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Abstract
This work presents a technique for the design of trans-reflective optical color filters employing a hybrid plasmonic nano-resonator with a dielectric cavity. The proposed filters exhibit wide-angle operation. They offer almost an omnidirectional field-of-view ($FOV$) (0°∼70°), an essential feature for light collection in miniaturized devices. Moreover, the proposed filters exhibit relatively high transmission and reflection (80%–92%) with at least a 14.3% enhancement than presented in literature. Moreover, the proposed filters are polarization independent manifesting a polarization dependent loss ($PDL$) of (−0.17 to −0.5 dB) at angle of incidence ($AOI$) of 70°. Variations in design parameters are introduced to evaluate the equivalent filters performances. Design rules of the filter are presented with physical justifications of the obtained performance curves, hence deducing design guidelines for the proposed color filters that may be further applied in infrared (IR) spectral region.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Color filters are known to be substantial elements for numerous applications such as organic light emitting diodes, display/imaging devices, organic solar cells, sensing, color printing and visible light communications (VLC) [1–5]. So far, distinct color filter designs have been demonstrated. These designs are mostly based on plasmonic devices, nano-structures, guided mode resonance filters, photonic crystals, single and cascaded etalon resonators [6–16]. Recently, etalon resonators have attracted much attention. They have been strongly adopted as potential color filters for their seamless no-lithography fabrication technique in addition to their ability to attain angle tolerance [15–19]. Angle tolerance is useful in applications involving imaging/display, sensing and communications. This is because a wide field-of-view ($FOV$) or the feature of the ability to collect light at a wide-angle is crucial in miniature devices [20].
Transmission, reflection and absorption-based angle tolerant color filters employing etalon resonators have been proposed in literature. Etalon resonators acting as trans-reflective color filters have also been reported [17]. Trans-reflective filters are known for their benefit in applications such as CCD imaging, holography and fluorescence microscopy [21,22]. Generally, two types of etalon resonator filters have been introduced in literature. The filter building block is either an all dielectric resonator with a high index cavity such as Silicon (Si) or amorphous silicon (a-Si) [23,24], or a metal-insulator-metal (MIM) resonator [12–15], [17,18]. MIM-based resonators operating in the visible spectrum mostly utilize thin and thick layers of silver (Ag) for transmission and reflection operations, respectively [13–15], [17,18]. This is due to its low extinction coefficient and inter-band transitions that cause low optical loss in the visible spectrum [25].
Transmission/reflection properties of recently proposed color filters either suffer from values that do not exceed 70% or from angle tolerance limited to a maximum of 60°. Hence, there exists a trade-off between increasing transmission or reflection along with preserving a wide-angle operation of the filter [12–18]. In [19] an induced transmission structure has been proposed as a visible spectrum filter with a wide-angle operation. However, its wide bandwidth prevents its usage as a color filter.
The primary goal of this work is to design and demonstrate a trans-reflective color filter structure that fills in the above challenging requirements at a low cost and limited complexity. In this work, the benefit of a high index cavity is combined with the induced transmission property of the IMI structure in [19] to produce an asymmetric nano-resonator that acts as a color filter. A transmission enhancement of 10%-32% compared to [17] is achieved along with preserving a trans-reflective operation under angles of incidence ($AOI$) from 0°−70°. The proposed filter embodies the use of titanium dioxide (TiO2), Si and only a single Ag layer to form an induced transmission configuration (IMI). A symmetric IMI is known to contribute to an enhanced transmission performance [19–26]. This comes in addition to preserving a relatively high reflection performance through phase compensation within the structure. The proposed structure may be engineered to operate in the infrared (IR) spectral region as well. To the best of the authors’ knowledge, this structure has not been demonstrated nor discussed elsewhere.
The paper is arranged such that first, the filter target characteristics are demonstrated, followed by an elaboration of the principle of operation of the proposed design. A design for blue-yellow, green-magenta and red-cyan filters are given. Motivations behind choosing the layer materials and thicknesses are discussed. The effects of different design parameters on the trans-reflective performance of the proposed filters are examined. The angle tolerant behaviour is verified and physically explained. Moreover, the polarization effect is studied in light of polarization dependent loss ($PDL$) at different angles of incidence ($AOI$). Finally, electromagnetic field profiles are plotted for different operating wavelengths for better understanding and insights of the obtained results.
2. Design approach
2.1 Filter target characteristics
Angle tolerant trans-reflective color filters based on two nano-resonator structures are proposed. Each of the proposed filters is required to transmit one color and reflect another. As shown in Fig. 1, the filters are designed to transmit blue (B), green (G) and red (R) and reflect yellow, magenta and cyan, respectively. A relatively high transmissions ($T$) and reflections ($R$) > 90% are targeted along with a wide rejection region beyond the visible spectrum. Hence, alleviating the effect of inevitably collected background noise by a photodetector. Thus, these filters may be adequate for VLC applications [15].
The proposed structure is based on IMI geometry employing a nano-resonator with a dielectric cavity. The filters are composed of titanium dioxide (TiO2) and silver (Ag) alternating layers on a fused silica substrate. An additional silicon (Si) layer is added for green and red filter operations. The choice of such specific materials along with the effects of variations in filter’s design parameters are discussed hereafter. Thus, providing guidelines for tuning the proposed IMI-based nano-resonator filter for different transmission requirements.
2.2 Principle of operation
Two asymmetric nano-resonators are proposed in this work. The first serves for blue-yellow trans-reflective filter while the second is used for green-magenta and red-cyan filters.
2.2.1 Nano-resonator I
A silver (Ag) of 20 nm layer on a fused silica substrate offers a transmission as shown in Fig. 2 (solid curve). An asymmetric nano-resonator is formed if a layer of TiO2 (cavity) is coated to Ag, thus altering the transmission peak to be in accordance with the TiO2 thickness as in Fig. 2 (dashed curve). Transmission may be further enhanced if the complex amplitudes of reflection at the upper and lower interfaces of the metal are the same. This is defined by Macleod as the induced transmission scheme [26]. This scheme may be satisfied by adding another TiO2 layer below the Ag layer to obtain a symmetric IMI geometry. The induced transmission is shown in Fig. 2 (dotted curve). This transmission enhancement follows from altering the reflection characteristics of the Ag / TiO2 geometry by adding another TiO2 layer below the metal layer.
Fig. 2. Transmission behaviour of a single metal layer versus MI and IMI geometries under normal incidence.
The above nano-resoantor is deemed to exhibit a bandpass filtering effect which may be expressed in terms of intensity transmission and reflection of $T = \frac{{{T_a}{T_b}}}{{1 + {R_a}{R_b} - 2\sqrt {{R_a}{R_b}} cos\delta }}$ and $R = \frac{{2\sqrt {{R_a}{R_b}} ({1 - cos\delta } )}}{{1 + {R_a}{R_b} - 2\sqrt {{R_a}{R_b}} cos\delta }}$ , respectively. ${T_a}$ and ${T_b}$ are the intensity transmissions of TiO2/Ag mirror into the TiO2 cavity, and the transmission of the TiO2 cavity into air, respectively, where ${R_a}$ and ${R_b}$ are the corresponding reflectivities [27]. The total reflection phase $\delta $ is defined as total phase accumulated due to a single round trip in the TiO2 cavity, which may be given by:
where ${\varphi _{{r_{a,b}}}}$ are the reflection phases at the mirror-cavity and cavity-air interfaces, respectively. The roundtrip propagation phase inside the TiO2 cavity is $2\beta .L$, where $\beta = 2\pi {n_d}/\lambda $ and $L = d/cos\theta $ is the effective cavity thickness under oblique incidence $\theta $. The cavity geometric thickness is d. The resonance condition may be deduced from (1) at $\delta = 2m\pi $, where m is a positive integer.To obtain a trans-reflective blue-yellow, green-magenta and red-cyan trans-reflective filters, the resonance condition in (1) needs to be satisfied at 450 nm, 535 nm and 650 nm, respectively. Hence, cavity thicknesses are 110 nm, 155 nm and 185 nm, respectively.
In this work, angle-tolerance is set as a design requirement. Angle tolerance may be guaranteed via applying several conditions. One condition is preserving the resonance condition in (1) under different angles of incidence ($AOI$) [15], [19] and [28]. This condition requires that the variation in the propagation phase built up within the dielectric layers under different $AOI$ to be abolished by the negative phase encountered at the metal-dielectric interface [28]. For a TiO2 cavity of 110 nm, angle tolerance is preserved. However, for larger cavity thicknesses, the propagation phase increases more than can be accommodated by adding a single metal layer.
Therefore, the above resonator is suitable for blue-yellow angle tolerant trans-reflective filter, but fails to satisfy angle tolerance for green-magenta and red-cyan applications.
Another method to achieve angle tolerance is employing a high index cavity such as silicon (Si) [13], [23,24]. Si is not suitable for blue transmission filters due to its relatively high absorption in the blue spectral range. Hence, replacing TiO2 in the above nano-resonator by Si is applied herein for green-magenta and red-cyan trans-reflective filters only. A lower Si layer is added for induced transmission as previously illustrated. Resonance conditions in (1) are thus satisfied at Si thicknesses of 78 nm and 95 nm for green-magenta and red-cyan trans-reflectance, respectively. The transmission of green and red colors are shown in Fig. 3 (solid curves). For further transmission performance enhancement, a proposed remedy is presented hereafter.
2.2.2 Nano-resonator II
Replacing TiO2 in nano-resonator I by Si, shall degrade the trans-reflective performance of the color filters as shown in Fig. 3 (solid curve). This is attributed to losses that Si exhibits in the visible spectrum [25]. In this work, another trans-reflective color filter structure is proposed. It combines the benefits of high index Si cavity along with IMI geometry based on quasi-plasmon mode excitation that has been previously proposed in [19]. The Si cavity preserves angle tolerance under different $AOI$. And the IMI structure in [19] offers induced transmission and guarantees angle tolerance up to ${60^{\circ}}$. Hence, the second asymmetric nano-resonator proposed in this work is a high index Si cavity along with the IMI structure of [19] at one side and air on the other side. This structure shall be employed to obtain green-magenta and red-cyan trans- reflective filters as shown in Fig. 1. The resonance thicknesses of the Si layer are chosen to be 65 nm and 84 nm for green-magenta and red-cyan operations, respectively. The filter performance of the proposed second resonator is shown in Fig. 3 (dotted curves) for green and red filtering in comparison to resonator I structure employing Si instead of TiO2 (solid curves).
2.3 Selection and engineering of material
Ag is known to be an adequate choice for filters employing metals and operating in the visible spectrum [29–31]. The imaginary part of a metal’s dielectric constant ($Im\{{\varepsilon (\omega )} \}$) expresses the metal’s absorption characteristic. In the visible spectrum (400–700 nm), the $Im\{ {\varepsilon _{Ag}}\} $ exhibits a relatively small value in comparison to its real part, therefore, it may be neglected in analysis [25]. This explains why Ag exhibits a negligible absorption in the visible range of interest which contributes to a higher transmission and a lower corresponding reflection. Moreover, metals offer strong reflection at wavelength regions where ${n_m}\sim \kappa $, with ${n_m}$. is the complex refractive index of the metal, and $\kappa $ is its extinction coefficient (imaginary part of refractive index) [31,32]. At $\lambda > 700nm$, ${n_{Ag}}\sim \kappa $ , according to Palik [25]. Hence, high reflection is obtained and a wide rejection band is observed. Reflection and absorption behaviour of metals may be further modified by adding carefully chosen dielectric layers as previously illustrated. Structures employing a symmetric IMI geometry are proved to induce transmission at resonance wavelengths of interest as seen in Fig. 2 and 3 [26–30].
In this work, two nano-resonators are introduced. The primary nano-resonator (Nano-resonator I), is an asymmetric resonator of {TiO2/Ag||TiO2||air} structure over a substrate of fused silica. TiO2 is chosen for its transparency in the visible spectral range, along with its good adhesion properties to Ag [33,34]. This structure is suitable for blue-yellow trans-reflective filters as shown in Fig. 2. For green-magenta and red-cyan filters, an asymmetric resonator of {Si/Ag||Si||air} is introduced. Si is chosen for its high refractive index that contributes to angle tolerance as illustrated previously. This structure gives a transmission less than that of the above proposed blue filter with TiO2. This is due to the complex dielectric constant of Si that dicates less transparency and higher absorption than TiO2 in the visible spectral region [25].
As a remedy to the deteriorated transmission of the above green and red filters, Nano-resonator II is proposed. Nano-resonator II combines the merits of employing a high index Si cavity with a symmetric IMI (TiO2/Ag/TiO2) that supports flat quasi-plasmon mode dispersion. To guarantee the operation under this mode, two conditions must be satisfied [28]; 1) ${n_{Ti{O_2}}} = {\kappa _{Ag}}$ at $\lambda $ of operation, and 2) ${d_{Ti{O_2}}} = {\lambda _{SP}}/({4{n_{Ti{O_2}}}} )$ . The over layer Si is then considered as a cavity as illustrated previously. Si and TiO2 exhibit good adhesion properties [35].
Both structures are deposited over fused silica substrates (exit medium) with n ∼ 1.47 as in [30], [34] and [36] with air as the superstrate (incidence medium). The transmission/reflection performances and results in this work are generated using the characteristic matrix approach of Abeles [37]. It may be constructed in MATLAB or utilizing OpenFilters software [38]. Dielectric constants of all materials in this work are extracted from [25].
3. Results and discussion
3.1 Trans-reflective characteristics
A schematic of the three trans-reflective color filters proposed in this work is given in Fig. 1. When white light is incident on the filter in Fig. 1, blue, green and red colors are transmitted, whereas yellow, magenta and cyan are reflected, respectively. Optimized filters dimensions along with refractive indices of the employed materials are given in Tables 1 and 2. The transmission and reflection behaviours of the above filters are shown in Fig. 4(a), (b) and (c), respectively. From Fig. 4(a) and (b), it is noted that all transmission peaks are concurrent with zero reflection dips. This occurs as a result of applying the induced transmission scheme by providing a symmetric IMI geometry as previously illustrated. The above filters reflect 80% of the incident light as shown in Fig. 4(b). Figure 4(c) provides a comparison of the proposed structures with high performance recently published color filters [17]. Comparison with [17] in particular is chosen as it offers the best performance in recently available results in literature [13], [15–18]. From Fig. 4(c), it is clear that the blue-yellow filter exhibits a transmission of above 90% with improvement of 31.46% compared to [17]. The green-magenta filter offers a transmission of 80% with improvement of 9% compared to [17]. And the red-cyan filter transmits around 80% of the incident light on it, manifesting an improvement of 14.7% when compared to [17]. The Si thicknesses of the proposed filters used to generate Fig. 4(c) are slightly altered from those given in Table 1. This is done in order to attain the same exact peak of [17] for fair comparison. Si thicknesses used are 70 nm and 90 nm for green-magenta and red-cyan filters, respectively. Generally, different shades of the same color may be obtained by tuning the cavity thickness as desired.
Table 1. Optimized proposed color filter structures of Fig. 1. First layer is adjacent to the substrate.
Fig. 4. (a) Transmission, (b) corresponding reflection behaviour of proposed color filters in Fig. 1 under normal incidence, and (c) Comparison of proposed filters transmission with recently published filter in [17].
3.2 Transmission engineering and filter tunability
The effect of varying the TiO2, Si and Ag thicknesses are studied in Fig. 5 under normal incidence. The symmetric IMI structure composed of TiO2/Ag/ TiO2 is operated herein in two distinct ways. Once to serve as nano-resonator I utilized as a blue - yellow filter, and another to act as a mirror for nano-resonator II structure. The operation in either of the two modes depends upon the TiO2 layers thicknesses surrounding the Ag layer. In Fig. 5(a), the TiO2 thickness is varied from 15–55 nm. The middle Ag layer is 20 nm. Within this TiO2 thickness range (${d_{Ti{O_2}}}\,<\,60$ nm), only one transmission peak (peak I) appears in the visible spectrum with properties given in Fig. 5(a). This peak may be attributed to quasi-plasmon mode excitation [19]. A maximum transmission value (${T_{max}}$) occurs at ${d_{Ti{O_2}}} = 30\,{\textrm{nm}}$ as appears in Fig. 5(a)i. The value ${d_{Ti{O_2}}} = 30$ resembles the quarter surface plasmon wavelength at the TiO2/Ag interface; ${\lambda _{SP}}/({4{n_{Ti{O_2}}}} )$. The dielectric constant of TiO2 is ${n_{Ti{O_2}}}$ and ${\lambda _{SP}}$ is the free-space surface plasmon wavelength of Ag ($= 2\pi c/{\omega _{SP}}$), and $c$ is the speed of light in free space [15], [28].
Fig. 5. (a) TiO2 thickness effect on (i) maximum transmission value (ii) cut-on and cut-off wavelengths, and (iii) transmission bandwidth, (b) Peaks I and II for different TiO2/Ag(20 nm)/TiO2 thicknesses, (c) Si over-layer (cavity) effect on (i) maximum transmission value (ii) cut-on and cut-off wavelengths, and (iii) transmission bandwidth, (d) Ag layer thickness effect on (i) maximum transmission value (ii) cut-on and cut-off wavelengths, and (iii) transmission bandwidth.
As ${d_{Ti{O_2}}}$ surpasses 60 nm, another peak (peak II) begins to appear at shorter wavelengths, with the previous peak getting broader and shifting towards the infra-red (IR) region as shown in Fig. 5(a)ii, iii and Fig. 5(b). Peak II shows an agreement with asymmetric Fabry-Perot resonator transmission peaks which occur at cavity thicknesses of ${L_{cavity}} = m.\lambda /2.\,{n_{cavity}}$, where $m$ is an integer and ${n_{cavity}}$ is the refractive index of the cavity [27]. The cavity in the above structure is considered the upper TiO2 layer adjacent to air. For the proposed filters in this work, IMI structure exhibiting peak II (in Fig. 5(b)) , i.e. ${d_{Ti{O_2}}}\,>\,60\,{\textrm{nm}}$ is employed in the design of the blue-yellow filter in Fig. 1. On the other hand, the IMI operating at peak I (in Fig. 5(b)), i.e., ${d_{Ti{O_2}}}\,<\,60$ nm are used in green-magenta and red-cyan proposed filter designs in Fig. 1. It is worth mentioning that the bandwidth in a symmetric IMI structure is tunable with variations in ${d_{Ti{O_2}}}$ as shown in Fig. 5(a)ii, iii, hence the choice of ${d_{Ti{O_2}}}$ is application based.
For the operation of green-magenta and red-cyan filters, a Si over-layer is added above the IMI structure. The overall structure acts then as an asymmetric Fabry-Perot resonator with a Si cavity which provides transmission peaks at cavity thicknesses of ${L_{Si}} = m.\lambda /2.{n_{Si}}$. The choice of Si material has been justified previously to be of use for the angle tolerant behaviour of the filters. This shall be discussed hereafter as well. In this work, first order peaks are considered. The effect of changing the Si cavity thickness from 35 nm to 100 nm on transmission characteristics is shown in Fig. 5(c). From Fig. 5(c)i, ${T_{max}}$ increases as Si cavity thickness increases till it reaches∼-1 dB. It then almost preserves its value. The wavelength at which resonance occurs is a function of the Si cavity thickness as shown in Fig. 5(c)ii; ${L_{Si}} = m.\lambda /2.{n_{Si}}$, with $m = 1$ and ${n_{Si}}$ is the refractive index of the Si cavity. Hence, the small ${T_{max}}$ value at ${d_{Si}} = 30$-60 nm may be due to Si losses in the visible spectrum (300–700 nm) which is maximum near the 300 nm edge and decreases as $\lambda $ of operation moves towards the IR. The bandwidth in Fig. 5(c) iii appears to be tunable with variations in the Si cavity thickness.
Variations in the Ag thickness affects mainly the ${T_{max}}$ value as shown in Fig. 5(d)i. The Ag layer thickness is varied from 15–60 nm. As expected, the transmission is higher for thinner layers of Ag. This may be due to the fact that the absorption, $A,$ of a single metal layer is directly proportional to its thickness. The minimum reflection value possible to maintain in thick Ag layers is ∼ 30%, along with another 25% of absorption (instead of 5% and 10%, respectively in case of thinner Ag layers), thus ${T_{max}}$ suffers a degradation of ∼ 70% when compared to thinner Ag cases.
A trade-off is encountered in practice, which is that Ag should be thin enough to allow light through the structure, yet thick enough such that it does not deviate from bulk metal film optical properties. Hence, a rule of thumb is that Ag layers are preferably chosen with thickness more than 15 nm in order to avoid metal islandization during fabrication. Metal islandization may result in large deviations from metal film expected performance [30], [32] and [36]. For the above mentioned reasons, Ag layer thickness throughout this work is chosen to be 20 nm.
3.3 Angle tolerance and color trajectory
To evaluate the angle tolerant performance of color filters, it is useful to examine their color trajectory. For a trans-reflective filter, the color trajectory of interest is the transmitted and reflected colors under different $AOI{\textrm{s}}$. For angle tolerant trans-reflective filters, preserved transmitted and reflected colors are expected for a wide range of $AOI{\textrm{s}}$. The trajectory is computed for the proposed filter designs in Fig. 1 with the aid of OpenFilters software [37,38] under unpolarized D65 illumination. The D65 illumination resembles the illumination of natural daylight-balanced light emitting diodes (LEDs) installed in homes or offices [39]. Figure 6 shows a colored representation to the results in Fig. 4(a, b). The color trajectories in Fig. 6 prove that the proposed filter structures offer acceptable trans-reflective operations under unpolarized light till an $AOI$ of 70° or slightly higher.
Fig. 6. Color trajectories from 0° to 89° for (a) blue-yellow, (b) green-magenta and (c) red-cyan filters of Fig. 1 and Fig. 4.
It is important to note that although D65 illumination is used to generate Fig. 6, but the proposed filters preserve their trans-reflective color performance under different cooler or warmer illuminations with a very slight discrepancy in the color shade but not the color itself.
Another method to demonstrate the proposed filters color behavior versus different AOIs is by observing the color maps of such filters. The CIE 1931 color space chromaticity diagram is presented in Fig. 7. The outer curved boundary has the wavelengths shown in nanometers. Calculated color maps of the proposed filters in Table 1 are presented in Fig. 8. The transmitted/reflected color variations with AOIs variation are also shown.
Fig. 7. The CIE 1931 color space chromaticity diagram. The outer curved boundary is the spectral locus, with wavelengths shown in nanometers [40].
Fig. 8. Calculated color maps of the proposed filters in Table 1. The transmitted/reflected color variation with AOIs variation is shown.
3.4 Polarization effect
The transmission/reflection performance of the proposed nano-resonator filters in this work is evaluated under unpolarized source illumination. Hence, the transmission and reflection behaviours are quantified as the average of transmissions/reflections under TM, and TE illuminations. It is worth mentioning that all previous Figures are generated under the assumption of unpolarized light where ${T_{unpolarized}} = \frac{1}{2}({{T_{TM}} + {T_{TE}}} )$, and ${R_{unpolarized}} = \frac{1}{2}({{R_{TM}} + {R_{TE}}})$ where $T$ and R indicate transmission and reflection, respectively [15], [41,42]. Although this averaging may indicate the angle tolerant behaviour of the filter, however, discussing the effect of polarization dependence is considered to be pivotal for accurate performance assessment. Transmission characteristics for the two extreme cases of TE and TM polarizations for the proposed filters in Fig. 1 are calculated with evaluation of the obtained results. Reflection characteristics are similar to those of transmission, hence not added to Figures.
To evaluate angle tolerance of the proposed filters, it is important to examine the polarization tolerance of the filters at different $AOI.$ This dictates the need to calculate the polarization dependence loss ($PDL$) of the proposed filters. Lower $PDL$ values indicate better angle tolerance. According to [43], $PDL$ maybe defined as:
where ${T_{TM,TE}}$ are the transmission values under TM and TE illumnations, respectively. $PDL$ along with variations in the central wavelength and filters bandwidth are studied for the three filters in Fig. 1. The results are given in Fig. 9.Fig. 9. (a). Blue-yellow filter transmission characteristics under different $AOI{\textrm{s}}$, (i) Maximum passband transmission, with $PDL$ computation, (ii) Variations in ${\lambda _o}$, and (iii) transmission bandwidth, all under TM and TE incident lights, (b). Green-magenta filter transmission characteristics under different $AOI{\textrm{s}}$, (i) Maximum passband transmission, with $PDL$ computation, (ii) Variations in ${\lambda _o}$, and (iii) transmission bandwidth, all under TM and TE incident lights, (c). Red-cyan filter transmission characteristics under different $AOI{\textrm{s}}$, (i) Maximum passband transmission, with $PDL$ computation, (ii) Variations in ${\lambda _o}$, and (iii) transmission bandwidth, all under TM and TE incident lights.
The performance of the blue-yellow filter in Fig. 1 across different $AOI{\textrm{s}}$ is given in Fig. 9(a). Figure 9(a)i, shows the variations in the passband maximum transmission values (${T_{max}}({TM,TE} )$) under TM and TE polarizations, respectively in addition to the $PDL$ of the proposed filters, at different $AOI$. TM and TE transmissions coincide till ∼ ${50^{\circ}}$, hence $PDL$ is zero. For larger $AOI{\textrm{s}}$, ${T_{max}}({TM} )$ suffers from more degradation than ${T_{max}}({TE} )$ causing a $PDL$ drop to −0.5 dB at 70°, which is still acceptable allowing for filter operation at further larger angles. However, to further ensure angle tolerance of the filter, wide angle performance of the filter’s central wavelength (${\lambda _o}$) as well as its bandwidth behaviour under different $AOI{\textrm{s}}$ must be examined. From Fig. 9(a)ii, it is clear that ${\lambda _o}$ almost preserves its values till 70° for both polarizations. A slight decrease is observed, from 448 nm to 420.4 nm, but does not affect the color performance of the filter. The bandwidth is affected by $AOI{\textrm{s}}$ as shown in Fig. 9(a)iii. The performance under TE polarization shows more angle tolerance than under TM at higher angles. However, the transmission of unpolarized light may be seen as the average between the TM and TE illuminations at the same angle. This suggests that the proposed blue-yellow filter is angle tolerant up to 70° under unpolarized light illumination.
Similar performances for green/magenta and red/cyan filters in Fig. 1 are obtained. Figure 9(b) and 9(c), show similar performances to those in Fig. 9(a) under TE and TM illuminations up to 60°. At larger angles, the average performance under unpoalrized light is observed to preserve its behaviour up to 70°. Visible LED sources which may be used to illuminate the above proposed filters are designed to generate unpolarized light [44]. Hence, the above proposed filters may be used for $AOI{\textrm{s}}$ up to 70°. This is due to the compensation in the average bandwidth performance between TE and TM illuminations under larger $AOI{\textrm{s}}$.
3.5 Field profiles
The electromagnetic field distribution across the proposed blue-yellow filter in Table 1 is shown in Fig. 10. In Fig. 10(a), the squared value of the normalized magnetic field ${|{{H_y}} |^2}$ is plotted at ${\lambda _o}$ of blue and yellow colors; 425 nm and 580 nm, respectively [17]. This shows the field behaviour at desired transmission and reflection wavelengths of the design. By observing the field at the superstrate (air), it is obvious that at a wavelength of blue resonance (425 nm), reflection is significantly mitigated. This appears in Fig. 10 as alleviated differences in amplitude between crests and troughs of the standing wave built up in the superstrate. This reduction of reflection implies a high transmission capability of the proposed filter design [30]. On the other hand, at 580 nm, which is the peak wavelength of the reflected yellow color, higher reflection is noted at the superstrate end. This implies a strong reflected yellow light from the filter as targeted by the proposed design.
Fig. 10. (a) Normalized squared TM field profiles at normal incidence for blue-yellow filter at λ = 425nm and 580nm, respectively, (b) Normalized squared TM field profiles at normal incidence for green-magenta filter at λ = 535nm and 415nm, respectively.
In Fig. 10(b), ${|{{H_y}} |^2}$ is also plotted at ${\lambda _o}$ of green and magenta colors; 535 nm and 415 nm, respectively for the green-magenta filter in Table 1 [17]. Similar to Fig. 10(a), mitigated reflections in air at 535 nm indicates strong green transmission resonance to the substrate, whereas strong reflection at 415 nm shows strong reflection of magenta spectrum as desired. It is however, obvious that the electromagnetic field value drops significantly after passing through the Si layer. This may be attributed to optical properties of Si and Ag. The losses encountered in the Si layer due to its absorption characteristics in the visible spectrum causes a significant drop in the field after passing through the Si layer.
Moreover, an additional decrease in the transmitted field value is seen after passing through the Ag layer. This decrease is ∼40% compared to 23% in Fig. 10(a) for the same Ag layer thickness of 20 nm. This is due to weak transmission Ag behaviour at higher $\lambda $ as shown in Fig. 2. Hence, it is worth mentioning that despite employing the induced transmission scheme (IMI) of [26], induced transmission is inevitably limited by natural properties of the materials used in the proposed filter design.
4. Conclusion
In this work, lithography-free, asymmetric, planar nano-resonator trans-reflective color filters incorporating a single metal layer are proposed. Two nano-resonator structures are demonstrated. The first, nano-resonator I, is a blue-yellow filter composed of a TiO2/Ag|| TiO2 planar structure, which gives an insertion loss of ∼ 0.33 dB, with at least a 31.46% transmission enhancement compared to equivalent recently designed MIM filters [13], [16–18]. And a 14.13% transmission enhancement than the blue filter previously proposed in [15]. Whereas the second proposed nano-resonator II is designed for green-magenta and red-cyan filter applications offering 9% and 14.7% enhancements in insertion loss, respectively. Nano-resonator II is a TiO2/Ag/TiO2||Si planar structure. Nano-resonator II benefits of the induced transmission of a TiO2/Ag/ TiO2 structure in addition to the angle tolerance provided by a high index Si cavity [19], [23,24] and [26]. An insertion loss enhancement of at least 14.3% compared to [13], [16–18] is achieved. The proposed filters preserve their trans-reflective capabilities for a wide range of angles (0°∼70°) since constructive interference for transmission and reflection passbands are satisfied over a wide range of $AOI{\textrm{s}}$. The performances of the proposed nano-resonator filters are examined for two extreme polarization cases, TE and TM. The filters’ $PDL$ are quantified and show acceptable wide $FOV$ (0°∼70°) performance under unpolarized light.
To the best of the authors’ knowledge, incorporating an IMI angle tolerant structure in a trans-reflective color filter in this manner has not been previously demonstrated.
Funding
Qatar National Research Fund (QNRF) (NPRP 9-077-2-036).
Acknowledgments
This work was made possible by the NPRP award [NPRP 9-077-2-036] from the Qatar National Research Fund (a member of the Qatar Foundation). The statements made herein are solely the responsibility of the author[s].
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