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Photonic structure engineering Design and fabrication of periodically ordered dielectric composites Periodicities at optical wavelengths All-optical information processing Diamond-based lattices are clear champions Successful fabrication in the IR regime Periodicities at visible wavelengths not yet realized

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Weevil optics Brilliant green iridescence of Lamprocyphus augustus Exoskeleton scales with interior diamond-based cuticular structure Near angle-independent coloration: elaborate multidomain photonic structure

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Photonic crystals Periodically structured electromagnetic media Possess photonic band gaps: ranges of frequency in which light cannot propagate through the structure EM analogue of a crystalline atomic lattice Intentionally introduced defects in the crystal give rise to localized EM states: linear waveguides, point-like cavities Perfect optical ‘insulator’, confine light losslessly around sharp bends

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Semiconductor review (nanohub.org) Schrodinger equation with potential V(x) = V(x + a) = V(x + 2a) a = periodicity of lattice

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EM wave propagation in periodic media Lord Rayleigh (1887) Peculiar reflective properties of a crystalline mineral with periodic ‘twinning’ planes Narrow band gap prohibiting light propagation through the planes Band gap is angle-dependent, different periodicities at non-normal incidence Reflected color that varies sharply with angle Yablonovitch and John (1987): EM and solid state physics for omnidirectional photonic bandgaps in 2D and 3D

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Photonic crystal schematic

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Maxwell’s equations Bloch (1928): wave propagation in 3D periodic media (extension of Floquet, 1883) Waves in such a medium can propagate without scattering Eigenproblem in analogue with Schrodinger’s equation Electric fields that lie in lower potential ( ) will have lower

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Bloch waves and Brillouin zones

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Photonic bandgap Range of in which there are no propagating (real k) solutions of Maxwell’s equations, surrounded by propagating states above and below the gap

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Perturbation is nontrivially periodic with period a Any periodic dielectric variation in 1D will lead to a band gap Dielectric/air bands are analogous to the valence/conduction bands

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SEM analysis of L. augustus Cross-sectional scanning electron microscopy Random cross-sectional cuts imaged with an electron microscope Domains of unique crystalline features: sheets of hexagonally arranged holes and rods, staircases

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Intrascale structure Serial sectioning: milling away 30 nm sections using an ion beam current (98 pA) and 30 kV accelerating voltage Stack of 2D SEM images with a thickness of 30 nm Individual scales consist of differently oriented single-crystalline domains of the same 3D lattice

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Dielectric function 3D structure of ABC stacked layers of hexagonally ordered air cylinders in a surrounding cuticular matrix Cylinder average r = 0.2a, h = 0.77a, a = 450 nm = 2.5

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Photonic band structure Remarkable proximity and overlap of three stop gaps, excellent photonic properties of diamond-based structures Entire green wavelength region, , and nm

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Iridescence Reflectance spectra of small (7 m diameter) subsections of individual scales Broad reflectance peak composed of three subbands Intensities varied with position

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SEM imaging 2D representations of calculated dielectric function along main crystal axes Individual single- crystal domains are oriented with their crystal axes normal or slightly off-normal to the scale top surface

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Conclusion Prevalence of numerous domains oriented at oblique angles = orientation of the single crystal domains is normal to the curved surface of the structureless shell Sophisticated microdomain orientation of diamond-based photonic structure = angle- independent reflection of a broad selective wavelength range Ingenuity of photonic structure engineering in biological systems

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Prospects Advanced optical materials design Biomimetic manufacturing

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