1. Introduction

Nanophotonic structural color filters are widely perceived to be indispensable in a variety of applications, such as display/imaging devices, photovoltaic cells, biosensors, and light modulators [1–8]. An asymmetric metal-dielectric-metal (MDM) configuration based on the Fabry-Perot resonance, which consists of a dielectric cavity sandwiched between a thin metal film and highly reflective substrate, is regarded as a leading candidate for constructing subtractive color filters. Subtractive colors, including cyan, magenta, and yellow (CMY), can be selected by simply controlling the thickness of the dielectric cavity [9–11]. For conventional filters relying on triple uniform layers, the depth of the dip in connection with the reflection is known to be somewhat dependent on the thickness of the top metal film [12, 13]. Under the critical coupling condition, where no power is reflected back from the resonant structure, incident optical power is completely transferred to the resonator. In order to achieve high color saturation, the filter is designed to exhibit a near-zero reflection dip by adjusting the thickness of the top metal film. The color saturation is an attribute of visual perception, indicating the degree to which color sensation differs from achromatic sensation at a constant brightness level, while the excitation purity represents a measure of the color saturation [14]. The thickness of the metal film required for fulfilling the reflection dip is usually several nanometers [10–13], which is extremely delicate for precise control. Therefore color saturation is critically susceptible to metal thickness. In a bid to mitigate this issue, we proposed and realized a set of subtractive color filters that exploit a nanoporous MDM resonant structure, enabling metal-thickness tolerant color saturation. The device is composed of a cavity made up of self-assembled nanoporous anodic aluminum oxide (AAO), sandwiched between a highly reflective aluminum (Al) substrate and thin Al film perforated with the same pores as the dielectric cavity. A hexagonal lattice of pores was previously cost effectively created in AAO on a large scale, via non-lithographic anodization process, taking into account its potential applications to biosensors and functional nanostructures [15–18]. The nanoporous structure embedded in the Al film, as well as the AAO cavity, is deemed to mimic a quasi-homogeneous medium with an effective refractive index, which can be customized by the volume fraction of the pores [18–21]. For the proposed filters based on a nanoporous structure, the resonance wavelength is expected to be efficiently tuned by tailoring the thickness of the porous AAO layer, so as to generate the CMY colors. The targeted subtractive color filters with a near-zero reflection dip, which is essential for attaining high color saturation, have been rigorously designed and analyzed using the finite-difference time-domain (FDTD) method. The sensitivity of the color saturation to the thickness of the porous Al film was explored for the proposed filters, in comparison with a typical filter with uniform layers.

2. Proposed nanoporous color filters featuring a stable reflection response

In this work, we aim to develop CMY color filters that employ a nanoporous MDM resonant configuration, giving rise to highly structure tolerant color saturation. Prior to pursuing the principle of the operation underlying the devices, a typical etalon filter involving no nanoporous structure is first discussed, as illustrated in Fig. 1(a), which comprises a thin metallic film at the top (layer 1), a dielectric cavity in the middle (layer 2), and an optically thick metal substrate at the base (layer 3). Al was selected for both the top and bottom metallic layers, due to its salient features of high reflectance and good process compatibility [22]. For the typical filter, the intensity reflectance R for the normal incidence is given by [23–26]:

 

Fig. 1 (a) Configuration of an asymmetric MDM structure. (b) Calculation of the required thickness of the top Al film (t₁) leading to a zero reflection dip based on Eq. (2), with t₂ changing from 250 to 340 nm. The spectral reflection was calculated according to Eq. (1). (c) Reflection characteristics in terms of t₁ for t₂ = 310 nm and n₂ = 1.48. (d) Relative depth of the reflection dip with t₁, to vary refractive indices of the metallic film, which is determined by n₁ = n_Ala, for a ranging from 0.6 to 1.4.

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We then examined the dependence of the spectral response on the properties of the top metal film, in terms of n₁ and t₁. For the dielectric cavity, the refractive index and the thickness were respectively set at n₂ = 1.48 and t₂ = 310 nm. As shown in Fig. 1(c), when t₁ changed from 5 to 30 nm, the depth of the dip was seriously susceptible to t₁. It is stated that a near-zero reflection dip was earned for t₁ = 5 nm, which is close to the thickness imposed by the critical coupling condition. However, the depth of the dip tends to deviate drastically from zero depending on the Al thickness, which is difficult to accurately control. As a result, the color saturation becomes unstable. According to Eq. (2), the tolerance of t₁, allowing for the negligibly small deviations from the zero-dip, can be readily enhanced by diminishing the imaginary part of index n_Im. Thus, the reflection dip was monitored by effectively manipulating the refractive index of the metallic film with respect to its true value, in accordance with $n_1=a\cdot n_{Al}$, where a, acting as a scaling factor, was varied from 0.6 to 1.4. As plotted in Fig. 1(d), the depth of the reflection dip was monitored in terms of t₁ for different values of n₁. The sensitivity of the dip to the metal thickness was substantially relaxed when n₁ was diminished to below n_Al, (for a < 1.0).

In this work, as illustrated in Fig. 2(a), we mainly endeavored to propose and construct subtractive color filters by incorporating a nanoporous structure into a top metallic film in conjunction with a dielectric cavity. The nanoporous Al film, behaving as a quasi-homogeneous medium, is expected to both elevate the transmission and lower the reflection, due to its small effective refractive index compared with the uniform Al film [29]. In light of the above analysis, the suggested filter is anticipated to offer a reflection dip, which is highly tolerant of the thickness of the Al film. In order to conduct the device fabrication on a large scale in a cost effective manner, we resorted to a non-lithographic process, where the nanoporous Al film was created via a self-assembled AAO layer with a hexagonal lattice of nanopores, serving as the dielectric cavity. The nanoporous AAO layer, which is directly grown from a thick Al substrate through the anodization process, has a fundamental pitch of Λ = 100 nm, defined as the distance between two adjacent pores, and a pore diameter size of d = 65 nm. The effective medium theory has been commonly utilized to elucidate the properties of such a nanoporous structure [18–21]. As depicted in Fig. 2(a), t₁ signifies the thickness of the top Al film while t_2C, t_2M, and t_2Y refer to the cavity thicknesses of the CMY filters, respectively. The proposed filters have been rigorously designed and assessed using the FDTD method based tool, FDTD Solutions from Lumerical, Canada [30]. The dispersion characteristics of the materials of concern, encompassing Al and Al₂O₃ constituting the AAO layer, were derived from the multi-coefficient model offered by the simulation tool. The thickness of the AAO cavity was pertinently determined to be t_2C = 160 nm, t_2M = 310 nm, and t_2Y = 250 nm for the CMY colors, respectively. For the perforated Al film, the thickness t₁ leading to a near-zero resonance dip was as thick as 15 nm, as plotted in Fig. 2(b). The corresponding near-zero dip was nearly centered at λ = 436, 526, and 612 nm for the CMY color filters, respectively. The corresponding color coordinates are presented in the 1931 CIE color diagram, as shown in Fig. 2(c), where appropriately enhanced color saturation was acquired for the three devices.

 

Fig. 2 (a) Schematic of the proposed CMY color filters with a nanoporous cavity inclusive of a hexagonal lattice of pores. (b) Observed optical responses for the proposed CMY color filters, with the near-zero reflection dip marked with a red circle. (c) Corresponding 1931 CIE color coordinates for the designed yellow, magenta and cyan filters, with the thickness of the AAO based cavity fixed at t_2Y = 250, t_2M = 310, and t_2C = 160 nm, respectively.

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The performance of the proposed nanoporous color filters was theoretically examined in terms of the reflection dip and the corresponding color saturation as a function of the thickness of the top nanoporous Al film. The performance was compared with that of a typical case, in which a uniform SiO₂ cavity, sandwiched between a top thin Al film and a thick Al substrate, is utilized. SiO₂ used for the uniform cavity was chosen in view of its refractive index similar to that of the nanoporous AAO cavity. The effective refractive index of the nanoporous cavity was n_2eff = ~1.48 for Λ = 100 nm and d = 65 nm, according to the Maxwell Garnett equation, which is given by $({\text{n}}^2{}_{2eff}-{\text{n}}^2{}_{AAO})/({\text{n}}^2{}_{2eff}{\text{+2n}}^2{}_{AAO})=V_P(1-{\text{n}}^2{}_{AAO})/(1{\text{+2n}}^2{}_{AAO})$ [19–21]. The refractive index of the AAO layer made of Al₂O₃ is n_AAO = 1.77 and the volume fraction of the pores within the cavity is $V_P=\pi {(d/\Lambda )}^2/2\sqrt{3}$. The spectral reflections of the proposed and conventional filters were investigated in the case of a magenta filter with t_2M = 310 nm, with t₁ varying from 5 to 30 nm. As shown in Fig. 3(a), the thickness t₁ in relation to the near-zero dip increased to 15 nm for the proposed filter. The reflection dip remained fairly stable, while t₁ ranged from 10 to 20 nm, implying that a high color saturation can be maintained regardless of variations in t₁. Meanwhile, for the typical filter, t₁ needed to be as thin as 5 nm while the reflection dip was noticeably deviated from zero with a larger t₁. The observed blue shift of the reflection dip in response to the larger t₁ is attributed to the shift in the reflection phase at the metal-dielectric interface [12, 13]. The influence of t₁ on the depth of the reflection dip is plotted in Fig. 3(b). The relative depth of the dip changed by ~0.8 and 0.2 for the typical and nanoporous cases, respectively, when t₁ increased from 5 to 30 nm. For the dependence of the color saturation on t₁, the color coordinates in the 1931 CIE chromaticity diagram were identified for the typical and proposed filters, as depicted in Fig. 3(c), where the magenta color drastically faded away to reach close to the white color for t₁ exceeding 10 nm. For the proposed nanoporous filter, satisfactory color saturation was stably retained, despite large variations of t₁, which is desirable for practical fabrication. The color saturation is quantitatively measured from the excitation purity, which is defined as the ratio of the length of the line segment (that connects the white point E (0.3333, 0.3333) to the point of interest) to the length of the line segment (which connects E to the dominant wavelength). Here, the dominant wavelength indicates the intersection between the perimeter and the extension of the segment from E to the point of interest [14]. The influence of t₁ on the excitation purity was checked from the plot in Fig. 3(d). For the typical filter, the purity degraded from the maximum of 0.37 to 0.17 when t₁ changed from 5 to 10 nm, and it approached zero with further increase in t₁. For the proposed filter, the high color purity reduced by only 0.1 from the maximum of 0.44 when t₁ was widely varied from 5 to 20 nm, signifying structure tolerant stable color saturation.

 

Fig. 3 (a) Observed optical responses for the typical and proposed magenta filter (t_2M = 310 nm) with the thickness of the top Al film t₁ changing from 5 to 30 nm. (b) Dependence of the reflection dips on t₁. (c) Corresponding 1931 CIE color coordinates and (d) excitation purity for the typical and proposed filter, with t₁ increasing from 5 to 30 nm.

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The proposed filter is presumed to exhibit no transmission due to its optically thick Al substrate, which potentially behaves as an absorber [12, 13, 24, 25]. A stable near-perfect absorption peak can be attained for certain values of t₁. The optical absorbance and reflectance were calculated for the filter with t₂ = 290 nm, as shown in Fig. 4(a), where a near-perfect absorption of as high as 99.98% was accomplished at a resonance wavelength of ~497 nm, which was synonymous with the near-zero reflection dip. The porous AAO cavity is equivalently modeled as a homogeneous medium with an effective refractive index [21]. For simplicity, a homogeneous cavity with an index of n_2eff = 1.48 was taken into consideration for the proposed filter, instead of a porous AAO layer. The normalized electric field intensity (|E|²) was analyzed at the resonance wavelength, as shown in Fig. 4(b), where light is found to be chiefly confined in the cavity as anticipated. It was hence confirmed that light has been substantially absorbed at the top and bottom metal-dielectric interfaces, translating into low reflection.

 

Fig. 4 (a) Calculated optical absorbance and reflectance for the filter with t₂ = 290 nm. (b) Normalized electric field intensity (|E|²) profile observed at a resonance wavelength of ~497 nm, assuming that the filter relies on an equivalent homogeneous cavity with an effective refractive index of n_2eff = 1.48.

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3. Fabrication of the proposed nanoporous color filters and their characterization

The proposed subtractive color filters, capitalizing on the nanoporous MDM resonant configuration, were manufactured through a two-step anodization process. The detailed fabrication procedure is described in Fig. 5. A substrate of Al foil with a high purity of over 99.99% was initially cleaned and electrochemically polished. On top of the cleaned Al foil a nanoporous AAO layer was roughly grown via anodization, which was then removed by immersing in a mixture of 6.0 wt% H₃PO₄ and 1.8 wt% H₂CrO₄ at 60 °C for 5 hours. The corrugated Al substrate underwent further anodization, thereby forming a well-aligned nanoporous AAO layer. The anodization time was meticulously controlled in order to create three different thicknesses for the AAO layer, including t_2C = 156 nm, t_2Y = 250 nm, and t_2M = 292 nm for the cyan, yellow, and magenta filters, respectively. In order to eliminate any unwanted barrier layer at the bottom, the prepared AAO template was dissolved in 6.0 wt% H₃PO₄ at 60 °C for 10 minutes. The AAO layer was made up of a hexagonal lattice of pores, of which the dimensions were tailored by means of the anodization voltage. A thin Al film with a thickness of t₁ = 15 nm was finally deposited on top of the AAO layer via e-beam evaporation at a rate of 0.5 Å/sec. Figures 6(a) and 6(b) show the top- and cross-sectional views of scanning electron microscope (SEM) images for the completed cyan filter, respectively. A hexagonal lattice of well-defined nanopores was formed as desired, exhibiting a fundamental pitch of Λ = 100 nm and a pore diameter of d = 65 nm. As shown in Fig. 6(b), the AAO layer, with a height of 156 nm, was observed to be sandwiched between the top porous Al film of 15-nm thickness and the Al substrate.

 

Fig. 5 Fabrication procedure for the proposed nanoporous color filters.

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Fig. 6 (a) Top-view and (b) cross-sectional-view of SEM images of the prepared cyan filter.

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In an attempt to evaluate the fabricated devices, their reflection characteristics were tested using a halogen lamp (Ocean Optics LS-1-LL) for the light source, a beam splitter, and a spectrometer (Ocean Optics USB4000). The measured results are shown in Fig. 7(a). It was observed that near-zero reflection dips were approximately obtained at the wavelengths of 436, 500, and 600 nm for the yellow, magenta, and cyan filters, respectively, which are well correlated with the calculation. The measured performance for the color filters was however discovered to be somewhat different from the simulated result. For the magenta filter, the measured spectral response in particular provided a broader bandwidth than calculated, as shown in Figs. 4(a) and 7(a), which may be due to the undesired optical loss stemming from the irregular nanopore patterns as well as the rough interfaces between the AAO layer and the top/bottom Al layers, as manifested in Fig. 6. It is also noted that while the magenta filter is based on the first order mode responsible for the resonance dip at λ = 500 nm, another dip relating to the fundamental resonance is in principle deemed to appear around λ = 1000 nm. As plotted in Fig. 7(a), the spectral reflectance relating to the fabricated magenta device was unexpectedly observed to decline starting from λ = 650 nm, which is attributed to the broadened fundamental resonance in the near infrared regime. As shown in Fig. 7(b), CMY colors with high color saturation were obtained from the three prepared filters. For the purpose of scrutinizing the color saturation with respect to the top Al film, we prepared nanoporous color filters coated with different thicknesses of Al film, under a constant cavity thickness of t₂ = 290 nm. Figure 8 shows the color images available from the proposed filters when the thickness of the top Al film changed from t₁ = 10 to 30 nm in steps of 5 nm. For the proposed filters, the magenta color could be stably maintained for t₁ ranging from 10 to 20 nm, leading to a large tolerance of ± 5 nm for t₁. Non-white color was then generated for t₁ ranging up to 30 nm, experimentally verifying the calculated results in Figs. 3(c) and 3(d). Meanwhile, for a conventional filter with a SiO₂ cavity, which was similarly prepared for comparison, the color was monitored to fluctuate from high to low color saturation when t₁ increased from 10 to 15 nm. It was observed that the color faded, reaching close to white for t₁ beyond 20 nm. It was consequently proven that the proposed filters were capable of retaining high color saturation, featuring large tolerance in the thickness of the top metal film.

 

Fig. 7 (a) Measured optical responses and (b) captured color images for the proposed color filters.

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Fig. 8 Observed color images of the proposed magenta filter and the typical filter based on a uniform SiO₂ cavity with t₁ ranging from 10 to 30 nm.

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4. Conclusion

Subtractive tri-color filters were successfully realized by tapping into a nanoporous Al-AAO resonant strucuture formed on an Al substrate, where the resonant wavelength was determined by altering the thickness of the porous AAO cavity in order to provide CMY colors. A near-zero reflection dip at the resonant wavelengths, which is crucial for achieving high color saturation, was stably obtained and was thus tolerant of the thickness of the porous Al film. This was made possible by non-lithographically producing a nanoporous Al layer on top of a self-assembled porous AAO cavity, with a view to effectively reducing its refractive index. As predicted, the fabricated CMY filters provided acceptable reflection dips, allowing for affordable tolerance for the top Al thickness.