Nanogap Engineering for Enhanced Transmission of Wire Grid Polarizers in Mid-Wavelength Infrared Region

Wire-grid polarizers (WGPs) have been widely used in various fields, such as polarimetry, imaging, display, spectroscopy, and optical isolation. However, conventional WGPs used in diverse mid-wavelength infrared (MWIR) applications show high reflection losses, which intrinsically arise from high refractive indices of their IR-transmitting substrates, such as silicon (Si) and germanium (Ge). This study demonstrated the enhanced transmittance of a transverse magnetic (TM) wave that surpassed ~80% over the entire MWIR range from 3000 to 5000 nm in a narrow air gap of a WGP, where aluminum (Al) was selectively deposited on a nanopatterned Si substrate using an oblique angle deposition method. Moreover, a higher TM wave transmittance was achieved by reducing the air gaps of the WGPs in the nanopatterns, which were distinctly different from the traditional WGPs comprising metal wires patterned directly on a flat substrate. A finite-difference time-domain simulation was performed to investigate optical properties of the proposed WGPs, which showed that the electric field in the air nanogap was remarkably enhanced. The characteristic performances were further investigated using a combination of an effective medium approximation and an admittance diagram, revealing that the broadband transmission enhancement could be attributed to a combined effect of a strong electric field and a better admittance matching. The approach and results described in this paper hold promise for the design and the fabrication of high-quality WGPs, as well as their numerous applications.


S1. Six-layer anti-reflection (AR) coating
Figure S1 (a) shows the schematic diagram of an exemplary 6-layer anti-reflection (AR) coating consisting of YF3 and ZnS with optimized thicknesses for eliminating the reflection occurring at a back surface. Transmission spectra of a bare Si substrate with (red) and without (black) the designed AR coating are provided in Figure S1 (b). The reflection without the AR coating from a one surface of the Si substrate would be about 30% ( Figure S1 (b) black solid line), which can be greatly suppressed by the optimized AR coating ( Figure S1 (b) red solid line). The AR coated Si substrate presents 99.6% of an average transmittance over a wide wavelength ranging from 3000 nm to 5000 nm. Any other AR approaches would also be suitable for the elimination of the reflection occurring at the bottom surface of the Si substrate.

S2. FDTD calculation results of the fsWGP
It has been found that the transmittance of the fsWGP structure ([air|Al nanowires|Si substrate]) for TM polarization decreases as the air gap decreases, which is different from what the psWGP structure ([air|Al nanowires|Si nanopatterns|Si substrate]) presents in Fig. 2(C). The psWGP structure with the air gap of 6 nm shows the average TM transmittance of 81% in the MWIR region, which is much higher than the average TM transmittance (46%) of the fsWGP structure with the same air gap (the surface reflection loss around 30% at the bottom part of the Si substrate is not considered). The TM transmittance of the fsWGP structure is pretty low over a wide wavelength range even with a large air gap of 30 nm, which indicates that anti-reflective (AR) coatings at the bottom of the Al nanowires are typically required to improve the transmittance of the conventional WGP structure (i.e., fsWGP) [RS1]. As can be seen from the cross-sectional SEM image in Fig. S3 (a), the cross-section of real Al-nanowires on top of Si-nanopatterns in the fabricated psWGP structure looks like a half-elliptic shape rather than a rectangle of ideal Al-nanowires and overfills in part the Si-nanopatterns. The half-elliptic shape that has been observed in other applications seems to be due to the intrinsic property of a thin film growth in the oblique angle deposition [RS2]. Although the psWGP structure looks like a mushroom in practice, it has been found that a difference between the TM transmittances attained from both the ellipsoidal and the rectangular models is quite negligible as shown in Fig. S3 (b), where the difference between the two curves is less than 1% (for the case of the psWGP with the air gap of 6 nm). Therefore, all the simulations in the main text were carried out by using the rectangular model for the simplicity. This originates from the Si-nanopatterns on a bare Si substrate. A line spacing of the Si-nanopatterns is wider than three. This could be happened in the stitching process of the spacer patterning technique of the Si-nanopatterns. As it has been found to be pretty difficult to fabricate the Si nanopatterns with a linewidth of 50 nm in a highly ordered manner over the large area, a top-down fabrication method based on stitchless stepper lithography and repetitive pattern downscaling technology was used for the fabrication of the Si nanopatterned substrate. After preparing the Si nanopatterns with a period of 100 nm, the pattern pitch was further reduced by the initial nanopatterns exploiting the spacer patterning technology. Details on the fabrication technique can be found in a reference RS3. Figures S4 (a) -(c) present schematic diagrams of the psWGP structures with the equal air gap (all air gaps are 6 nm, (a)), the unequal air gap (6 nm, 6 nm, 6 nm, 20 nm, (b)), and (6 nm, 8 nm, 7 nm, 20 nm, (c)). As is seen from the Figure 1 (e), a 20 nm gap exists and three nanopatterns whose spacing is close to 6 nm are repeated within a unit cell having a pitch of 400 nm, which is different from the structure dimension in the simulation where a 6 nm air gap and a 100 nm pitch are used. Figure S4  and 20 nm in a unit cell (blue solid line) at normal incidence are displayed. Since a trivial discrepancy between the three curves, which is about 3% averaged from the MWIR range (3000 nm -5000 nm), is observed, all the simulations with the period of 100 nm and the air gap of 6 nm were carried out to explore the optical properties of the psWGPs in the main text.

S5. Additional EMA analysis results
in Figure 2(b) of the main text, which corresponds to the complex refractive index of the anisotropic uniaxial Al-nanowires layer for TM polarization, shows a very small imaginary part, whereas in Figure S5 of the SI that is the anisotropic uniaxial refractive index of the Al-nanowires for TE polarization shows a very high imaginary part as compared to a real part. This implies that the Al nanowires function as the dielectric (metal) for TM (TE) polarization, which can transmit (reflect) the incident light of TM (TE) polarization.

Figure S6. Complex refractive index ( ) of an anisotropic uniaxial Al-nanowires layer for TE
polarization at 4000 nm as a function of the air gap, calculated by using the EMA method.
In Figure S6  Simulation results of TM transmittances of the psWGP structure with 70-nm Al height obtained from FDTD (black) and EMA (red) methods, along with some measured data points, at normal incidence (0˚) and oblique incidence (45˚) are provided in Figure S7. In the EMA method, optical transmittances of the psWGPs are calculated by approximating each structure to an anisotropic uniaxial thin film according to the air gap of the Al structure. FDTD results are used as a reference. A negligible discrepancy between the simulation results attained by using FDTD and EMA is observed, which are in good agreement with the measured results. Similarly, admittance of an EMA Al nanowire layer starts from as shown in Figure S9 which is the same as Eq. (7) in the main text.