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Abstract
Optical diffusers are widely used in a variety of light sources to create uniform illumination over a wide field of view. Inspired by the diffraction-based light diffusion of the Morpho butterfly, here we demonstrate a novel diffuser which fulfils (i) high transmittance, (ii) wide angular spread, and (iii) low color dispersion. Two-dimensional nanopatterns were designed using optical simulations to enable simple fabrication. By introducing anisotropy into the surface nanopatterns, we achieved control of anisotropic light diffusion, which has been challenging for conventional diffusers. Next, the designed diffuser was implemented over a large area (100 × 100 mm2) via nanoimprint lithography. The obtained diffuser demonstrated a high transmittance of ∼85% and full width at half maximum (FWHM) of >60° with low color dispersion, outperforming conventional diffusers. Since the presented diffuser has the controllable diffusion properties with low light loss, it has many applications including LED lighting, displays, and daylight harvesting systems.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical diffusers spread incident light in various directions and this function plays an important role in generating a uniform light distribution. In fact, optical diffusers are widely used in light-emitting diode (LED) luminaires and liquid crystal displays. Diffusers also have a wide range of applications, such as daylight harvesting [1–4], laser optics [5,6], and chemical sensors [7].
Although there are several types of diffusers, the most general one is based on multiple scattering and refraction, in which organic/inorganic scatterers are embedded in a plastic film. However, the inherent multiple scattering—light travelling inside the film is scattered repeatedly at the interfaces between a base medium and scatterers—leads to a significant reduction in transmittance and lowers the energy efficiency in lighting [8–14]. In addition, the light diffusion is only isotropic due to the spherical shape of the scatterers, which not only limits the variety of light shaping, but also dims the diffused light because the brightness per solid angle decreases when the light is diffused isotropically/spherically. Therefore, anisotropic light diffusion is preferable for several applications such as specific luminaires and monitors, where light needs to be diffused mainly into horizontal directions.
To overcome these problems, many researchers have developed novel diffusers through various methods, e.g., wrinkles formation [15], chemical treatment of wood [16,17], the use of specific crystal morphologies [18,19], and laser processing [20–22]. However, owing to the limitation in formed shapes and/or some undesirable phenomena (absorption, multiple scattering, etc.), it still remains a challenge to produce a diffuser that fulfils all the following characteristics: (i) high transmittance, (ii) wide angular spread, and (iii) low color dispersion.
In contrast, the nanostructure of the Morpho butterfly is promising for an excellent diffuser because the light diffusion is achieved by diffraction (neither multiple scattering nor refraction), allowing for the light diffusion with high transmittance. Based on this diffraction-based light diffusion, we recently proposed a biomimetic model with superb diffusion properties, which meets all the aforementioned characteristics in optical simulation [23]. However, the current model requires complex nanostructures with three-dimensional (3D) disorder, hindering practical fabrication of the Morpho-type diffuser. There was also an attempt to use Morpho butterfly wings as a diffuser, but the need for intact wings is unsuitable for mass production, and the optical properties (angular spread, anisotropy, etc.) cannot be controlled [24].
Here, we report the first demonstration of an artificial Morpho-type diffuser. Using the finite-difference time-domain (FDTD) simulation, the original 3D model was simplified into a 2D design to enable straightforward nanofabrication. Next, the designed diffuser was fabricated over a large area (100 × 100 mm2) via nanoimprint lithography. Lastly, structural and optical characterization was performed to investigate the performance of the created diffuser.
2. Optical principles
A vast number of creatures exhibit vivid colors as a result of different kinds of photonic crystals [25–31]. In particular, the brilliant blue color of some species of the Morpho butterfly (Fig. 1(a)) is intriguing because of its low angular dependence. The butterfly wing appears blue in a wide angular range (> ±40° from the normal), while the intense blue color (reflectivity > 60%) is induced by multilayered structures which typically show angle-dependent colors (i.e. iridescence). This exceptional feature can be explained by the discrete multilayers shown in Fig. 1(b) and summarized as follows: (i) periodic alternating layers of air and chitin cause multilayer interference and produce the intense blue reflection; (ii) small widths of the multilayers diffract the reflected blue waves into wide angles; and (iii) random configuration of the multilayers prevents the formation of diffraction gratings, thereby alleviating the angular dependence of reflectivity [25,32–38].
Fig. 1. (a) Photograph of a male Morpho didius. (b) Cross-sectional nanostructure of a blue wing scale of M. didius. Reproduced with permission from Ref. [33]. Copyright (2012) Taylor & Francis Group. (c) Schematic of the diffraction-based light diffusion of the Morpho-type diffuser. Note that Fig. 1(c) depicts a cross-sectional view.
Considering that the high reflectivity arises from the multiple reflections at the multilayers, the skillful diffusion properties of the Morpho butterfly can be converted into transmission mode by omitting the reflective multilayers. Figure 1(c) illustrates how the transmitted light is diffracted into a wide angular range by randomly distributed nanopillars. In this scheme, all the three requirements can be met at the same time: (i) high transmittance can be attained by the absence of multiple scattering (diffraction occurs only at the surface region and thus the number of scattering events is limited); (ii) wide angular spread by the diffraction from the small pillar widths; and (iii) low color dispersion due to the randomness [23]. Moreover, the degree of light diffusion is tunable by modifying the pillar widths, because the diffraction spread is determined by the width of a diffracting object. Indeed, the Morpho butterfly’s nanostructure is highly anisotropic (widths are small in one direction as in Fig. 1(b) but large in the orthogonal direction), exhibiting anisotropic reflection and thereby enhancing its brightness [25,36].
3. Results and discussion
3.1 Structural design using FDTD simulations
Despite the remarkable potential of the Morpho-type diffuser, it remains elusive to implement the disordered yet well-defined morphology in Fig. 1(c). Therefore, the complex 3D structure must be simplified into a 2D design for practical fabrication. Recently, we clarified that in-plane randomness with binary height, rather than 3D randomness, is sufficient for creating a Morpho-colored material [39]. Based on this concept, we designed a 2D (in-plane) structural model with random widths to enable the simple fabrication of the Morpho-type diffuser (Fig. 2(a–c)). Although this design does not directly comprise the 3D morphology as in Fig. 1, our diffuser is analogous to the Morpho butterfly in terms of (i) nanoscale randomness, (ii) wide diffraction spread, and (iii) anisotropy.
Fig. 2. (a) Schematic of the 2D Morpho-type diffuser containing anisotropic nanopatterns on both sides. (b,c) Surface nanopatterns on the bottom and top sides, respectively. The minimum widths W0 and the groove depths d were set to (W0, d) = (b) (300 nm, 440 nm), (c) (470 nm, 690 nm), and the distribution function f was optimized to be the half-normal distributions (denoted as σ) with standard deviations of 0–3W0 and 6W0 for the x- and y-directions, respectively. See Supplementary Note 1 (Figs. S3–S6, Supplement 1) for the detailed procedure. (d) Simulated total transmittance spectrum. (e,f) Simulated angular distributions of the transmitted light in the x- and y-directions, respectively.
Figure 2(a) shows a schematic of the 2D Morpho-diffuser. The surface nanopattern was defined to be anisotropic to achieve anisotropic light diffusion—incident light is diffused widely in the x-direction but tightly in the y-direction, which is unavailable with the conventional diffusers. The nanopattern is characterized as a lattice of rectangles with varying widths, W = W0 + f, and a depth d, where W0 is the minimum feature size, and f is a positive distribution function to introduce randomness. This design allows the simple optimization of the structural parameters, because the x- and y-directions are independent of each other. The optimization of the structural parameters was performed using the FDTD simulations, and the detailed procedure is described in Supplement 1 (Supplementary Methods and Supplementary Note 1), but the essence can be summarized as follows:
- (i) The diffraction spread depends on the wavelength of incidence, and the light is strongly diffracted by structures of comparable size to its wavelength. To aim for homogeneous light diffusion over the entire visible spectrum, we placed two differently sized nanopatterns on the bottom and top sides so that the short and long wavelengths would be diffracted predominantly at the bottom- and top-side patterns, respectively (Fig. 2(b,c)).
- (ii) To suppress the strong normal transmission (zeroth-order diffraction), the groove depths d were set to 440 nm and 690 nm for the bottom and top patterns, respectively. These values correspond to the destructive interference of blue and red light, respectively, assuming that the nanostructure is composed of UV-curable resin with a refractive index of 1.51. Note that weakening the normal transmission does not reduce the total transmittance; this component is distributed in other directions since there is no light absorption in the material.
3.2 Fabrication of the designed diffuser
To realize the practical fabrication of the designed Morpho-type diffuser, we employed nanoimprint lithography, namely photolithography and UV nanoimprint (Fig. 3(a); see Supplementary Methods in Supplement 1 for more experimental details). Firstly, the bottom and top patterns were created on 6-inch Si wafers separately by photolithography and dry etching. Next, the nanostructures on the Si molds were transferred to a UV-curable resin on a poly(methyl methacrylate) (PMMA) film with a thickness of 125 µm. As the UV resin and PMMA film have high transparency and similar refractive indices in the visible spectral range, the designed diffuser can be obtained with low light loss.
Fig. 3. (a) Schematic of the fabrication process of the designed diffuser (nanoimprint lithography). (b,c) Photographs of the Si molds with the bottom and top patterns, respectively (patterned area: 100 × 100 mm2). (d,e) SEM images of the bottom and top patterns on the Si molds, respectively. The red circles in (d) represent the missing tiny structures due to underexposure. (f) Photograph of the fabricated diffuser film (patterned area: 100 × 100 mm2) placed ∼10 cm above university logos.
Figures 3(b,c) show photographs of the Si molds (patterned area: 100 × 100 mm2). The bottom and top patterns appear bluish and reddish at an oblique angle, respectively, indicating that the respective nanopatterns well diffuse the light with short and long wavelengths. The scanning electron microscopy (SEM) images shown in Figs. 3(d) and 3(e) reveal that nanostructures of the order of the visible wavelengths were successfully obtained. Although tiny structures smaller than the exposure wavelength (365 nm) shrunk or are missing in the bottom pattern (red circles in Fig. 3(d)), these defects account for a small portion of the overall area and thus would make little contribution to the optical properties. These defects largely stem from the diffraction phenomenon in photolithography which distorts the image patterned on the photoresist by rounding sharp corners and shortening narrow line ends [40,41].
After the simple nanoimprint process, a diffuser film was acquired over a large area with high reproducibility (Fig. 3(f), patterned area: 100 × 100 mm2). The opacity of the patterned region demonstrates effective light diffusion of the diffuser, because opacity is a result of redirecting the light coming from the back. In contrast, the outer part (unpatterned region) exhibits high transparency. This indicates low light loss (high optical efficiency) owing to the matched refractive indices between the UV resin (1.51) and PMMA film (∼1.5).
3.3 Structural/optical characterization
To evaluate the 3D morphology of the imprinted diffuser film, we performed atomic force microscopy (AFM). Figures 4(a) and 4(b) show 3D AFM images and representative cross-sectional profiles of the bottom and top patterns, respectively. The 3D images verify the satisfactory replication of the UV nanoimprint for both patterns, without any collapse of the nanoprotrusions. In addition, we analyzed the cross-sectional profiles and obtained groove depths of 450 ± 15 nm and 673 ± 11 nm for the bottom and top patterns, respectively (n > 30). These values are in good agreement with the designed depths (440 nm and 690 nm, respectively). Therefore, the fabricated diffuser is expected to exhibit optical properties similar to the simulation results shown in Figs. 2(d–f).
Fig. 4. AFM analysis of (a) the bottom and (b) top patterns on the imprinted film (top: 3D AFM images; bottom: cross-sectional profiles along the black lines).
To reveal the diffusing characteristics, we performed optical characterization using two different light sources: a collimated white beam as a well-defined experimental light source (Fig. 5) and an LED light as a practical light source (as shown later in Fig. 7). Figure 5(a) illustrates the experimental setup, where the distribution of the transmitted light for a collimated white beam is projected onto a screen. Unlike the conventional diffusers [8–14], our Morpho-type diffuser clearly demonstrates anisotropic light diffusion, so that the incident light is diffused widely in the x-direction but tightly in the y-direction (Fig. 5(b)). However, a cross mark (orthogonal bright lines in the x- and y-directions) and a bright spot are present in the diffusion pattern. The cross mark can be attributed to diffraction caused by the rectangular structures. The bright spot, on the other hand, is thought to result from the deviated area fraction of the nanoprotrusions and/or the high coherency of the experimental light source, as discussed in Supplementary Note 2 (Supplement 1).
Fig. 5. (a) Experimental setup to verify the diffusing characteristics. (b) Photograph of the diffusion pattern of a collimated white beam. (c) Measured total transmittance spectrum. (d,e) Measured angular distributions of the transmitted light in the x- and y-directions, respectively.
Fig. 6. Plots of (a) diffusion factors and (b) angular FWHMs versus transmittance for different types of diffusers.
Fig. 7. (a,b) Photographs of the LED light distribution without and with the diffuser, respectively. (c) Measured angular distributions of (a,b).
Next, we measured the total transmittance and angular spread of the transmitted light to quantify the optical properties. Figure 5(c) shows the total transmittance spectrum measured with an integrating sphere. The total transmittance of ∼85% represents high optical efficiency, which coincides with the simulation result (Fig. 2(d)). We also obtained the diffuse transmittance (= total transmittance – direct transmittance) of ∼73% by eliminating the direct transmission (bright spot) in measurement. This indicates that ∼86% (known as “haze value”) of the transmitted light is diffused into non-zero directions. Figures 5(d), and 5(e) show the angle-resolved spectra measured in the x- and y-directions, respectively. Although large transmittance peaks emerge at 0° corresponding to the bright spot, an anisotropic angular spread was confirmed with low color dispersion. Excluding the transmittance peak at 0°, a wide angular spread of FWHM ≈ 66°, and a small spread of FWHM ≈ 27° were confirmed in the x- and y-directions, respectively. These values are in good agreement with the simulation results (∼69° and ∼24°, respectively; Figs. 2(e), and 2(f)), showing the validity of our design principles.
To clarify the difference between our Morpho-type diffuser and the conventional diffusers, we plotted the diffusion factor—one of the performance indicators for market diffusers [11–14]—versus transmittance (Fig. 6(a)). The diffusion factor (%) is given as
To ensure a fair assessment, we further conducted a performance comparison with the other novel diffusers [15–22,24]. As seen in Fig. 6(a), the diffusion factor is an effective indicator for visualizing the relationship between the degree of diffusion and transmittance. However, it has yet to be utilized in academia; angular FWHM is mainly used as a diffusion indicator for the other novel diffusers. Therefore, here we plotted the angular FWHMs instead of the diffusion factor, versus transmittance (Fig. 6(b)). It is obvious that the FWHMs of the other novel diffusers do not exceed 60°, whereas our Morpho-type diffuser exhibits the largest FWHM (>60°) and a high transmittance (85%), displaying the superiority of the diffraction-based light diffusion.
Although a cross mark and a bright spot emerged in the diffusion pattern for a collimated white beam (Fig. 5(b)), diffusers are generally used for LED light. Hence, the diffusing capability with respect to LED light was examined, as shown in Fig. 7. Notably, using an LED flashlight that makes a spotlight distribution (Fig. 7(a)), the cross mark and bright spot disappeared (Fig. 7(b)). This can be attributed to the lower directivity of the LED light compared to that of the collimated white beam. Figure 7(c) shows the angular spread of the light patterns in Figs. 7(a) and 7(b). The FWHM of ∼21° in Fig. 7(a) is anisotropically broadened to ∼63° in the x-direction and ∼30° in the y-direction in Fig. 7(b), indicating effective light diffusion for a practical light source. Therefore, our Morpho-type diffuser has high potential for many applications, such as LED lighting, displays, and daylight harvesting systems.
Regarding optical measurement techniques, it would be interesting to examine the diffusion properties for the collimated white beam (Figs. 5(d) and 5(e)) for different incident angles; weighted summation of which would provide diffusion properties for a light source with an arbitrary angular profile. While the multiple experiments might be time-consuming, this method would be useful in the case that the analysis of diffusion properties for various light sources are required.
4. Conclusions
Based on the diffraction-based light diffusion of the Morpho butterfly, we demonstrated a novel optical diffuser which fulfils (i) high transmittance, (ii) wide angular spread, and (iii) low color dispersion. Using the FDTD simulations, the nanopattern of the Morpho-type diffuser was designed in 2D. The anisotropic nanodesign enabled anisotropic light diffusion, which cannot be achieved with the conventional diffusers. Next, the designed diffuser was implemented over a large area (100 × 100 mm2) via nanoimprint lithography. Structural characterization by SEM and AFM verified the successful fabrication of the designed nanopattern with a slight error. Although the fabricated diffuser produced a cross mark and a bright spot in the diffusion pattern for a collimated white beam, anisotropic light broadening with FWHMs of ∼66° and ∼27°, a high transmittance of 85% were obtained in optical measurements. Furthermore, the cross mark and bright spot were not present for a practical LED light source, and the circular angle distribution of FWHM ≈ 21° was broadened to ∼63° in the wide-angle direction and ∼30° in the narrow-angle direction, indicating satisfactory light diffusion for LED light. Since our Morpho-type diffuser has the controllable diffusion properties (diffusion angle, directionality, etc.) with high optical efficiency, it has many potential applications including LED lighting, displays, and daylight harvesting systems.
Funding
Japan Society for the Promotion of Science (JP19K22062).
Acknowledgments
The authors thank Kyoto University Nano Technology Hub for providing access to photolithography equipment, S. Kishimura and H. Seto (Kyoto University Nano Technology Hub) for technical assistance in photolithography, and Prof. Y. Hirai (Osaka Prefecture University) and T. Ohsaki (Toyo Gosei Co. Ltd.) for technical support in nanoimprint.
Disclosures
The authors declare no conflicts of interest
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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