We propose omnidirectional reflective color filters based on metal-dielectric-metal subwavelength grating structure. By particle swarm optimization, the structural parameters of three color filters (yellow, magenta, cyan) are obtained. The optimized filters can present the same perceived specular color at unpolarized illumination for a broad range of incident angles. The reflectance curves at different incident angles keep almost invariable and the color difference is less than 6 in CIEDE2000 formula up to 45°. Angle-insensitive properties including the incident angular tolerance, azimuthal angular tolerance and the polarization effect are investigated thoroughly to construct a real omnidirectional color filter. Through the analysis of the magnetic field, the physical origin is verified that the total absorption band at specific wavelength results from the localized surface plasmon resonance responsible for the angle insensitive spectral filtering.
© 2014 Optical Society of America
Color filter displays various colors by selectively transmitting or reflecting a specific wavelength in the visible region. Nowadays, color filters are widely used in the fields of display, colorful decoration, anti-counterfeiting and so forth. The optical thin film filters by multi-layer interference and the guided mode resonance (GMR) filters are high angle sensitive and the angular tolerance is quite poor, with so called blue shift [1–6]. The traditional chemical color filters have a relatively high angular tolerance, which are attributed to the wavelength-selective absorption of the particular functional groups of the comprised chemical pigment. However, such chemical pigments are not stable to a variety of processing chemicals, cannot stand long-time illumination with strong light intensities, require lots of processes for filter patterns, and cause a significant environmental burden simultaneously. For recent years, color filters combined with structural color have been investigated extensively and developed in different aspects, owing to the development of numerical simulation algorithms and nano/micro fabrication techniques. Ting Xu theoretically and experimentally demonstrated plasmon nanoresonators to disperse light with efficiency. By arranging different resonators, arbitrary colored patterns on a micrometer scale are achievable . Karthik Kumar presented an approach for full-color printing at the optical diffraction limit by encoding color information into silver/gold nanodisks raised above a holey backreflector . Jeppe Clausen showed that the cheap large area color filters, based on surface scattering, can be fabricated in dielectric materials by the replication of random structures in silicon . However, almost all these proposed color filters are sensitive to the angle of incidence, which leads to a shift of spectrum with different incidence angles. For many applications, e.g., special illumination, display and spectral analysis, the same perceived specular color of the filters is required to be kept for a broad range of incident angles. Therefore, it is essential to improve the incident angular tolerance of the color filters. Yi-Kuei Ryan Wu proposed a new scheme through the localized resonance in metallic nanoslits by light funneling. Angle insensitive color filters have been achieved, capable of tuning a wide color across the entire visible band . Nonetheless, only TM polarization of the incident light was considered and cone of the incident light characterized by the azimuthal angle was neglected, which limits its further application in many fields. In our previous work , high angular tolerant color filters of two dimensional sub-wavelength silicon grating structure were proposed. The reflectance curves at different incidence angles were coincident and the color difference was less than 8 for the incident angle up to 45°. In addition, the intensity of the reflection and the saturation of specular colors at different incidence angles had approving performance. Nevertheless, cone of the incident light characterized by the azimuthal angle was neglected as well and the spectral filtering property could be further improved.
In this paper, we propose an omnidirectional reflective color filter based on metal-dielectric-metal (MDM) subwavelength grating structure. Taking advantage of the surface plasmon resonance, the total absorption band at specific wavelength comes out successfully. By particle swarm optimization (PSO), the optimal structure parameters are obtained. The optimized filters present the same perceived specular color at unpolarized illumination for a broad range of incident angles. The reflectance curves at different incident angles keep almost invariable and the color difference is less than 6 in CIEDE2000 formula up to 45°. Angle-insensitive properties including the incident angular tolerance, azimuthal angular tolerance and the polarization effect are investigated thoroughly to construct a real omnidirectional color filter. Through the analysis of the magnetic field, the physical origin is verified that the localized surface plasmon resonance confined in the structure is responsible for the angle insensitive spectral filtering.
2. Structure and design
The proposed angle-insensitive reflective color filter based on metal-dielectric-metal structure is shown in Fig. 1. Two dimensional sub-wavelength double-layered gating with square pattern is adapted. It consists of a layer of thin aluminum grating and an aluminum film with thickness larger than 100nm, separated by a thin SiO2 dielectric grating layer, serving as the modulating layer. Aluminum is chosen as the metal material because it is easier for fabrication and more stable than gold and silver. The side lengths of square grating is denoted by a, the interval between the units is denoted by d and the period of the structure is denoted by p while the thicknesses of the top aluminum layer and the SiO2 dielectric layer are represented by t1 and t2, respectively. A simple geometric relationships p = a + 2d could be obtained. The linearly polarized light is launched at an incident angle θ and an azimuthal angle φ towards the color filter, as shown in Fig. 1. In the paper, the incidence angle θ varies from 0° to 60° while the azimuthal angle changes from 0° to 45° due to the symmetry of the square “pixels”. The incident medium and substrate are air and quartz, whose refractive indices are n0 = 1.0 and ns = 1.46 respectively. The refractive index of silicon dioxide is set to nSiO2 = 1.5. The material coefficient of aluminum comes from the data in the book  (data between the nodes derived from linear interpolation).
Finite-Difference Time-Domain (FDTD) method is employed to simulate the optical properties of the structure including angle resolved reflection spectra and the magnetic field distribution for TE and TM polarized light with the wavelength ranged from 380nm to 780 nm. FDTD method, proposed by K. S. Yee in 1966 , is a powerful numerical analysis technique to compute the electromagnetic field and through it, a wide frequency range can be covered with a single simulation run [13–16]. To obtain desired optical properties at different incident angles, PSO method is applied for the filter design owing to its advantage of fast convergence speed and less dependence on the initial parameters. PSO, first developed by Eberhart and Kennedy , is derived from the social behavior of large number of birds or fish, with a simple but effective working schedule. The implicit rules of cooperation and competition in social swarms increase the performance for global optimization with the help of memory rather than a simple random search. In addition, merit functions employed during the optimization procedure must be constructed reasonably. In our work, two parts are included in the merit function : one focuses on the reflectance curve at normal incidence to assure high intensity efficiency and a specified reflected color with good saturation; the other is concentrated on the optical property deviation at different incident angles. Note that the optical property deviation could be either reflectance difference or color difference calculated by CIEDE2000 formula. The optimized parameters in our work are the top aluminum thickness t1, SiO2 thickness t2, side length a and the interval d of the grating.
3. Results and analysis
The optimal structural parameters of the proposed filter for the cyan, magenta, and yellow (CMY) color could be received by the appropriate merit functions and PSO method mentioned above, shown in Table 1. From Table 1, the interval between the units remains similar for all three filters while the dimension of the pattern decreases for CMY filters correspondingly. It is noted that the dielectric material of the subwavelength grating is not restricted within low refractive index materials. A material of high refractive index is applicable and the wavelength filtering property could be obtained as well. But, in our work, if a higher index of refraction material is chosen, a much thinner dielectric layer will be needed according to Table 1, which is more difficult for practical fabrication. Therefore, SiO2 was chosen as the subwavelength dielectric material. Figure 2 shows the reflectance curves of the optimized color filters for unpolarized incidence. The optimized structures are able to trap light as much as 94% at the specific resonant wavelength. Since the thickness of the bottom aluminum film is thick enough (>100nm), there is no light transmitting the structure. Thus, the equation A + R = 1 could be obtained apparently. So the efficient color filtering feature could be ascribed to the strong absorption at the selected wavelength range, excited by the MDM structure as seen in the insert. The absorption band is red-shifted as the size of the constituent unit increases. Moreover, if the pattern chooses the circle pattern instead of the square one, the bandwidth will become wider and the color saturation will deteriorate. This is the reason why the square pattern is chosen.
Good incident angular behavior for the CMY color filters could be obtained with the optimized structural parameters. The angle resolved reflection spectra of these three color filters for unpolarized incidence are displayed in Fig. 3. Obviously, all the three filters present a great feature of the angle robust spectrum response up to 60° with the reflection dip wavelength invariable (@445nm, @516nm, @631nm). The coincidence of the reflectance spectrum at various incident angles can be observed. Besides, as the incidence angle is increased, the reflection of the dip increases accordingly, resulting in a narrower band. It is worth noting that a small dip appears at short wavelengths for the cyan filter at large incidence angles due to the red-shift of reflectance spectrum, which is attributed to the increase in dimension of the structure.
According to these reflectance spectrums, the chromaticity coordinates at different angles of incidence are calculated and marked in Fig. 4. The illuminant used in the color difference calculation is a standard illuminant E, which has constant spectral power distributions over the visible spectrum. Intuitively, the reflected specular color has no large change with incidence angles for all the three optimized color filters. As the incidence angle increases, the chromaticity coordinates move towards the central white point owing to the increased reflectance at the reflection dip. Compared with magenta and cyan color filters, the yellow filter presents higher color saturation because it has a more efficient absorption at the resonance wavelength. The luminance values of the reflected color at various incident angles are Y∈[41, 52] for cyan color, Y∈[30, 42] for magenta color, Y∈[61, 67] for yellow color, when the luminance value of illuminant is set to 100.
However, the distance between two coordinates on CIE 1931 chromaticity diagram is not uniform for actual human eyes sense of the color difference, that is, a shorter distance between two chromaticity coordinates may cause a more sensitive color difference than a longer one does. So CIEDE2000 formula [18,19] is under our consideration to evaluate the color difference. The calculated results are shown in Fig. 5. Apparently, the visual color difference increases with an increased incidence angle. When the incidence angle is less than 25°, the color difference keeps a low level which could not be perceived by human eyes. The cyan color filter has a relatively larger color difference for its small dip located at short wavelength region at large incidence. Overall, the three filters show a much slighter color variation for human visual sense compared with the multilayer filters .
Moreover, good angle-insensitivity properties can be obtained for both TM and TE polarizations though the angle resolved spectral characteristic at TM polarized incidence is a little better than TE mode. Figure 6 shows the reflectance of the optimized magenta filter for TE and TM polarization at different incidence angles. For TE polarized light, as the incidence angle increases gradually, a little red shift of the reflection dip could be observed, with an increased reflectance over the whole visible region. Different from the behavior for TE polarization, the reflectance dip position does not change for TM polarization and only a small deviation of the reflectance exists.
As a core displaying component or detecting element, the cone angular tolerance of a color filter must be taken into account for its practical application. Figure 7 shows the cone angular property of the optimized yellow filter at the oblique incidence of 45°. According to the symmetry of the square structures, the largest cone angle is 45°. There is no doubt that the cone angular property is excellent, and inappreciable variation exists when the azimuthal angle changes.
To reveal the physical origin of the spectral filtering feature of the proposed omnidirectional color filter, the magnetic field distribution is studied. Figures 8(a)-8(b) illustrate the magnetic field profile of the structure with the optimal parameters for yellow color at the reflection dip wavelength λ = 445nm and high-reflection wavelength λ = 780nm. The magnetic field profile in Fig. 8 records the magnetic field in YZ-plane, while the incident light propagating along the z-axis with TM polarization. By comparing the two figures, the difference in the magnetic field distribution could be observed apparently. From Fig. 8(a), it is clear that an intense resonance exists at the interface between the spacing layer SiO2 and top aluminum grating at the reflection dip wavelength. Though Fabry–Pérot resonance could be excited by the MDM structure in most cases, considering such a thin cavity constructed, this resonance is absent in this work. Only surface plasmon resonance  is excited in the structure. Specifically, it is the localized surface plasmon resonance excited upon the periodic subwavelength surface. Thereby, the spectral filtering of the structure results from the efficient absorption which is induced by the surface plasmon resonance. And the localized surface plasmon resonance, which is relatively independent of the wave vector, is responsible for the high incident angular tolerance.
In conclusion, an omnidirectional reflective color filter based on metal-dielectric-metal subwavelength grating structure is proposed. The simulation reveals that the obtained color filters offer a high incident angular tolerance, keeping the same perceived color at the incident angles, up to 60°. Furthermore, the cone angular tolerance, the reflective intensity as well as the color purity of the color filter has a satisfied performance. It is the localized surface plasmon resonance confined in the grating that brings out the angle insensitive spectral filtering property. Consequently, the angle-insensitive reflective color filter has potential applications in display, colorful decoration, anti-counterfeiting and so forth.
It is a pleasure for authors to acknowledge the funding support from National High Technology Research and Development Program 863(2012AA040401), National Natural Science Foundation of China (No. 61275161), the Fundamental Research Funds for the Central Universities (2014FZA5004) and the Open Project of Jiangsu Province Key Laboratory of Advanced Optical Manufacturing Technology (KJS1304).
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