The enhancement of color saturation and color gamut has been demonstrated, by taking advantage of a dual-band color filter based on a subwavelength rectangular metal-dielectric resonant grating, which exhibits an adjustable spectral response with respect to its relative transmittances at the two bands of green and red, thereby producing any color in between green and red, through the adjustment of incoming light polarization. Also, the prominent features of the spectral response of the filter, namely the bandwidth and resonant wavelength, can be readily adjusted by varying the dielectric layer thickness and the grating pitch, respectively. The dependence of chromaticity coordinates of the filter in the CIE (International Commission on Illumination) 1931 chromaticity diagram upon the parameters of the spectral response, including the center wavelength, spectral bandwidth and sideband level, has been rigorously examined, and their influence on the color gamut and the excitation purity, which is a colorimetric measure of saturation, has been analytically explored at the same time, in order to optimize the color performance of the filters. In particular, a device with wider spectral bandwidth was observed to efficiently extend the color gamut and enhance the color saturation, i.e. the excitation purity for a given sideband level. Two dual-band green-red filters, exhibiting different bandwidths of about 17 and 36 nm, were specifically designed and fabricated. As compared with the case with narrower bandwidth, the device with wider bandwidth was observed to provide both higher excitation purity leading to better color saturation and greater separation of the chromaticity coordinates for the filter output for different incident polarizations, which provides extended color gamut. The proposed device structure may permit the color tuning span to encompass all primary color bands, by adjusting the grating pitch.
© 2014 Optical Society of America
Color filters exploiting nano-photonic structures are regarded as an integral element for the implementation of display/imaging devices, biosensors, photovoltaic cells, active color pixels, polarization detectors, security tags, and so forth [1–6]. In particular, guided-mode resonance (GMR) based color filters are recognized as being conspicuously attractive, in light of their numerous advantages, such as high efficiency in tandem with proper bandwidth, flexible transfer characteristics, compact size, and simple structure [7–10]. Such filters have been mostly developed to ameliorate the performance, in terms of high transmittance, narrow bandwidth, polarization independence, high angular tolerance, and broad spectral tuning range [11–16]. Their transfer characteristics were dynamically tailored, by means of the angle of incidence, micro-mechanical actuation, and electro-optic effect. It is also noted that for a rectangular grating structure an efficient spectral tuning was attained with the assistance of incident light polarization . To date, as a figure of merit of color filters, the center wavelength and transmittance were mostly taken into account. However, in order to optimize the color response of those filters, features of the spectral response such as the spectral bandwidth and sideband level should be attentively considered. From the viewpoint of their practical applications to the display and imaging fields, the color filters ought to be rigorously evaluated in terms of essential parameters including the color saturation and color gamut. The color saturation is known to be an attribute of visual perception, indicating the degree to which color sensation differs from achromatic sensation regardless of its perceived brightness. The color saturation is quantitatively measured in terms of the excitation purity in a colorimetric analysis, while the color gamut is the range of colors reproducible from a device or system [18–20]. The color saturation and color gamut are to be preferably expanded, so as to enhance the imitation of the natural color of an object [21, 22]. To the best of our knowledge, no attempts have yet been made towards the schemes to improve the color saturation or color gamut through a resonant grating-based visible filter.
In this paper, we present a meticulous study of the dependence of the physical aspects of the color response of a filter upon the properties of its spectral response, including the center wavelength, the spectral bandwidth, and the sideband level, in terms of the chromaticity coordinates in a CIE (International Commission on Illumination) 1931 chromaticity diagram, dominant wavelength and excitation purity. Furthermore, we propose and demonstrate a method to enhance the color saturation and gamut of the filter. A device with wider spectral bandwidth is shown to play a pivotal role in enhancing the color saturation, and extending the color gamut for a given sideband level. Here, we are primarily concerned with a resonant grating-based dual-band color filter incorporating a nanophotonic two-dimensional (2D) rectangular grating, which features a polarization sensitive spectral response exhibiting two primary resonant peaks at green and red colors for two orthogonal polarizations. For arbitrary polarizations formed by two orthogonal cases, the filter is capable of producing any color in between green and red. For the filters having different bandwidths, which could be obtained by simply adjusting the cladding thickness of the device, a detailed comparison of the color saturation associated with the excitation purity and the color gamut has been conducted. We also provide a numerical and experimental proof of the enhancement of the color saturation and color gamut of the filter, using a similar configuration to our previous device , which showed good performance in terms of the spectral tunability, yet exhibiting a low saturation and small gamut. For a color filter with enlarged bandwidth, which results from reduction in the cladding thickness, the performance has been demonstrated to be substantially enhanced in terms of the color saturation and gamut.
2. Dual-band color filter proposed to improve the color saturation and color gamut
As illustrated in Fig. 1, the proposed dual-band color filter involves a 2D asymmetric rectangular subwavelength grating made of Al films, with periods of Λx and Λy along the x- and y-direction, which is integrated with a slab waveguide, consisting of an Si3N4 core (n = 2.023), an SiO2 upper cladding (n = 1.457), and a lower cladding formed on a quartz substrate. The operation of the filter is based on the GMR between the guided modes of the planar waveguide and the diffracted light generated by the grating. The device is supposed to exhibit two transmittance peaks corresponding to green and red, each with a 3-dB bandwidth Δω, depending on two light polarizations of Lx and Ly. For the transmitted color output, the chromaticity coordinates in the CIE 1931 chromaticity diagram are determined by the polarization angle θ, corresponding to the alignment of the electric field with respect to the x-direction. The color saturation, which is quantitatively measured in terms of the excitation purity that depends on the distance running from the white point (completely unsaturated) to the outer edge of the chromaticity diagram (fully saturated), hinges on the Δω of the resonance peak, as will be later explained [18–20]. Taking into account the fact that the change in light polarization alters the color output of the proposed dual-band filter, color gamut of the device is defined as the range of the colors available from the device and it depends on the separation of the coordinates on the chromaticity diagram, corresponding to the points for polarization angles of θ = 0° and 90°. Larger separation of the chromaticity coordinates would lead to greater color gamut, and vice versa.
For the case of a filter device that engages a metallic grating with pitches of Λx = 355 nm and Λy = 395 nm, and a planar waveguide with a 100-nm thick core in Si3N4 and SiO2 cladding layer of 100-nm thickness, we have theoretically explored the transmittance characteristics for different incident polarizations with θ = 0°, 45°, and 90°, via a finite difference time domain (FDTD) method based simulation tool, FDTD Solutions, Lumerical, Canada. The fill factor for the grating, defined as the ratio of the width of the metallic pattern to the grating pitch, is set at 0.7 in light of the transmittance in the visible spectral band. The calculated transfer curves are plotted in Fig. 2(a). Primary resonant peaks at λ = 558 and 612 nm were respectively observed with a transmittance near 85%, for the Lx (θ = 0°) and Ly (θ = 90°) polarizations, while the transmittance for the case with θ = 45° is the average of the two former cases . The reason for this may be explained as follows: The output power when a light is incident with its electric field (E) aligned at an angle θ with the x-axis is proportional to Tθ(λ)E2, where Tθ(λ)is the transmittance for a polarization angle θ of incident light. Also, the field (E) of the incident light may be resolved into two components, Ecosθ and Esinθ, along the x- and y-axes, respectively. When the transmittance for the light polarized along x- and y-axes are respectively denoted as Tx(λ) and Ty(λ), the transmitted power due to the first and second components will be proportional to Tx(λ)E2cos2θ and Ty(λ)E2sin2θ, respectively. Thus, the total output depends on E2[Tx(λ)cos2θ + Ty(λ)sin2θ]. As a consequence, for the proposed filter the transmittance for a polarization angle θ is given by Tθ(λ)=Tx(λ)cos2θ + Ty(λ)sin2θ, which is valid irrespective of the state of polarization of the output light.
As shown in Fig. 2(a), the bandwidths for the main peaks were ~13 and 15 nm for the green and red spectral bands, respectively. Using the transmittance of the color filters, displayable colors can be calculated using the standard equations as provided in . In order to calculate the chromaticity coordinates in the CIE 1931 chromaticity diagram, we first calculated XYZ tristimulus values for a color with a spectral transmittance T(λ), using the following formulae.
Here, are CIE 1931 standard colorimetric observer color-matching functions; S(λ) is the relative spectral power distribution of the standard illuminant, which was chosen to be the CIE normalized illuminant E; The summation was carried out over the visible spectral band ranging from 360 to 830 nm, in wavelength intervals of Δλ equal to 1 nm, and the constant k was chosen in such a way that Y equals 100 for objects for which T(λ) = 1 for all wavelengths. Finally, the chromaticity coordinates (x, y) are given as:
Figure 2(b) depicts the resulting chromaticity coordinates on the CIE 1931 chromaticity diagram in accordance with the spectral responses, for different polarizations varying from θ = 0° to 90° in steps of 45°, where the output color changes from green to red, signifying efficient polarization-mediated tuning of the output color. Although the proposed filter device shows resonant wavelengths pertaining to green and red, the chromaticity coordinates of the output colors are positioned in the vicinity of the white point E(0.3333, 0.3333) in the chromaticity diagram, indicating poor color saturation. It is also evident from the chromaticity diagram that the chromaticity coordinates corresponding to the two polarizations for θ = 0° and 90° are slightly separated from each other, resulting in a small gamut.
The poor color saturation is presumed to arise from appreciable transmittance in the non-resonance sideband. In order to better recreate the natural color of an object, the color saturation and color gamut need to be desirably enhanced. The sideband transmittance may be efficiently diminished by relying on a configuration incorporating a multi-layered Bragg reflector [23, 24]. However, this approach works merely under a limited spectral and angular range. Its implementation is complicated, requiring a number of layers whose thicknesses should be accurately controlled . Meanwhile, our device based on a single dielectric waveguide, loaded up with a metallic grating layer, which ensures reflective properties over a wide spectral and angular range, is expected to achieve a transmission peak via the GMR . Thus, for the configuration of the proposed device, we endeavored to search for a scheme to elevate the color saturation as measured by the excitation purity and to extend the color gamut, by checking on the spectral response that is responsible for the chromaticity coordinates. The resonance spectra of filters capitalizing on the GMR effect are typically expressed by a Lorentzian function, as defined in the following Eq. (3), where To is the sideband transmittance level, T1 the peak transmittance of the resonant peak, Δω the 3-dB bandwidth of the resonant peak, λ the wavelength, and λo the center wavelength of the resonant peak [26, 27].
In an effort to keenly inspect the influence of the transmittance characteristics, including λo, Δω and To, upon the output color, the chromaticity coordinates were traced with respect to the aforementioned parameters, for an arbitrarily fixed transmittance of 90%. Two different cases were considered for the transmittance spectra in the presence and absence of the sideband level, i.e. To = 0 and To≠0. First, in the case of a negligible sideband level (To = 0), the chromaticity coordinates were identified for Δω ranging from 5 to 30 nm in steps of 5 nm, with λo varying from 450 to 650 nm in steps of 10 nm. As shown in Fig. 3(a), the output color shifts from blue to green and eventually to red, along a direction marked by the black arrow in a clockwise direction, which closely follows the direction of the “horseshoe” contour of the chromaticity diagram, thereby meaning that by adjusting the center wavelength λo determined by the grating pitches , we could continuously scan the output color on the chromaticity diagram through all of the three primary colors. It is to be mentioned that as Δω increases, the chromaticity coordinates corresponding to the filter transmittance with a given λo shift towards the white point E of the chromaticity diagram, as indicated by the blue arrow. Hence the color purity/saturation degrades. Meanwhile, as depicted in Fig. 3(b), for the case of a constant sideband level (To = 0.05), for a fixed Δω the chromaticity coordinates shift with λo, sweeping the chromaticity diagram from blue through green to red, in a similar manner to the previous case. However, with increasing Δω, the chromaticity coordinates corresponding to the filter transmittance with a given λo, deviate progressively from the white point E towards the spectral curve of the diagram (as implied by the blue arrow), unlike the previous case with a zero sideband level (To = 0). This intuitively indicates that the color saturation is accordingly elevated as Δω is increased. Similar behaviors with the chromaticity coordinates shifting away from the white point towards the spectral curve of the chromaticity diagram were also observed for any other non-zero side band transmittance. Consequently, as regards a dual-band color filter with a given transmittance and sideband level, the color saturation may be improved by enlarging the bandwidth Δω.
We then investigated the excitation purity of the colors corresponding to the filter transmittance, in order to look into the quantitative aspect of color saturation [18–20]. The dominant wavelength (λD) for a given chromaticity coordinate in the chromaticity diagram was first determined, then the excitation purity was calculated as the ratio of the length of the line segment that connects the chromaticity coordinates of the reference white point E and the point of interest in the diagram, to the length of the line segment that connects the reference white point to the dominant wavelength . Figure 4(a) shows the effect of variation in Δω on the excitation purity of the colors for the Lorentzian filter response given by Eq. (3) with λo = 450, 550 and 650 nm, corresponding to the blue, green and red regimes, particularly considering two cases in relation to the presence and absence of the sideband level (To = 0 and To = 0.05). It is evident from Fig. 4(a) that when Δω increases from 5 to 60 nm, the excitation purity decreases and increases for the cases of To = 0 and To = 0.05, respectively. As shown in Fig. 4(b), for both of zero and non-zero sideband cases, the dominant wavelength for a Lorentzian response with a given λo is observed to show merely a small change as Δω is increased. The excitation purity reaches a maximum value for λo = 450 and 550 nm, while it continues to increase for λo = 650 nm. We thus intended to increase Δω οf the filter, which is presented in Fig. 2, up to 30 nm, thereby improving the excitation purity of both the green and red color output available from the filter.
The spectral bandwidth Δω of the pass band can be readily increased by diminishing the thickness of the upper cladding, in light of the fact that the loss associated with the waveguide modes is dominantly induced by the metallic grating [8, 11]. In order to probe into the possibility of adjusting the bandwidth for the proposed device, the spectral response was examined for different upper cladding thicknesses, ranging from 30 to 210 nm in steps of 30 nm. As shown in Fig. 5(a), the bandwidth increased from about 3 to 29 nm when the cladding thickness decreased from 210 to 30 nm for the green spectral band for the Lx polarization, whereas the bandwidth increased from 8 to 32 nm or so in the red spectral band for the Ly polarization. The bandwidth could be adjusted by altering the cladding thickness, incurring a minimal shift in the resonant wavelength. For the cladding thickness changing from 30 to 210 nm, the shift in the resonant wavelength Δλo was first estimated with respect to the case when the cladding thickness is 210 nm. As presented in Fig. 5(b), the relative wavelength shift, which is defined as Δλo/λo, was found to be much smaller.
For the same planar waveguide with a 100-nm thick core in Si3N4 and an SiO2 cladding layer of 100-nm thickness, we could also obtain blue-green(BG), blue-red(BR), and green-red (GR) filters by adjusting the grating periods, where the grating periods in the x- and y-directions were set to Λx/Λy = 285/355 nm, Λx/Λy = 285/395 nm, and Λx/Λy = 355/395 nm with center wavelengths at 462, 558 and 612 nm corresponding to the blue, green and red bands, respectively, with a transmittance exceeding 85% and a bandwidth of ~15 nm for different bands, as shown in dashed lines in Fig. 6. Also, when the cladding thickness was reduced to 30 nm, the spectral bandwidth Δω could be widened to ~32 nm for different transmission bands of the filters, incurring a minimal shift in λo, as shown in solid lines in Fig. 6. The former three, which have a cladding thickness of t = 100 nm and thus have narrow bandwidths, are designated as BG-1, BR-1 and GR-1, while the latter three which have a cladding thickness of t = 30 nm and wider bandwidths are designated as BG-2, BR-2 and GR-2.
Figure 7 shows the chromaticity coordinates of the filters, BG-1, BR-1, GR-1, BG-2, BR-2 and GR-2, where the coordinates of the former three and latter three filters for different polarizations are shown connected by a dashed and solid line, respectively. Here, the direction of the arrows represents the change in the chromaticity coordinates, with θ varying from 0° to 90°, and the dots in the chromaticity diagram for each filter represent the chromaticity coordinates for the particular cases of θ = 0°, 45° and 90°. It is clear from Fig. 6 that the triangle-like area is enclosed by the three cases of BG, BR and GR, indicating the subset of colors reproducible by the use of the filters. For the devices of BG-1, BR-1 and GR-1, the chromaticity coordinates are closer to the white point E in the chromaticity diagram, thereby indicating poor saturation and low excitation purity. To the contrary, in the case of the filters of BG-2, BR-2 and GR-2, the chromaticity coordinates are farther from the white point E, leading to high excitation purity or color saturation. Moreover, the separation of chromaticity coordinates of the filters for different polarizations is larger for the latter case, hence providing larger color gamut. Thus, the color saturation as well as the color gamut turned out to be better for a broader spectrum corresponding to the cladding of 30-nm thickness than for the case of a 100-nm thick cladding. The calculated chromaticity coordinate, dominant wavelength and excitation purity for each of the points in chromaticity diagram for the calculated spectral response of those six different filters have been summarized in Tables 1, 2 and 3, for different incident polarization angles θ. When no well-defined dominant wavelength exists, the complementary wavelengths have been indicated with a letter 'c' enclosed in parenthesis in the tables. The wavelength associated with the point on the horseshoe-shaped curve, at which the line extrapolated in the other direction (from the point of interest towards the reference white point) intersects, is called the “complementary wavelength” [18–20]. It is understood from Fig. 7 and Tables 1, 2 and 3 that the excitation purity and color gamut are enhanced for the filters with wider bandwidth Δω.
3. Application of the implemented dual-band color filters for enhancing the color saturation and color gamut
The proposed visible filters, which exhibit two transmittance peaks corresponding to green and red depending on two light polarizations of Lx and Ly, were fabricated exploiting conventional e-beam lithography in conjunction with dry etching technique. Initially, a Si3N4 and SiO2 thin film, each 100 nm thick, were successively deposited on a quartz substrate via plasma enhanced chemical vapor deposition, and a 40-nm thick Al film was subsequently formed via thermal evaporation. With an e-beam resist pattern serving as a soft mask, the Al film was selectively dry etched to create an asymmetric 2D grating with the pitches of Λx = 355 nm and Λy = 395 nm, which are responsible for the green and red bands, respectively. In this way, one filter device designated as Dev-I, with a cladding thickness of 100 nm, was completed. The other device, designated as Dev-II, was similarly created with a smaller cladding thickness of 30 nm. Both Dev-I and II have effective dimensions of 40x40 μm2. Figure 8(a) displays a scanning electron microscope (SEM) image of Dev-I, which is monitored to have clearly defined metal patterns. The revealed nano-grating structures of the samples were characterized using a scanning electronic microscopy (CD-SEM System, Hitachi, S-9260A, Japan) with an accelerating voltage of 800 V and a magnification of 100,000. The grating pitches were prepared as designed. As revealed in Fig. 8(b), for Dev-II, the grating pitches along the x-and y-directions were slightly changed to be Λx = 340 nm and Λy = 405 nm due to process errors.
In order to evaluate the transfer characteristics of the prepared dual-band filters, light available from a halogen lamp (AvaLight-HA, Avantes) was properly polarized and launched to the device under test, with the output detected by a spectrometer (Avaspec-3648, Avantes). As plotted in Fig. 9, the optical response was first scrutinized in terms of two orthogonal polarizations. The calculated and measured results are shown by a dashed and solid line, respectively. For the Lx polarization, the main transmittance for Dev-I and Dev-II was centered at the wavelength determined by the x-direction pitch Λx. The transmittance was found to surpass 80%. For the Ly polarization, the primary resonant wavelengths shifted to the red band in accordance with the y-direction pitch Λy. For Dev-I, as plotted in Fig. 9(a), the main resonant wavelengths in compliance with the phase matching for Λx and Λy were measured to be ~558 and 612 nm, respectively, for the two orthogonal polarizations. The maximum transmittance for each of the bands at the resonant wavelengths was around 80%. For the Dev-II, the corresponding peaks were centered at λ = 530 and 612 nm, as presented in Fig. 9(b). The maximum transmittance for each of the bands was beyond 78%. The measured spectral bandwidth was 17 and 36 nm or so for the Dev-I and Dev-II, respectively, for both of the two polarizations. On the whole, the measured results were in good agreement with the simulation results, with the realized structural parameters being reflected.
Finally, we endeavored to actually verify that the prepared dual-band visible filters could play the role of helping improve both the color saturation and color gamut. As revealed in Fig. 10, the measured spectra for both the Dev-I and Dev-II, exhibiting a polarization sensitive operation, were represented in the CIE 1931 chromaticity diagram, where the dots represent the particular cases of θ = 0°, 45° and 90°. The line joining the two points corresponding to the cases of θ = 0° and 90° indicates that the color could be successfully scanned from green to red along the direction of the arrows, when the polarization angle θ changed from 0° to 90°. The dashed arrow is used for the Dev-I with Δω = 17 nm, while the solid arrow is for the Dev-II with Δω = 36 nm. The chromaticity coordinates pertaining to the output of the Dev-II were observed to be farther away from the white point E of the chromaticity diagram, implying that, as anticipated, the color saturation has been elevated and the separation of the chromaticity coordinates for different incident polarizations of the filter output was larger, indicating that the color gamut has been extended due to the extension of the color range between the green and red points. For the measured spectral response of the fabricated green-red filters, Dev-I and Dev-II, at different incident polarization angles, the chromaticity coordinates, dominant wavelength (λD), and excitation purity for each of the points in the chromaticity diagram have been summarized in Table 4. The complementary wavelengths were indicated with a letter 'c' enclosed in parenthesis in the table for the cases of no well-defined dominant wavelength. It is clearly implied from Table 4 that, in comparison to Dev-I, the separation of the chromaticity coordinates for different polarizations are larger for Dev-II, thereby exhibiting larger color gamut. Also, the excitation purity is raised by a factor of ~4 for Dev-II for θ = 45 ° and 90°, while it has a similar value for θ = 0°. It is to be noted that, as evident from its dominant and complementary wavelengths, Dev-I with a narrower bandwidth provides a color perception in blue and purple regions, as opposed to our prediction of obtaining green and red colors. This is attributed to the undesirably high sideband transmission in the blue band, seriously affecting the color output. To the contrary, Dev-II with a wider bandwidth is less affected by the undesirable sideband transmission, exhibiting enhanced color saturation (excitation purity) and color gamut. It was therefore validated that, for the proposed GMR filter devices containing a certain level of sideband, not only the excitation purity, which provides a measure of color saturation, could be enhanced but also the color gamut could be improved by increasing the bandwidth of the pass band, as manifested by the thick blue arrow in Fig. 10. In order to optimize the quality of color reproducible by the filters, the spectral bandwidth and sideband level of the spectral response should be considered, in addition to the location of the resonant wavelength and maximum transmittance. Although we have experimentally demonstrated the enhancement of color saturation and color gamut for the green and red spectral bands, the proposed approach is readily applicable to the other spectral bands like blue/red or blue/green, which may be easily accomplished by tailoring the grating pitches as aforementioned, thereby embracing all three primaries. This will be highly applicable in creating display systems with an extended triangular color gamut. Thus, the dual-band color filter as proposed in this work, exhibiting an adjustable spectral response that features polarization sensitivity, center wavelength determined by the grating period, and bandwidth controlled by the upper cladding thickness, may be highly useful in accomplishing the flexible design of color filters to enhance the color saturation and extend the color gamut. The proposed scheme may be equally valid for the spectral responses in other cases, such as thin-film filters or surface plasmon resonance based filters.
The enhancement of excitation purity, which is a measure of color saturation and extension of the color gamut, has been demonstrated by taking advantage of a dual-band color filter incorporating a 2D asymmetric resonant grating structure, which exhibits a polarization-tailored spectral response with two resonant peaks at green and red colors. In particular, the effect of the spectral bandwidth, the resonant wavelength and the sideband transmittance upon the color saturation and color gamut was theoretically and experimentally inspected, by relating the spectral response to the chromaticity coordinates in the CIE 1931 chromaticity diagram. Between the two dual-band color filters with bandwidths of ~17 and 36 nm, the latter device with wider bandwidth was observed to result in higher excitation purity, signifying better color saturation and more extended color gamut. It is predicted that the proposed scheme resorting to a GMR-based dual-band filter will be readily exploited for upgrading the performance of various types of display applications.
This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2013-008672, 2013-067321), and a research grant from Kwangwoon University in 2014. The authors are grateful to Mr. C. H. Park and Dr. Y. T. Yoon for their valuable help.
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