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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 8 — Apr. 11, 2011
  • pp: 7750–7755
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Ultranegative angular dispersion of diffraction in quasiordered biophotonic structures

Feng Liu, Biqin Dong, Fangyuan Zhao, Xinhua Hu, Xiaohan Liu, and Jian Zi  »View Author Affiliations


Optics Express, Vol. 19, Issue 8, pp. 7750-7755 (2011)
http://dx.doi.org/10.1364/OE.19.007750


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Abstract

We report that a three-dimensional quasiordered photonic structure, found in the cuticles of beetle H. sexmaculata, can diffract light in a “wrong” way and its angular dispersion is about one order of magnitude larger than that of a conventional diffraction grating. A new diffraction type of photonic bandgap (from an anticrossing of longitudinal and transverse modes) and additional disorder effect are found to play important roles in this phenomenon. Mimicking the structure could lead to novel optical devices with ultralarge angular dispersion.

© 2011 OSA

1. Introduction

Conventionally, when light is normally incident on a periodic structure with in-plane period a larger than the wavelength λ, it can be partially reflected into an angle θ ≠ 0 [24

24. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, England, 1999).

]. Such a diffraction phenomenon is described by a grating equation sinθ=mλ/a. For the same order m of diffraction, the diffraction angle of green light θ is smaller than that of yellow light [Fig. 1(a)
Fig. 1 (a) When a green light beam is normally incident on a mirror with periodic grooves on the surface, it is diffracted into an angle θ smaller than that of a yellow one (for the first order). (b)-(e) When a white light beam with a diameter of 1 mm is normally incident on an elytron of beetle H. sexmaculata, green light is diffracted into an angle larger than that of yellow light and the angular dispersion dθ/dλ is eight times the value in (a). (b) Schematic of the experimental setup for (c). For more vivid photos of the beetle, see http://www.dannesdjur.com/bilder/heterorrhina_sexmaculata_sexmaculata_1.jpg (c) Diffraction pattern on the screen. (d) and (e) Reflectivity of the elytron as a function of the wavelength λ and emergence angle θ. R(λ,θ) is defined as the ratio of the measured reflected intensity from the elytron to the value of specular reflection from a mirror.
]. The angular dispersion (dθ/dλ=tanθ/λ) is much larger than that of a prism so that this phenomenon is widely used to decompose light in modern optical technologies [25

25. E. G. Loewen and E. Popov, Diffraction gratings and applications (Marcel Dekker, New York, 1997).

].

In this paper, we study the structural and optical properties of the elytra of beetle Heterorrhina sexmaculata by electron microscopy and optical spectroscopy. We find that the elytra are composed of a three-dimensional (3D) quasiordered photonic structure which can diffract light in a “wrong” way. In addition, the angular dispersion is about one order of magnitude higher than that of a conventional diffraction grating. Based on theoretical derivation and modeling, we identify that an interesting diffraction photonic bandgap (from an anticrossing of longitudinal and transverse modes) and additional disorder effect play important roles in this phenomenon.

2. Experimental results

Beetle H. sexmaculata belongs to a family of Cetoniinae (flower beetles), found in the rainforests of Indonesia and Malaysia. The elytra of the beetle display mainly green and orange colors, depending on both the incident and viewing angles. Here, we focus on the diffraction at normal incidence. When a white light beam is normally incident on an elytron [Fig. 1(b)], a diffraction pattern of colorful rings is formed on the screen above the elytron [Fig. 1(c)]. In contrast to conventional diffraction phenomena, yellow light is found to be diffracted into an angle smaller than that of green light. From measured spectra of reflectivity [Figs. 1(d) and 1(e)], a large angular dispersion (0.013 rad/nm) is found where the value is much higher than that in a conventional diffraction grating (tan42°/580nm = 0.0016 rad/nm). Hence, a narrow band of light (564.2 nm < λ < 596.5 nm) is diffracted into a wide angle range (56.3° > θ > 32.5°). In this frequency range, a high efficiency of diffraction is found where RD/Rall > 90% with RD and Rall being obtained by integrating R(λ, θ) sinθ over |θ | > 15° and > 0°, respectively [sinθ is used in the integration because the reflection is the same for different angles φ, giving rise to uniform colorful rings in Fig. 1(c)]. Due to a bandgap effect (shown below), this diffraction efficiency is higher than that of surface gratings [15

15. H. M. Whitney, M. Kolle, P. Andrew, L. Chittka, U. Steiner, and B. J. Glover, “Floral iridescence, produced by diffractive optics, acts as a cue for animal pollinators,” Science 323(5910), 130–133 (2009). [CrossRef] [PubMed]

,17

17. A. R. Parker and Z. Hegedus, “Diffractive optics in spiders,” J. Opt. A, Pure Appl. Opt. 5(4), S111–S116 (2003). [CrossRef]

]. We notice that although a small peak occurs at wavelength of 610 nm, the specular reflectivity is almost uniform in the whole visible frequency range [Fig. 1(e)], giving rise to a white spot at the center of the screen.

Figures 2(a)
Fig. 2 (a)-(b) Transmission electron micrographs of the elytron of beetle H. sexmaculata, where the light and dark areas represent chitin (A) and melanoprotein (B), respectively. (a) Transverse cross section of the elytron. (b) Longitudinal cross section of the elytron showing that the middle part II is pierced by an array of rods. Inset is the Fourier Transform of (b). (c) Enlarged plot of (b). (d) Radial distribution function of the rod array in (b), indicating an average rod spacing of 850 nm. (e) Part II is simulated by a periodic layered structure (AB)100 which is inserted by a triangular lattice of rods with diameter D = 500 nm and lattice constant a. The layer thickness dA = dB = d/2 = 93 nm. The refractive index nA = 1.56 and nB = nrod = 1.68. A triangular lattice was used because it has a Fourier transform image (with 6 nearest neighbor points for the origin) more close to the ring the inset to (b) than a square lattice (with 4 nearest neighbor points for the origin).
, 2(b) and 2(c) show the transmission electron micrographs (TEM) for the microstructures of elytra, where the light and dark areas represent chitin (A) and melanoprotein (B), respectively. The top part (I) has three layers of large thickness (ABA, about 400 nm in each layer) and thus contributes slightly to the reflection of visible light [5

5. J. Zi, X. Yu, Y. Li, X. Hu, C. Xu, X. Wang, X. Liu, and R. Fu, “Coloration strategies in peacock feathers,” Proc. Natl. Acad. Sci. U.S.A. 100(22), 12576–12578 (2003). [CrossRef] [PubMed]

]. In the middle part (II), the stacking layers (AB)L have a small layer thickness (93 nm each) and are inserted by melanoprotein rods. Due to the existence of the rod array, light can be diffracted. The layers below part II have a layer thickness chirping from 50 nm to 500 nm, which can present a specular reflection for all visible wavelengths [6

6. A. R. Parker, D. R. Mckenzie, and M. C. J. Large, “Multilayer reflectors in animals using green and gold beetles as contrasting examples,” J. Exp. Biol. 201, 1307–1313 (1998).

]. This explains the white spot observed in Fig. 1(c).

Figure 2(d) shows the radial distribution function (RDF) of the rod array in part II. Here, the RDF is defined as f(r) = Σ i Ni(r)/Σi N0, where Ni(r) is the average rod density in the circular ring (r, r + dr) around rod i and N 0 is the total rod density [26

26. B. Q. Dong, X. H. Liu, T. R. Zhan, L. P. Jiang, H. W. Yin, F. Liu, and J. Zi, “Structural coloration and photonic pseudogap in natural random close-packing photonic structures,” Opt. Express 18(14), 14430–14438 (2010). [CrossRef] [PubMed]

,27

27. K. Edagawa, S. Kanoko, and M. Notomi, “Photonic amorphous diamond structure with a 3D photonic band gap,” Phys. Rev. Lett. 100(1), 013901 (2008). [CrossRef] [PubMed]

]. When the array is fully random, f(r) should be a constant of 1. In Fig. 2(d), the first peak at r = 0.85 μm and the second peak at r = 1.62 μm can be clearly seen. This indicates that the rod array has weak order and the average rod spacing is 0.85 μm. From Fourier transform of the rod array [3

3. R. O. Prum, R. H. Torres, S. Williamson, and J. Dyck, “Coherent light scattering by blue feather barbs,” Nature 396(6706), 28–29 (1998). [CrossRef]

], a circle can also be obtained, indicating the isotropy of the array (see the inset to Fig. 2(b)).

3. Theoretical analysis

To understand the observed diffraction phenomenon, part II in the elytra is simplified as periodic dielectric layers (AB)100 that are inserted by a triangular lattice of rods [Fig. 2(e)]. The layer thicknesses are d A = d B = d/2 = 93 nm. The refractive index n A = = 1.56 and nB = n rod = εB = 1.68 [7

7. J. A. Noyes, P. Vukusic, and I. R. Hooper, “Experimental method for reliably establishing the refractive index of buprestid beetle exocuticle,” Opt. Express 15(7), 4351–4358 (2007). [CrossRef] [PubMed]

]. The diameter of rods is 500 nm. Figure 3(a)
Fig. 3 (a) Photonic band structure (kx = ky = 0) and (b) reflectance at normal incidence for the structure in Fig. 2(d) (a = 850 nm). The results in (a) and (b) are calculated by plane-wave and scattering-matrix methods, respectively. (c) Dependence of the two gaps in (a) on the rod spacing a. (d) Emergence angles for the diffraction gap in (b), compared with the experimental results in Fig. 1(d). The blue line in (d) is the result for a periodic structure with a = 850 nm. The lines and gray areas in (c) and (d) are calculated by a plane-wave method and the dots are obtained from Eqs. (1)-(3).
shows the band structure (k x = k y = 0) calculated by a plane-wave method [28

28. K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990). [CrossRef] [PubMed]

] for such a 3D photonic crystal with a = 0.85 μm [29

29. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987). [CrossRef] [PubMed]

31

31. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University Press, Princeton, NJ, 2008).

]. Here curves A1 (with ne2π/λ=kz) are the lowest frequency band, curves A2 (with ne2π/λ=kz+2π/d) are the folding band of A1, and curves B1 (with (ne2π/λ)2=kz2+(2π/a')2) have a nonzero parallel wavenumber |q|=2π/a' with a'=3a/2. Due to the periodicity along the z direction, a gap occurs between bands A1 and A2 and it remains when the rods are eliminated from the structure. The wavelength of gap center can be analytically obtained by:
λ0=2dne,
(1)
where ne=εeis the effective refractive index, εe=εAfA+εB(1fA), and fA is the volume fraction of chitin. Figure 3(b) shows the reflectance spectra calculated by a scattering-matrix method [32

32. Z. Y. Li and L. L. Lin, “Photonic band structures solved by a plane-wave-based transfer-matrix method,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046607 (2003). [CrossRef] [PubMed]

,33

33. Z. Xiong, F. Zhao, J. Yang, and X. Hu, “Comparison of optical absorption in Si nanowire and nanoporous Si structures for photovoltaic applications,” Appl. Phys. Lett. 96(18), 181903 (2010). [CrossRef]

]. For wavelengths in the lowest gap, light is strongly reflected in the specular direction. The gap is centered at wavelength of 610 nm, agreeing well with the experimental value in Fig. 1(e).

Above the lowest bandgap, another gap is formed by an anticrossing of bands A2 and B1. This gap does not exist for layered structures without rods and its central wavelength can be expressed as:
λ1=2dne/(1+d2/a'2).
(2)
For wavelengths in this anticrossing gap, light is diffracted into the direction of the first order (sinθ = λ/a') [Fig. 3(b)]. The diffraction angle can be derived for the wavelength of gap center:

sinθ=λ1d2dne/λ11.
(3)

For a = 850 nm, a narrow band (572 nm < λ < 577 nm) of light is diffracted into a small angle range (51° < θ < 51.6°). Such a kind of diffraction can be found from the measured reflectivity in Fig. 1(d).

To fully understand the experimental results, we consider part II in the elytra as a combination of a series of 3D photonic crystals with the same volume fraction of chitin fA and different rod spacings a. When the rod spacing a is increasing, bands A1 and A2 do not move while bands B1 shift down in frequencies. As a result, the Bragg gap persists while the diffraction gap redshifts [Fig. 3(c)]. Since the lattice constant is ranging in a wide range (from 0.75 μm to 1.35 μm) for the quasiordered rod array, the central wavelength of the diffraction gap changes from 565 nm to 596 nm, giving rise to a wide range of diffraction angle (31° < θ < 60°). According to Eq. (3), the diffraction angle θ decreases with increasing λ1, which explains the unusual experimental results in Fig. 3(d). At a certain emergence angle, the observed diffraction peak has a width (25 nm) wider than the theoretical value (5 nm) [Fig. 1(e)]. From integrating sphere experiments, the measured total reflectance is found to have a maximum of 36% (at λ = 569 nm, not shown) smaller than the ideal case. The discrepancies may result from the structural imperfection in the layers and rods and the absorption from the melanoprotein [7

7. J. A. Noyes, P. Vukusic, and I. R. Hooper, “Experimental method for reliably establishing the refractive index of buprestid beetle exocuticle,” Opt. Express 15(7), 4351–4358 (2007). [CrossRef] [PubMed]

].

4. Discussion

It is interesting to note that the disorder of rods can induce an ultranegative angular dispersion in diffraction. Disordered photonic structures have been studied extensively due to intriguing phenomena such as Anderson localization and random lasing [30

30. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987). [CrossRef] [PubMed]

,34

34. H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random Laser Action in Semiconductor Powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999). [CrossRef]

]. Due to the absence of periodicity, such systems are difficult to handle in theory and a supercell is usually needed in numerical simulations [26

26. B. Q. Dong, X. H. Liu, T. R. Zhan, L. P. Jiang, H. W. Yin, F. Liu, and J. Zi, “Structural coloration and photonic pseudogap in natural random close-packing photonic structures,” Opt. Express 18(14), 14430–14438 (2010). [CrossRef] [PubMed]

,27

27. K. Edagawa, S. Kanoko, and M. Notomi, “Photonic amorphous diamond structure with a 3D photonic band gap,” Phys. Rev. Lett. 100(1), 013901 (2008). [CrossRef] [PubMed]

,35

35. Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic Band Gaps in Two Dimensional Photonic Quasicrystals,” Phys. Rev. Lett. 80(5), 956–959 (1998). [CrossRef]

]. Here, we present an interesting approach that considers a quasiordered structure (which is nonperiodic and disordered, but has short-range order) as a combination of some periodic ones. The good agreement between theoretical and experimental results suggests that this method is valid at least to random weak scattering systems (nA/nB ~1). We note that this method (using RDF in Fig. 2) does not include particular structural symmetry such as those in quasiperiodic photonic crystals (QPCs, which are nonperiodic but has long-range order) [35

35. Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic Band Gaps in Two Dimensional Photonic Quasicrystals,” Phys. Rev. Lett. 80(5), 956–959 (1998). [CrossRef]

]. If this method is applied to QPCs, the total bandgap could be estimated while special results such as various defect modes may not be predicted by this method.

5. Conclusion

In summary, we have discovered that the elytra of beetle H. sexmaculata display unusual diffractive colors, where the angular dispersion is abnormal and has amplitude about one order larger than the value of a conventional diffraction grating. A novel diffraction photonic bandgap (from an anticrossing of longitudinal modes A2 and transverse modes B1) of the 3D structures in the elytra and additional disorder effects are found to be responsible for the intriguing phenomenon. This ultralarge dispersive ability could be advantageous for camouflage [2

2. M. Srinivasarao, “Nano-optics in the biological world: Beetles, butterflies, birds, and moths,” Chem. Rev. 99(7), 1935–1962 (1999). [CrossRef]

,14

14. F. Liu, H. Yin, B. Dong, Y. Qing, L. Zhao, S. Meyer, X. Liu, J. Zi, and B. Chen, “Inconspicuous structural coloration in the elytra of beetles Chlorophila obscuripennis (Coleoptera),” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(1), 012901 (2008). [CrossRef] [PubMed]

] and mimicking the structures may lead to novel optical devices [20

20. R. A. Potyrailo, H. Ghiradella, A. Vertiatchikh, K. Dovidenko, J. R. Cournoyer, and E. Olson, “Morpho butterfly wing scales demonstrate highly selective vapour response,” Nat. Photonics 1(2), 123–128 (2007). [CrossRef]

23

23. H. Kim, J. Ge, J. Kim, S. E. Choi, H. Lee, H. Lee, W. Park, Y. Yin, and S. Kwon, “Structural colour printing using a magnetically tunable and lithographically fixable photonic crystal,” Nat. Photonics 3(9), 534–540 (2009). [CrossRef]

].

Acknowledgement

This work was supported by the 973 Program (Grant Nos. 2007CB613200 and 2006CB921700), the Shanghai Science and Technology Committee (Grant Nos. 09PJ1402000 and 08dj1400302), the Shanghai Normal University Research Programs (Grant Nos. RE920, 307-A-3501-11-005005, and DXL 902), and NSFC. F. Liu is further supported by Shanghai Municipal Natural Science Foundation (No. 11ZR1426000).

References and links

1.

P. Vukusic and J. R. Sambles, “Photonic structures in biology,” Nature 424(6950), 852–855 (2003). [CrossRef] [PubMed]

2.

M. Srinivasarao, “Nano-optics in the biological world: Beetles, butterflies, birds, and moths,” Chem. Rev. 99(7), 1935–1962 (1999). [CrossRef]

3.

R. O. Prum, R. H. Torres, S. Williamson, and J. Dyck, “Coherent light scattering by blue feather barbs,” Nature 396(6706), 28–29 (1998). [CrossRef]

4.

A. R. Parker, R. C. McPhedran, D. R. McKenzie, L. C. Botten, and N. A. Nicorovici, “Photonic engineering. Aphrodite’s iridescence,” Nature 409(6816), 36–37 (2001). [CrossRef] [PubMed]

5.

J. Zi, X. Yu, Y. Li, X. Hu, C. Xu, X. Wang, X. Liu, and R. Fu, “Coloration strategies in peacock feathers,” Proc. Natl. Acad. Sci. U.S.A. 100(22), 12576–12578 (2003). [CrossRef] [PubMed]

6.

A. R. Parker, D. R. Mckenzie, and M. C. J. Large, “Multilayer reflectors in animals using green and gold beetles as contrasting examples,” J. Exp. Biol. 201, 1307–1313 (1998).

7.

J. A. Noyes, P. Vukusic, and I. R. Hooper, “Experimental method for reliably establishing the refractive index of buprestid beetle exocuticle,” Opt. Express 15(7), 4351–4358 (2007). [CrossRef] [PubMed]

8.

V. Welch, V. Lousse, O. Deparis, A. Parker, and J. P. Vigneron, “Orange reflection from a three-dimensional photonic crystal in the scales of the weevil Pachyrrhynchus congestus pavonius (Curculionidae),” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(4), 041919 (2007). [CrossRef] [PubMed]

9.

J. W. Galusha, L. R. Richey, J. S. Gardner, J. N. Cha, and M. H. Bartl, “Discovery of a diamond-based photonic crystal structure in beetle scales,” Phys. Rev. E 77, 050904(R) (2008). [CrossRef]

10.

P. Vukusic, J. R. Sambles, and C. R. Lawrence, “Structural colour: Colour mixing in wing scales of a butterfly,” Nature 404(6777), 457 (2000). [CrossRef] [PubMed]

11.

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Structural origin of circularly polarized iridescence in jeweled beetles,” Science 325(5939), 449–451 (2009). [CrossRef] [PubMed]

12.

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Now you see it - now you dont,” Nature 410(6824), 36 (2001). [CrossRef] [PubMed]

13.

S. Kinoshita, S. Yoshioka, and K. Kawagoe, “Mechanisms of structural colour in the Morpho butterfly: cooperation of regularity and irregularity in an iridescent scale,” Proc. Biol. Sci. 269(1499), 1417–1421 (2002). [CrossRef] [PubMed]

14.

F. Liu, H. Yin, B. Dong, Y. Qing, L. Zhao, S. Meyer, X. Liu, J. Zi, and B. Chen, “Inconspicuous structural coloration in the elytra of beetles Chlorophila obscuripennis (Coleoptera),” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(1), 012901 (2008). [CrossRef] [PubMed]

15.

H. M. Whitney, M. Kolle, P. Andrew, L. Chittka, U. Steiner, and B. J. Glover, “Floral iridescence, produced by diffractive optics, acts as a cue for animal pollinators,” Science 323(5910), 130–133 (2009). [CrossRef] [PubMed]

16.

H. Noh, S. F. Liew, V. Saranathan, S. G. J. Mochrie, R. O. Prum, E. R. Dufresne, and H. Cao, “How noniridescent colors are generated by quasi-ordered structures of bird feathers,” Adv. Mater. (Deerfield Beach Fla.) 22(26-27), 2871–2880 (2010). [CrossRef]

17.

A. R. Parker and Z. Hegedus, “Diffractive optics in spiders,” J. Opt. A, Pure Appl. Opt. 5(4), S111–S116 (2003). [CrossRef]

18.

M. Rassart, J. F. Colomer, T. Tabarrant, and J. P. Vigneron, “Diffractive hygrochromic effect in the cuticle of the hercules beetle Dynastes hercules,” N. J. Phys. 10(3), 033014 (2008). [CrossRef]

19.

F. Liu, B. Q. Dong, X. H. Liu, Y. M. Zheng, and J. Zi, “Structural color change in longhorn beetles Tmesisternus isabellae,” Opt. Express 17(18), 16183–16191 (2009). [CrossRef] [PubMed]

20.

R. A. Potyrailo, H. Ghiradella, A. Vertiatchikh, K. Dovidenko, J. R. Cournoyer, and E. Olson, “Morpho butterfly wing scales demonstrate highly selective vapour response,” Nat. Photonics 1(2), 123–128 (2007). [CrossRef]

21.

N. W. Roberts, T. H. Chiou, N. J. Marshall, and T. W. Cronin, “A biological quarter-wave retarder with excellent achromaticity in the visible wavelength region,” Nat. Photonics 3(11), 641–644 (2009). [CrossRef]

22.

M. Kolle, P. M. Salgard-Cunha, M. R. J. Scherer, F. Huang, P. Vukusic, S. Mahajan, J. J. Baumberg, and U. Steiner, “Mimicking the colourful wing scale structure of the Papilio blumei butterfly,” Nat. Nanotechnol. 5(7), 511–515 (2010). [CrossRef] [PubMed]

23.

H. Kim, J. Ge, J. Kim, S. E. Choi, H. Lee, H. Lee, W. Park, Y. Yin, and S. Kwon, “Structural colour printing using a magnetically tunable and lithographically fixable photonic crystal,” Nat. Photonics 3(9), 534–540 (2009). [CrossRef]

24.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, England, 1999).

25.

E. G. Loewen and E. Popov, Diffraction gratings and applications (Marcel Dekker, New York, 1997).

26.

B. Q. Dong, X. H. Liu, T. R. Zhan, L. P. Jiang, H. W. Yin, F. Liu, and J. Zi, “Structural coloration and photonic pseudogap in natural random close-packing photonic structures,” Opt. Express 18(14), 14430–14438 (2010). [CrossRef] [PubMed]

27.

K. Edagawa, S. Kanoko, and M. Notomi, “Photonic amorphous diamond structure with a 3D photonic band gap,” Phys. Rev. Lett. 100(1), 013901 (2008). [CrossRef] [PubMed]

28.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990). [CrossRef] [PubMed]

29.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987). [CrossRef] [PubMed]

30.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987). [CrossRef] [PubMed]

31.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University Press, Princeton, NJ, 2008).

32.

Z. Y. Li and L. L. Lin, “Photonic band structures solved by a plane-wave-based transfer-matrix method,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046607 (2003). [CrossRef] [PubMed]

33.

Z. Xiong, F. Zhao, J. Yang, and X. Hu, “Comparison of optical absorption in Si nanowire and nanoporous Si structures for photovoltaic applications,” Appl. Phys. Lett. 96(18), 181903 (2010). [CrossRef]

34.

H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random Laser Action in Semiconductor Powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999). [CrossRef]

35.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic Band Gaps in Two Dimensional Photonic Quasicrystals,” Phys. Rev. Lett. 80(5), 956–959 (1998). [CrossRef]

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(330.1690) Vision, color, and visual optics : Color
(160.5298) Materials : Photonic crystals

ToC Category:
Diffraction and Gratings

History
Original Manuscript: March 2, 2011
Revised Manuscript: March 25, 2011
Manuscript Accepted: March 25, 2011
Published: April 6, 2011

Virtual Issues
Vol. 6, Iss. 5 Virtual Journal for Biomedical Optics

Citation
Feng Liu, Biqin Dong, Fangyuan Zhao, Xinhua Hu, Xiaohan Liu, and Jian Zi, "Ultranegative angular dispersion of diffraction in quasiordered biophotonic structures," Opt. Express 19, 7750-7755 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-8-7750


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References

  1. P. Vukusic and J. R. Sambles, “Photonic structures in biology,” Nature 424(6950), 852–855 (2003). [CrossRef] [PubMed]
  2. M. Srinivasarao, “Nano-optics in the biological world: Beetles, butterflies, birds, and moths,” Chem. Rev. 99(7), 1935–1962 (1999). [CrossRef]
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