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

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

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

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

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

Photonic crystal schematic

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 

Bloch waves and Brillouin zones

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

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

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

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

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

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

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

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

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

Prospects Advanced optical materials design Biomimetic manufacturing

Local context