Structural color filters based on nano-photonic structures are regarded as an integral element for the implementation of display devices, image sensors, digital photography and projectors, security tags, color printing, multispectral imaging, and so forth [1-6]. Such structural filters may act as an attractive replacement for conventional colorant pigment-based filters due to their appealing merits in terms of enhanced efficiency, ease of fabrication, and eco-friendliness. Recently, multilayer stacks composed of periodical layers of high (H) and low (L) index layers, particularly received extensive attention as a vehicle to realize structural color filters. Such multilayered structural colors incorporating dense or nano-porous TiO₂ and SiO₂ were actively studied thanks to their excellent properties, such as high transparency, non-toxicity, chemical stability, good film adhesion, and mechanical durability [7-13].

TiO₂ is conspicuously promising from the perspective of its high refractive index (n=~2.3) and good transparency in the visible range. Under the limited availability of low-index materials, multilayered structural colors were actively developed by drawing upon porous or columnar SiO₂ or TiO₂ as a low-index layer, focusing mainly on the reflection mode while ignoring the transmission color response [7-11]. However, this method suffered from a couple of drawbacks that mostly stem from the porous and/or columnar microstructure of the films. The performance of such devices is potentially vulnerable to the environment, considering that gases or fluids diffusing or penetrating into the device might change the optical properties of the material undesirably [14]. The columnar structure, as in the case of obliquely deposited TiO₂ film, renders it optically anisotropic [14]. MgF₂, which was widely used for optical coatings in light of its prominent properties in terms of a wide transmission window spanning from UV up to mid-infrared (200 nm ~ 7 μm), high robustness against humidity and mechanical abrasion, is perceived to be an outstanding candidate as a low-index layer associated with BSs with a high index contrast, leading to enhanced reflectivity with a minimal number of pairs [15]. Driven by those advantages, numerous works on TiO₂-MgF₂ multilayer stacks have been reported for different applications such as bandpass filtering and anti-reflection and high-reflection coatings [16-19]. However, the application of the material combination towards the realization of structural color filters has rarely been discussed. It should also be remarked that the previous reports on multilayered structural colors mostly dealt with their operation in the reflection mode while ignoring the color filtering in transmission-mode [7-13]. A transmission-type color filter is of paramount importance in view of its potential applications in transmissive displays and sensors and thus the investigation of color filtering of such multilayer stacks in both reflection and transmission modes would be highly desirable. By resorting to elevated index contrast between high and low index materials in a multilayer stack, we could acquire enhanced reflectivity while the transmission is significantly suppressed over a spectral range, thereby enabling the development of highly efficient structural trans-reflective colors, which may serve as subtractive and additive color filters in the transmission and reflection mode, respectively. Such trans-reflective color filters are key elements for various optical applications, including holography, CCD imaging, multispectral sensor, and fluorescence microscopy [20, 21]. However, multilayer stacks serving as color filters in such trans-reflective configurations, which require an optimal stop band assuming an appropriate bandwidth within the visible regime, still have not been investigated.

In this paper, we propose and realize highly efficient transreflective color filters operating under normal incidence by exploiting a multilayer stack structure which consists of a stack of five bi-layers of TiO₂ and MgF₂. We inspect the performance in both transmission and reflection mode in terms of the transmission and reflection efficiencies, chromaticity coordinates, and demonstrated colors. The angular dependence of the transmission/reflection spectra was also meticulously monitored with respect to light polarization. The proposed structural colors, tapping into multilayer stacks incorporating dense multilayers of TiO₂ and MgF₂, are anticipated to lead to more stable color response compared to porous and columnar counterparts, which are either anisotropic or are potentially vulnerable to the environment, considering that gases or fluids diffusing or penetrating into the device might change the optical properties of the material undesirably [7-11, 14]. The appeal of the work is not only the scope of the material composition that has been utilized for structural color filter applications but also the realization of trans-reflective color filters, featuring an optimal stop band assuming an appropriate bandwidth within the visible regime, which has not been rigorously examined yet.

As illustrated in Fig. 1, the proposed color filter capitalizes on a multilayered structure, comprising periodic stacks of alternating layers of high (H) and low (L) index materials of TiO₂ and MgF₂, respectively. The periodic stack of two materials is supposed to create a photonic band gap where wave propagation is prohibited. Within the corresponding spectral stop band that is centered at a certain wavelength, incident light is remarkably reflected and thus the transmission is suppressed. Hence, the device is anticipated to serve as a structural color filter, delivering red, green, and blue (RGB) color output in the reflection mode and cyan, magenta, and yellow (CMY) color output in the transmission mode. With regard to the structure, the position of the stop band for the normal incidence is determined by m λ_ₒ=2(n_ld_l+n_hd_h), where λ_ₒ is the wavelength in vacuum, m is the order of the stop band, and n_h, n_l, d_h, and d_l are the respective refractive indices and thicknesses of the H- and L-index layers. Therefore, the position of the stop band can be tailored by altering the optical path length of the layers. For light impinging upon the filter, the angle of incidence is denoted as θ_o while the light is either s- or p-polarized in accordance with the direction of the electric field.

The design of the trans-reflective visible filter was conducted with the assistance of a commercially available tool specialized for analyzing thin-film structures, Essential Macleod (Version 9.8.436). For the numerical simulations, the glass substrate was considered to be semi-infinite while the dispersion properties for deposited TiO₂ films were actually taken into account as depicted in Fig. 2(a), while the dispersion for MgF₂ films was taken from the refractive index database [22]. The number of TiO₂-MgF₂ pairs and their thicknesses were varied to attain selectively suppressed transmission spectra and selectively elevated reflection spectra. We first endeavored to examine the effect of d_h and d_l on the transmission spectra of the device with five bi-layers of TiO₂-MgF₂. d_h and d_l were varied as integer (q) multiples of 73.23 and 61.95 nm respectively. In response to q=1, 2, and 3, three dominant stop bands were obtained in the visible band. It was clearly seen from Fig. 2(b) that the 3-dB bandwidths were 200, 95, and 30 nm for q=1, 2, and 3, respectively. In order to concoct a subtractive color filter, where the band corresponding to blue, green, or red should be individually suppressed in terms of the transmission, a bandwidth close to 100 nm would be desirable. In this way, we could engage the stop band corresponding to q=2 which accompanies an appropriate bandwidth of ~95 nm, by setting d_h and d_l at 146.46 and 123.9 nm, respectively.

In an effort to probe the influence of the number of TiO₂-MgF₂ pairs on the optical characteristics of the multilayer structure, we observed the transmission and reflection spectra for the normal incidence. Figures 2(c) and 2(d) respectively illustrate the simulated transmission and reflection spectra for one, three, five and seven pairs within the stack. The thickness of each of the TiO₂ and MgF₂ layers was uniformly kept at 146.5 nm and 123.9 nm, respectively. As shown in Figs. 2(c) and 2(d), the reflection was selectively enhanced while the transmission was profoundly suppressed around a particular wavelength, when the number of bi-layer pairs was varying from one to seven. However, the off-resonance transmission decreased in the case of seven bi-layers as compared to the case of five bi-layers. This is the reason why we decided to further consider the case of five bi-layers. For a multilayer stack that is made up of five bi-layers or more, the reflection reached as high as 96% and a properly broad reflection peak was observed at λ=518 nm. Similarly, the roll-off characteristics in relation to the transmission dip improved on the whole, with the transmission level held below 4% at the location of the reflection peak. The transmission was over 80% on average over the wavelength range away from the transmission dip. It was readily signified that the proposed device can act as a highly efficient trans-reflective color filter, offering subtractive and additive filtering characteristics in the transmission and reflection modes, respectively.

As supported through the additional simulations, the position of the transmission dip and the reflection peak could be tuned across the entire visible band by controlling the thickness of the layers belonging to the stack. Figures 3(a) and 3(b) respectively display the theoretical transmission and reflection spectra of the three devices, designated as Dev1, Dev2, and Dev3, which are composed of five bi-layers with different thicknesses of high- and low-index layers, i.e. d_h and d_l. For each of the devices, the thickness of layers and the refractive index of the TiO₂ and MgF₂ films are arranged in Table 1 alongside the resonant wavelength. The three devices each produced a transmission dip in conjunction with a reflection peak pertaining to the blue, green, and red bands.

The proposed trans-reflective color filters were fabricated over a footprint of 7.63 × 2.54 cm² , by forming alternating layers of TiO₂ and MgF₂ thin films via electron-beam evaporation (Balzers BAK 600). Prior to film deposition, the substrate was ultrasonically cleaned with acetone, isopropanol, and deionized water in sequence. Five TiO₂-MgF₂ pairs were successively formed on a glass substrate via planetary rotation to obtain uniform films, when the evaporation chamber was evacuated to a base pressure of 6×10⁻⁶ Torr. During TiO₂ evaporation a small amount of oxygen with a gas pressure of 5×10⁻⁵ Torr was introduced to make the film composition as stoichiometric as possible; otherwise oxygen-deficit titanium oxide would be obtained. The substrate temperature was kept at 100 ℃ during deposition. The deposition rates for TiO₂ and MgF₂ films were monitored by a quartz crystal microbalance to keep them at 3 and 39 nm/min, respectively. Figure 4 reveals scanning electron microscopy (SEM) images of the crosssections of the fabricated filters Dev1, Dev2 and Dev3, manifesting clearly defined dielectric layers with good fidelity to design.

In an attempt to evaluate the transmission spectra for the normal and oblique incidence, a collimated light beam from a halogen lamp (Model LS-1, Ocean Optics) was irradiated upon the prepared device mounted on a motorized rotation stage, while the transmitted light was captured by a multimode fiber linked to a spectrometer (Model USB-4000-VIS-NIR, Ocean Optics). Meanwhile, in the course of measuring the reflection spectra, the collimated beam was illuminated on the device via a 50:50 non-polarizing beam splitter cube (BS016, Thorlabs) while the reflected light from the device was deviated by the beam splitter and similarly coupled to a spectrometer. A broadband dielectric mirror with ~99% reflectivity (BB1-E02, Thorlabs) was utilized as a reference for reflection measurements. To investigate the transfer characteristics for different polarizations, the incident light was properly polarized by use of a calcite crystal polarizer (GTH 10M-A, Thorlabs). The transmission and reflection responses were scrutinized under the normal incidence and are presented in Fig. 5, where the measured and calculated spectra are plotted in solid and dashed curves, respectively. As shown in Fig. 5(a), the transmission was found to be selectively suppressed at λ=422 nm, 518 nm, and 646 nm for Dev1, Dev2, and Dev3, respectively, where the reflection peaks coincided with the transmission dips, thereby resulting in a good agreement with the simulated values. Outside of the resonance wavelengths all the three devices delivered a transmission efficiency surpassing 90%. It is to be noted that there are ripples in the transmission windows, giving rise to variations of the transmission efficiency and degrading the color response of the filters. Such ripples are reported to be attributed to multiple wave interference, which can be alleviated by adding a pair of antireflection layers to either side of the multilayer stack [23, 24]. For the transmission dips, the measured reflection presented a peak of as high as 94% as seen in Fig 5(b). Good correlations between simulated and measured results were attained for both transmission and reflection spectra. The chromaticity coordinates in accordance with the simulated and measured spectral responses were estimated [25, 26] and plotted in the standard CIE (International Commission on Illumination) 1931 chromaticity diagram. It was implied from the coordinates in the chromaticity diagram that Dev1, Dev2, and Dev3 respectively demonstrated yellow, magenta, and cyan colors for the transmission mode as depicted in Fig. 5(c), while the complementary colors, such as blue, green, and red, were obtained for the reflection mode as shown in Fig. 5(d). Remarkable agreement between the simulated and measured color responses was witnessed in the chromaticity diagram.

We took a photograph of the color output from fabricated filters, in a bid to prove that the prepared filters are capable of practically demonstrating colors. The photographic images of the three devices including Dev1, Dev2, and Dev3 are displayed from left to right in the transmission mode, as shown in Fig. 6(a), exhibiting bright and distinct colors of yellow, magenta, and cyan, respectively. The corresponding responses in the reflection mode are presented from left to right, as shown in Fig. 6(b), producing bright and vivid colors of blue, green, and red. The filters delivered uniform colors over the developed footprint of 7.63 cm × 2.54 cm both in the transmission and reflection mode. As a result, the fabricated devices were corroborated to act as a highly efficient trans-reflective color filter as intended under normal incidence.

The optical transmission and reflection characteristics of the filters were then explored as a function of the angle of incidence θ_o for different light polarizations. The transmission and reflection spectra were measured over the range of from 400 to 700 nm under different angles of incidence and polarizations using a PHOTON RT UV-VIS-NIR scanning spectrophotometer (EssentOptics Ltd. 23A-81, Republic of Belarus). As shown in Fig. 6, the transmission spectra for a magenta filter (Dev2) over an angular range of from θ_o =0° to 75° are displayed in a contour map. The simulated results are respectively plotted in Figs. 7(a), 7(b), and 7(c) for unpolarized, p-polarized, and s-polarized incident light while the corresponding measured transmission spectra are respectively depicted in Figs. 7(d), 7(e), and 7(f). For the normal incidence with θ_o =0°, both p- and s-polarized light exhibited the same spectral response. With increasing angle, the bands of suppressed transmission were blue shifted for the p- and s-polarized light. The bandwidth of the transmission dips were notably enlarged for the case of s-polarized incidence, whereas the bandwidth slightly decreased for the case of p-polarized incidence. Hence, for the unpolarized light, with increasing angle the transmission dips were blue shifted and the bandwidth diminished. The maximum transmission was measured to be ~60% and the transmission at the dip was kept below 5%. The measurement results were verified to follow the same trend as predicted by the simulations for different polarizations. It was proved that the other two devices, Dev1 (yellow) and Dev3 (cyan), gave rise to similar angle-sensitive transmission characteristics.

Finally, we looked into the dependence of the reflection characteristics of the filters upon the angle of incidence θ_o for different polarized lights, as shown in Fig. 8. For the magenta color filter (Dev2), the contour maps for the simulated reflection spectra over an angular range of θ_o=10° to 75° are plotted in Figs. 8(a), 8(b), and 8(c) for unpolarized, p-polarized, and s-polarized incidence, respectively. The corresponding measured reflection spectra are depicted in Figs. 8(d), 8(e), and 8(f). We observed the same spectral shape for the normal incidence for p- and s-polarized light. As θ_o is increased, the bands relevant to the reflection peaks were blue shifted. The bandwidth for the reflection peaks was fairly broadened with increasing angle for the s-polarized case, but it slightly narrowed for the p-polarized case. As a consequence, for the unpolarized light the reflection peaks were blue shifted and the bandwidth decreased for larger θ_o. The maximum reflection was beyond 92% throughout the whole angular range. The simulation and measured results matched together. The other two filters, Dev1 (yellow) and Dev3 (cyan), were also observed to provide similar angle dependent reflection characteristics. It is remarked that all the transmission and reflection spectra presented in this paper were simulated by using a commercial simulation tool, Essential Macleod (Version 9.8.436).

Highly efficient trans-reflective color filters were presented counting on a high index contrast multilayer stack structure constituted of periodically arranged five bi-layers of TiO₂ and MgF₂ as high and low index materials. The devices featured high efficiencies beyond 90% in both transmissive and reflective configurations, exhibiting vivid primary colors in subtractive as well as additive schemes respectively for those configurations. By adjusting the thicknesses and the numbers of bi-layers, an optimal stop band with an appropriate bandwidth was achieved. The color performance of the filters was scrutinized by referring to the chromaticity coordinates of the transmission and reflection spectra, alongside photographed vivid color images in both modes. The angular dependence and polarization sensitivity were thoroughly assessed for both transmission and reflection spectra. It is definitely predicted that the proposed devices, simply involving deposited bi-layers of TiO₂ and MgF₂, are conspicuously advantageous in terms of simple and cost-effective fabrication, desirable for scalability and volume production. Inferring from their high efficiency as well as low sensitivity to the angle and polarization, the proposed color filters are categorically predicted to play a pivotal role in display, imaging, and sensor applications.