Photonic structure engineeringPhotonic structure engineering

Design and fabrication of periodically Design and fabrication of periodically ordered dielectric compositesordered dielectric compositesPeriodicities at optical wavelengthsPeriodicities at optical wavelengthsAll-optical information processingAll-optical information processingDiamond-based lattices are clear Diamond-based lattices are clear championschampionsSuccessful fabrication in the IR regimeSuccessful fabrication in the IR regimePeriodicities at visible wavelengths not yet Periodicities at visible wavelengths not yet realizedrealized

Weevil opticsWeevil opticsBrilliant green iridescence of Brilliant green iridescence of Lamprocyphus Lamprocyphus augustusaugustus

Exoskeleton scales with interior diamond-based Exoskeleton scales with interior diamond-based cuticular structurecuticular structure

Near angle-independent coloration: elaborate Near angle-independent coloration: elaborate multidomain photonic structuremultidomain photonic structure

Photonic crystalsPhotonic crystals

Periodically structured electromagnetic mediaPeriodically structured electromagnetic mediaPossess photonic band gaps: ranges of Possess photonic band gaps: ranges of frequency in which light cannot propagate frequency in which light cannot propagate through the structurethrough the structureEM analogue of a crystalline atomic latticeEM analogue of a crystalline atomic latticeIntentionally introduced defects in the crystal Intentionally introduced defects in the crystal give rise to localized EM states: linear give rise to localized EM states: linear waveguides, point-like cavitieswaveguides, point-like cavitiesPerfect optical ‘insulator’, confine light losslessly Perfect optical ‘insulator’, confine light losslessly around sharp bendsaround sharp bends

Semiconductor review Semiconductor review (nanohub.org)(nanohub.org)

Schrodinger equation with potential Schrodinger equation with potential

V(x) = V(x + a) = V(x + 2a)V(x) = V(x + a) = V(x + 2a)

a = periodicity of latticea = periodicity of lattice

EM wave propagation EM wave propagation in periodic mediain periodic media

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

Photonic crystal schematicPhotonic crystal schematic

Maxwell’s equationsMaxwell’s equations

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

Bloch waves and Brillouin zonesBloch waves and Brillouin zones

Photonic bandgapPhotonic bandgap

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

PerturbationPerturbation

is nontrivially is nontrivially periodic with period aperiodic with period a

Any periodic dielectric Any periodic dielectric variation in 1D will variation in 1D will lead to a band gaplead to a band gap

Dielectric/air bands Dielectric/air bands are analogous to the are analogous to the valence/conduction valence/conduction bandsbands

SEM analysis of SEM analysis of L. augustusL. augustus

Cross-sectional scanning electron Cross-sectional scanning electron microscopymicroscopy

Random cross-sectional cuts imaged with Random cross-sectional cuts imaged with an electron microscopean electron microscope

Domains of unique crystalline features: Domains of unique crystalline features: sheets of hexagonally arranged holes and sheets of hexagonally arranged holes and rods, staircasesrods, staircases

Intrascale structureIntrascale structure

Serial sectioning: milling away 30 nm Serial sectioning: milling away 30 nm sections using an ion beam current (98 sections using an ion beam current (98 pA) and 30 kV accelerating voltagepA) and 30 kV accelerating voltage

Stack of 2D SEM images with a thickness Stack of 2D SEM images with a thickness of 30 nmof 30 nm

Individual scales consist of differently Individual scales consist of differently oriented single-crystalline domains of the oriented single-crystalline domains of the same 3D latticesame 3D lattice

Dielectric functionDielectric function

3D structure of ABC stacked layers of 3D structure of ABC stacked layers of hexagonally ordered air cylinders in a hexagonally ordered air cylinders in a surrounding cuticular matrixsurrounding cuticular matrix

Cylinder average r = 0.2a, h = 0.77a, a = Cylinder average r = 0.2a, h = 0.77a, a = 450 nm450 nm

= 2.5= 2.5

Photonic band structurePhotonic band structure

Remarkable proximity Remarkable proximity and overlap of three and overlap of three stop gaps, excellent stop gaps, excellent photonic properties of photonic properties of diamond-based diamond-based structuresstructures

Entire green Entire green wavelength region, wavelength region, 541-598, 555-614 and 541-598, 555-614 and 586-647 nm586-647 nm

IridescenceIridescence

Reflectance spectra Reflectance spectra of small (7 of small (7 m m diameter) subsections diameter) subsections of individual scalesof individual scales

Broad reflectance Broad reflectance peak composed of peak composed of three subbandsthree subbands

Intensities varied with Intensities varied with positionposition

SEM imagingSEM imaging

2D representations of 2D representations of calculated dielectric calculated dielectric function along main function along main crystal axescrystal axes

Individual single-Individual single-crystal domains are crystal domains are oriented with their oriented with their crystal axes normal or crystal axes normal or slightly off-normal to slightly off-normal to the scale top surfacethe scale top surface

ConclusionConclusion

Prevalence of numerous domains oriented at Prevalence of numerous domains oriented at oblique angles = orientation of the single crystal oblique angles = orientation of the single crystal domains is normal to the curved surface of the domains is normal to the curved surface of the structureless shellstructureless shell

Sophisticated microdomain orientation of Sophisticated microdomain orientation of diamond-based photonic structure = angle-diamond-based photonic structure = angle-independent reflection of a broad selective independent reflection of a broad selective wavelength rangewavelength range

Ingenuity of photonic structure engineering in Ingenuity of photonic structure engineering in biological systemsbiological systems

ProspectsProspects

Advanced optical materials designAdvanced optical materials design

Biomimetic manufacturingBiomimetic manufacturing

Local contextLocal context