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Tunable color filter with non-subwavelength grating at oblique incidence
Journal Pre-proof Tunable Color Filter with Non-subwavelength Grating at Oblique Incidence Haitao Li, Kangni Wang, Linyong Qian
PII:
S0030-4026(20)30266-7
DOI:
https://doi.org/10.1016/j.ijleo.2020.164432
Reference:
IJLEO 164432
To appear in:
Optik
Received Date:
7 January 2020
Accepted Date:
16 February 2020
Please cite this article as: Li H, Wang K, Qian L, Tunable Color Filter with Non-subwavelength Grating at Oblique Incidence, Optik (2020), doi: https://doi.org/10.1016/j.ijleo.2020.164432
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier.
Tunable Color Filter with Non-subwavelength Grating at Oblique Incidence Haitao Li1, Kangni Wang1, 2, 3*, and Linyong Qian1,4* 1
School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, PR China School of Physical Science and Technology, Yangzhou University, Yangzhou 225002, PR China *E-mail: 3 [email protected] 4 [email protected] 2
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Abstract—An angle controlled guided-mode resonant (GMR) color filter with 1D grating is proposed for resonant wavelength at oblique incidence. A Ta2O5 grating based GMR filter was fabricated, which exhibits tunable filtering feature. The grating with a period of 574 nm was fabricated utilizing a two-beam interference system and ion beam etching. A resonant wavelength varying in the entire visible spectrum is demonstrated experimentally. For TM -polarization, as the incident angle increases from 20° to 50°, the resonant wavelength decreases from 670.32 nm to 463.21 nm, which covers the entire visible wavelength. The grating period is larger than the resonant wavelength when the incident angle is larger than 30.6°, i.e. the structure works under non-subwavelength conditions, which leads to a reduction of the difficulties associated with pattern production. The structure was calculated by rigorous coupled-wave analysis method. Our design may promote the application of the GMR color filter. Keywords: gratings, interference lithography, resonant filter.
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1. Introduction
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Color filters are widely used inside computer monitors, imaging cameras, and projection display systems. Traditionally, liquid crystal displays are widely used often with dye-based color filters [1]. These filters transmit a particular color while absorbing the undesired surrounding spectral components under the illumination of white light. However, intrinsic heating and low color selectivity hamper conventional filters made with liquid crystals and dye molecules [2]. Recently, many types of thin-film color filters have been suggested. Among them, guided -mode resonance (GMR) based devices, particularly GMR filters, are presently attracting a lot of interest [3-5]. The GMR is due to the excitation of leaky guided modes in the periodic waveguide structure. Thus, lossless spectral filters with narrow bandwidth appear to be feasible by using GMR filters. In addition, the optical filters fashioned with such photonic nanostructures possess advantages over dye -based filters in the areas of tunability [6-8], compactness [9], stability [10], and multi-functionality [11]. Since the GMR wavelength is much affected by the grating period, color filters of different wavelengths can be designed through changing the grating period [12]. For example, Uddin et al. fabricated GMR filters based on Si3N4 gratings which exhibited blue, green, and red color response for periods of 274, 327, and 369 nm, respectively [13]. Wang et al. used GMR filter arrays to generate different color s and reproduced colored images [14]. These structures were realized by deploying multiple filters in which pixels with different grating periods produce individual colors. Recently, tunable GMR color filter whose peak can be tuned continuously based on one structure gets more attention. Among them, the tunable mechanism by rotating incident angle and polarization angle [15, 16] have attracted much interest. However, in the mentioned structures above, the grating periods are all less than the resonant wavelength value, which regarded as “sub-wavelength” grating [17]. To our knowledge, in order to exploit GMR easily, most research has focused on sub-wavelength devices, i.e., the grating period is much smaller than the wavelength. Actually, larger - period structures are less susceptible to parameter deviations during manufacture [18]. In the interference exposure, smaller period means the preparation environment should be more precise, which leading a greater difficulty in fabrication process. Although nano-imprint printing can be accurately prepared, it is still difficult to demodulate in the preparation of the small-period grating, and expensive equipment is always required. For practical applications, it is desirable to reduce the fabrication difficulties of making GMR structure. Some studies have focused
on reducing these difficulties, for example, high refractive index substrate [19], shallow gratings [20] were designed. However, less attention has been drawn to the GMR structure whose period is non-sub-wavelength. In this work, we describe a tunable color pixel which covers the entire visible range. Based on the angle-sensitive GMR structure, a “non-subwavelength” structure, whose period is close to or larger than the resonant wavelength. As the angle of incidence increases, the peak wavelength tunes continuously because of the GMR which is based on the coupling of the -1th diffraction order (due to a leaky mode). The filter was fabricated using laser lithography technology which is used for creating surface grating patterns. The computational results presented here were obtained through rigorous coupled-wave analysis (RCWA). This is the first time a GMR color filter based on such design has been verified experimentally. The results in this letter will show that the GMR color filter will be easier to use by reducing the grating density and that it also has practical applications.
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2. Proposed structure and simulation
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Fig .1(a) Basic GMR filter showing structure parameters. (b) Resonance regimes of the proposed GMR structure.
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The typical double-layer GMR structure is shown in Fig. 1(a). It consists of two layers upon the substrate, the waveguide layer and the grating layer. As shown in Fig.1(a), the grating layer has refractive indices of nh and nc (cover layer); dg and dw are the thicknesses of grating layer and waveguide layer; nw and ns are the refractive indices of the waveguide film and substrate material; Λ is the grating period and f is the fill factor. Assume β is the propagation constant, λ is the wavelength, and k=2π/λ. For GMR exciting, the value of N= β/k should be satisfied [21] max {nc, ns} ≤ | N | ＜neff (1) where neff represents the value of the grating average refractive index. The effective propagation constant β can be approximated as follows: β→ βi= k (neff sinθ’-iλ/Λ). (2) It can be obtained that max {nc, ns} ≤ | nc sinθ- iλ/Λ|＜neff (3) where we use neffsinθ’ = ncsinθ, with θ being the external angle of incidence, as shown in Fig. 1. The above inequations are applied to calculate the locations of GMR as functions the structure parameters, and the equations are all useable for TM and TE-polarization. In particular, the TM and TE polarizations refer to the cases of φ= 90 and 0°, respectively. From Eq.3, if the grating period is unchanged, as the angle θ increases, which means an oblique incidence is introduced, the Λ for upper limit can be also increased for a fixed resonant wavelength. We can infer that under at a particular incident angle, the resonant wavelength will be equal to grating period, i.e. non -subwavelength GMR condition can be realized. Hence, the GMR wavelength value is close to or even less than the grating period. Based on the above equations, plots to describes the structure parameters for various orders can be obtained too. In Eq.1, the neff is obtained according to the effective medium theory, however a rigorous value, especially working in the non-subwavelength condition, is hard to provide [22]. Even though, the dispersion equation of the waveguide slab can be used to estimate the resonance locations approximately, as shown in Fig. 1(b). The structure parameters are assumed to be nh=nw=2.16, nc=1, f=0.5, and ns=1.51. The shaded regions indicate the conditions for which a GMR occurs. When dg=100nm, dw=63 nm, and the resonant wavelength is fixed at 570 nm, the grating period
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as a function of incident angle was shown in the blue lines. At the intersection of the two blue curves, i.e. under normal incidence, higher order diffraction will be suppressed and only the 0th diffracted propagate, which means highest GMR efficiency can be obtained. Here Λ=367.35nm, the GMR is excited at the wavelength of 570 nm. When it couples to the ±1th diffraction waves, the GMR can be also excited under non-normal incidence. As a result, in contrast to the classical picture of a TM-polarized wave at a dielectric interface, the reflected 0th order is re-radiated in a specular direction even though the polarization vector of the incident wave in the film is oriented parallel to the direction of reflection. In addition, in order to insure coupling the -1th diffraction order, as the angle of incidence increases, the grating period should also be increased. On the right -hand side of λ/Λ=1 (λ=Λ=570 nm), the resonant wavelength is larger than the value of the grating period, which means a sub - wavelength condition. However, on the left side of λ/Λ=1, i.e. the angle θ, is larger than 31.93°, non -subwavelength condition is introduced. Therefore, a GMR structure with larger period can excite the same resonant wavelength.
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Fig. 2(a) Simulated spectral response under different incident angles of 25°, 35° and 45°. (b) Simulated TM -polarized reflectance spectra corresponding to -1th diffraction order, for incident angles from 20° and 50°
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For the GMR based on the coupling of the -1th diffraction order, when the incidence angles are25°, 35° and 45°, the peak wavelengths corresponding to red, green, and blue and are 623.5nm, 548nm, and 487nm, respectively. The changing rate of wavelength with angle is 6.825nm/degree. For structures under oblique incidence, it is difficult to obtain a resonance efficiency of 100%, since the GMR occurs due to coupling of the -1th diffraction order (due to a leaky waveguide), and not all higher-order diffractions are stopped. The calculated reflectance of these three peak wavelengths are 84%, 87% and 95%. In addition, the full width at half maximum (FWHM) increases with the increase of angle of incidence, likewise the FWHM decreases as it decreases. This is also seen in Fig. 2(b) which presents the calculated spectral response as a function of angle of incidence and wavelength. When the angle of incidence is 20°, the corresponding resonant wavelength is 463.3nm and its FWHM is 25.5nm. When the angle of incidence is tuned to 50°, the corresponding resonant wavelength is 667.4 nm and FWHM is 4.2 nm. The value of FWHM can affect the color purity of visible filters. The narrower the bandwidth, the smaller the FWHM and the purer the color, which is desirable for color pixels. From the figure, we see that the color purity corresponding to the long wavelength is better. Actually, the FWHM can be reduced by optimizing further, for example, by using a material with a smaller refractive index or by reducing the grating thickness to reduce the adjustment strength of the grating layer.
3. Experiment results and discussion In the experiment, the structure fabrication started with the deposition of a 170 nm-thick Ta2O5 film on a BK7 substrate using a sputtering system. Thereafter, a 300 nm AZ1500 photo-resist layer is spin coated onto the substrate. The 1D grating pattern is recorded using an interferometric lithography system using a He-Cd laser with a wavelength of 441.6 nm. During the pattern writing process, the contrast of the interference strips and the exposure and development time will basically determine the fill factor. The interference contrast can be mostly controlled by tuning the relative intensity ratio of the coherent beams. Finally, ion beam etching was used to transfer the pattern to the Ta2O5 film. Ion etching using Ar gas was used to etch the film. All materials have different etching rates and so the etching ratio of materials should be determined to get the desired depth of groove as accurately as possible. The resulting
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grating structures were investigated by atomic force microscopy (AFM), and the results are shown in Fig. 3. From the AFM image, the grating parameters are found to be dg ≈ 106 nm, and Λ=574nm. An exact rectangle profile is hard to obtain. However, the final grating parameters are close to the initial design, especially for this period.
Fig. 3 AFM image of the fabricated grating profile.
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To evaluate the spectral characteristics of the proposed filters, a tungsten halogen light source with a wavelength range of 360 nm-2000 nm serves as the light source and illuminates through the collimating lens toward the structure. A linear polarizer is mounted behind the source to select a specific polarization. The beam was tuned using the angle of incidence by rotating the sample stage. The spectral response of the fabricated filter was measured using a spectrometer (USB4000, Ocean Optics, wavelength range: 200 nm-1100 nm). The measured reflection spectra for three different angles are illustrated in Fig. 4. The simulated spectra, using the fabricated structure parameters, match the experimental results. With angles of incidence of 25°, 35° and 45°, we observe blue, green, and red color responses which correspond to the wavelength of 627.41 nm, 550.03 nm and 480.64 nm, respectively. This produces a 146.8 nm wavelength shift when the angle of incidence changes to 20°. The spectral curve information is shown in Table 1. Like the calculated results, the FWHM is smaller for longer wavelengths, which means a purer color. Deviations from the theoretically predicted reflection at resonance maybe caused by the loss due to scattering from the waveguide interface and variations of the parameters, such as the refractive index or the grating uniformity. The increase of the FWHM in measurement may be due to the increase of the fill factor. In Fig. 3 it can be clearly seen that the fill factor of the grating is larger than 0.5. The larger fill factor will increase the modulation intensity of the grating layer, thus increasing the bandwidth. An exact rectangle grating profile is hard to obtain; however, the final period is close to the initial design and a large resonant wavelength shift in the visible spectrum is achieved.
Fig. 4 Measured and calculated spectral response of the GMR filter under three different angles.
Table 1 Reflection spectra information at three different angles Incident angle Peak wavelength FWHM Peak reflectance (%) (a) (b)
25° 35° 45°
36.1 nm 45.2 nm 49.6 nm
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627.41 nm 550.03 nm 480.64 nm
Fig. 5 Measured GMR reflectance spectra for different angles of incidence
4. Conclusion
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The angular tuning of the device is achieved by continuously rotating the sample stage allowing the resonant wavelength to be continuously tuned. Figure 5 shows the measured reflectance spectra as a function of the angle of incidence from 20° to 50°. The result of the measurement is the approximation to the simulation; as the angle of incidence increases, the resonant wavelength moves from long to short wavelength. As a result, the GMR wavelength changes from 670.32 nm to 463.21 nm. It is apparent that the relationship between the resonant wavelength and the angle of incidence is not exactly linear, particularly when the angle increases to about 40°; similar conclusions can be obtained from Fig. 2(b). When the incident angle is 30.6°, the grating period is 574 nm, which is equal to the grating period value. In other word, when the incidence angle is larger than 30.6°, the filter works in the case of non -sub -wavelength. In addition, from the measured results, the FWHM increases monotonically, which verifies that a larger FWHM is observed for short wavelengths. This also indicates that the modulation intensity of the grating layer increases with the increase of angle. A narrower resonant wavelength means a purer color, so for a color pixel, when the angle of incidence increases, the color purity decreases for short wavelengths. Work is still being done to reduce the sidebands and FWHM, and this will reduce crosstalk amongst red, blue, and green pixel -states and increase the color purity, i.e., increase the color gamut.
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In summary, we have demonstrated a GMR color filter with a resonant wavelength tunable function based on a classical two-layer structure. The GMR wavelength can be tuned continuously by varying the angle of incidence on the structure. For TM-polarization, the grating period is larger than the resonant wavelength when the angle of incidence is larger than 30.6°, i.e. the structure works under non-subwavelength conditions, which will reduce the difficulties of pattern production. The device was designed utilizing numerical methods based on a rigorous coupled-wave analysis. Our design will improve the practical application for color filters based on the GMR effect.
Funding National Natural Science Foundation of China (11704162, 61771227); Foundation of Xuzhou city (KC18002); Natural Science Research of Jiangsu Higher Education Institutions of China (18KJB510048). Declaration of interests
☑The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
☑The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
Reference
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[1] R. W. Sabnis, “Color filter technology for liquid crystal display,” Displays, vol. 20, no. 3, pp.119 –219, Nov. 29, 1999. [2] Koo, H. S., Chen, M. and Pan, P. C., “LCD -based color filter films fabricated by a pigment -based colorant photo resist inks and printing technology,” Thin solid films, vol. 515, no. 3, pp. 896 -901, Nov. 23, 2006. [3] Quaranta, G., Basset, G., Martin, O. J. and Gallinet, B., “Recent Advances in Resonant Waveguide Gratings,” Laser Photonics Rev., vol. 12, no.9, pp. 1800017(1 -31), July.30, 2018. [4] S. S. Wang and R. Magnusson, “Theory and applications of guided -mode resonance filters,” Appl. Opt., vol. 32, no. 14, pp. 2606 -2613, May.10, 1993. [5] Ian D. Block, et al., “A Sensitivity Model for Predicting Photonic Crystal Biosensor Performance,” IEEE Sen. J. vol. 8, no. 3, pp.274 -280, Mar., 2008. [6] M. J. Uddin, R. Magnusson, “Efficient Guided -Mode -Resonant Tunable Color Filters,” IEEE Photon. Technol. Lett., vol. 24, no. 17, pp. 1552 –1554, Sep. 1, 2012. [7] Q. Wang, et al., “Type of tunable guided -mode resonance filter based on electro -optic characteristic of polymer -dispersed liquid crystal,” Opt. Lett., vol. 35, no. 8, pp. 1236 –1238, Apr. 2010. [8] M. J. Uddin and R. Magnusson, “Guided -mode resonant thermo -optic tunable filters,” IEEE Photon. Technol. Lett., vol. 25, no. 15, pp. 1412 –1415, Aug. 1, 2013. [9] R. Magnusson, D. Shin, and Z. S. Liu, “Guided -mode resonance Brewster filter,” Opt. Lett., vol. 23, no. 8, pp. 612 –614, Apr. 15, 1998. [10] S. S. Wang, R. Magnusson, and J. S. Bagby, “Guided -mode resonances in planar dielectric -layer diffraction gratings,” J. Opt. Soc. Am. A, vol.7, no.8, pp.1470 –1474, Aug. 1990. [11] Wang, et al., “Guided -mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett., vol. 88, pp. 251115(1 -3), June. 22, 2006. [12] Kanamori, Y., Ozaki, T., and Hane, K., “Fabrication of ultrathin color filters for three primary colors using guided -mode resonance in silicon subwavelength gratings,” Optical Rev., vol.21, no.5, pp.723 -727, Oct. 1, 2014. [13] M. J. Uddin, and R. Magnusson, “Highly efficient color filter array using resonant Si 3 N 4 gratings,” Opt. Express, vol.20, no.10, pp. 12495 -12506, May. 14, 2013. [14] Wang, Q., Zhang, D., Xu, B., Huang, Y., Tao, C., Wang, C., and Zhuang, S. “Colored image produced with guided -mode resonance filter array,” Opt. Lett., vol. 36, no. 23, pp. 4698 -4700, Dec.1,2011. [15] Park, C. H., Yoon, Y. T., Shrestha, V. R., Park, C. S., Lee, S. S., and Kim, E. S., “Electrically tunable color filter based on a polarization -tailored nano -photonic dichroic resonator featuring an asymmetric subwavelength grating,” Opt. Express, vol.21, no.23, pp.28783 -28793, Nov. 15, 2013. [16] M. J. Uddin, T. Khaleque., and R. Magnusson, “Guided -mode resonant polarization -controlled tunable color filters,” Opt. Express, vol.22, no.10, pp.12307 -12315, May. 13, 2014. [17] R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett., vol. 61, no. 9, pp.1022 –1024, Aug.3, 1992. [18] Qian, L., Zhang, D., Huang, Y., Tao, C., Hong, R., and Zhuang, S, “Performance of a double -layer guided mode resonance filter with non -subwavelength grating period at oblique incidence,” Opt. Laser Technology, no. 72, pp. 42 -47, Feb., 2015. [19] Liu, W., Chen, H. and Lai, Z., “Guided -mode resonance filter with high -index substrate,” Opt. Lett., vol. 37, no. 22, pp. 4648 – 4650, Nov.15,2012. [20] Liu, W., Lai, Z., Guo, H. and Liu, Y., “Guided -mode resonance filters with shallow grating,” Opt. Lett., vol. 35, no. 6, pp. 865 –867, March.15, 2010. [21] X. Liu, Sh. Chen, and J. Tian, “Triple -layer guided -mode resonance Brewster filter consisting of a homogenous layer and coupled gratings with equal refractive index,” Opt. Express, vol. 19, no.9, pp.8233 – 8241, Apr. 25, 2011. [22] S. Tibuleac and R. Magnusson, “Reflection and transmission guided -mode resonance filters,” J. Opt. Soc. Am. A, vol. 14, no.14, pp1617 -1626, July.7, 1997.
PII:
S0030-4026(20)30266-7
DOI:
https://doi.org/10.1016/j.ijleo.2020.164432
Reference:
IJLEO 164432
To appear in:
Optik
Received Date:
7 January 2020
Accepted Date:
16 February 2020
Please cite this article as: Li H, Wang K, Qian L, Tunable Color Filter with Non-subwavelength Grating at Oblique Incidence, Optik (2020), doi: https://doi.org/10.1016/j.ijleo.2020.164432
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier.
Tunable Color Filter with Non-subwavelength Grating at Oblique Incidence Haitao Li1, Kangni Wang1, 2, 3*, and Linyong Qian1,4* 1
School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, PR China School of Physical Science and Technology, Yangzhou University, Yangzhou 225002, PR China *E-mail: 3 [email protected] 4 [email protected] 2
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Abstract—An angle controlled guided-mode resonant (GMR) color filter with 1D grating is proposed for resonant wavelength at oblique incidence. A Ta2O5 grating based GMR filter was fabricated, which exhibits tunable filtering feature. The grating with a period of 574 nm was fabricated utilizing a two-beam interference system and ion beam etching. A resonant wavelength varying in the entire visible spectrum is demonstrated experimentally. For TM -polarization, as the incident angle increases from 20° to 50°, the resonant wavelength decreases from 670.32 nm to 463.21 nm, which covers the entire visible wavelength. The grating period is larger than the resonant wavelength when the incident angle is larger than 30.6°, i.e. the structure works under non-subwavelength conditions, which leads to a reduction of the difficulties associated with pattern production. The structure was calculated by rigorous coupled-wave analysis method. Our design may promote the application of the GMR color filter. Keywords: gratings, interference lithography, resonant filter.
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1. Introduction
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Color filters are widely used inside computer monitors, imaging cameras, and projection display systems. Traditionally, liquid crystal displays are widely used often with dye-based color filters [1]. These filters transmit a particular color while absorbing the undesired surrounding spectral components under the illumination of white light. However, intrinsic heating and low color selectivity hamper conventional filters made with liquid crystals and dye molecules [2]. Recently, many types of thin-film color filters have been suggested. Among them, guided -mode resonance (GMR) based devices, particularly GMR filters, are presently attracting a lot of interest [3-5]. The GMR is due to the excitation of leaky guided modes in the periodic waveguide structure. Thus, lossless spectral filters with narrow bandwidth appear to be feasible by using GMR filters. In addition, the optical filters fashioned with such photonic nanostructures possess advantages over dye -based filters in the areas of tunability [6-8], compactness [9], stability [10], and multi-functionality [11]. Since the GMR wavelength is much affected by the grating period, color filters of different wavelengths can be designed through changing the grating period [12]. For example, Uddin et al. fabricated GMR filters based on Si3N4 gratings which exhibited blue, green, and red color response for periods of 274, 327, and 369 nm, respectively [13]. Wang et al. used GMR filter arrays to generate different color s and reproduced colored images [14]. These structures were realized by deploying multiple filters in which pixels with different grating periods produce individual colors. Recently, tunable GMR color filter whose peak can be tuned continuously based on one structure gets more attention. Among them, the tunable mechanism by rotating incident angle and polarization angle [15, 16] have attracted much interest. However, in the mentioned structures above, the grating periods are all less than the resonant wavelength value, which regarded as “sub-wavelength” grating [17]. To our knowledge, in order to exploit GMR easily, most research has focused on sub-wavelength devices, i.e., the grating period is much smaller than the wavelength. Actually, larger - period structures are less susceptible to parameter deviations during manufacture [18]. In the interference exposure, smaller period means the preparation environment should be more precise, which leading a greater difficulty in fabrication process. Although nano-imprint printing can be accurately prepared, it is still difficult to demodulate in the preparation of the small-period grating, and expensive equipment is always required. For practical applications, it is desirable to reduce the fabrication difficulties of making GMR structure. Some studies have focused
on reducing these difficulties, for example, high refractive index substrate [19], shallow gratings [20] were designed. However, less attention has been drawn to the GMR structure whose period is non-sub-wavelength. In this work, we describe a tunable color pixel which covers the entire visible range. Based on the angle-sensitive GMR structure, a “non-subwavelength” structure, whose period is close to or larger than the resonant wavelength. As the angle of incidence increases, the peak wavelength tunes continuously because of the GMR which is based on the coupling of the -1th diffraction order (due to a leaky mode). The filter was fabricated using laser lithography technology which is used for creating surface grating patterns. The computational results presented here were obtained through rigorous coupled-wave analysis (RCWA). This is the first time a GMR color filter based on such design has been verified experimentally. The results in this letter will show that the GMR color filter will be easier to use by reducing the grating density and that it also has practical applications.
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2. Proposed structure and simulation
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Fig .1(a) Basic GMR filter showing structure parameters. (b) Resonance regimes of the proposed GMR structure.
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The typical double-layer GMR structure is shown in Fig. 1(a). It consists of two layers upon the substrate, the waveguide layer and the grating layer. As shown in Fig.1(a), the grating layer has refractive indices of nh and nc (cover layer); dg and dw are the thicknesses of grating layer and waveguide layer; nw and ns are the refractive indices of the waveguide film and substrate material; Λ is the grating period and f is the fill factor. Assume β is the propagation constant, λ is the wavelength, and k=2π/λ. For GMR exciting, the value of N= β/k should be satisfied [21] max {nc, ns} ≤ | N | ＜neff (1) where neff represents the value of the grating average refractive index. The effective propagation constant β can be approximated as follows: β→ βi= k (neff sinθ’-iλ/Λ). (2) It can be obtained that max {nc, ns} ≤ | nc sinθ- iλ/Λ|＜neff (3) where we use neffsinθ’ = ncsinθ, with θ being the external angle of incidence, as shown in Fig. 1. The above inequations are applied to calculate the locations of GMR as functions the structure parameters, and the equations are all useable for TM and TE-polarization. In particular, the TM and TE polarizations refer to the cases of φ= 90 and 0°, respectively. From Eq.3, if the grating period is unchanged, as the angle θ increases, which means an oblique incidence is introduced, the Λ for upper limit can be also increased for a fixed resonant wavelength. We can infer that under at a particular incident angle, the resonant wavelength will be equal to grating period, i.e. non -subwavelength GMR condition can be realized. Hence, the GMR wavelength value is close to or even less than the grating period. Based on the above equations, plots to describes the structure parameters for various orders can be obtained too. In Eq.1, the neff is obtained according to the effective medium theory, however a rigorous value, especially working in the non-subwavelength condition, is hard to provide [22]. Even though, the dispersion equation of the waveguide slab can be used to estimate the resonance locations approximately, as shown in Fig. 1(b). The structure parameters are assumed to be nh=nw=2.16, nc=1, f=0.5, and ns=1.51. The shaded regions indicate the conditions for which a GMR occurs. When dg=100nm, dw=63 nm, and the resonant wavelength is fixed at 570 nm, the grating period
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as a function of incident angle was shown in the blue lines. At the intersection of the two blue curves, i.e. under normal incidence, higher order diffraction will be suppressed and only the 0th diffracted propagate, which means highest GMR efficiency can be obtained. Here Λ=367.35nm, the GMR is excited at the wavelength of 570 nm. When it couples to the ±1th diffraction waves, the GMR can be also excited under non-normal incidence. As a result, in contrast to the classical picture of a TM-polarized wave at a dielectric interface, the reflected 0th order is re-radiated in a specular direction even though the polarization vector of the incident wave in the film is oriented parallel to the direction of reflection. In addition, in order to insure coupling the -1th diffraction order, as the angle of incidence increases, the grating period should also be increased. On the right -hand side of λ/Λ=1 (λ=Λ=570 nm), the resonant wavelength is larger than the value of the grating period, which means a sub - wavelength condition. However, on the left side of λ/Λ=1, i.e. the angle θ, is larger than 31.93°, non -subwavelength condition is introduced. Therefore, a GMR structure with larger period can excite the same resonant wavelength.
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Fig. 2(a) Simulated spectral response under different incident angles of 25°, 35° and 45°. (b) Simulated TM -polarized reflectance spectra corresponding to -1th diffraction order, for incident angles from 20° and 50°
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For the GMR based on the coupling of the -1th diffraction order, when the incidence angles are25°, 35° and 45°, the peak wavelengths corresponding to red, green, and blue and are 623.5nm, 548nm, and 487nm, respectively. The changing rate of wavelength with angle is 6.825nm/degree. For structures under oblique incidence, it is difficult to obtain a resonance efficiency of 100%, since the GMR occurs due to coupling of the -1th diffraction order (due to a leaky waveguide), and not all higher-order diffractions are stopped. The calculated reflectance of these three peak wavelengths are 84%, 87% and 95%. In addition, the full width at half maximum (FWHM) increases with the increase of angle of incidence, likewise the FWHM decreases as it decreases. This is also seen in Fig. 2(b) which presents the calculated spectral response as a function of angle of incidence and wavelength. When the angle of incidence is 20°, the corresponding resonant wavelength is 463.3nm and its FWHM is 25.5nm. When the angle of incidence is tuned to 50°, the corresponding resonant wavelength is 667.4 nm and FWHM is 4.2 nm. The value of FWHM can affect the color purity of visible filters. The narrower the bandwidth, the smaller the FWHM and the purer the color, which is desirable for color pixels. From the figure, we see that the color purity corresponding to the long wavelength is better. Actually, the FWHM can be reduced by optimizing further, for example, by using a material with a smaller refractive index or by reducing the grating thickness to reduce the adjustment strength of the grating layer.
3. Experiment results and discussion In the experiment, the structure fabrication started with the deposition of a 170 nm-thick Ta2O5 film on a BK7 substrate using a sputtering system. Thereafter, a 300 nm AZ1500 photo-resist layer is spin coated onto the substrate. The 1D grating pattern is recorded using an interferometric lithography system using a He-Cd laser with a wavelength of 441.6 nm. During the pattern writing process, the contrast of the interference strips and the exposure and development time will basically determine the fill factor. The interference contrast can be mostly controlled by tuning the relative intensity ratio of the coherent beams. Finally, ion beam etching was used to transfer the pattern to the Ta2O5 film. Ion etching using Ar gas was used to etch the film. All materials have different etching rates and so the etching ratio of materials should be determined to get the desired depth of groove as accurately as possible. The resulting
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grating structures were investigated by atomic force microscopy (AFM), and the results are shown in Fig. 3. From the AFM image, the grating parameters are found to be dg ≈ 106 nm, and Λ=574nm. An exact rectangle profile is hard to obtain. However, the final grating parameters are close to the initial design, especially for this period.
Fig. 3 AFM image of the fabricated grating profile.
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To evaluate the spectral characteristics of the proposed filters, a tungsten halogen light source with a wavelength range of 360 nm-2000 nm serves as the light source and illuminates through the collimating lens toward the structure. A linear polarizer is mounted behind the source to select a specific polarization. The beam was tuned using the angle of incidence by rotating the sample stage. The spectral response of the fabricated filter was measured using a spectrometer (USB4000, Ocean Optics, wavelength range: 200 nm-1100 nm). The measured reflection spectra for three different angles are illustrated in Fig. 4. The simulated spectra, using the fabricated structure parameters, match the experimental results. With angles of incidence of 25°, 35° and 45°, we observe blue, green, and red color responses which correspond to the wavelength of 627.41 nm, 550.03 nm and 480.64 nm, respectively. This produces a 146.8 nm wavelength shift when the angle of incidence changes to 20°. The spectral curve information is shown in Table 1. Like the calculated results, the FWHM is smaller for longer wavelengths, which means a purer color. Deviations from the theoretically predicted reflection at resonance maybe caused by the loss due to scattering from the waveguide interface and variations of the parameters, such as the refractive index or the grating uniformity. The increase of the FWHM in measurement may be due to the increase of the fill factor. In Fig. 3 it can be clearly seen that the fill factor of the grating is larger than 0.5. The larger fill factor will increase the modulation intensity of the grating layer, thus increasing the bandwidth. An exact rectangle grating profile is hard to obtain; however, the final period is close to the initial design and a large resonant wavelength shift in the visible spectrum is achieved.
Fig. 4 Measured and calculated spectral response of the GMR filter under three different angles.
Table 1 Reflection spectra information at three different angles Incident angle Peak wavelength FWHM Peak reflectance (%) (a) (b)
25° 35° 45°
36.1 nm 45.2 nm 49.6 nm
65 66 61
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(c)
627.41 nm 550.03 nm 480.64 nm
Fig. 5 Measured GMR reflectance spectra for different angles of incidence
4. Conclusion
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The angular tuning of the device is achieved by continuously rotating the sample stage allowing the resonant wavelength to be continuously tuned. Figure 5 shows the measured reflectance spectra as a function of the angle of incidence from 20° to 50°. The result of the measurement is the approximation to the simulation; as the angle of incidence increases, the resonant wavelength moves from long to short wavelength. As a result, the GMR wavelength changes from 670.32 nm to 463.21 nm. It is apparent that the relationship between the resonant wavelength and the angle of incidence is not exactly linear, particularly when the angle increases to about 40°; similar conclusions can be obtained from Fig. 2(b). When the incident angle is 30.6°, the grating period is 574 nm, which is equal to the grating period value. In other word, when the incidence angle is larger than 30.6°, the filter works in the case of non -sub -wavelength. In addition, from the measured results, the FWHM increases monotonically, which verifies that a larger FWHM is observed for short wavelengths. This also indicates that the modulation intensity of the grating layer increases with the increase of angle. A narrower resonant wavelength means a purer color, so for a color pixel, when the angle of incidence increases, the color purity decreases for short wavelengths. Work is still being done to reduce the sidebands and FWHM, and this will reduce crosstalk amongst red, blue, and green pixel -states and increase the color purity, i.e., increase the color gamut.
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In summary, we have demonstrated a GMR color filter with a resonant wavelength tunable function based on a classical two-layer structure. The GMR wavelength can be tuned continuously by varying the angle of incidence on the structure. For TM-polarization, the grating period is larger than the resonant wavelength when the angle of incidence is larger than 30.6°, i.e. the structure works under non-subwavelength conditions, which will reduce the difficulties of pattern production. The device was designed utilizing numerical methods based on a rigorous coupled-wave analysis. Our design will improve the practical application for color filters based on the GMR effect.
Funding National Natural Science Foundation of China (11704162, 61771227); Foundation of Xuzhou city (KC18002); Natural Science Research of Jiangsu Higher Education Institutions of China (18KJB510048). Declaration of interests
☑The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
☑The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
Reference
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[1] R. W. Sabnis, “Color filter technology for liquid crystal display,” Displays, vol. 20, no. 3, pp.119 –219, Nov. 29, 1999. [2] Koo, H. S., Chen, M. and Pan, P. C., “LCD -based color filter films fabricated by a pigment -based colorant photo resist inks and printing technology,” Thin solid films, vol. 515, no. 3, pp. 896 -901, Nov. 23, 2006. [3] Quaranta, G., Basset, G., Martin, O. J. and Gallinet, B., “Recent Advances in Resonant Waveguide Gratings,” Laser Photonics Rev., vol. 12, no.9, pp. 1800017(1 -31), July.30, 2018. [4] S. S. Wang and R. Magnusson, “Theory and applications of guided -mode resonance filters,” Appl. Opt., vol. 32, no. 14, pp. 2606 -2613, May.10, 1993. [5] Ian D. Block, et al., “A Sensitivity Model for Predicting Photonic Crystal Biosensor Performance,” IEEE Sen. J. vol. 8, no. 3, pp.274 -280, Mar., 2008. [6] M. J. Uddin, R. Magnusson, “Efficient Guided -Mode -Resonant Tunable Color Filters,” IEEE Photon. Technol. Lett., vol. 24, no. 17, pp. 1552 –1554, Sep. 1, 2012. [7] Q. Wang, et al., “Type of tunable guided -mode resonance filter based on electro -optic characteristic of polymer -dispersed liquid crystal,” Opt. Lett., vol. 35, no. 8, pp. 1236 –1238, Apr. 2010. [8] M. J. Uddin and R. Magnusson, “Guided -mode resonant thermo -optic tunable filters,” IEEE Photon. Technol. Lett., vol. 25, no. 15, pp. 1412 –1415, Aug. 1, 2013. [9] R. Magnusson, D. Shin, and Z. S. Liu, “Guided -mode resonance Brewster filter,” Opt. Lett., vol. 23, no. 8, pp. 612 –614, Apr. 15, 1998. [10] S. S. Wang, R. Magnusson, and J. S. Bagby, “Guided -mode resonances in planar dielectric -layer diffraction gratings,” J. Opt. Soc. Am. A, vol.7, no.8, pp.1470 –1474, Aug. 1990. [11] Wang, et al., “Guided -mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett., vol. 88, pp. 251115(1 -3), June. 22, 2006. [12] Kanamori, Y., Ozaki, T., and Hane, K., “Fabrication of ultrathin color filters for three primary colors using guided -mode resonance in silicon subwavelength gratings,” Optical Rev., vol.21, no.5, pp.723 -727, Oct. 1, 2014. [13] M. J. Uddin, and R. Magnusson, “Highly efficient color filter array using resonant Si 3 N 4 gratings,” Opt. Express, vol.20, no.10, pp. 12495 -12506, May. 14, 2013. [14] Wang, Q., Zhang, D., Xu, B., Huang, Y., Tao, C., Wang, C., and Zhuang, S. “Colored image produced with guided -mode resonance filter array,” Opt. Lett., vol. 36, no. 23, pp. 4698 -4700, Dec.1,2011. [15] Park, C. H., Yoon, Y. T., Shrestha, V. R., Park, C. S., Lee, S. S., and Kim, E. S., “Electrically tunable color filter based on a polarization -tailored nano -photonic dichroic resonator featuring an asymmetric subwavelength grating,” Opt. Express, vol.21, no.23, pp.28783 -28793, Nov. 15, 2013. [16] M. J. Uddin, T. Khaleque., and R. Magnusson, “Guided -mode resonant polarization -controlled tunable color filters,” Opt. Express, vol.22, no.10, pp.12307 -12315, May. 13, 2014. [17] R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett., vol. 61, no. 9, pp.1022 –1024, Aug.3, 1992. [18] Qian, L., Zhang, D., Huang, Y., Tao, C., Hong, R., and Zhuang, S, “Performance of a double -layer guided mode resonance filter with non -subwavelength grating period at oblique incidence,” Opt. Laser Technology, no. 72, pp. 42 -47, Feb., 2015. [19] Liu, W., Chen, H. and Lai, Z., “Guided -mode resonance filter with high -index substrate,” Opt. Lett., vol. 37, no. 22, pp. 4648 – 4650, Nov.15,2012. [20] Liu, W., Lai, Z., Guo, H. and Liu, Y., “Guided -mode resonance filters with shallow grating,” Opt. Lett., vol. 35, no. 6, pp. 865 –867, March.15, 2010. [21] X. Liu, Sh. Chen, and J. Tian, “Triple -layer guided -mode resonance Brewster filter consisting of a homogenous layer and coupled gratings with equal refractive index,” Opt. Express, vol. 19, no.9, pp.8233 – 8241, Apr. 25, 2011. [22] S. Tibuleac and R. Magnusson, “Reflection and transmission guided -mode resonance filters,” J. Opt. Soc. Am. A, vol. 14, no.14, pp1617 -1626, July.7, 1997.