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A polarization-mediated color filter featuring a high angular tolerance is proposed incorporating a metal-dielectric-metal etalon based on a nanostructured cavity, where a one-dimensional subwavelength grating of a high refractive index is embedded in a base layer of a low refractive index. The aim of the nanostructured cavity is mimicking of the equivalent birefringent medium whereby different effective refractive indices are exhibited depending on the incident polarization. As the transmission peak of the etalon is effectively tuned through the tailoring of the refractive index of the cavity, the proposed filter is capable of providing a continuum of vivid output colors through a dynamic control of the polarization. The effective medium theory is chiefly applied for an investigation of the birefringent characteristics of the nanostructured cavity. A dielectric overlay that acts as an anti-reflection coating is specifically adopted for the etalon to enhance the transmission efficiency. The proposed polarization-tuned filter evidently provides a high transmission of ~71% and a high angular tolerance of ~35° in conjunction with a wide polarization-mediated color tuning.
© 2016 Optical Society of America
Corrections
10 August 2016: A correction was made to the author affiliations.
1. Introduction
Nanostructured color filters have received a substantial amount of attention as the central element of numerous applications including digital displays, image sensing, anti-counterfeiting, and high-resolution photorealistic color printing [1–7]. Such filters are a prominent alternative to the conventional dye-based filters, which are susceptible to serious performance degradation over time due to their severe sensitivity to temperature and ultraviolet illumination. The eminent nanostructures that are associated with the filtering device encompass a Fabry-Perot (FP) etalon, a plasmonic resonator, and a grating device that invokes the guided-mode resonance (GMR) [8–14]. In applications like display/imaging devices, the color filter is typically supposed to enable the additive coloration based on red, green, and blue, as well as the subtractive coloration that entails cyan, magenta, and yellow. To embody a compact, rapid color display and high-density optical data storage, a color filter with a fixed geometry that allows for a continuum of colors is essentially required [15,16]. Several color filters with dynamically tuned output colors were previously built through an alteration of the polarization of incident light, resorting to asymmetric plasmonic nanostructures, such as a metallic cross embedded in a dielectric layer or a cross-shaped aperture in a metallic film [17,18]; however, the design and fabrication of such a two-dimensional (2D) geometry poses critical issues. A report regarding a polarization-tuned color filter that features simple structures, like a one-dimensional (1D) subwavelength grating (SWG) in Si3N4, or a 1D Al nanowire that initiates a combination of the surface plasmon resonance (SPR) and the GMR, was recently published [19,20]. For the SPR- and GMR-mediated color filters, it is evident that the color output is intolerably vulnerable to the angle of incidence because the resonant coupling apparently depends on the polarization state in relation to the geometry of the nanostructured constituents [21]; to mitigate this obstacle, which prohibits the construction of an angle-insensitive color filter, an FP etalon of a metal-dielectric-metal (MDM) configuration is regarded as a potential prime candidate [8,22].
In this paper, a polarization-mediated color filter that enables a high angular tolerance and for which an etalon of a dielectric-metal-dielectric-metal (DMDM) configuration that capitalizes on a nanostructured cavity, where a 1D SWG of a high-refractive index is embedded in a base layer with a low-refractive index, is proposed and designed; here it is presumed that the nanostructured cavity plays the role of a birefringent medium. Given that the transmission peak for an etalon based filter can be efficiently tuned through a simple tailoring of the effective index of the cavity [23], it is anticipated that the proposed color filter will give rise to a continuum of output colors through a dynamic control of the polarization of the incident light. With respect to the polarization, the optical characteristics of the SWG-based cavity are explored with the assistance of the effective medium theory (EMT). In particular, a dielectric overlay, working as an effective anti-reflection (AR) coating, is integrated into the etalon of the MDM configuration, resulting in a profound boosting of the transmission efficiency. This study confirms that the proposed color filter can provide a high transmission and a substantial angular tolerance in conjunction with a wide color tuning.
2. Proposed polarization-mediated color filter featuring an enhanced angular tolerance
The aim of this work is the demonstration of a polarization-mediated color filter that renders a relaxed angular tolerance. As illustrated in Fig. 1, the proposed device, formed on a glass substrate, comprises an FP etalon that capitalizes on a nanostructured cavity, which is sandwiched between a pair of thin metallic mirrors in silver (Ag), overlaid with a dielectric film in TiO2. The thicknesses of the TiO2 overlay, the Ag mirror, and the cavity are denoted by td, tm, and tc, respectively. For the creation of the nanostructured cavity, a 1D SWG, made of TiO2 with a high refractive index of n2, is embedded in a base layer that is made of PMMA with a low refractive index of n1. Here tg, P, and W signify the thickness, pitch, and width of the embedded grating, respectively. The polarization of the incident light is indicated by an angle φ for the alignment of the corresponding electric (E) field with respect to the x direction. A transmission peak is supposed to occur at a resonance wavelength, where the total phase shift that is accumulated during a single round trip in the nanostructured cavity becomes integer multiples of 2π [24]. The resonance wavelength might be effectively tuned by the tailoring of either the thickness of the cavity or its refractive index. Regarding the proposed color filter, it is expected that the cavity that involves a 1D SWG will emulate a birefringent medium, whereby different effective refractive indices are exhibited depending on the incident polarization. Specifically, two different color outputs of blue and green are produced for the transverse-magnetic (TM) and transverse-electric (TE) polarizations that correspond to φ = 0° and φ = 90°, respectively.
Fig. 1 Schematic of the proposed polarization-mediated color filter that is capitalizing on a nanostructured FP cavity incorporating a 1D SWG. The filter gives birth to color outputs of blue and green in accordance with the incident TM and TE polarizations, respectively.
3. Design of the proposed angle-tolerant polarization-tuned color filter and its characterization
An SWG-based cavity, regarded as a crucial element of the proposed filter, is initially investigated in terms of the birefringence that is governed by its polarization-dependent refractive index. As depicted in Fig. 2, the 1D SWG, for which alternating layers with low- and high-refractive indices of n1 and n2, are drawn upon, is equivalently treated as a birefringent medium with effective refractive indices of nTM and nTE for the TM and TE polarizations, respectively; furthermore, the treatment of the 1D SWG is under the assumption that the grating period P is sufficiently small compared with the wavelength of interest. As listed in Eq. (1), it is known that the EMT can be safely applied for the estimation of the effective index that corresponds to the modeled birefringent layer, as follows [25,26]:
Here, the superscripts 0 and 2 that pertain to nTM and nTE respectively indicate the zeroth- and second-order approximations for the EMT. The refractive indices of the alternating layers that constitute the SWG are determined as n1 = 1.47 and n2 = 2.3 in the cases of the PMMA and TiO2, respectively. The zeroth-order approximation is only valid as long as the grating pitch P is smaller than λ/10; meanwhile, for the case of a pitch P that satisfies, the second-order EMT should be exploited. As the grating pitch is selected as P = 150 nm in this work, the second-order EMT is applied to derive the effective indices of the SWG structure. The nTM and nTE change with the λ and W for the given values of P, n1, and n2. The dependence of nTM and nTE on the wavelength is plotted in Fig. 2(b) for a constant width of W = 100 nm. The resulting variations of nTM and nTE are slightly less than 0.06 for the wavelength range from 400 nm to 700 nm, whereby the resonance wavelength is rarely shifted. The effective indices of the SWG-based cavity are therefore calculated for the TM and TE polarizations at a specific wavelength of λ = 550 nm via the second-order EMT. As shown in Fig. 2(c), the effective indices for the SWG are calculated at λ = 550 nm through a varying of the grating width W from 20 nm to 120 nm in steps of 10 nm. The nTM and nTE are respectively monitored to increase from 1.53 to 2.06 and 1.62 to 2.17 as the width W increases; accordingly, the index contrast between the nTM and nTE changes from 0.09 to 0.18 reaching a maximum for W = P/2. For the etalon-based color filters, it is desirable for the nanostructured cavity to exhibit a large birefringence that leads to a high index contrast, thereby broadening the color tuning range. It is noteworthy that the SWG-based artificial medium offers a much stronger birefringence compared with the birefringent materials that exist in nature, such as cadmium selenide (CdSe) and cadmium sulfide (CdS) [25].Fig. 2 (a) A nanostructured cavity composed of alternating low-index (n1) and high-index (n2) layers is approximated as a birefringent medium, which is characterized by the effective refractive indices of nTM and nTE for the TM and TE polarizations, respectively, according to the EMT. The effective indices of nTM and nTE are derived from the second-order EMT as a function of (b) the wavelength under a fixed grating width of W = 100 nm, and (c) the grating width at the specific wavelength of 550 nm.
To validate the derived effective index of the nanostructured cavity through the EMT method, as depicted in Fig. 3(a), an actual case that directly represents an SWG-based cavity was explored in comparison with a modeled case that involves an equivalent birefringent medium with the calculated effective indices. Toward that end, simulations have been rigorously conducted with the assistance of the finite-difference time-domain (FDTD)-method-based tool “FDTD Solutions” that is available from Lumerical, Canada [27]. The thicknesses of the Ag mirror, the PMMA cavity, and the TiO2 overlay are set as tm = 25 nm, tc = 240 nm, and td = 60 nm, respectively. The selected grating thicknesses for the actual case and the modeled birefringent medium are both tg = 0.8tc, and the grating pitch for the actual case is set as P = 150 nm. Also, the transmission spectra of the filters were examined for different grating widths. For the nanostructured cavity with grating widths of W = 50 nm, W = 100 nm, and W = 120 nm, the calculated effective indices in accordance with the EMT are nTM = 1.66, 1.94, and 2.06 for the TM polarization, respectively, and nTE = 1.82, 2.09, and 2.17 for the TE polarization, respectively. In consideration of the transmission spectra that are shown in Fig. 3(b), a sound correlation is obtained between the actual case and the modeled case, proving the validity of the EMT. Transmission efficiencies approaching 65% and 71% were respectively acquired for the TM and TE cases; as expected, the index contrast between the nTM and nTE translates into the available spectral tunability.
Fig. 3 (a) Configurations of an actual case with a nanostructured cavity with a grating width of W and a modeled case with a birefringent cavity that exhibits the effective indices of nTM and nTE. The thicknesses of the Ag mirror, the PMMA cavity, and the TiO2 overlay are set as 25 nm, 240 nm, and 60 nm, respectively. The grating thicknesses for the actual case and the modeled birefringent medium are both 192 nm, and the grating pitch for the actual case is fixed at 150 nm. (b) Polarization-dependent transmission spectra with different grating widths of W = 50 nm, W = 100 nm, and W = 120 nm.
For the proposed filters, the polarization-controlled color tuning has been thoroughly scrutinized in terms of the transmission spectra and the corresponding chromaticity coordinates in a standard International Commission on Illumination (CIE) 1931 chromaticity diagram. Figure 4(a) shows the transmission spectra for the grating widths of W = 50 nm, W = 100 nm, and W = 120 nm when the incident polarization is rotated from φ = 0° to φ = 90° in steps of 10° . As the polarization angle increases, the transmission peak eventually red shifts from λ = 474 nm, λ = 538 nm, and λ = 569 nm to λ = 511 nm, λ = 571 nm, and λ = 594 nm for the different grating widths, respectively. For intermediate polarization angles between φ = 0° and φ = 90°, the transmission is represented by , where TTM and TTE represent the transmissions for the TM and TE cases, respectively. The chromaticity coordinates that correspond to the transmission spectra are plotted in the CIE 1931 chromaticity diagram, as shown in Fig. 4(b). Through a dynamic adjustment of the polarization angle, the color output evolves from blue to green, green to yellow, and yellow to red for W = 50 nm, W = 100 nm, and W = 120 nm, respectively, indicating a high purity. The large spectral shift from the TM case to the TE case implies the large color tunability of the proposed filter.
Fig. 4 (a) Transmission spectra of the proposed polarization-tuned color filter with grating widths of W = 50 nm, W = 100 nm, and W = 120 nm for a constant grating pitch of 150 nm, when the incident polarization varies from φ = 0° to 90°. (b) Corresponding chromaticity coordinates in the CIE 1931 chromaticity diagram.
The angle-dependent property of the proposed color filter has been meticulously assessed for different polarizations in terms of the relative resonance wavelength shift and variations of the peak transmission; here, the relative shift of the resonance wavelength is given by |Δλ/λ0|, where λ0 is the resonance wavelength for the normal incidence and Δλ is the spectral deviation from λ0. As the incident angle increases from 0° to 35°, the transmission spectra for the different widths of W = 50 nm, W = 100 nm, and W = 120 nm are studied for the TM and TE polarizations, as depicted in Fig. 5. The resonance wavelength and the peak transmission are almost invariant to the incident angle ranging up to 35° for both of the two polarizations, confirming a wide field of view; moreover, the relative wavelength shift and the reduction of the peak transmission are less than 4% and 1%, respectively. In an attempt to scrutinize the underlying mechanism of the high angular tolerance, a typical case that is based on a DMDM configuration is considered with respect to the contributions of different types of phase shift in relation to the cavity, as depicted in Fig. 6(a). For the TE polarization, the refractive index of the cavity is set as nc = 2.09, in correspondence to the effective index of the nanostructured cavity with a grating width of 100 nm. For the etalon, the peak transmission occurs at a resonance wavelength where the total round-trip phase shift within the cavity equals ϕ = 2mπ, where the integer m stands for the mode that relates to the order of the resonance peak. ϕ is specifically given by , where ϕr1 and ϕr2 are the phase shifts that are caused by the reflection at the bottom and top interface between the Ag mirror and the cavity, respectively. The round-trip propagation phase is given by , where nc and tc are respectively the refractive index and the thickness of the cavity, and θt is the propagation angle inside the cavity [24]. As plotted in Fig. 6(b), the phase shift at the resonance wavelength of λ = 599 nm is estimated when θt is altered from 0° to 16°, in correspondence to the incident angles θ0 that change from 0° to 35°, by means of a simulation tool that is based on the transfer matrix method, Essential MacLeod from Thin Film Center, U.S.A [28]. The total phase shift is roughly equal to ϕ = 2π for the propagation angles that range up to 16°, and this supports the finding that the proposed color filter, which is based on a resonance mode of m = 1, exhibits an enhanced angular tolerance of ~35°.
Fig. 5 Contour map of polarization-sensitive transmission spectra for grating widths of W = 50 nm, W = 100 nm, and W = 120 nm, and a constant grating pitch of 150 nm, with respect to the angle of incidence.
Fig. 6 (a) Light propagation in a typical filter of a DMDM configuration. The thicknesses of the Ag mirror, the cavity with a refractive index of nc = 2.09, and the TiO2 overlay are set as 25 nm, 240 nm, and 60 nm, respectively. (b) Total phase shift ϕ at a resonance wavelength of λ = 599 nm for a typical filter when the propagation angle inside the cavity (θt) increases from 0° to 16°.
For the purpose of elevating the resonant peak transmission for the color filter for which an MDM etalon is utilized, the TiO2 dielectric overlay needs to be a quarter-wave thick to serve as an efficient AR coating. For practical convenience, the thickness of the overlay is uniformly chosen as 60 nm. As shown in Fig. 7, for the case of a device with a grating width of W = 100 nm, the introduction of the TiO2 overlay is checked to account for increases of the peak transmission of 12% and 15% in for the TM and TE polarizations, respectively. For an understanding of the performance of the proposed polarization-tuned color filters, the transmission spectra are shown in Fig. 8(a) in terms of the dispersion of TiO2. The resonance wavelength and the peak transmission are negligibly affected by the practical dispersion of the constituent materials of the filter in the case of grating widths of W = 100 nm and W = 120 nm. For a width of W = 50 nm, the resonance wavelength slightly red shifts due to the increased refractive index of the TiO2. The corresponding color coordinates are plotted in the CIE 1931 chromaticity diagram, as shown in Fig. 8(b). Devices with different grating widths could scan the output color from blue to green, green to yellow, and yellow to red, by tailoring the polarization from the TM to the TE. The proposed device incorporating a nanostructured cavity may be possibly implemented by virtue of the following procedure [29]. A thin PMMA film is first spin-coated on top of an Ag-coated glass substrate and properly baked. A 1D TiO2 grating structure is subsequently patterned via the e-beam lithography process. Another PMMA layer is similarly spin-coated while the spacing associated with the high-index grating is filled up. Finally, the device is completed by forming a combination of the top metallic layer and the dielectric overlay.
Fig. 7 Polarization-dependent transmission spectra of the color filter with and without a 60-nm thick TiO2 overlay. The color filter with a grating width and pitch of 100 nm and 150 nm has been respectively investigated.
Fig. 8 (a) Polarization-dependent transmission spectra of the color filter with different grating widths of W = 50 nm, W = 100 nm, and W = 120 nm and a constant grating pitch of P = 100 nm that depend on the dispersion of TiO2. (b) Corresponding 1931 CIE color coordinates.
4. Conclusion
A polarization-mediated color filter that enables a high angular tolerance, taking advantage of an etalon with a nanostructured cavity, which comprises a TiO2 SWG that is embedded in a PMMA base layer, was presented in this paper. The nanostructured cavity plays the role of a birefringent medium with polarization-dependent effective refractive indices, which has been examined via the second-order EMT method. For the proposed filter, a continnum of output colors could be readily tuned through an adaptive alteration of the incident polarization. A TiO2 overlay, serving as a decent AR coating, is taken advantage of to significantly elevate the transmission efficiency up to ~71%. By analyzing the contributions of the variety of phase shifts that are associated with the cavity, a high angular tolerance of ~35° has been achieved. Lastly, it has been confirmed that the proposed device provides a capability whereby the output color can be dynamically scanned by virtue of the incident polarization.
Acknowledgments
This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (2011-0030079 and 2016R1A2B2010170) and a research grant from Kwangwoon University in 2016. The authors are grateful to Mr. Chanwoo J. Lee, Seoul Foreign School, Seoul, S. Korea, for his help with the preparation of this manuscript.
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