Abstract

The departure from strict periodic order in two-phase dielectric materials can offer properties that are otherwise inaccessible to perfectly ordered photonic crystals. Herewith, we investigate the circular dichroism of the single gyroid photonic crystal in the presence of spatial distortions. FDTD simulations and microwave transmission measurements on 3D-printed replicas show that certain harmonic long-wavelength spatial distortions (“sinusoidal chirp”) nearly doubles the imbalance of the circular polarisation reflectances, as well as significantly strengthens polarisation-incoherent reflectance. The observed changes are partially rationalised by comparison with simpler distortion models (linear chirp and tetragonal deformation) of the Gyroid.

© 2017 Optical Society of America

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2017 (1)

B. P. Cumming, G. E. Schroder-Turk, S. Debbarma, and M. Gu, “Bragg-mirror-like circular dichroism in bio-inspired quadruple-gyroid 4srs nanostructures,” Light Sci Appl. 6, e16192 (2017).
[Crossref]

2016 (1)

J. A. Dolan, M. Saba, R. Dehmel, I. Gunkel, Y. Gu, U. Wiesner, O. Hess, T. D. Wilkinson, J. J. Baumberg, U. Steiner, and B. D. Wilts, “Gyroid optical metamaterials: Calculating the effective permittivity of multidomain samples,” ACS Photonics 3, 1888–1896 (2016).
[Crossref] [PubMed]

2015 (2)

M. Saba and G. E. Schröder-Turk, “Bloch modes and evanescent modes of photonic crystals: Weak form solutions based on accurate interface triangulation,” Crystals 5, 14–44 (2015).
[Crossref]

B. Winter, B. Butz, C. Dieker, G. E. Schröder-Turk, K. Mecke, and E. Spiecker, “Coexistence of both gyroid chiralities in individual butterfly wing scales of callophrys rubi,” PNAS 112, 12911–12916 (2015).
[Crossref] [PubMed]

2014 (5)

M. Saba, B. D. Wilts, J. Hielscher, and G. E. Schröder-Turk, “Absence of circular polarisation in reflections of butterfly wing scales with chiral gyroid structure,” Mater. Today: Proc. 1, 193–208 (2014).
[Crossref]

Y. Jiao, T. Lau, H. Hatzikirou, M. Meyer-Hermann, J. C. Corbo, and S. Torquato, “Avian photoreceptor patterns represent a disordered hyperuniform solution to a multiscale packing problem,” Phys. Rev. E 89, 022721 (2014).
[Crossref]

M. Burresi, L. Cortese, L. Pattelli, M. Kolle, P. Vukusic, D. S. Wiersma, U. Steiner, and S. Vignolini, “Bright-white beetle scales optimise multiple scattering of light,” Scientific Reports 4, 6075 (2014).
[PubMed]

B. P. Cumming, M. D. Turner, G. E. Schröder-Turk, S. Debbarma, B. Luther-Davies, and M. Gu, “Adaptive optics enhanced direct laser writing of high refractive index gyroid photonic crystals in chalcogenide glass,” Opt. Express 22, 689–698 (2014).
[Crossref] [PubMed]

V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Bouligand structures underlie circularly polarized iridescence of scarab beetles: A closer view,” Mater. Today: Proc. 1, 161–171 (2014).
[Crossref]

2013 (3)

M. D. Turner, M. Saba, Q. Zhang, B. P. Cumming, G. E. Schröder-Turk, and M. Gu, “Miniature chiral beamsplitter based on gyroid photonic crystals,” Nature Photon. 7, 801–805 (2013).
[Crossref]

M. Saba, M. D. Turner, K. Mecke, M. Gu, and G. E. Schröder-Turk, “Group theory of circular-polarization effects in chiral photonic crystals with four-fold rotation axes applied to the eight-fold intergrowth of gyroid nets,” Phys. Rev. B 88, 245116 (2013).
[Crossref]

S. Yoshioka, H. Fujita, S. Kinoshita, and B. Matsuhana, “Alignment of crystal orientations of the multi-domain photonic crystals in Parides sesostris wing scales,” J. Royal Soc. Interf. 11, 20131029 (2013).
[Crossref]

2012 (3)

C. Pouya and P. Vukusic, “Electromagnetic characterization of millimetre-scale replicas of the gyroid photonic crystal found in the butterfly parides sesostris,” Interface Focus 2, 645–650 (2012).
[Crossref]

A. Demetriadou, S. S. Oh, S. Wuestner, and O. Hess, “A tri-helical model for nanoplasmonic gyroid metamaterials,” New J. Phys. 14, 083032 (2012).
[Crossref]

A. H. Schoen, “Reflections concerning triply-periodic minimal surfaces,” Interface Focus 2, 658–668 (2012).
[Crossref]

2011 (5)

M. Saba, M. Thiel, M. D. Turner, S. T. Hyde, M. Gu, K. Große-Brauckmann, D. N. Neshev, K. Mecke, and G. E. Schröder-Turk, “Circular dichroism in biological photonic crystals and cubic chiral nets,” Phys. Rev. Lett. 106, 103902 (2011).
[Crossref] [PubMed]

S. Vignolini, N. A. Yufa, P. S. Cunha, S. Guldin, I. Rushkin, M. Stefik, K. Hur, U. Wiesner, J. J. Baumberg, and U. Steiner, “A 3D optical metamaterial made by self-assembly,” Adv. Mater. 24, OP23–OP27 (2011).
[PubMed]

K. Hur, Y. Francescato, V. Giannini, S. A. Maier, R. G. Hennig, and U. Wiesner, “Three-dimensionally isotropic negative refractive index materials from block copolymer self-assembled chiral gyroid networks,” Angew. Chem., Int. Ed. 50, 11985–11989 (2011).
[Crossref]

G. E. Schröder-Turk, S. Wickham, H. Averdunk, F. Brink, J. D. Fitz Gerald, L. Poladian, M. C. J. Large, and S. T. Hyde, “The chiral structure of porous chitin within the wing-scales of callophrys rubi,” J. Struct. Biol. 174, 290–295 (2011).
[Crossref] [PubMed]

B. D. Wilts, K. Michielsen, H. De Raedt, and D. G. Stavenga, “Iridescence and spectral filtering of the gyroid-type photonic crystals in parides sesostris wing scales,” Interf. Focus 2, 681–687 (2011).
[Crossref]

2010 (3)

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 1038–1052 (2010).
[Crossref]

V. Saranathan, C. O. Osuji, S. G. J. Mochrie, H. Noh, S. Narayanan, A. Sandy, E. R. Dufresne, and R. O. Prum, “Structure, function, and self-assembly of single network gyroid (I 4132) photonic crystals in butterfly wing scales,” PNAS 107, 11676–11681 (2010).
[Crossref]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

2009 (5)

A. F. Oskooi, C. Kottke, and S. G. Johnson, “Accurate finite-difference time-domain simulation of anisotropic media by subpixel smoothing,” Opt. Lett. 34, 2778 (2009).
[Crossref] [PubMed]

B. Wang, J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A: Pure Appl. Opt. 11, 114003 (2009).
[Crossref]

M. Florescu, S. Torquato, and P. J. Steinhardt, “Designer disordered materials with large, complete photonic band gaps,” PNAS 106, 20658–20663 (2009).
[Crossref] [PubMed]

K. Michielsen, H. De Raedt, and D. G. Stavenga, “Reflectivity of the gyroid biophotonic crystals in the ventral wing scales of the green hairstreak butterfly, callophrys rubi,” J. Royal Soc. Interf. 7, 765–771 (2009).
[Crossref]

M. Thiel, M. S. Rill, G. von Freymann, and M. Wegener, “Three-dimensional bi-chiral photonic crystals,” Adv. Mater. 21, 4680–4682 (2009).

2008 (3)

K. Michielsen and D. G. Stavenga, “Gyroid cuticular structures in butterfly wing scales: biological photonic crystals,” J. Royal Soc. Interf. 5, 85–94 (2008).
[Crossref]

S. T. Hyde, M. O’Keeffe, and D. M. Proserpio, “A short history of an elusive yet ubiquitous structure in chemistry, materials, and mathematics,” Angew. Chem., Int. Ed. 47, 7996–8000 (2008).
[Crossref]

A. F. Oskooi, L. Zhang, Y. Avniel, and S. G. Johnson, “The failure of perfectly matched layers, and towards their redemption by adiabatic absorbers,” Opt. Express 16, 11376 (2008).
[Crossref] [PubMed]

2007 (3)

S. A. Jewell, P. Vukusic, and N. W. Roberts, “Circularly polarized colour reflection from helicoidal structures in the beetle plusiotis boucardi,” New J. Phys. 9, 99 (2007).
[Crossref]

P. Vukusic, B. Hallam, and J. Noyes, “Brilliant whiteness in ultrathin beetle scales,” Science 315, 348 (2007).
[Crossref] [PubMed]

M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Polarization stop bands in chiral polymeric three-dimensional photonic crystals,” Adv. Mater. 19, 207–210 (2007).
[Crossref]

2006 (1)

2005 (1)

2003 (1)

K. Michielsen and J. S. Kole, “Photonic band gaps in materials with triply periodic surfaces and related tubular structures,” Phys. Rev. B 68, 115107 (2003).
[Crossref]

2001 (2)

M. O’Keeffe, J. Plévert, Y. Teshima, Y. Watanabe, and T. Ogama, “The invariant cubic rod (cylinder) packings: symmetries and coordinates,” Acta Cryst. A 57, 110–111 (2001).
[Crossref]

S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173 (2001).
[Crossref] [PubMed]

1999 (1)

A. Fogden and S. T. Hyde, “Continuous transformations of cubic minimal surfaces,” Eur. Phys. J. B 7, 91–104 (1999).
[Crossref]

1996 (2)

J. Lekner, “Optical properties of isotropic chiral media,” Pure Appl. Opt. A 5, 417–443 (1996).
[Crossref]

C. A. Lambert, L. H. Radzilowski, and E. L. Thomas, “Triply periodic level surfaces as models for cubic tricontinuous block copolymer morphologies,” Philos. Trans R. Soc. London, Ser. A 354, 2009–2023 (1996).
[Crossref]

1991 (1)

H. G. von Schnering and R. Nesper, “Nodal surfaces of Fourier series: Fundamental invariants of structured matter,” Z. PhysikB – Condensed Matter 83, 407–412 (1991).
[Crossref]

1987 (2)

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

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

1985 (1)

R. A. Steinbrecht, W. Mohren, H. K. Pulker, and D. Schneider, “Cuticular interference reflectors in the golden pupae of danaine butterflies,” Proc. Roy. Soc. B 226, 367–390 (1985).
[Crossref]

1977 (1)

A. C. Neville, “Metallic gold and silver colours in some insect cuticles,” J. Insect Physiol. 23, 1267–1274 (1977).
[Crossref]

1974 (1)

W. B. Weir, “Automatic measurement of complex dielectric constant and permeability at microwave frequencies,” Proc. IEEE 62, 33–36 (1974).
[Crossref]

1970 (1)

A. M. Nicolson and G. F. Ross, “Measurement of the intrinsic properties of materials by time-domain techniques,” IEEE Transactions on Instrumentation and Measurement 19, 377–382 (1970).
[Crossref]

1887 (1)

J. W. S. Rayleigh, “On the maintenance of vibrations by forces of double frequency, and on the propagation of waves through a medium endowed with a periodic structure,” Phil. Mag. 24, 145–159 (1887).
[Crossref]

Averdunk, H.

G. E. Schröder-Turk, S. Wickham, H. Averdunk, F. Brink, J. D. Fitz Gerald, L. Poladian, M. C. J. Large, and S. T. Hyde, “The chiral structure of porous chitin within the wing-scales of callophrys rubi,” J. Struct. Biol. 174, 290–295 (2011).
[Crossref] [PubMed]

Avniel, Y.

Baumberg, J. J.

J. A. Dolan, M. Saba, R. Dehmel, I. Gunkel, Y. Gu, U. Wiesner, O. Hess, T. D. Wilkinson, J. J. Baumberg, U. Steiner, and B. D. Wilts, “Gyroid optical metamaterials: Calculating the effective permittivity of multidomain samples,” ACS Photonics 3, 1888–1896 (2016).
[Crossref] [PubMed]

S. Vignolini, N. A. Yufa, P. S. Cunha, S. Guldin, I. Rushkin, M. Stefik, K. Hur, U. Wiesner, J. J. Baumberg, and U. Steiner, “A 3D optical metamaterial made by self-assembly,” Adv. Mater. 24, OP23–OP27 (2011).
[PubMed]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in FDTD,” Opt. Lett. 31, 2972–2974 (2006).
[Crossref] [PubMed]

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Burresi, M.

M. Burresi, L. Cortese, L. Pattelli, M. Kolle, P. Vukusic, D. S. Wiersma, U. Steiner, and S. Vignolini, “Bright-white beetle scales optimise multiple scattering of light,” Scientific Reports 4, 6075 (2014).
[PubMed]

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G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 1038–1052 (2010).
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B. Winter, B. Butz, C. Dieker, G. E. Schröder-Turk, K. Mecke, and E. Spiecker, “Coexistence of both gyroid chiralities in individual butterfly wing scales of callophrys rubi,” PNAS 112, 12911–12916 (2015).
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Chan, C. T.

Corbo, J. C.

Y. Jiao, T. Lau, H. Hatzikirou, M. Meyer-Hermann, J. C. Corbo, and S. Torquato, “Avian photoreceptor patterns represent a disordered hyperuniform solution to a multiscale packing problem,” Phys. Rev. E 89, 022721 (2014).
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M. Burresi, L. Cortese, L. Pattelli, M. Kolle, P. Vukusic, D. S. Wiersma, U. Steiner, and S. Vignolini, “Bright-white beetle scales optimise multiple scattering of light,” Scientific Reports 4, 6075 (2014).
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V. Sharma, M. Crne, J. O. Park, and M. Srinivasarao, “Bouligand structures underlie circularly polarized iridescence of scarab beetles: A closer view,” Mater. Today: Proc. 1, 161–171 (2014).
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B. P. Cumming, M. D. Turner, G. E. Schröder-Turk, S. Debbarma, B. Luther-Davies, and M. Gu, “Adaptive optics enhanced direct laser writing of high refractive index gyroid photonic crystals in chalcogenide glass,” Opt. Express 22, 689–698 (2014).
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M. D. Turner, M. Saba, Q. Zhang, B. P. Cumming, G. E. Schröder-Turk, and M. Gu, “Miniature chiral beamsplitter based on gyroid photonic crystals,” Nature Photon. 7, 801–805 (2013).
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S. Vignolini, N. A. Yufa, P. S. Cunha, S. Guldin, I. Rushkin, M. Stefik, K. Hur, U. Wiesner, J. J. Baumberg, and U. Steiner, “A 3D optical metamaterial made by self-assembly,” Adv. Mater. 24, OP23–OP27 (2011).
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B. D. Wilts, K. Michielsen, H. De Raedt, and D. G. Stavenga, “Iridescence and spectral filtering of the gyroid-type photonic crystals in parides sesostris wing scales,” Interf. Focus 2, 681–687 (2011).
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B. P. Cumming, G. E. Schroder-Turk, S. Debbarma, and M. Gu, “Bragg-mirror-like circular dichroism in bio-inspired quadruple-gyroid 4srs nanostructures,” Light Sci Appl. 6, e16192 (2017).
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B. P. Cumming, M. D. Turner, G. E. Schröder-Turk, S. Debbarma, B. Luther-Davies, and M. Gu, “Adaptive optics enhanced direct laser writing of high refractive index gyroid photonic crystals in chalcogenide glass,” Opt. Express 22, 689–698 (2014).
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M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Polarization stop bands in chiral polymeric three-dimensional photonic crystals,” Adv. Mater. 19, 207–210 (2007).
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J. A. Dolan, M. Saba, R. Dehmel, I. Gunkel, Y. Gu, U. Wiesner, O. Hess, T. D. Wilkinson, J. J. Baumberg, U. Steiner, and B. D. Wilts, “Gyroid optical metamaterials: Calculating the effective permittivity of multidomain samples,” ACS Photonics 3, 1888–1896 (2016).
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A. Demetriadou, S. S. Oh, S. Wuestner, and O. Hess, “A tri-helical model for nanoplasmonic gyroid metamaterials,” New J. Phys. 14, 083032 (2012).
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M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Polarization stop bands in chiral polymeric three-dimensional photonic crystals,” Adv. Mater. 19, 207–210 (2007).
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B. Winter, B. Butz, C. Dieker, G. E. Schröder-Turk, K. Mecke, and E. Spiecker, “Coexistence of both gyroid chiralities in individual butterfly wing scales of callophrys rubi,” PNAS 112, 12911–12916 (2015).
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J. A. Dolan, M. Saba, R. Dehmel, I. Gunkel, Y. Gu, U. Wiesner, O. Hess, T. D. Wilkinson, J. J. Baumberg, U. Steiner, and B. D. Wilts, “Gyroid optical metamaterials: Calculating the effective permittivity of multidomain samples,” ACS Photonics 3, 1888–1896 (2016).
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V. Saranathan, C. O. Osuji, S. G. J. Mochrie, H. Noh, S. Narayanan, A. Sandy, E. R. Dufresne, and R. O. Prum, “Structure, function, and self-assembly of single network gyroid (I 4132) photonic crystals in butterfly wing scales,” PNAS 107, 11676–11681 (2010).
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G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 1038–1052 (2010).
[Crossref]

Farjadpour, A.

Fitz Gerald, J. D.

G. E. Schröder-Turk, S. Wickham, H. Averdunk, F. Brink, J. D. Fitz Gerald, L. Poladian, M. C. J. Large, and S. T. Hyde, “The chiral structure of porous chitin within the wing-scales of callophrys rubi,” J. Struct. Biol. 174, 290–295 (2011).
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S. Yoshioka, H. Fujita, S. Kinoshita, and B. Matsuhana, “Alignment of crystal orientations of the multi-domain photonic crystals in Parides sesostris wing scales,” J. Royal Soc. Interf. 11, 20131029 (2013).
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K. Hur, Y. Francescato, V. Giannini, S. A. Maier, R. G. Hennig, and U. Wiesner, “Three-dimensionally isotropic negative refractive index materials from block copolymer self-assembled chiral gyroid networks,” Angew. Chem., Int. Ed. 50, 11985–11989 (2011).
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M. Saba, M. Thiel, M. D. Turner, S. T. Hyde, M. Gu, K. Große-Brauckmann, D. N. Neshev, K. Mecke, and G. E. Schröder-Turk, “Circular dichroism in biological photonic crystals and cubic chiral nets,” Phys. Rev. Lett. 106, 103902 (2011).
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Gu, M.

B. P. Cumming, G. E. Schroder-Turk, S. Debbarma, and M. Gu, “Bragg-mirror-like circular dichroism in bio-inspired quadruple-gyroid 4srs nanostructures,” Light Sci Appl. 6, e16192 (2017).
[Crossref]

B. P. Cumming, M. D. Turner, G. E. Schröder-Turk, S. Debbarma, B. Luther-Davies, and M. Gu, “Adaptive optics enhanced direct laser writing of high refractive index gyroid photonic crystals in chalcogenide glass,” Opt. Express 22, 689–698 (2014).
[Crossref] [PubMed]

M. D. Turner, M. Saba, Q. Zhang, B. P. Cumming, G. E. Schröder-Turk, and M. Gu, “Miniature chiral beamsplitter based on gyroid photonic crystals,” Nature Photon. 7, 801–805 (2013).
[Crossref]

M. Saba, M. D. Turner, K. Mecke, M. Gu, and G. E. Schröder-Turk, “Group theory of circular-polarization effects in chiral photonic crystals with four-fold rotation axes applied to the eight-fold intergrowth of gyroid nets,” Phys. Rev. B 88, 245116 (2013).
[Crossref]

M. Saba, M. Thiel, M. D. Turner, S. T. Hyde, M. Gu, K. Große-Brauckmann, D. N. Neshev, K. Mecke, and G. E. Schröder-Turk, “Circular dichroism in biological photonic crystals and cubic chiral nets,” Phys. Rev. Lett. 106, 103902 (2011).
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J. A. Dolan, M. Saba, R. Dehmel, I. Gunkel, Y. Gu, U. Wiesner, O. Hess, T. D. Wilkinson, J. J. Baumberg, U. Steiner, and B. D. Wilts, “Gyroid optical metamaterials: Calculating the effective permittivity of multidomain samples,” ACS Photonics 3, 1888–1896 (2016).
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S. Vignolini, N. A. Yufa, P. S. Cunha, S. Guldin, I. Rushkin, M. Stefik, K. Hur, U. Wiesner, J. J. Baumberg, and U. Steiner, “A 3D optical metamaterial made by self-assembly,” Adv. Mater. 24, OP23–OP27 (2011).
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J. A. Dolan, M. Saba, R. Dehmel, I. Gunkel, Y. Gu, U. Wiesner, O. Hess, T. D. Wilkinson, J. J. Baumberg, U. Steiner, and B. D. Wilts, “Gyroid optical metamaterials: Calculating the effective permittivity of multidomain samples,” ACS Photonics 3, 1888–1896 (2016).
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Y. Jiao, T. Lau, H. Hatzikirou, M. Meyer-Hermann, J. C. Corbo, and S. Torquato, “Avian photoreceptor patterns represent a disordered hyperuniform solution to a multiscale packing problem,” Phys. Rev. E 89, 022721 (2014).
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K. Hur, Y. Francescato, V. Giannini, S. A. Maier, R. G. Hennig, and U. Wiesner, “Three-dimensionally isotropic negative refractive index materials from block copolymer self-assembled chiral gyroid networks,” Angew. Chem., Int. Ed. 50, 11985–11989 (2011).
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J. A. Dolan, M. Saba, R. Dehmel, I. Gunkel, Y. Gu, U. Wiesner, O. Hess, T. D. Wilkinson, J. J. Baumberg, U. Steiner, and B. D. Wilts, “Gyroid optical metamaterials: Calculating the effective permittivity of multidomain samples,” ACS Photonics 3, 1888–1896 (2016).
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K. Hur, Y. Francescato, V. Giannini, S. A. Maier, R. G. Hennig, and U. Wiesner, “Three-dimensionally isotropic negative refractive index materials from block copolymer self-assembled chiral gyroid networks,” Angew. Chem., Int. Ed. 50, 11985–11989 (2011).
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S. Vignolini, N. A. Yufa, P. S. Cunha, S. Guldin, I. Rushkin, M. Stefik, K. Hur, U. Wiesner, J. J. Baumberg, and U. Steiner, “A 3D optical metamaterial made by self-assembly,” Adv. Mater. 24, OP23–OP27 (2011).
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M. Saba, M. Thiel, M. D. Turner, S. T. Hyde, M. Gu, K. Große-Brauckmann, D. N. Neshev, K. Mecke, and G. E. Schröder-Turk, “Circular dichroism in biological photonic crystals and cubic chiral nets,” Phys. Rev. Lett. 106, 103902 (2011).
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G. E. Schröder-Turk, S. Wickham, H. Averdunk, F. Brink, J. D. Fitz Gerald, L. Poladian, M. C. J. Large, and S. T. Hyde, “The chiral structure of porous chitin within the wing-scales of callophrys rubi,” J. Struct. Biol. 174, 290–295 (2011).
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S. T. Hyde, M. O’Keeffe, and D. M. Proserpio, “A short history of an elusive yet ubiquitous structure in chemistry, materials, and mathematics,” Angew. Chem., Int. Ed. 47, 7996–8000 (2008).
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Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
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A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in FDTD,” Opt. Lett. 31, 2972–2974 (2006).
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K. Michielsen and J. S. Kole, “Photonic band gaps in materials with triply periodic surfaces and related tubular structures,” Phys. Rev. B 68, 115107 (2003).
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M. Burresi, L. Cortese, L. Pattelli, M. Kolle, P. Vukusic, D. S. Wiersma, U. Steiner, and S. Vignolini, “Bright-white beetle scales optimise multiple scattering of light,” Scientific Reports 4, 6075 (2014).
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G. E. Schröder-Turk, S. Wickham, H. Averdunk, F. Brink, J. D. Fitz Gerald, L. Poladian, M. C. J. Large, and S. T. Hyde, “The chiral structure of porous chitin within the wing-scales of callophrys rubi,” J. Struct. Biol. 174, 290–295 (2011).
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Y. Jiao, T. Lau, H. Hatzikirou, M. Meyer-Hermann, J. C. Corbo, and S. Torquato, “Avian photoreceptor patterns represent a disordered hyperuniform solution to a multiscale packing problem,” Phys. Rev. E 89, 022721 (2014).
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G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 1038–1052 (2010).
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K. Hur, Y. Francescato, V. Giannini, S. A. Maier, R. G. Hennig, and U. Wiesner, “Three-dimensionally isotropic negative refractive index materials from block copolymer self-assembled chiral gyroid networks,” Angew. Chem., Int. Ed. 50, 11985–11989 (2011).
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S. Yoshioka, H. Fujita, S. Kinoshita, and B. Matsuhana, “Alignment of crystal orientations of the multi-domain photonic crystals in Parides sesostris wing scales,” J. Royal Soc. Interf. 11, 20131029 (2013).
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B. Winter, B. Butz, C. Dieker, G. E. Schröder-Turk, K. Mecke, and E. Spiecker, “Coexistence of both gyroid chiralities in individual butterfly wing scales of callophrys rubi,” PNAS 112, 12911–12916 (2015).
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M. Saba, M. Thiel, M. D. Turner, S. T. Hyde, M. Gu, K. Große-Brauckmann, D. N. Neshev, K. Mecke, and G. E. Schröder-Turk, “Circular dichroism in biological photonic crystals and cubic chiral nets,” Phys. Rev. Lett. 106, 103902 (2011).
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Y. Jiao, T. Lau, H. Hatzikirou, M. Meyer-Hermann, J. C. Corbo, and S. Torquato, “Avian photoreceptor patterns represent a disordered hyperuniform solution to a multiscale packing problem,” Phys. Rev. E 89, 022721 (2014).
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B. D. Wilts, K. Michielsen, H. De Raedt, and D. G. Stavenga, “Iridescence and spectral filtering of the gyroid-type photonic crystals in parides sesostris wing scales,” Interf. Focus 2, 681–687 (2011).
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K. Michielsen, H. De Raedt, and D. G. Stavenga, “Reflectivity of the gyroid biophotonic crystals in the ventral wing scales of the green hairstreak butterfly, callophrys rubi,” J. Royal Soc. Interf. 7, 765–771 (2009).
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S. T. Hyde, M. O’Keeffe, and D. M. Proserpio, “A short history of an elusive yet ubiquitous structure in chemistry, materials, and mathematics,” Angew. Chem., Int. Ed. 47, 7996–8000 (2008).
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Osuji, C. O.

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[Crossref]

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Zhang, Q.

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ACS Photonics (1)

J. A. Dolan, M. Saba, R. Dehmel, I. Gunkel, Y. Gu, U. Wiesner, O. Hess, T. D. Wilkinson, J. J. Baumberg, U. Steiner, and B. D. Wilts, “Gyroid optical metamaterials: Calculating the effective permittivity of multidomain samples,” ACS Photonics 3, 1888–1896 (2016).
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M. Saba and G. E. Schröder-Turk, “Bloch modes and evanescent modes of photonic crystals: Weak form solutions based on accurate interface triangulation,” Crystals 5, 14–44 (2015).
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Light Sci Appl. (1)

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Mater. Today: Proc. (2)

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Figures (11)

Fig. 1
Fig. 1

Schematic setup of the microwave experiments and FDTD simulations: A slab of right-handed single Gyroid PhC, irradiated with RCP circular-polarised light (i. e. “↺↺” relative rotatory sense). One of the Gyroid’s implicit 41 helices is highlighted in green; cubic unit cells indicated by wire frame. Note that, for illustration purposes, geometrical details (slab thickness, volume fraction) are chosen differently from the studied structures.

Fig. 2
Fig. 2

Experimental transmission data of ↻↺ (top) and ↺↺ (bottom) microwave radiation through 3D printed single Gyroid PhC replica. Both “contracted” and “expanded” sinusoidal chirp cases pronouncedly affect the spectra, which are superimposed with noise from the experimental setup. Detailed discussion in sect. 3.1.

Fig. 3
Fig. 3

Reflectance spectra of the undistorted single Gyroid, resolved for relative circular polarisations (FDTD simulations, bottom). Ellipticities (top panel) quantify the degree of circular polarisation of the reflected and transmitted light. Cumulative circular contrast (CCR, middle) expresses the imbalance between the CP reflectances. Steep CCR slope corresponds to large circular reflectance imbalance (unity slope marked by skew dashed line).

Fig. 4
Fig. 4

Mock-illustration of chirp deformations for a multi-layer PhC (amplitudes greatly exaggerated, irradiation from below). Sinusoidal chirp at its two extreme terminations expanded/contracted, spatially constant distortion (tetragonal), and linear change of lattice constant; each compared to the undistorted structure in the middle (grey).

Fig. 5
Fig. 5

The Gyroid structured objects used in the simulations and experiments. Left: FDTD simulation boxes containing the chunks of the PhC slab (thickness Lz = 4a, 2a × 2a extent in lateral directions, periodically continued; surface staircasing reminds of the voxelisation of ε(r⃗) and the FDTD grid). Photographs, right: 3D-printed replicas, which have come to use in microwave transmission and reflectance experiments. The middle panel on both sides depicts the undistorted PhC, strictly periodic to translation by a in z (normal/vertical) direction; while the outer sides show PhCs with sinusoidal chirp: Left contracted, i. e. z lattice constant shortest in the middle of the slab and longest at the surfaces (arrows indicate directions of decreasing lattice constant); the reverse (expanded) situation is depicted on the right sides.

Fig. 6
Fig. 6

Cumulative circular contrast spectra: transmission experiments (thick lines) and FDTD simulations (thin lines) of a single Gyroid PhC superimposed with sinusoidal chirps and undistorted. CCR simplifies comparison between methods and chirp situations, and facilitates the distinction of frequency regions with strong circular dichroism. Symbols identify distinct features within the spectra (see text); cumulation start Ω0 = 0.55.

Fig. 7
Fig. 7

Comparison of CCR spectra (FDTD simulations) for sinusoidal, constant tetragonal (BCT), and linear lattice constant variations (see Fig. 4). Additionally, for sinusoidal chirp, the “mid-way” terminations τ = 0 and 0.5 are drawn along the expanded/contracted sinusoidal phases τ = 0.25/0.75 (see also the figure in appendix 2).

Fig. 8
Fig. 8

Undistorted (middle), oblate (left) and prolate (right) tetragonal distorted single Gyroid: Partial band structures in [0 0 1] direction (lower abscissa), and CCR spectra (coloured, upper abscissa). Shaded area: frequency range between BZ boundary and minimum of circular dichroic stop-band. Bottom row: sketches of the Brillouin zones of the respective distortion situations (exaggerated c/a). The oblate BCT path is extended up to the M point of the second BZ, half the way to the next reciprocal lattice point.

Fig. 9
Fig. 9

Construction of the single Gyroid geometry by overlapping helices: Within the Gyroid network (red), the ‘octagon’ helices are traced with solid helices (left [1 0 0], middle: all three 〈1 0 0〉 directions, right: all I4132 copies). The union of these helices closely resembles the single Gyroid geometry (right).

Fig. 10
Fig. 10

Chirp termination dependence of integral reflectance measures (i↺↺R and i↻↺R) and circular dichroism (iCCR) of a Gyroid PhC (FDTD data integrated over frequency; purple lines: values of the undistorted PhC) points the prominence of the special terminations τ = 0.25 and 0.75 out. In black, some exemplary error bars are shown to indicate the standard deviation due to structure termination averaging. Splines are guides to the eye. Cumulation range [Ω0; Ω1] = [0.51; 1.01].

Fig. 11
Fig. 11

Distortion amplitude σr of sinusoidal chirp influences polarisation-resolved and -incoherent reflectances, and circular contrast (iCCR); cumulation range [Ω0; Ω1] = [0.51; 1.01]. The value chosen for the experimental samples is marked by the dashed lines at σr /a = 0.074. The integral reflectance ranges accessible by chirp amplitude manipulation are indicated by the shaded areas.

Equations (4)

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e = ( equal ) : RCP light + RH Gyroid , or LCP light + LH Gyroid or e = ( opposite ) : LCP light + RH Gyroid , or RCP light + LH Gyroid ,
CCR ( Ω ) = Ω 0 Ω d Ω ( R ( Ω ) R ( Ω ) ) = = Ω 0 Ω d Ω ( R + R ) 2 × tan θ R
G ( r ) = sin ( q a x ) cos ( q a y ) + sin ( q a y ) cos ( q a z ) + sin ( q a z ) cos ( q a x ) ,
ϕ approx = 1 2 + t 3

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