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Wavelength-Independent Optical Polarizer Based on Metallic Nanowire Arrays Volume 3, Number 6, December 2011 Qiaoqiang Gan Haifeng Hu Huina Xu Ke Liu Suhua Jiang Alexander N. Cartwright

DOI: 10.1109/JPHOT.2011.2173478 1943-0655/$26.00 ©2011 IEEE

IEEE Photonics Journal

Wavelength-Independent Optical Polarizer

Wavelength-Independent Optical Polarizer Based on Metallic Nanowire Arrays Qiaoqiang Gan, 1 Haifeng Hu, 1;2 Huina Xu, 1 Ke Liu, 1 Suhua Jiang, 3 and Alexander N. Cartwright 1 1

Department of Electrical Engineering, The State University of New York at Buffalo, Buffalo, NY 14260 USA 2 Institute of Semiconductors, Chinese Academy of Science, Beijing 100083, China 3 Material Science Department, Fudan University, Shanghai 200433, China DOI: 10.1109/JPHOT.2011.2173478 1943-0655/$26.00 Ó2011 IEEE

Manuscript received September 23, 2011; revised October 19, 2011; accepted October 19, 2011. Date of publication October 26, 2011; date of current version November 14, 2011. Q. Gan was supported by the National Science Foundation under Award 1128086. S. Jiang was supported by the National Natural Science Foundation of China under Award 51001029. A. Cartwright was supported by the National Institutes of Health under NIBIB 5R21EB009506 and the U.S. Air Force Office of Scientific Research Award FA95501010216. This paper has supplementary downloadable material available at http:// ieeexplore.ieee.org, provided by the authors. Corresponding author: Q. Gan and (e-mail: qqgan@ buffalo.edu).

Abstract: We propose a design of high-performance wavelength-independent optical polarizer for ultraviolet/visible to terahertz (THz) spectral region based on metallic nanowire (NW) arrays on ultrathin substrates, which can reduce the influence of the substrate material. This NW-based polarizer is anticipated to have far-reaching impact on numerous existing devices including polarimetric imagers in the mid-infrared and THz domains, complementary metal–oxide semiconductor (CMOS) imagers, and DVD/CD players. Index Terms: Polarizer, nanowire, metallic optics, nanomembrane.

1. Introduction Over the past two decades, the field of nanowire (NW)-based structures has become one of the most active research areas within the nanoscience community. Extensive efforts have been made in developing new fundamental science as well as applications, including NW electronics [1], NW photonics and optoelectronics [2], [3], NWs for energy conversion and storage [4], and life science [5]. However, people working in this field usually addressed the Byes-or-no[ question when proposing various potential applications for NWs by emphasizing the novelty but paid less attention to the Bbetter-or-worse[ question [5]. To further reveal the advantages and potential of NWs, it is critical to achieve equivalent or even better performance using NW structures compared with other technologies or corresponding commercially available products. Optical polarizers are important optical elements for spectroscopic analysis of sample orientation, polarimetric imaging [6], measuring thin films on reflective surfaces, etc. However, the working spectral ranges of different polarizers are usually limited by the optical properties of their substrate materials. There is currently no device in the market that can work for an ultrabroad wavelength range from the ultraviolet (UV) or visible to terahertz (THz) or even to the millimeter-wave domain. In this paper, we propose the design of a high-performance wavelength-independent optical polarizer based on periodic metallic NW arrays. Theoretical analysis will be performed to reveal the outstanding polarization properties of free-standing NW arrays. To mimic the optical properties of

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Fig. 1. Conceptual illustration of a free-standing NW polarization filter.

free-standing NW arrays, we then propose to employ ultrathin layers (e.g., dielectric nanomembranes) as the substrate to realize an ultrabroadband optical polarizer from the UV/visible to the THz domain. Theoretical analysis and preliminary experimental results demonstrate the potential of this structure to work as a high-performance optical polarizer that does not currently exist commercially but is critical for overcoming the working spectral range barriers of conventional technologies. This NW-based polarizer is anticipated to have far-reaching impact on numerous existing devices including polarimetric imagers [7] in mid-infrared (mid-IR) and THz domains [8], complementary metal–oxide semiconductor (CMOS) imagers, and DVD/CD players. This paper is organized as follows. In Section 2, we first employ the coupled mode method (CMM) to investigate the polarization-dependent transmission properties of free-standing metallic NW arrays. Design principles and underlying physics will be analyzed systematically. In Section 3, we fabricate a metallic NW grating on a glass substrate and characterize its broadband polarization performance which is limited by the substrate material. Then, in Section 4, we propose to employ ultrathin layers (e.g., dielectric nanomembranes) as the substrate to minimize the influence of the substrate material. CMM modeling outlined in Section 2 will be developed to further investigate the polarization-dependent transmission properties through NW arrays on these ultrathin substrates. Finally, we draw our conclusions in Section 5 and introduce potential applications of the proposed wavelength-independent optical polarizer.

2. Proposal of a Wavelength-Independent Polarizer Based on Free-Standing NW Arrays 2.1. CMM Formalism We first analyze the transmission properties of free-standing metallic NW arrays to explore their potential for ultrabroadband optical polarizer, which is illustrated in Fig. 1 conceptually. In our proposed structure, the period of the NW arrays is P, the width of the slit is w , and the height of the NW array is t. Here, we employ CMM [9] to calculate its polarization-dependent optical transmission. Under this formalism, the electromagnetic (EM) field can be expressed as a linear combination of a waveguide mode in the slit region and a plane wave in the free space outside the NW array, respectively. The parallel components of the EM field should be matched at the top and bottom interfaces of the NW array. Using the periodic boundary condition, we only need to deal with a unit cell instead of the infinite array for the entire NW structure. The basic set of linear equations for the CMM can be written as X X 0 0 ðG Þ E þ G E GV E0 ¼ I ; G E0 þ G E0 GV E ¼ 0 (1) 6¼


6¼

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where E and E 0 are the modal amplitudes of the electric field at the two interfaces of the NW array. When the width of the slit is much smaller than the wavelength, only the fundamental waveguide mode in the slit needs to be considered ( ¼ 0 for TM mode and ¼ 1 for TE mode) because the contribution of the higher-order modes to the transmission are negligible [10]. By considering the surface-impedance boundary conditions and the effective index mode calculation, the formalism has been used to interpret the physics of the optical transmission associated with real metals [11]. In (1), I is the illumination term, and is related to the bouncing back and forth of the EM field inside the slits. GV is the coupling between the two ends of the slit, and G represents the coupling coefficient from ji to ji. The detailed expressions of these terms are given by [9, eqs. A8–A9]. To solve (1), the primary task is to calculate the overlap integral between the fundamental mode ji and the plane wave jk i. The parallel components of the plane wave vectors are determined by the Floquet condition (i.e., Bloch condition/periodical boundary condition) and given by k ¼ k0 þ 2m=P, where m is an integer. In the case of s-polarized incident light, only TE modes exist in the slit. Under the single mode approximation, the overlap integral is written as rffiffiffiffiffiffiffi w ½sincðkw =2 þ =2Þ þ sincðkw =2 =2Þ: (2) h ¼ 1jksi ¼ 2P In (2), the function sincðx Þ ¼ sinðx Þ=x . Similar to the s-polarization case, when the incident light is p-polarized, the fundamental TM mode is j ¼ 0i, and the overlap integral is pffiffiffiffiffiffiffiffiffiffi h ¼ 0jkpi ¼ w =P sincðkw =2Þ: (3) For a perfect electric conductor (PEC), the propagation constant of the waveguide mode in the slit qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi is qz ¼ k!2 ð=w Þ2 . However, for a real metal with finite dielectric constants qz should be obtained by solving the following transcendental equations (see (4) and (5) below) using waveguide mode theory [11]: ffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 k 2" q M z ! 2 w =2 ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðfor TE modesÞ (4) tan k!2 "0 qz 2 k!2 "0 qz pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 k 2" "0 qz ! M 2 2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ðfor TM modesÞ: (5) tanh qz k! "0 w =2 ¼ 2 "M qz k!2 "0 In (4) and (5), k! is the vacuum wave vector and "0 and "M are the dielectric constants of vacuum and the metal, respectively. Based on the CMM formalism outlined above, the transmission efficiency K through the NW array can be calculated by XX XZZ Y~k0 K ¼ E0 E0 d~ k k ih~ k ji: (6) 2 hj~ 0 1 þ Z Y s ~ SðPÞ k

2.2. Polarization Filter Performance of Free-Standing NW Arrays In this section, we employ the CMM modeling to analyze the optical transmission through the free-standing NW arrays in the spectral range of 0:3 m 100 m. In addition, two important parameters will also be analyzed based on the numerical results to evaluate the performance of the polarizer, i.e., degree of polarization (DOP) ¼ ðK1 K2 Þ=ðK1 þ K2 Þ and extinction ratio (ER) ¼ K1 =2K2 . Here, K1 and K2 are transmission efficiencies for normally incident TM and TE polarized light, respectively. Period-dependence: As shown in Fig. 2(a)–(d), when the period of the NW array is tuned from 100 nm to 400 nm ðwidth ¼ 70 nm and t ¼ 100 nmÞ, the transmission efficiency for the normal incidence is calculated to vary from 102 107 for s-polarized light [see Fig. 2(a)]. While for p-polarized light, when the period is 100 nm (i.e., the incident wavelength is much larger than the period), the transmission efficiency is higher than 89% in the spectral range of 0.3–2 m, and


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Fig. 2. Period dependence of the transmission spectrum through NW arrays for (a) s-polarization and for (b) p-polarization, when h ¼ 100 nm and width ¼ 70 nm. Thickness dependence of the transmission spectrum through the NW arrays for (e) s-polarization and for (f) p-polarization, when the Period ¼ 140 nm and width ¼ 70 nm. Angle dependence of the transmission spectrum through the NW arrays for (i) s-polarization and for (j) p-polarization, when the Period ¼ 140 nm, h ¼ 200 nm, and width ¼ 70 nm. The optical constants from [17] for the Al material in this spectral region is employed in our calculation.

higher than 99% in the mid-IR and THz region (2–100 m) due to the fact that the metal loss is negligible in the mid-IR and THz regions. It should be noted that in the short wavelength region several narrow transmission peaks can be observed [see the black line in the inset of Fig. 2(b)] due to the excitation of surface plasmons at the surfaces of metal films [10], [12], which is undesirable for application as a wavelength-independent optical polarizer. Moreover, the transmission minima that appear in Fig. 2(b) are attributed to the Rayleigh–Wood anomaly [see the white line in the inset of Fig. 2(b)]. Along this line, the transmission for the TM case may even be lower than the transmission for the TE case. The DOP will become negative as shown in Fig. 2(c), and the ER will become extremely low ðG 102 Þ. Consequently, in order to achieve excellent broadband polarizer performance, the period of the NW array should be chosen in the region of 100 nm 150 nm. The DOP for structures with various periods is plotted in Fig. 2(c), which is larger than 99.99% over a wide range, indicating that the polarization performance has great tolerance to the period of the NW array. As shown in Fig. 2(d), an ER of 102 could be achieved by reducing the period of the NW array to 100 150 nm. Remarkably, the ER is higher than 105 in the mid-IR and THz regions ð2 100 mÞ. Thickness-dependence: Similarly, in Fig. 2(e)–(h), we numerically tune the thickness of the NW array layer using the CMM formalism ðP ¼ 140 nm and width ¼ 70 nmÞ. One can see that the transmission of s-polarized normal incident light decreases rapidly from 102 to 1010 as the thickness increases. This strong thickness dependence is due to the cutoff fundamental mode when G 2w . In this case, electric and magnetic field components decay rapidly in the slit area. Consider that the transmission is determined by the magnitude of the field reaching the other end of


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Fig. 3. Transmission spectra of TE and TM polarized light through the free-standing nanowire array by RCWA and CMM. The period and width of the Al nanowire are 140 nm and 70 nm, respectively. The thickness of the metal layer is 180 nm.

the slit, the TE-mode transmission is therefore suppressed significantly. For the case of p-polarized light, Fabry–Pe´rot (FP) resonance will occur in the UV/visible spectral region, which will lead to oscillations in the transmission spectrum. As shown in Fig. 2(f), one can see that the transmission peak is associated with the FP resonance condition ð ¼ 2nÞ [see the white dots in Fig. 2(f)]. The DOP still remains 9 99.9% over a wide thickness range (i.e., t can be tuned from 130 nm to 300 nm) [see Fig. 2(g)]. However, as shown in Fig. 2(h), if the thickness is decreased to the 20–100 nm range, the ER of the NW polarizer is only in the 101 103 level, which cannot compete with commercial products (usually in 105 level) [13]–[15]. Consequently, to achieve an equivalent or even better performance compared with the currently available commercial products, the thickness of the metallic NW layer should be larger than 150 nm [with an extinction ratio 9 104 ; see Fig. 2(h)]. Angle-tolerance: Besides the polarization-dependence for normal incidence, the angular tolerance of the metallic NW array is an important figure of merit to evaluate its performance as a practical polarization filter. As shown in Fig. 2(i), for the s-polarized incidence, the transmission drops rapidly as the incident angle increases. At large incident angles (e.g., 9 70 ), the overlap between the zero-order diffraction plane wave and the fundamental mode ðhjk0 0 iÞ becomes weak, resulting in a significantly suppressed transmission. For the p-polarized incidence shown in Fig. 2(j), the transmission remains higher than 80% when the incident angle is smaller than 70 in the mid-IR and THz domains, demonstrating the wide angle tolerance of the proposed free-standing NW-based polarizer. One can see that the DOP remains larger than 99.8% [see Fig. 2(k)], and an ER higher than 105 is achieved over almost the entire incident angle range [see Fig. 2(l)].

2.3. Rigorous Coupled-Wave Analysis Modeling of the Polarization Filter Performance To validate the theoretical prediction based on the CMM formalism shown in Section 2.2, we then perform numerical simulation to model the transmission spectra through an aluminum (Al) NW array using the rigorous coupled-wave analysis (RCWA) method1 (see Fig. S1 in the supplementary material). The optical constants of Al material from 300 nm to 100 m2 are substituted into the modeling. It is revealed that the theoretical prediction (Fig. 2) and numerical simulation results (Fig. S1) are generally consistent with each other. In addition, the duty cycle of the periodic NW array could also be controlled to optimize the performance of the proposed broad-band polarizer further (see Fig. S2 in the supplementary material). Remarkably, when the feature size of the metallic grating is scaled down to the several-hundred-nanometer range (e.g., G 200 nm), these metallic NW gratings will work as a polarizer for a very broad spectral range from the UV to THz domain. As shown in Fig. 3, we select a set of grating parameters ðP ¼ 140 nm; w ¼ 70 nm; and t ¼ 180 nmÞ and show the ultrabroadband polarization-dependent transmission through a free-standing metallic 1 RCWA simulation with the commercial solver, i.e., Diffraction mode (Rsoft Inc.), is used to calculate the transmission spectra of the Al grating structures. 2 The optical data for Al in the spectral range between 300 nm and 30 m is taken from [16]. The data beyond this range (up to 100 m) are using the built-in fitting parameter in a commercial software package Rsoft.


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grating calculated by CMM (see the red and green curves) and RCWA modeling (see the black and blue curves). One can see that the transmission for the TM mode is very high from the UV (G 400 nm) to the THz domain (up to 100 m), while the TE mode transmission is suppressed significantly through the entire spectrum, indicating that the free-standing metallic NW array can work as a highperformance ultrabroadband polarizer which is currently not available in the market. It should be noted that the CMM calculation is an approximate formalism which can provide accurate predictions on optical transmission properties of subwavelength apertures in metallic films for the long wavelength region but may fail in the short wavelength region (especially when the light frequency is above the plasma frequency of the metal). By comparing the modeling results shown in Figs. 2 and S1, we can find that the transmission for TE-polarized light predicted by CMM formalism is lower than that obtained by RCWA modeling in the UV to visible region. Particularly, as shown in Fig. 3, the predicted TE-mode transmission in UV-visible region is approximately a half of the one simulated by RCWA. However, the absolute values for the TE-mode transmission obtained by these two methods are both extremely low ðG 104 Þ, indicating that this inconsistency in modeling results is negligible in this case. Based on the analysis shown in Figs. 2, 3, and S1, we conclude that the metallic NW array can work as a high-performance ultrabroadband optical polarizer. Towards the realization of the proposed polarizer, two challenges have to be addressed: 1) to fabricate the periodic metallic NW array with a feature size of 100–200 nm and 2) to achieve or mimic the property of the Bfree-standing[ NW structure. In the subsequent two sections, we consider practical issues to address these two challenges and demonstrate the feasibility of this device.

3. Preliminary Experiment: Metallic NW Arrays on Dielectric Substrates To realize a practical optical polarizer, a large area NW array with a very small feature size (e.g., G 200 nm) is required. As shown in Fig. 4(a), we deposit a 180 nm-thick Al film on a UV-fused glass substrate and employ the nanoimprint technique to fabricate the NW array. The period and width of the Al NW array is 140 nm and 70 nm, respectively. To characterize the performance of the NW polarizer, UV–VIS spectroscopy (HP 8452A diode array spectrophotometer) and Fourier transform infrared spectroscopy (FTIR, Bruker Vertex 70) were employed to measure the transmission spectra of the glass substrate and the NW array in UV to mid-IR domain, respectively. It is wellknown that the performance of a polarizer is mainly determined by the optical properties of substrate materials, particularly in the UV [17], mid-IR [8], [18]–[20], and THz domains. For example, in conventional developments, various IR-transmitting materials were used as substrates for mid-IR polarizers, including halogenides (CaF2 , TlBrI, CsI, etc.), chalcognides (ZnSe, As2 S3 , etc.), and semiconductors (Si, Ge) [18], [19]. More recently, novel materials or structures were applied as substrates to improve the performance of mid-IR polarizers (e.g., WSi [8], Y2 O3 [20], etc.). Consequently, the working spectral range of this sample is limited by the optical properties of the glass substrate used in our nanofabrication. The measured data of the substrate at normal incidence are shown in Fig. 4(b). One can see a flat and high transmission spectrum from 300 nm to 2.7 m (the data in the spectral range from 800 nm to 1.4 m is missing because of the spectral response limitation of our facilities), which, however, decreases and oscillates significantly beyond the wavelength of 2.7 m. Based on this relatively broadband substrate, we believe that the fabricated Al NW polarizer should work from 300 nm to 2.7 m. As shown in Fig. 4(c), the measured angular transmission spectra of the NW sample for TE and TM polarized incidence are both plotted (normalized by the transmission through a reference glass substrate at corresponding incident angles). Remarkably, a weak TE-polarized transmission and a high TM-polarized transmission can be obtained in the upper and central panels of Fig. 4(c), respectively, agreeing reasonably well with the modeling results shown in Fig. 3. The measured DOP of the NW polarizer on the glass substrate remains larger than 90% in the UV region (300–350 nm) and larger than 98.5% from 450 nm to 2.7 m [see the lower panel in Fig. 4(c)], revealing the large angulartolerance of the proposed NW polarizer. Although the performance of the NW array on the glass substrate from UV to 2.7 m in the mid-IR domain is generally good, these measurements also demonstrate that the working spectral range of a real device is significantly limited by the optical


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Fig. 4. (a) SEM image of Al NW array fabricated by nanoimprint technique on UV-fused glass substrate. The period and width of the Al NW are 140 nm and 70 nm, respectively. The thickness of the metal layer is 180 nm. (b) The measured transmission spectrum of a flat glass substrate. (c) Characterizations of the NW array in visible to near IR and mid-IR domains. (Left column) Measured transmission spectra of TE and TM polarized light from 300 nm to 800 nm wavelength range. The degree of polarization of the device in visible to near IR domain is calculated by ðTTM TTE Þ=ðTTM þ TTE Þ, which is over 99.2% in the UV to near-IR domain. (Right column) Measured transmission spectra of TE and TM polarized light in near-IR to mid-IR domain. The degree of polarization of the device in the near IR to mid-IR domain is also plotted, which is over 99.8% through the entire wavelength range.

properties of substrate materials (i.e., the high TM-polarized transmission performance cannot be retained beyond the wavelength of 2.7 m). Consequently, if the free-standing structure can be realized, we can finally overcome the limitation of the substrate and achieve an ultrabroadband polarization filter, which would have a revolutionary impact on optical polarizer market. It should be noted that free-standing metal wire-grids with tens of micrometers have been used for THz polarizers [21], [22]. However, free-standing NW arrays should be extremely fragile, which are challenging to fabricate based on known materials and nanofabrication technologies. In the next section, we propose to employ ultrathin substrates to minimize the limitation of the optical properties of substrate materials and mimic the optical properties of free-standing structures.

4. Mimic Optical Properties of BFree-Standing[ NW Arrays Using Ultrathin Nanomembranes Rigid ultrathin semiconductor/dielectric nanomembranes [23] have been widely employed in investigations of TEM characterizations, DNA sequencing [24], nanoplasmonic sensing [25], and metamaterials [26]. Currently, 5–20-nm-thick semiconductor/dielectric nanomembranes are available in the market [27]. Here, we perform theoretical analyses to demonstrate the feasibility of the highperformance wavelength-independent optical polarizer based on nanomembrane substrates. First, we further develop the CMM formalism outlined in Section 2 to incorporate the dielectric nanomembrane layer into the theoretical modeling. According to (1), G and I need to be modified


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Fig. 5. (a) Calculated transmission efficiency through a SiO2 nanomembrane for various thicknesses (i.e., 5 nm, 10 nm, and 20 nm). One can see that there are two transmission valleys at 9 m 10 m and 11 m 12 m due to the optical characteristics of the SiO2 membrane. In all calculations in (b) and (c), the metallic grating parameters Period ¼ 140 nm, width ¼ 70 nm, and thickness ¼ 180 nm.

to consider the additional dielectric layer as follows: I ¼

iu~k0 0 Y~k0 0 l 1 þ Zs v~k0 0 Y~k0 0 l

hj~ k0 0 i;

G ¼

X ~ k

v~k Y~k l hj~ k ih~ k ji: 1 þ Zs v~k Y~k l

(7)

Compared with (1) for a free-standing NW array, two parameters (v~k and u~k ) are introduced in (7) which are related to the dielectric layer. Their expressions are as follows: Y~k cosðklz dl Þ iY~k l sinðklz dl Þ Y~k l cosðklz dl Þ iY~k sinðklz dl Þ 1 ¼ ðY~k þ v~k Y~k l Þcosðklz dl Þ þ ðY~k l þ v~k Y~k Þisinðklz dl Þ : Y~k l

v~k ¼

(8a)

u~k

(8b)

It should be noted that without the dielectric layer (i.e., dl ¼ 0 and Yk ¼ Yk l ), one can get v~k ¼ 1 and u~k ¼ 2, and then, (7) will be reduced to a form for the free-standing NW arrays (see [9, eqs. A8–A9]). Subsequently, we apply (7) and (8) to estimate the polarizer performance of metallic NW arrays on ultrathin SiO2 and Si nanomembranes, respectively. In this modeling, the optical constants of SiO2 and Si materials taken from[16] are considered in the following calculations. As shown in Fig. 5(a), the optical transmission spectra of the SiO2 nanomembranes without the NW arrays are calculated for different thicknesses by using the characteristic matrix of the stratified medium [28]. One can see that a high transmission larger than 95% can be obtained throughout the spectral region from 300 nm to 100 m, except for the regions between 8 m 9 m and 11 m 12 m due to the lattice vibration absorption of the material [29]. Using these nanomembranes as the substrate, we calculate the polarization-dependent transmission through the NW arrays on top of them using the CMM formalism [see (7) and (8)], as shown in Fig. 5(b). For TMpolarized incident light, a transmission resonance from 50% to 80% is obtained in the wavelength range from 300 nm to 1 m because of the FP resonance (see corresponding discussion in Section 2.2). In the near-IR to THz region, the transmission increases to 9 97%. Due to the lattice vibration resonance, the transmission slightly reduces to 80%, 85%, and 92% for the 20 nm-thick, 10 nm-thick and 5 nm-thick substrate, respectively [see the upper curves in Fig. 5(b)]. For TEpolarized incident light, the transmission is lower than 104 throughout the entire spectral region [see the lower curves in Fig. 5(b)]. The DOP is therefore calculated to be larger than 99.98% from the UV to THz domains. However, because of the intrinsic property of SiO2 material, the transmission dips introduced by lattice vibration resonances are not desirable for the optimization of the high-performance wavelength-independent polarizer in the mid-IR to far-IR region. Consequently, we then consider Si nanomembranes as alternative substrates. As shown in Fig. 6(a), the optical transmission of the Si nanomembrane is much lower than those for SiO2 nanomembranes in the visible to near-IR domain due to the relatively strong absorption and large refractive index of the Si material in this spectral region. However, the transmission spectra for various thicknesses are pretty high and flat in the mid-IR and THz range, leading to a high transmission for TM-polarized incident light and a low transmission for TE-polarized light in the long wavelength region [see


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Fig. 6. (a) Calculated transmission efficiency through the Si nanomembrane for various thicknesses (i.e., 5 nm, 10 nm, and 20 nm). In all calculations in (b) and (c), the metallic grating parameters are Period ¼ 140 nm, width ¼ 70 nm, and thickness ¼ 180 nm.

Fig. 6(b)]. Consequently, the DOP of the NW polarizer on Si nanomembranes is larger than 99.99% in the near-IR to THz domain [from 700 nm–100 m, see Fig. 6(c)], which is better than the one on SiO2 in this spectral region.

5. Conclusion In conclusion, the design of a high-performance wavelength-independent optical polarizer based on free-standing NW arrays is proposed, which is not limited by the properties of substrate materials. By properly designing the geometric parameters of the NW array, the polarizer can work well for an ultrabroadband spectral region from the UV/visible to the THz domains. Preliminary experimental results of NW arrays fabricated on glass substrates by nanoimprint lithography were provided to demonstrate the feasibility of the proposed NW polarizer. The working range of this device is from 300 nm to 2.7 m, which, however, is still limited by the glass substrate. To further reduce the influence of the substrate material, we propose to employ dielectric nanomembranes (e.g., SiO2 and Si nanomembranes) as the substrate of the NW polarizer. Theoretical predictions reveal that these NW arrays on nanomembranes are promising to function as an ultrabroadband polarizer for the UV/visible to THz frequencies, which is integrable with portable optoelectronic devices [30]. It should be noted that in a latest theoretical work, metallic nanoslit, and rectangular nanoaperture arrays were proposed to realize a broadband polarization-dependent high transmission in mid-IR domain [31], which, however, neglected the substrate limitation in the numerical modeling. Consequently, the concept of employing nanomembranes as the substrate is also applicable to these novel designs. Importantly, if these metallic nanostructures are fabricated on monolayers of graphene [32], with its excellent optical transmission properties, a robust, flexible, and ultrabroadband polarizer is achievable, which will lead to a path-breaking product for the optical devices market.

Acknowledgment The authors thank J. Wang in NanoNuvo for assistance in nanoimprint fabrications.

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