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Abstract
High-performance omnidirectional transmissive chromatic polarizers based on a one-dimensional dielectric-metal-dielectric subwavelength grating structure are proposed. The incident angle-insensitive properties, azimuthal angle-insensitive properties and polarization features are investigated thoroughly to realize the proposed omnidirectional transmissive chromatic polarizers. The color difference at different angles for the proposed yellow polarizers is less than 0.9746, and the extinction ratio at different angles for the proposed cyan polarizers exceeds 26. Analysis of the power density profiles for the transverse electric (TE) and transverse magnetic (TM) polarizations show that surface plasmon resonance and high refractive index contrast properties lead to excellent polarization features and high angular tolerance.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
A variety of polarizers are used in fields including optical communications, displays, and imaging systems. This has led many researchers to develop a number of different polarizers with various materials [1–6]. Several different aspects of wire grid polarizers have been researched widely [5–9], since these devices were first put forward by Heinrich Hertz for the application of radio wave. I. Yamada et al. fabricated a wire-grid polarizer on a low-toxicity chalcogenide glass. The experimental extinction ratio of this polarizer was more than 20 dB in the near-infrared region [7]. A polarizer utilizing the guided-mode resonance, as proposed by Shiraishi, was based on a sinusoidal or triangular thin metallic-film-based-subwavelength grating for use in the infrared and terahertz regions. The high performance of this device includes a high extinction ratio and high tolerance to structural parameters [9]. Although researchers have been working for several years on wire grid polarizers, chromatic polarizers, which are derived from wire grid polarizers, are also sufficiently interesting to require further research [10–13]. Generally, the two essential components of a liquid crystal display (LCD) can be regarded as a color filter and a polarizer. A chromatic polarizer can be regarded as a combination of a color filter and a polarizer, which would not only low the device cost but also would make the device more compact. T. Ellenbogen et al. proposed chromatic plasmonic polarizer based on metallic optical nanoantennas arrays for use in polarimetry and active visible color filtering [10]. In contrasted to conventional chromatic devices, their device can control the color output. However, insufficient attention was paid to the polarization features in their work. Reflective chromatic polarizer, which was proposed by Yang, is based on a metal-dielectric-metal structure with oblique incidence at 45° [12]. Although this polarizer demonstrated high tolerance with respect to the structural parameters, the specific incident angle required restricts its practical applications. In practical applications, it is desirable for a polarizer to have a wide angular bandwidth, high extinction ratios, and a compact device size [14].
Here, we propose omnidirectional transmissive chromatic polarizers (for the cyan, magenta and yellow (CMY) colors) based on a one-dimensional dielectric-metal-dielectric (DMD) subwavelength grating structure, which can exhibit good angle-insensitive properties and good polarization features. These polarizers pass the transverse magnetic (TM) polarized light, but block the transverse electric (TE) polarized light. Additionally, the transmittance spectra for the TM-polarized light can roughly coincide at different angle of incidence. The color difference up to 60° for the proposed yellow polarizers is less than 0.9746 in term of the CIEDE2000 formula and the extinction ratio up to 60° for the proposed cyan polarizers is more than 26. The good angle-insensitive properties of these polarizers consist of good incident angle-insensitive properties and excellent azimuthal angle-insensitive properties. We also investigate the azimuthal angular tolerance thoroughly to realize the proposed omnidirectional CMY chromatic polarizers. Analysis of the power density profiles for TM polarization and TE polarization in the cross section indicate that the surface plasmon resonances and high refractive index contrast confined in the structures enable the good angle-insensitive properties and excellent polarization properties of the proposed polarizers.
2. Structure and design
The omnidirectional transmissive CMY chromatic polarizers based on the dielectric-metal-dielectric (DMD) structure proposed in this work adopt a one-dimensional subwavelength triple-layer grating structure, which is illustrated in Fig. 1. Sliver (Ag) is selected as the metal material because of its considerable superiority to excited surface plasmon resonances at the interfaces between the layers and its low absorption loss. Zinc sulfide (ZnS) is chosen as the material for the bottom and top layers, because of high refractive index contrast between the medium of ZnS and Ag. The surface plasmon resonance and high refractive index contrast in this structure are the physical origins of the characteristics of the proposed omnidirectional CMY chromatic polarizers and these properties will be analyzed in a later section. The width of the grating ridge is denoted by a, the width of the grating groove is denoted by d and the period of this grating is denotes by p, additionally, the thickness of the layers from bottom to top in the sandwich structure are designated as t1, t2 and t3. Hence, the calculated duty cycle could be defined as $f = a/(a + d)$ and the relationship of simple geometric parameters is $p = a + d$.
In this structure, the dielectric material SiO2 is selected as the glass substrate whose refractive index is characterized with the following formula [15].
Table 1. The refractive index of silica.
The refractive index of ZnS is characterized with Eq. (2) [16].
Table 2. The refractive index of zinc sulfide.
The coefficient of sliver (Ag) is quoted from Ref. [17] and the refractive index of Ag in the wavelength region of interest is shown in Table 3. This structure is illuminated by the plane wave in the air (c).
Table 3. The refractive index of sliver.
In our work, we perform finite difference time domain (FDTD) solutions commercial software simulating this structure to investigate its optical properties. Here, we choose the bloch boundary conditions to simulate a period section in the x and y axis and choose perfectly matched layer (PML) in the z axis. Based on the results, the transmissive spectra and power density profiles for TM polarization and TE polarization in the visible region are analyzed, as will be shown in a later section.
3. Results and analysis
The appropriate optical parameters for the proposed omnidirectional CMY chromatic polarizers are shown in Table 4. The structures of the cyan, magenta and yellow chromatic polarizers are designed and constructed by utilizing FDTD solutions commercial software. From Table 4, the thicknesses of the bottom and top ZnS layers remain the same for three chromatic polarizers, while the thickness of the metal layer decreases for the CMY chromatic polarizers correspondingly. The transformation between the cyan polarizer and the yellow polarizer can be achieve by adjusting the thickness of the metal layer, which represents a highly efficient color tuning method for tuning between the cyan and yellow colors. However, adjusting this parameter alone is not sufficient to achieve the transformation between the magenta polarizer and the other one.
Table 4. Optimal structure parameters for CMY chromatic polarizers.
Furthermore, the use of a dielectric material with high refractive index is of great importance for the optical properties of the proposed omnidirectional chromatic polarizers. In our work, if a dielectric material with lower refractive index, such as TiO2 or SiO2, is chosen as the material of the top and bottom layers, realization of the cyan polarizer will become almost impossible. For the chromatic polarizers, the absence of color is unacceptable. It is a fact that the material with high refractive index has a larger modulation in this sandwich structure to achieve cyan, magenta and yellow (CMY) colors. If a dielectric material with higher refractive index, such as Si, GaAs or GaP, are chosen, it will have large modulation to achieve three desired colors. However, the dielectric material with higher refractive index have low transmissive efficiency in the visible spectrum. Therefore, ZnS is chosen as material of the bottom and top layers.
The optical properties of the proposed omnidirectional CMY chromatic polarizers can divided into two aspects, which are illustrated in Fig. 2. The first aspect is the good polarization features of these proposed CMY chromatic polarizers and the second is the good incident angle-insensitive properties of the polarizers.
Fig. 2. (a) (c) (e) The transmittance spectra of the proposed CMY chromatic polarizers at normal incidence. (b) (d) (f) The spectral transmittance curves of the proposed CMY chromatic polarizers for TM polarized light at different incident angles. (a) and (b) Yellow polarizer; (c) and (d) Magenta polarizer; (e) and (f) Cyan polarized.
The transmittance spectra of the CMY chromatic polarizers for the TE and TM polarized lights at normal incidence are shown in Figs. 2(a), 2(c) and 2(e). These CMY chromatic polarizers pass TM-polarized light, but block TE-polarized light. Apparently, these polarizers present good polarization features at normal incidence and their transmittance for TE-polarized light at different wavelengths is less than 4%. In fact, this kind of good polarization features can be preserved at different incident angles, which will be corroborated by the results shown in Fig. 4. The TM-pass/TE-stop polarization features also provide a great convenience for our investigation on incident angle-insensitive properties of the proposed polarizers. Therefore, for the investigation of the high angular tolerance properties of these polarizers, it is sufficiently exhaustive to consider the incident angle-insensitive properties for TM-polarized light alone.
The spectral transmittance curves of the CMY chromatic polarizers with the optical structural parameters listed in Table 4 for TM-polarized light at different incident angles are shown in Figs. 2(b), 2(d) and 2(f). Obviously, the wavelengths of the transmission valleys for the proposed chromatic polarizers remain roughly invariable when the incident angle increases from 0° to 60°. Here, the enlarged views of transmissive valleys for TM-polarized light are shown in Figs. 2(b), 2(d) and 2(f). The wavelength range of the enlarged view is 15 nm. It is observed that the full width at half maximum (FWHM) of the transmittance curve of the magenta polarizer is wider than that of the other one’s when the light illuminates the polarizers at different incident angles, which is resulted by the increase in the period of this structure. In addition, a new shallow valley appears at large wavelengths for the cyan polarizer at large incidence angles due to the blue-shift in the transmittance spectra, which owns in the thicker metal layer in this structure. It is worth noting that a new valley also appears at short wavelengths for the magenta polarizer at large incident angles due to the red-shift in the transmittance spectrum, which is attributed to the increase in the period of the structure [18]. To give a clearer explanation for this phenomenon, the magnetic field distributions of the wavelength at the new transmission valley for the proposed magenta polarizer is calculated, shown in Fig. 3. Figure 3(a) shows the magnetic field distribution for the magenta polarizer at 0° incidence and Fig. 3(b) shows the magnetic field distribution for the magenta polarizer at 60° incidence. Apparently, the structure of the proposed magenta polarizer excites mainly surface plasmon resonance at the wavelength at the new transmission valley which appears at large incident angles when the light illuminate at 0° incidence but it excites mainly guided mode resonance that exists in the top ZnS layer when the light illuminate at 60° incidence, which is the reason why a new valley appears at short wavelengths for the magenta polarizer at large incident angles.
Fig. 3. The magnetic field distributions of the wavelength at the new transmission valley. (a) The magnetic field distribution for the magenta polarizer at 0° incidence. (b) The magnetic field distribution for the magenta polarizer at 60° incidence.
The maps of the transmittance spectra of the proposed omnidirectional CMY chromatic polarizers for TE-polarized and TM-polarized lights when the angle increases from 0° to 60° are shown in Fig. 4. Good incident angle-insensitive properties and good polarization features of the CMY chromatic polarizers are thus verified. It is observed that the transmittance spectrum for TM polarization at different angles of incidence is almost coincident. Obviously, these CMY chromatic polarizers present a good polarization features at different incidence angles and the transmittance of these polarizers for TE-polarized light is at a low level. Apparently, the transmittance of the cyan and yellow polarizers for TE-polarized light decreases at short wavelengths as the incident angle varies from 0°to 60°. Additionally, a low peak appears at short wavelengths for the magenta polarizer when the TE polarized light illuminates at large angles of incidence, because the increase of the period in this structure results in a red-shift in the transmittance spectrum at large incident angles.
Fig. 4. The maps of transmittance spectrum of the proposed CMY chromatic polarizers for TE and TM polarization when the incident angle varies from 0° to 60°. (a) Yellow polarizer, TM polarization; (b) Yellow polarizer, TE polarization; (c) Magenta polarizer, TM polarization; (d) Magenta polarizer, TE polarization; (e) Cyan polarizer, TM polarization; (f) Cyan polarizer, TE polarization.
Here, the power density profiles of the proposed polarizers are analyzed to account for their good polarization properties. Figures 5(a) and 5(b) show the power density profiles of the proposed yellow chromatic polarizer for TE and TM polarizations at normal incidence. Apparently, the TE polarized light is reflected fully at the interface between the top dielectric layer and the metal layer. In contrast, for TM-polarized light, surface plasmon resonances are excited at the interfaces between the dielectric layers and the metal layer to produce a transmissive phenomenon [19].
Fig. 5. The power density profile of the proposed yellow polarizer for TE and TM polarizations at normal incidence. (a) TE polarization (b) TM polarization.
When the metal grating period is smaller than the wavelength of the incident light, the free oscillation of the electrons that are blocked on the surface of the metal layer will cause the TM polarized light to pass through this structure while the free oscillation of the electrons moving along the grating slot will cause the TE polarized light to be reflected completely [20]. In Fig. 5(b), the transmission phenomenon for TM-polarized light occurs in the sandwich grating structure. To verify the good angle-insensitive properties of the CMY chromatic polarizers, the phase shift properties of the multilayer structure are studied. The transmittance of this multilayer sandwich grating structure can be calculated by using Smith method [21]. When the light passes through the top ZnS layer, it has larger refractive angles at different incident angles between the medium of air and ZnS than at the angle of total internal reflection between the medium of ZnS and Ag layers, which seems that the TM polarized light will be reflected completely at the interface between the top ZnS layer and the metal layer. However, the strong surface plasmon resonance that is excited at the interface between the top ZnS layer and the metal layer causes the TM polarized light to pass through the metal layer. In other words, the function of the top ZnS layer is to enable the TM polarized light to pass through the metal layer. Therefore, the phase shift in the transmission is mainly considered in the bottom ZnS layer. The bottom ZnS layer is thus analyzed by using Smith method and a simplified model is proposed as shown in Fig. 6. The total Fresnel coefficient of transmission in this model is as following.
Fig. 6. The simplified model of the proposed chromatic polarizers for the analysis of the phase shift.
According to the transmittance spectra for TM-polarized light in Figs. 4(a), 4(c) and 4(e), the chromaticity coordinates for three chromatic polarizers at different incident angles are calculated and are marked in the chromaticity diagram shown in Fig. 7. The colors corresponding to the different transmission curves are not only dependent on the transmission efficiency of this structure but also have a close relationship with the spectral energy distribution of the light source. The CIE standard illuminant D65 is selected as the light source here because its relative spectral power distribution is the closest distribution to natural light. As Fig. 7 shows, the colors corresponding to the different transmission spectra for the yellow and cyan polarizers show no large changes as the angle of incidence increases. However, the chromaticity coordinate at different angles of incidence shows large changes for the magenta polarizer due to the red-shift in the transmittance spectrum that occurs at large incident angles. The proposed yellow polarizer presents better color saturation than the other one does, because its transmittance curves have a narrower bandwidth.
Fig. 7. The CIE 1931 chromaticity coordinates of the proposed CMY chromatic polarizers for TM polarized light at the incident angle of 0°, 10°, 20°, 30°, 40°, 50°, 60°.
However, it is not accurate to define the distance between two coordinates on the CIE 1931 chromaticity diagram directly as a color difference. Therefore, the CIEDE2000 formula [22] is used to evaluate color differences between two coordinates on the CIE 1931 chromaticity diagram. The calculated results are listed in Table 5.
Table 5. CIEDE2000 color-difference in transmission at different incident angle.
Apparently, the color difference increases with the increase of the incident angle. The color differences of three chromatic polarizers are maintained to an acceptable level up to 60°. Compared with the cyan and yellow polarizers, the magenta polarizer shows a larger change at the incident angles of 0°, 20°, 40°, 60°, because its transmittance curve at different incident angles shown in Fig. 2(d) appears large changes. The color difference is regarded as a measure of the angular tolerance of the proposed omnidirectional CMY chromatic polarizers. Likewise, the extinction ratio is also considered to be the measure of the polarization features. The extinction ratio (ER) is defined by the following formula [23]:
where ${\textrm{T}_{\textrm{TM}}}$ is the total transmission for TM-polarized light and ${\textrm{T}_{\textrm{TE}}}$ is the total transmission for TE-polarized light.According to the transmittance spectra in Fig. 4, the ER value calculated at oblique angles of incidence up to 60°with respect to the normal incidence is shown in Fig. 8. Obviously, the ER value also increases with the increase in the incident angle and the variation of the extinction ratio increases with the increase in the incident angle. However, it is worth noting that the ER curve of the proposed magenta polarizer show a decreasing trend when the incident angle varies from 45° to 60° because of a new valley that appears to reduce the total transmittance for TM-polarized light and a new peak that appears to increase the total transmittance for TE-polarized light at large incident angles. Additionally, the transmittance spectra of the cyan polarizer show the lowest total transmittance for TE-polarized light at different incident angles in Figs. 4(b), 4(d) and 4(f), which is the reason why the cyan polarizer owns the highest ER values.
Finally, as core elements of the liquid crystal displays (LCDs), good azimuthal angle-insensitive properties are of major importance to polarizers in the practical applications. Figure 9 shows the azimuthal angle-insensitive properties of the yellow polarizer for the TM-polarized and TE-polarized lights at an incident angle of 45°. These results demonstrate that the azimuthal angle-insensitive properties are extremely excellent.
Fig. 9. The maps of transmittance spectra of the proposed yellow polarizers for TE and TM polarization at various azimuthal angles with the incident angle of 45°. (a) TM polarization; (b) TE polarization.
4. Conclusions
In summary, the proposed omnidirectional transmissive CMY chromatic polarizers based on a one-dimensional dielectric-metal-dielectric subwavelength grating structure are constructed via a thorough investigation of their incident angle-insensitive properties, azimuthal angle-insensitive properties and the polarization features. These polarizers have good incident angle-insensitive properties and also demonstrate excellent polarization features at different incident angles. The polarizers allow the TM polarized light to pass but block the TE polarized light. Furthermore, the excellent azimuthal angle-insensitive properties of the polarizers make it possible to use in the practical applications. The surface plasmon resonances and high refractive index contrast of the polarizers take responsible for their good angle-insensitive properties and excellent polarization properties.
Funding
National Natural Science Foundation of China (61775140).
Disclosures
The authors declare no conflicts of interest.
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