Open Access
Add to BibSonomyAbstract
We explore plasmon-enhanced wire-gird polarizers (WGPs) to achieve improved polarimetric performance with more relaxed fabrication parameters compared to conventional WGP. A WGP designed with a blazed wire-grid profile was considered for plasmonic enhancement. The results show that a blazed WGP can achieve extremely high polarimetric extinction at a longer wire-grid period (Λ) compared to conventional WGP structure. Under the optimum geometrical parameters, a blazed WGP may attain an extinction ratio of over 40 dB at Λ = 800 nm, which may allow photolithography for fabrication. In contrast, conventional WGPs obtained comparable performance at Λ = 200 nm, requiring more difficult lithographic techniques. The study can therefore be of significant importance for WGPs to be more widely available for diverse applications.
© 2017 Optical Society of America
1. Introduction
A wire-grid polarizer (WGP) is a polarization-sensitive device based on wire-grids made of good conductor: light in transverse magnetic (TM) polarization mode has its electric field aligned in an orientation orthogonal to the wire-grid grating and is dominantly transmitted. In contrast, light in transverse electric (TE) polarization with an electric field parallel to the grating is largely absorbed and reflected and the field strength of a TE polarized light after transmission becomes much weaker than that of TM polarized light [1]. As a result, electric fields transmitted through a WGP oscillate orthogonally for the most part with respect to grating wires and hence TM-polarized, while reflected fields become TE-polarized. Light incident at an angle θin satisfies grating equation for momentum conservation so that the angle of diffracted light orders θout is given by
for ambient modes andfor substrate modes (ns: substrate refractive index) [2]. In Eqs. (1) and (2), free-space wave number of incident light k0 = 2π⁄λ (λ: wavelength of light). Grating vector Kg is given by Kg = 2π⁄Λ with Λ as the wire-grid period. m is an integer representing diffraction orders.A WGP has drawn significant attention since the fabrication by Bird and Parrish for near-infrared waveband in 1960 [3] because of the excellent polarization performance and planar structure that allows easy integration to other optical components. Therefore, a WGP has long been investigated in many aspects of optical science regarding, for example, fabrication issues [4–9], implementation and applications in the ultraviolet, infrared and terahertz waveband [3,10–20], and for imaging polarimetry [21], spectro-polarimetry [22,23], liquid-crystal display [24–27], projection display [28], fiber-optic sensor [29], and integration into a CMOS sensor [30]. A biologically inspired WGP based on DNA hybridization has been reported [31] and effects of surface roughness were explored [32]. Also, a WGP was analyzed on a rotating platform [33] and flexible surface [34–37]. Despite broad interests and even commercial availability, however, a WGP has not been widely used up to the full potential. This is mainly because extremely fine wire-grids need to be fabricated with a grid period typically on the order of λ/10 or even shorter in order to achieve high extinction of light polarization. In general, a WGP with a longer grid period performs worse in terms of polarization extinction and may suffer from Wood’s anomaly due to the excitation and redistribution of light power in the higher order diffraction modes [38,39], thus a small grating pitch represents improved performance as a WGP.
In this paper, we explore a plasmon-enhanced WGP: surface plasmon (SP) refers to a longitudinal electron density wave that is formed in metal/dielectric interface when incident photon is momentum-matched under the dispersion relation [40]:
In Eq. (3), ksp represents the momentum of SP. εm and εd are the permittivity of metal and dielectric ambience (εd = 1 in air ambiance). ω and c denote the angular frequency and speed of light in the free space. SP resonance (SPR) that arises from the momentum-matching described in Eq. (3) is highly polarization specific and takes place with TM polarized light. Therefore, SPR in its own right has been the basis for implementation of a polarizing device [41,42]. Nevertheless, direct combination of wire-grids and SPR has not been explicitly attempted for the following reasons: first, formation of propagating SP occurs over a narrowband of wavelength so that the combination can only be effective in the narrow waveband. On the other hand, grating on a nanometer scale may induce localization of SP. Although SP localization has been useful in many biosensing and imaging applications [43–50], the spectrum associated with localized SP is often quite broad, in which case polarization extinction tends not to be significant. Also, the momentum-matching between SP and incident photon represented by Eq. (3) is typically achieved by off-axis light incidence, while a WGP is often used under on-axis illumination and the momentum matching condition of Eq. (3) is not satisfied without exciting SP.Here, we aim to implement a SP-enhanced WGP with large grating pitch requirement to achieve given extinction performance, thereby more lenient fabrication processes. To attain this goal, blazed wire-grids are considered for a WGP. A blazed grating has been historically adopted to optimize grating efficiency in a specific diffraction order [51]. Fabrication of a blazed grating is a traditional yet perennial topic [2], which may be performed using e-beam lithography [52], molding [53], imprint lithography [54], and holography [55,56]. Despite the historic use of blazed grating, we find it rather surprising that a blazed surface profile has not been considered to improve the performance of WGPs. In this work, blazed surface was introduced to allow facilitated momentum matching for excitation of SP and enhanced polarization extinction, while the periodic grating structure implements a WGP. In other words, we consider blazed WGPs (bWGPs) for momentum matching from Eqs. (1) and (3) to come up with a first-principles plasmon resonance condition in terms of grating geometrical parameter
with a blazed angle θB. In order to confirm the feasibility, we compared the performance of a SP-enhanced WGP with that of a conventional WGP (cWGP) by evaluating the improvement in terms of the required grating pitch. The requirement on the grating pitch was used as a measure of the grating's fabrication complexity.2. Numerical method and model
2.1 Numerical method
For calculation of optical characteristics produced by WGP structures, rigorous coupled-wave analysis (RCWA) was employed with 50 spatial harmonics under periodic boundary conditions. RCWA has been used successfully to describe experimental properties of periodic and random optical structures [57–59]. The calculation is based on wavelength scanning in the visible waveband between λ = 400 and 600 nm with a step of Δλ = 1 nm at normal incidence.
2.2 Numerical model for plasmon-enhanced WGP
The schematic of the numerical model that we adopted for a plasmon-enhanced WGP is presented in Fig. 1. Wire-grid of gold in a blazed surface profile is assumed to be formed on a BK7 glass substrate in air ambiance. Despite strong absorption below λ = 550 nm, gold provides good polarimetric performance in the visible and NIR wavebands [60]. Wire-grid periods for numerical computation were selected to be Λ = 100 nm ~1 μm in a step of 100 nm for a blazed profile and Λ = 50 nm ~1 μm in a step of 50 nm for a conventional rectangular profile. For the simplicity of numerical computation, the blazed grating profile was approximated by five rectangular segments of identical thickness ( = dbWGP/5) and the total thickness depends on the period and the blaze angle, as shown in Fig. 1. The segment width is set to be Λ/6. Blaze angle θB is in general designed to match the resonance angle (θspr), i.e., θspr = θin at which Eq. (3) is satisfied, by adjusting the total thickness of blazed wire-grids to be dbWG = ΛtanθB. In air ambiance, θspr ≈45° at λ = 600 nm and 60° at λ = 400 nm for 50-nm thick gold thin film on a BK7 substrate, therefore θB was varied to be 30°, 45°, and 60°. Light illumination is assumed from substrate to ambiance to measure ambient modes in transmission. Incident light is normal to the substrate surface and only the zeroth order reflection or transmission (m = 0) is assumed to be collected by detectors. Polarization direction corresponding to TM polarized light is also shown in Fig. 1. TE polarization is in the direction into and out of paper.
Fig. 1 Schematic illustrations: (a) a blazed WGP (bWGP) with geometrical parameters. Segments to approximate a blazed surface profile are shown. For comparison, conventional WGP (cWGP) structure is presented in (b). cWGP is assumed to have a 50% fill factor. Polarization direction of TM polarized light is shown: TE polarization into and out-of-paper. In both cases, normal light incidence is assumed in the calculation as illustrated.
For comparison, control WGPs of conventional structure with a rectangular profile was also considered. For each bWGP structure, control cWGPs were assumed to have a 50% fill factor, i.e., metallic grid occupying half the period, and the thickness at dcWGP = ΛtanθB such that the cross-section area of control and bWGPs is identical. The thickness effectively makes the metallic volume of bWGP and cWGP structures identical per unit period thereby for the structureless absorption by metal to be equal. On the other hand, the grid period of control cWGPs was varied from Λ = 50 nm to 1 μm. Throughout computation, optical parameters of BK7 glass and gold were taken from [61] and fitted to a polynomial function for interpolation.
2.3 Metrics
Polarimetric performance of a WGP was evaluated based on two metrics: transmittance of preferred TM polarized light through a WGP (TR), i.e., TR = ITM between 0 and 100% and extinction ratio (ER), which is a measure of polarization extinction, defined as
ITM and ITE denote normalized light intensity for TM and TE polarization. ER defined in Eq. (5) ranges from 1 (no extinction) to ∞ (perfect extinction for TM polarization). ER may become smaller than 1 for low TM transmittance and is not desired.3. Results and discussion
3.1 Pitch analysis of polarimetric extinction by a bWGP
Figure 2 shows TR and ER for cWGP and bWGP at θB = 30°, 45°, and 60° under normal light incidence, as the wavelength and the wire-grid period are varied. While TR shows largely monotonous decreases with a longer period Λ for both cWGPs and bWGPs, the rate of decrease tends to be much higher in the case of bWGPs. Maximum of TR at each wire-grid period depends on the material dispersion n(λ) of substrate and metal, but was also affected by the excitation of higher-order diffraction. For example, the decreased TRmax at Λ = 350 and 550 nm is associated with the excitation of the ± 1st order in reflection and transmission, respectively (marked by arrows). ER, on the other hand, reaches a maximum when Λ = 200 nm (marked in blue arrow in Fig. 2(a)) for cWGPs. For bWGPs, the behavior of ER is drastically different in that it becomes a maximum at a much longer wire-grid period at Λ = 800 nm (denoted in red arrow in Fig. 2(b)). This is clear in Fig. 3, which presents the maximum TR and ER obtained over the entire spectral range (λ = 400 ~600 nm) at each wire-grid period. Quite visibly, TRmax decreases monotonously to a degree that is more obvious for a bWGP. Also note lower TRmax through a bWGP than through a cWGP. This is due mainly to the 100% fill factor of blazed surface which affects transmittance of TM polarized light. Interestingly, ERmax is in general higher with a bWGP, in particular at a longer period. By comparison, a cWGP showed the highest ERmax, i.e., ERmax = 13,040 ~41.15 dB, at Λ = 200 nm. For a bWGP, ERmax was slightly higher at ERmax = 15,740 ~41.97 dB (measured at λ = 600 nm): however, this is with Λ = 800 nm. This strongly suggests that the best polarimetric performance in terms of ER can be obtained using much easier lithographic techniques such as photolithography, if a blazed surface profile is employed. For comparable performance based on conventional structure, one needs to use more sophisticated therefore expensive equipment including electron-beam lithography, a significant advantage of blazed surface structure.
Fig. 2 (a) TR and (b) ER of conventional WGP (cWGP) and blazed WGP (bWGP) structures at normal incidence for λ = 400 ~600 nm and Λ = 100 ~1000 nm in a step of 100 nm. Blaze angle (θB) is changed: θB = 30° (left), 45° (middle), and 60° (right). Blue and red arrow marks the wire-grid period at which the maximum ER appears for cWGP and bWGP structure.
Fig. 3 (a) TR and (b) ER at a maximum obtained over λ = 400 ~600 nm at each wire-grid period (Λ) for θB = 30°, 45°, and 60°. TR and ER were fitted, respectively, to a rational and a Pearson VII function. Correlation coefficient R2 was higher than 99% and 85% for cWGP and bWGP.
For more quantitative comparison, we have presented relative TR (RTR) and ER (RER) defined respectively as RTR = TRbWGP/TRcWGP and RER = ERbWGP/ERcWGP in Fig. 4 at λ = 400, 500, and 600 nm. As we have seen in Figs. 2 and 3, RTR is lower than unity and tends to become lower with a longer period, indicating that a smaller number of photons may be available through a bWGP, which may affect an SNR in a negative way. In contrast, RER increases significantly with a grid period. Highest RER was RER = 41,880 at Λ = 1 μm. Note that RER in Fig. 4(b) is plotted on a logarithmic scale in the y-axis. In other words, for bWGPs, ER increases almost exponentially with Λ, while TR decreases more slowly as the grid period increases: this offers a performance optimum at a longer wire-grid period, thereby a WGP structure that is much more affordable with a more accessible fabrication possibilities. A different blazed surface profile may be considered to increase TR so as to avoid penalty in SNR, for example, blazing with a reduced fill factor < 100% appears to affect transmittance for an increase, albeit this may cause the fabrication to be less relaxed.
Fig. 4 (a) Relative TR (RTR) between cWGP and bWGP defined as RTR = TRbWGP/TRcWGP and (b) relative ER (RER) = ERbWGP/ERcWGP. A trend of decreasing RTR and exponentially increasing RER with a longer wire-grid period and larger blaze angle is clearly visible.
Throughout the results of Figs. 3 and 4, the highest ER in the range of θB considered was obtained at θB = 60°. Partly, this is due to more severe absorption of TE polarized light at a larger blaze angle. This also indicates that the momentum-matching between incident photon and SP described by Eq. (4) occurs at a higher momentum than in films due to enhancement associated with SP excitation and localization that may be induced. For more complete understanding, near-field distribution produced by a bWGP with Λ = 800 nm at λ = 600 nm and by a cWGP with Λ = 200 nm at λ = 400 nm is presented, respectively, in Figs. 5(a) and 5(b). This shows clear localization of evanescent light fields for both bWGP and cWGP: in the case of bWGP, the localization is much stronger in Fig. 5(a) than in a cWGP. TE polarized light, on the other hand, is largely extinguished as shown in Figs. 5(c) and 5(d), respectively for bWGP and cWGP structure. The strong localized field observed in a bWGP for TM polarized light may hint at enhanced polarimetric performance being directly associated with plasmonic localization of near-fields.
Fig. 5 Near-field distribution produced by WGPs: (a) bWGP (5 periods) with Λ = 800 nm for λ = 600 nm and (b) cWGP (20 periods) with Λ = 200 nm for λ = 400 nm for TM polarized light. (c) bWGP and (d) cWGP for TE polarization. These geometrical parameters produce the highest ER in each structure. For both bWGP and cWGP structures, θB = 60°.
3.2 Effects of higher-order diffraction on the performance of a bWGP
In the previous section, it was observed that the highest ER can be obtained at a longer wire-grid period using blazed surface. From Eqs. (1) and (2), and under normal incidence, the wire-grid period at which higher-order diffraction does not occur is given by Λ < λ⁄ns . Using given parameters, the wire-grid period that corresponds to optimum polarimetric extinction of a bWGP is longer than λ⁄ns, thus excitation of higher diffraction orders is accompanied with an optimum bWGP. In fact, the presence of higher-order diffraction is partly responsible for reduced transmittance through a bWGP. Figure 6 shows TR and ER of a bWGP with Λ = 800 nm and θB = 60° for ± 1st and 0th diffraction orders as well as the total intensity sum. For the 1st order, ER increases by up to 100 times with respect to the 0th order, although TR was shown to decrease by approximately 5 times. At Λ = 400 nm, ER was found to increase 6 times for the 1st order diffraction compared to the 0th order mode. If a sufficient number of photons are available, the result suggests that one may take advantage of a higher-order mode, rather than 0th order, for improved polarimetric extinction.
Fig. 6 (a) TR and (b) ER of a bWGP with Λ = 800 nm and θB = 60° for the ± 1st and the 0th diffraction orders. Also shown is the total transmittance.
4. Concluding remarks
In this study, we have investigated WGPs with a blazed surface profile for plasmonic field enhancement. For evaluation of polarimetric performance, TR and ER that can be achieved by a bWGP were calculated relative to a cWGP. It was shown that a bWGP can improve ER almost exponentially with a wire-grid period while TR may decrease more slowly. Maximum ER was obtained as 15,740 at Λ = 800 nm and θB = 60° for λ = 600 nm. Also, the highest RER was found to be 41,880 at Λ = 1 μm. If sufficient photon budget is available so that signal intensity after transmission is above noise (SNR > 1), bWGP may be a practical consideration. An optimum wire-grid period for bWGPs is much longer than that of a conventional structure and can thus allow much simplified and accessible fabrication processes.
Funding
National Research Foundation of Korea (NRF) grants (NRF-2012R1A4A1029061, 2015R1A2A1A10052826, NRF-2014R1A1A3049671); Yonsei University Future-Leading Research Initiative (2015–22–0147).
References and links
1. E. Hecht, Optics (Pearson, 2016), Chap. 8.
2. E. G. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997), Chap. 2 and 16.
3. G. R. Bird and M. Parrish, “The wire grid as a near-infrared polarizer,” J. Opt. Soc. Am. 50(9), 886–891 (1960). [CrossRef]
4. H. Tamada, T. Doumuki, T. Yamaguchi, and S. Matsumoto, “Al wire-grid polarizer using the s-polarization resonance effect at the 0.8-microm-wavelength band,” Opt. Lett. 22(6), 419–421 (1997). [CrossRef] [PubMed]
5. X. J. Yu and H. S. Kwok, “Optical wire-grid polarizers at oblique angles of incidence,” J. Appl. Phys. 93(8), 4407–4412 (2003). [CrossRef]
6. S. W. Ahn, K. D. Lee, J. S. Kim, S. H. Kim, J. D. Park, S. H. Lee, and P. W. Yoon, “Fabrication of a 50 nm half-pitch wire grid polarizer using nanoimprint lithography,” Nanotechnology 16(9), 1874–1877 (2005). [CrossRef]
7. J. J. Wang, L. Chen, X. Liu, P. Sciortino, F. Liu, F. Walters, and X. Deng, “30-nm-wide aluminum nanowire grid for ultrahigh contrast and transmittance polarizers made by UV-nanoimprint lithography,” Appl. Phys. Lett. 89(14), 141105 (2006). [CrossRef]
8. S. H. Ahn, J. S. Kim, and L. J. Guo, “Bilayer metal wire-grid polarizer fabricated by roll-to-roll nanoimprint lithography on flexible plastic substrate,” J. Vac. Sci. Technol. B 25(6), 2388–2391 (2007). [CrossRef]
9. F. Schlachter, J. Barnett, U. Plachetka, C. Nowak, M. Messerschmidt, M. Thesen, and H. Kurz, “UV-NIL based nanostructuring of aluminum using a novel organic imprint resist demonstrated for 100nm half-pitch wire grid polarizer,” Microelectron. Eng. 155, 118–121 (2016). [CrossRef]
10. J. B. Young, H. A. Graham, and E. W. Peterson, “Wire grid infrared polarizer,” Appl. Opt. 4(8), 1023–1026 (1965). [CrossRef]
11. I. Yamada, K. Kintaka, J. Nishii, S. Akioka, Y. Yamagishi, and M. Saito, “Mid-infrared wire-grid polarizer with silicides,” Opt. Lett. 33(3), 258–260 (2008). [CrossRef] [PubMed]
12. I. Yamada, K. Takano, M. Hangyo, M. Saito, and W. Watanabe, “Terahertz wire-grid polarizers with micrometer-pitch Al gratings,” Opt. Lett. 34(3), 274–276 (2009). [CrossRef] [PubMed]
13. T. Weber, T. Käsebier, E. B. Kley, and A. Tünnermann, “Broadband iridium wire grid polarizer for UV applications,” Opt. Lett. 36(4), 445–447 (2011). [CrossRef] [PubMed]
14. K. Takano, H. Yokoyama, A. Ichii, I. Morimoto, and M. Hangyo, “Wire-grid polarizer sheet in the terahertz region fabricated by nanoimprint technology,” Opt. Lett. 36(14), 2665–2667 (2011). [CrossRef] [PubMed]
15. I. Yamada, N. Yamashita, K. Tani, T. Einishi, M. Saito, K. Fukumi, and J. Nishii, “Fabrication of a mid-IR wire-grid polarizer by direct imprinting on chalcogenide glass,” Opt. Lett. 36(19), 3882–3884 (2011). [CrossRef] [PubMed]
16. T. Weber, T. Käsebier, M. Helgert, E. B. Kley, and A. Tünnermann, “Tungsten wire grid polarizer for applications in the DUV spectral range,” Appl. Opt. 51(16), 3224–3227 (2012). [CrossRef] [PubMed]
17. J. S. Cetnar, J. R. Middendorf, and E. R. Brown, “Extraordinary optical transmission and extinction in a Terahertz wire-grid polarizer,” Appl. Phys. Lett. 100(23), 231912 (2012). [CrossRef]
18. Z. Huang, H. Park, E. P. Parrott, H. P. Chan, and E. Pickwell-MacPherson, “Robust thin-film wire-grid THz polarizer fabricated via a low-cost approach,” IEEE Photonics Technol. Lett. 25(1), 81–84 (2013). [CrossRef]
19. K. Asano, S. Yokoyama, A. Kemmochi, and T. Yatagai, “Fabrication and characterization of a deep ultraviolet wire grid polarizer with a chromium-oxide subwavelength grating,” Appl. Opt. 53(13), 2942–2948 (2014). [CrossRef] [PubMed]
20. T. Weber, S. Kroker, T. Käsebier, E. B. Kley, and A. Tünnermann, “Silicon wire grid polarizer for ultraviolet applications,” Appl. Opt. 53(34), 8140–8144 (2014). [CrossRef] [PubMed]
21. D. Kim, “Performance uniformity analysis of a wire-grid polarizer in imaging polarimetry,” Appl. Opt. 44(26), 5398–5402 (2005). [CrossRef] [PubMed]
22. D. Kim, C. Warde, K. Vaccaro, and C. Woods, “Imaging multispectral polarimetric sensor: single-pixel design, fabrication, and characterization,” Appl. Opt. 42(19), 3756–3764 (2003). [CrossRef] [PubMed]
23. D. Kim and K. Burke, “Design of a grating-based thin-film filter for broadband spectropolarimetry,” Appl. Opt. 42(31), 6321–6326 (2003). [CrossRef] [PubMed]
24. M. Xu, H. Urbach, D. de Boer, and H. Cornelissen, “Wire-grid diffraction gratings used as polarizing beam splitter for visible light and applied in liquid crystal on silicon,” Opt. Express 13(7), 2303–2320 (2005). [CrossRef] [PubMed]
25. S. H. Kim, J. D. Park, and K. D. Lee, “Fabrication of a nano-wire grid polarizer for brightness enhancement in liquid crystal display,” Nanotechnology 17(17), 4436–4438 (2006). [CrossRef]
26. Z. Ge, T. X. Wu, and S. T. Wu, “Single cell gap and wide-view transflective liquid crystal display using fringe field switching and embedded wire grid polarizer,” Appl. Phys. Lett. 92(5), 051109 (2008). [CrossRef]
27. J.-S. Seo, T.-E. Yeom, and J.-H. Ko, “Experimental and simulation study of the optical performances of a wide grid polarizer as a luminance enhancement film for LCD backlight applications,” J. Opt. Soc. Korea 16(2), 151–156 (2012). [CrossRef]
28. X.-J. Yu and H.-S. Kwok, “Application of wire-grid polarizers to projection displays,” Appl. Opt. 42(31), 6335–6341 (2003). [CrossRef] [PubMed]
29. J. Feng, Y. Zhao, X. W. Lin, W. Hu, F. Xu, and Y. Q. Lu, “A transflective nano-wire grid polarizer based fiber-optic sensor,” Sensors (Basel) 11(12), 2488–2495 (2011). [CrossRef] [PubMed]
30. K. Sasagawa, S. Shishido, K. Ando, H. Matsuoka, T. Noda, T. Tokuda, K. Kakiuchi, and J. Ohta, “Image sensor pixel with on-chip high extinction ratio polarizer based on 65-nm standard CMOS technology,” Opt. Express 21(9), 11132–11140 (2013). [CrossRef] [PubMed]
31. H. Yu, Y. Oh, S. Kim, S. H. Song, and D. Kim, “Polarization-extinction-based detection of DNA hybridization in situ using a nanoparticle wire-grid polarizer,” Opt. Lett. 37(18), 3867–3869 (2012). [CrossRef] [PubMed]
32. H. Ryu, S. Joon Yoon, and D. Kim, “Influence of surface roughness on the polarimetric characteristics of a wire-grid grating polarizer,” Appl. Opt. 47(30), 5715–5721 (2008). [CrossRef] [PubMed]
33. D. Kim, “Polarization characteristics of a wire-grid polarizer in a rotating platform,” Appl. Opt. 44(8), 1366–1371 (2005). [CrossRef] [PubMed]
34. D. Kim and E. Sim, “Segmented coupled-wave analysis of a curved wire-grid polarizer,” J. Opt. Soc. Am. A 25(3), 558–565 (2008). [CrossRef] [PubMed]
35. F. Meng, G. Luo, I. Maximov, L. Montelius, J. Chu, and H. Xu, “Fabrication and characterization of bilayer metal wire-grid polarizer using nanoimprint lithography on flexible plastic substrate,” Microelectron. Eng. 88(10), 3108–3112 (2011). [CrossRef]
36. Y. J. Shin, C. Pina-Hernandez, Y. K. Wu, J. G. Ok, and L. J. Guo, “Facile route of flexible wire grid polarizer fabrication by angled-evaporations of aluminum on two sidewalls of an imprinted nanograting,” Nanotechnology 23(34), 344018 (2012). [CrossRef] [PubMed]
37. A. Ferraro, D. C. Zografopoulos, M. Missori, M. Peccianti, R. Caputo, and R. Beccherelli, “Flexible terahertz wire grid polarizer with high extinction ratio and low loss,” Opt. Lett. 41(9), 2009–2012 (2016). [CrossRef] [PubMed]
38. R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Philos. Mag. 4(21), 396–402 (1902). [CrossRef]
39. A. Hessel and A. A. Oliner, “A new theory of Wood’s anomalies on optical gratings,” Appl. Opt. 4(10), 1275–1297 (1965). [CrossRef]
40. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988), Ch. 2 Surface Plasmons on Smooth Surfaces.
41. A. Lehmuskero, B. Bai, P. Vahimaa, and M. Kuittinen, “Wire-grid polarizers in the volume plasmon region,” Opt. Express 17(7), 5481–5489 (2009). [CrossRef] [PubMed]
42. C. H. Dong, C. L. Zou, X. F. Ren, G. C. Guo, and F. W. Sun, “In-line high efficient fiber polarizer based on surface plasmon,” Appl. Phys. Lett. 100(4), 041104 (2012). [CrossRef]
43. S. J. Yoon and D. Kim, “Target dependence of the sensitivity in periodic nanowire-based localized surface plasmon resonance biosensors,” J. Opt. Soc. Am. A 25(3), 725–735 (2008). [CrossRef] [PubMed]
44. K. Kim, D. J. Kim, E.-J. Cho, J.-S. Suh, Y.-M. Huh, and D. Kim, “Nanograting-based plasmon enhancement for total internal reflection fluorescence microscopy of live cells,” Nanotechnology 20(1), 015202 (2009). [CrossRef] [PubMed]
45. S. Moon, D. J. Kim, K. Kim, D. Kim, H. Lee, K. Lee, and S. Haam, “Surface-enhanced plasmon resonance detection of nanoparticle-conjugated DNA hybridization,” Appl. Opt. 49(3), 484–491 (2010). [CrossRef] [PubMed]
46. K. Kim, Y. Oh, W. Lee, and D. Kim, “Plasmonics-based spatially activated light microscopy for super-resolution imaging of molecular fluorescence,” Opt. Lett. 35(20), 3501–3503 (2010). [CrossRef] [PubMed]
47. Y. Oh, W. Lee, and D. Kim, “Colocalization of gold nanoparticle-conjugated DNA hybridization for enhanced surface plasmon detection using nanograting antennas,” Opt. Lett. 36(8), 1353–1355 (2011). [CrossRef] [PubMed]
48. S. Moon, Y. Kim, Y. Oh, H. Lee, H. C. Kim, K. Lee, and D. Kim, “Grating-based surface plasmon resonance detection of core-shell nanoparticle mediated DNA hybridization,” Biosens. Bioelectron. 32(1), 141–147 (2012). [CrossRef] [PubMed]
49. J. Choi, K. Kim, Y. Oh, A. L. Kim, S. Y. Kim, J.-S. Shin, and D. Kim, “Extraordinary transmission based plasmonic nanoarrays for axially super-resolved cell imaging,” Adv. Opt. Mater. 2(1), 48–55 (2014). [CrossRef]
50. W. Lee, Y. Kinosita, Y. Oh, N. Mikami, H. Yang, M. Miyata, T. Nishizaka, and D. Kim, “Three-dimensional superlocalization imaging of gliding Mycoplasma mobile by extraordinary light transmission through arrayed nanoholes,” ACS Nano 9(11), 10896–10908 (2015). [CrossRef] [PubMed]
51. E. G. Loewen, M. Nevière, and D. Maystre, “Grating efficiency theory as it applies to blazed and holographic gratings,” Appl. Opt. 16(10), 2711–2721 (1977). [CrossRef] [PubMed]
52. T. Fujita, H. Nishihara, and J. Koyama, “Blazed gratings and Fresnel lenses fabricated by electron-beam lithography,” Opt. Lett. 7(12), 578–580 (1982). [CrossRef] [PubMed]
53. Y. Xia, E. Kim, X. M. Zhao, J. A. Rogers, M. Prentiss, and G. M. Whitesides, “Complex optical surfaces formed by replica molding against elastomeric masters,” Science 273(5273), 347–349 (1996). [CrossRef] [PubMed]
54. C. H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of sawtooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21(6), 2755–2759 (2003). [CrossRef]
55. N. K. Sheridon, “Production of blazed holograms,” Appl. Phys. Lett. 12(9), 316–318 (1968). [CrossRef]
56. N. Kawatsuki, E. Nishioka, A. Emoto, H. Ono, and M. Kondo, “Blazed surface relief formation in azobenzene-containing polymeric films by asymmetric polarization holography,” Appl. Phys. Express 5(4), 041601 (2012). [CrossRef]
57. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005). [CrossRef] [PubMed]
58. K. M. Byun, S. J. Yoon, D. Kim, and S. J. Kim, “Sensitivity analysis of a nanowire-based surface plasmon resonance biosensor in the presence of surface roughness,” J. Opt. Soc. Am. A 24(2), 522–529 (2007). [CrossRef] [PubMed]
59. Y. J. Lee, D. S. Ruby, D. W. Peters, B. B. McKenzie, and J. W. Hsu, “ZnO nanostructures as efficient antireflection layers in solar cells,” Nano Lett. 8(5), 1501–1505 (2008). [CrossRef] [PubMed]
60. Y. Ekinci, H. H. Solak, C. David, and H. Sigg, “Bilayer Al wire-grids as broadband and high-performance polarizers,” Opt. Express 14(6), 2323–2334 (2006). [CrossRef] [PubMed]
61. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
