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Omnidirectional light absorption of disordered nano-hole structure inspired from Papilio ulysses Wanlin Wang,1 Wang Zhang,1,3 Xiaotian Fang,1 Yiqiao Huang,1 Qinglei Liu,1 Mingwen Bai,2 and Di Zhang1,4 1
State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, China 2 School of Materials, University of Manchester, Manchester M13 9PL, UK 3
e-mail:
[email protected] 4
e-mail:
[email protected]
Received April 16, 2014; revised June 4, 2014; accepted June 10, 2014; posted June 10, 2014 (Doc. ID 210190); published July 11, 2014 Butterflies routinely produce nanostructured surfaces with useful properties. Here, we report a disordered nanohole structure with ridges inspired by Papilio ulysses that produce omnidirectional light absorption compared with the common ordered structure. The result shows that the omnidirectional light absorption is affected by polarization, the incident angle, and the wavelength. Using the finite-difference time-domain (FDTD) method, the stable omnidirectional light absorption is achieved in the structure inspired from the Papilio ulysses over a wide incident angle range and with various wavelengths. This explains some of the mysteries of the structure of the Papilio ulysses butterfly. These conclusions can guide the design of omnidirectional absorption materials. © 2014 Optical Society of America OCIS codes: (140.3490) Lasers, distributed-feedback; (060.2420) Fibers, polarization-maintaining; (060.3735) Fiber Bragg gratings; (060.2370) Fiber optics sensors. http://dx.doi.org/10.1364/OL.39.004208
The light absorption property play a key role in optical detectors and photovoltaics. Inspired by nature, two different routes have been investigated to achieve perfect absorption. The first one consists of relying on diffusion in disordered lossy surfaces. Engineered materials have been synthesized following this solution to produce extraordinary broadband light absorption [1]. The second approach consists in using ordered periodic structures, as found in some insects such as butterfly [2,3]. Several efforts have been made in this field to achieve near total but directionally dependent absorption using periodic grating structures [4–6]. However, the ability to absorb light completely from any incident direction of light remains a challenge. Absorption in periodic structures is highly sensitive to the angle of incidence. This directionality prevents their application to photovoltaic cells and microscale lighting, where wide collection and emission angles are generally required [7]. Here, we design an effective microstructure for an omnidirectional absorption effect that relies on a disordered nano-hole structure inspired from the Papilio ulysses. The scales of the Papilio ulysses are mainly comprised of chitin and diffused melanin. The refractive index (RI) of butterfly chitin has been established to be around 1.56 [8], while the RI of melanin has been much less certain. Because melanin is an absorbing pigment, the value of the RI is a complex number, which is difficult to measure accurately. The RI of sepia melanin at wavelength 633 nm was reported as 1.655 0.008 i0.12 0.07 [9]. Similar data were reported as 1.55 i0.14 with melanin elytra of a buprestid beetle [10]. The index values were also studied in the damselfly [11]. In this Letter, we focus on the study of the omnidirectional light absorption property. Thus the RI is set as 1.56 i0.2 with thin nano-hole structures to prevent too small an absorption. Our goal is not to create an exact computational model and then get the exact absorption of the Papilio ulysses, but to discover the mystery of the disordered structure of Papilio 0146-9592/14/144208-04$15.00/0
ulysses and then to guide the design of omnidirectional light absorption material. The black scales of the Papilio ulysses butterfly were chosen for this study because of their deep black. The structure of these black scales is typical of dark brown and black scales found on many other Lepidoptera [2]. These scales are constructed by periodic ridges and aperiodic nano-holes between the ridges that extend from the surface toward the scale substrate beneath. Common ordered nano-hole structures were proved to yield nontrivial effects [12–15], such as larger enhancement and redshift of the transmission peaks with respect to the Rayleigh condition for light polarized along the short axis of elongated apertures. In this Letter, we will compare the omnidirectional light absorption properties of these common ordered nano-hole structures with the disordered nano-hole structure inspired from Papilio ulysses. The 3D-model of our simulation is shown in Fig. 1. The structure (M0) was derived from transmission electron micrographs of Papilio ulysses [2]. Figure 1(a), a-1, shows the polar angle θ and the azimuth angle φ in the coordinate system. The φ is set from 0 to 360°. The θ is set from 0 to 45° which is limited by the ability of our computer. Figure 1(a), a-2, shows one period of the structure. Figure 1(a), a-3, shows the tapered ridges. The RI of these ridges is set as 1.56 i0.06. The 3-D models of three common ordered structures (M1, M2, and M3) are shown in Fig. 1(b). In this Letter, the absorption with omnidirectional incident light in studied in the structure of Papilio ulysses. We concentrated our efforts to complete the omnidirectional light study, thus the mean value of the absorption with the same wavelength was kept roughly the same. The filling ratio and the hole’s area, and depth were fixed at 0.27, 0.176 μm2 , and 1000 nm, respectively. In this study, we use the finite-difference time-domain (FDTD) method to numerically calculate the absorption © 2014 Optical Society of America
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Fig. 1. Structure model and boundary conditions. (a) M0: the disordered model with ridges derived from the Papilio ulysses. a-1, the sketch map of polar angle θ, azimuth angle φ and coordinate system; a-2, one period of the M0; and a-3, the tapered ridges of the Papilio ulysses. (b) Three ordered model of M1, M2, and M3. The filling ratio and the hole’s area are fixed at 0.27 and 0.176 μm2 . (c) The boundary conditions in vertical (x & y) directions are absorbing (perfectly matched layer, PML) and in horizontal (z) direction is periodic (periodic boundary condition, PBC).
produced by the sophisticated microstructures in the Papilio ulysses’ wing. The boundary conditions are shown in Fig. 1(c). The boundary condition in the z direction is absorbing (perfectly matched layer, PML) and in the x and ydirections is periodic (periodic boundary condition, PBC). A plane wave source illuminates the structure. The polar contour plots of absorption with M0 to M3 are shown in Fig. 2. The structure M0 was constructed from the SEM of the Papilio ulysses [2]. The structure M0 is not an ordered structure and has tapered ridges. The results for a wavelength of 600 nm are given in different columns. The s and p polarizations are shown in the second row and the mean value of s and p polarization is given in the fourth row labeled “unpolarized” condition. The color bar is located in the right of the picture. It should be noted that the limitation of the color bar is 50% to 100%. The angles of θ and φ were marked in the plot of unpolarized condition, while the information of θ and φ was not given in the s and p polarization to save space.
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The results of omnidirectional light absorption were as follows. (1) The omnidirectional light absorption of M0 is the most stable structure. (2) The difference of p polarization and s polarization is smaller than the condition of structures M1 to M3. (3) The peaks and the troughs in Fig. 2 are all in the directions of symmetry axes. Thus symmetry structure produces unsteady omnidirectional light absorption. (4) The omnidirectional light absorption of p polarization is very different with s polarization. The value of unpolarized illumination is more stable than that of the s or p polarization. (5) The omnidirectional absorption of structures M2 and M3 are more stable than the absorption of structure M1, while the absorption of structure M2 is similar to that of the absorption of structure M3. Thus the symmetry of the structure affects the absorption with different incident light. The polar contour plots with a wavelength of 500 and 700 nm were also finished. The results confirmed the above conclusions with a wavelength of 600 nm. These plots were not shown here to saving space. The line plots of ΔA [shown in Eq. (1)] as a function of wavelength at different angles of incidence were provided to evaluate the stability of omnidirectional light absorption in the visible spectrum as shown in Fig. 3: ΔA
Aθ . Aθ0
(1)
The line cuts from polar plots were compared for normal and oblique incidences. Here the results of structure M1 were compared to structure M0. With the fixed azimuth angle φ, the stability of different polar angles θ was shown. The results are as follows. (1) The stability with different θ of structure M0 is much better than that of structure M1 in the visible spectrum. (2) The absorption decreases with an increase of θ at a shorter wavelength, while the absorption increases with an increase of θ at a longer wavelength. (3) The absorption with different φ changes a little in structure M0, while there is much more changes with different φ in structure M1. Thus the stability with a different φ in structure M0 is better than that in structure M1.
Fig. 2. Polar contour plots of absorption with model M0 to M3 at a wavelength of 600 nm. The s and p and unpolarized light were applied. The mean value, standard deviation value, minimum value, and maximum value are given below each contour plot.
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Fig. 4. Electric field intensity slice plot of structure M0 and M1 with different polarization and incident angle under wavelength 100 nm. (a) structure M1 with p polarization and incident angle θ and φ, both equal 0°; (b) structure M1 with p polarization and incident angle θ and φ equal 45° and 0°; (c) structure M1 with s polarization and incident angle θ and φ equal 45° and 0°; (d) structure M0 with p polarization and incident angle θ and φ equal 45° and 0°; and (e) structure M0 with s polarization and incident angle θ and φ equal 45° and 0°.
In order to investigate the absorption in the nano-hole structure, electric field intensity slice plots of M0 and M1 are shown in Fig. 4 with a wavelength of 600 nm. The slice plot of h 100 nm, h 300 nm, h 500 nm, and h 700 to 1000 nm was chosen. The red double-headed arrow shows the polarization direction. Figure 4(a) shows the absorption of M1 with p polarization, and both the incident angles θ and φ are set to 0°. It also shows that the absorption is mainly completed by the rectangle parallel to the polarization (along the x axis) while the absorption of the rectangle perpendicular to the polarization is much smaller. The condition of s polarization
Fig. 3. Line plots of ΔA spectra with different viewing angle θ and φ in structure M0 and M1. (a) ΔA spectra with φ equals 0° in M0 structure; (b) ΔA spectra with φ equals 90° in M0 structure; (c) ΔA spectra with φ equals 0° in M1 structure; (d) ΔA spectra with φ equals 45° in M1 structure. The unpolarized light is applied.
is similar with p polarization. The difference is that the absorption is mainly completed by the rectangle along the y axis to respond to the change in polarization direction. Please note that the absorption is high when incident light, polarization, and rectangle are in the same plane. The absorption of this condition is 91% as shown in the bottom of the slice plot. Then we change the incident angle θ to 45° and the result is shown in Figs. 4(b) and 4(c). With the p polarization the incident light, polarization, and rectangle (the one along the x axis) are still in the same plane as shown in Fig. 4(b), and the absorption is still high at 92%. With s polarization, though, the incident light, polarization, and rectangle are not in one plane, and the absorption is decreased to 59% as shown in Fig. 4(c). Thus the omnidirectional light absorption is highly sensitive to the symmetry of the structure. Then the slice plots with the disordered structure M0 are given with the same conditions. The results show that with the disordered structure and the tapered ridges, the absorption is 92% with p polarization and 82% with s polarization. In conclusion, we have studied the omnidirectional absorption of disordered nano-hole structure inspired from Papilio ulysses using the FDTD method and proved that the omnidirectional absorption of this structure was more stable than the ordered structure. These optical properties were performed with different polarizations and wavelengths. The structure M0 inspired from Papilio ulysses can enhance not only the stability of absorption between the different incident angles but also between different polarizations and wavelengths. These conclusions can guide the design of omnidirectional absorption materials. This work was supported by the National Natural Science Foundation of China (no. 51202145, no. 51131004
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