact that the light transmitted through the first wire-grid layer was partially reflected by the second grating and it traveled back and forth between the two layers, leading to constructive or destructive interference at certain separations. The transmittance of a typical F-P interferometer with two identical interfaces is given by the following equations :
where T0 is the transmittance of the interface, R0 the reflectance of the interface, λ the light wavelength, d the spacing between the interfaces, n the refractive index between the layers, and m an integer. As shown in both equations, when the wavelength is increased the oscillation period of the transmittance is increased, which can be found in the simulation results shown in Fig. 10. From the figures, it is also found that when the spacing is 20 nm the polarizer will have better optical performances in the region from 0.3 to 5 µm.
3.5 A broadband nanowire-grid polarizer covering the UV, visible, and NIR regions
Based on the simulation results, a broadband nanowire-grid polarizer on a calcium fluoride (CaF2) substrate is proposed. Figure 11 shows the cross-section of the polarizer. On both surfaces of the substrate, there are dual-layer Al wire grids. The period of the grid is 80 nm with a fill ratio of 50%. The spacing between the two layers is 20 nm. The thickness is 40 nm. Since CaF2 is a transparent material in a broad band (from 0.25 to 7 µm) and has a very low refractive index (n=1.4), polarizers based on it will have a broad transparent spectrum and low reflection loss. The optical transmittances and extinction ratios calculated using the FDTD method are shown in Fig. 12(a). As seen in the results, the polarizer has an average extinction ratio higher than 70 dB and transmission efficiency over 64% in the wavelength range from 0.3 to 5 µm. In order to compare the difference between the F-P like dual-layer structure and the single-layer structure, we also performed the calculations of the single-layer structure on both surfaces of the substrate. The period of the grid is 80 nm with a fill ratio of 50% and a thickness of 40 nm. The calculation results are shown in Fig. 12(b). Although the transmission efficiency of the single-layer structure is higher than that of the F-P like dual-layer structure, the extinction ratio of the single-layer structure is much lower.
The optical performances of nanowire-grid polariers in UV-visible-NIR regions were studied using the FDTD method. Comparing with several different metals, Al wire-grid polarizers have better optical performances in the regions from 0.3 to 5 µm. The geometrical parameters, such as the grid period, the fill ratio, and the spacing, can greatly affect the optical performances of the polarizers. In the UV-visible-NIR regions, small grid periods, appropriate fill ratios between 50% and 62.5%, and small spacing between layers are the key factors to improve the optical performances of the wire-grid polarizers.
Based on the simulation results, a broadband nano-wire-grid polarizer was designed and simulated. The proposed polarizer has an average extinction ratio over 70 dB and transmission efficiency over 64% in a wide range from 0.3 to 5 µm. In general, nanowire-grid polarizers have ideal optical performances in the infrared region, as long as the substrate materials are transparent in this region. For wire-grid polarizers, therefore, how to fabricate wire grids as small as possible is the most important issue. Although this work was not intended to optimize all design parameters, it is expected that with the development of nanotechnology wire-grid polarizers will be widely used in the UV, visible, and infrared regions.
The authors are grateful to Y.X. Han and M. Zhao for their assistance. This work is financially supported by the National Science Foundation (Grant No. ECS 0629280) and Air Force Science Foundation under (Grant No. FA9550-05-1-0453).
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