Individual, unsupported scales of two male butterflies with dorsal blue and ventral green color were compared by
microscpectrometric measurements, optical and electronic microscopy. All the scales are colored by photonic band gap
type materials built of chitin (n = 1.58) and air. The different scales are characterized by different degrees of order from
fully ordered single crystalline blue scales of the <i>Cyanophrys remus</i> butterfly through polycrystalline green scales on the
ventral side of the same butterfly, to the most disordered dorsal blue scales of the <i>Albulina metallica</i>, where only the
distance of the first neighbors is constant. The different scale nanoarchitectures and their properties are compared.
We present the optical characterization of an all-dielectric photonic crystal (PC)-based guided resonance filter sensitive to index-of-refraction changes in aqueous solutions. Spectral peak width was found to be 9.8 and 4.4 nm around 816 nm (water media), corresponding to a quality factor Q of 83 and 181, respectively. A spectral shift of peak wavelength with index change of 130 nm/RIU was observed for bulk fluid experiments. Measured peak shift (&Dgr;&lgr;=0.2nm) corresponds to a detectable index change &Dgr;n=1.5×10<sup>-3</sup>.
The structural origin of the weak iridescence from the very peculiar ribbon-shaped feathers of the African
open-bill stork, <i>Anastomus lamelligerus </i>(Ciconiidae) is investigated, using a combination of spectrophotometry,
electron microscopy, and theoretical modelling. The cortex of these feathers can be described as a slab of keratin,
transformed into a multilayer by the insertion of thin parallel planes containing harder nodules, disposed sideby-
side and oriented along the feather axis. These nodules each show a sperically capped cylindrical shape. An
empty cylindrical channel - the vacuole - occupies the long axis of the nodule. These nodules act in a collective
and individual way to produce the frequency selection giving rise to the observed dark-green coloration of these
<i>Hoplia coerulea </i>is known for its spectacular blue-violet iridescence. The blue coloration is caused by the presence
of a photonic structure inside the scales which cover the dorsal parts of the insect's body, including the head,
the thorax, and the wing cases. The structure can be described by a stack of chitin plates wearing arrays of
parallel rods. This arrangement leads to a multilayer structure which only uses a single solid material. The shift
of the reflected wavelength to the ultraviolet (passing through violet iridescence) is described and explained on
the basis of the optical properties of this structured metamaterial.
The structural origin of the weak iridescence on some of the dark feathers of the black-billed magpie, <i>Pica pica</i> (Corvidae), is found in the structure of the ribbon-shaped barbules. The cortex of these barbules contains
cylindrical holes distributed as the nodes of an hexagonal lattice in the hard layer cross-section. The cortex
optical properties are described starting from a photonic-crystal film theory. The yellowish-green coloration of
the bird's tail can be explained by the appearance of a reflection band related to the photonic-crystal lowest-lying
gap. The bluish reflections from the wings are produced by a more complicated mechanism, involving the
presence of a cortex "second gap".
We report simulations showing tunable terahertz oscillations of the electromagnetic field provided by the Bloch oscillations of a short photonic wave packet in a tilted band structure. The structure consists in a finite one-dimensional photonic crystal inhomogeneously chirped by a slowly-varying refractive index gradient. Tunability is obtained by relocating the Bloch oscillations center in regions characterized by different local band structure gradients. With reasonable refractive indexes, this mechanism may allow the generation of signals which cover a wide continuous part of the electromagnetic terahertz range, when used in combination of appropriate detection schemes.
The optical reflectance of photonic-crystal films is revisited,
while focussing on the variety of coloration produced by different
surface orientations. The needed tools for this analysis are first
described. These include a number of simple rules that help
locating the useful spectral features of the photonic-crystal
reflectance with a minimal knowledge of the structure, and make
explicit a full multiple-scattering algorithm (often cited, but
not explicitly described so far) for the precise computation of
reflectance spectra. It is seen that a face-centered cubic
structure of low refractive index can span a wide region of the
chromaticity diagram with just a few high-symmetry surfaces.
The effect of a long-range, slowly varying, modulation of the refractive index of a photonic crystal is investigated. It is shown that the Bloch modes are modified by essentially being modulated by an envelope function which adapts to the long-range dielectric function perturbation. This envelope function obeys a simple linear
Schroedinger equation of classical (non-quantum) origin. Close to a band extremum, at a gap edge, the envelope functions can be interpreted as wave functions of relativistic particles possessing a finite rest mass. These effective energy carriers come as two species, referred to as “effective photons” (for positive band curvatures) or “photonic holes” (for negative band curvatures). The energy transfer through the chirped structure can be viewed as resulting from the migration of these particles under forces implied by the long-range dielectric function modulation.
Periodicity implies the creation of discretely diffracted beams while various departures from periodicity lead to broadened scattering angles. This effect is investigated for disturbed lattices exhibiting randomly varying periods. In the Born approximation, the diffused reflection is shown to be related to a pair correlation function constructed from the distribution of the
film scattering power. The technique is first applied to a natural photonic crystal found on the ventral side of the wings of the butterfly <i>Cyanophrys remus</i>, where scanning electron microscopy reveals the formation of polycrystalline photonic structures. Second, the disorder in the distribution of the cross-ribs on the scales another butterfly, <i>Lycaena virgaureae</i>, is investigated. The irregular arrangement of scatterers found in chitin structure of this insect produces light reflection in the long-wavelength part of the visible range, with a quite unusual broad directionality. The use of the pair correlation function allows to propose estimates of the diffusive spreading in these very different systems.
Periodic inhomogeneities of linear dielectric materials are known to give rise to highly complex transmission spectra, widely adjustable by tuning geometric parameters. In this work, the theory of optical periodic structures is extended to materials exhibiting the nonlinear Kerr effect. A new computational scheme, based on the transfer-matrix method, is introduced in order to perform, in a selfconsistent way, the simultaneous adjustment of the refractive index and transisting electric field and compute the intensity-dependent transmittance of nonlinear films. For adequate geometries and with a suitably adjusted frequency, hysteresis loops can appear in the transmittance vs. intensity diagrams, signaling bistability. We observe that a bistable behavior can appear without the construction of a Fabry-Perot structure. For a nonlinear film structured by a periodic side variation of the refractive index, we provide evidence that bistability can also take place for frequencies corresponding to Fano resonances. Depending on the geometry of the film, we observe a wide variety of shapes for the transmittance hysteresis loops.
Electromagnetic modes of photonic-crystal slabs can be excited by
charged particles which remain outside the slab. The theory
assumes a classical trajectory for the particle and computes the
dielectric response of the slab photonic structure to the Coulomb
fields emitted by the moving charge. The power applied by this
response force on the charged particle describes the energy
transfer between the charge and the electromagnetic modes of the
slab. It is shown that the photonic crystal film responds
according to an effective dielectric function which is easily
calculated using a transfer matrix scheme.
When the unit cell of the photonic crystal contains material which undergoes an optical Kerr effect, internal illumination will change the refractive index distribution without modifying the crystal periodicity and induce significant modifications of the dispersion relations. We describe these modifications by a self-consistent computation of the band structure where the occupation of a photon mode with specific frequency, Brillouin-zone vector and polarization is kept fixed. This requires to solve a sequence of ordinary, linear, photonic band structure problems. The resulting non-linear photonic band structure explicitly depends on the mode occupation, itself determined by the level of illumination. We carry out specific non-linear band structure calculations for the woodpile structure where rods are considered experiencing refractive index changes according to various types of illumination. It is shown that, for positive Kerr coefficient, a strong illumination moves the photonic band gap to lower frequency while slightly modifying its width. The use of different illumination polarizations and frequencies results in modifications of the band structure and the spectral location of the Van Hove singularities in the density of states.
A photonic crystal efficiently controls the radiation rate of an embedded dipolar emitter. The influence of the periodic refractive index patterning on the emitter characteristics is assessed and the efficiency of a dipolar photonic source is calculated for a realistic, three-dimensional photonic crystal. Taking as a starting point the photonic band structure, it is shown that the emission rate is strongly correlated with the density of modes. For an infinite crystal, the computation of the field propagator confirms, in particular, that the emission rate falls to zero in the frequency range defined by the photonic band gap. We specifically consider a photonic crystal with a woodpile structure, offering a wide gap, with a monochromatic oscillating dipole at specific points (in or outside the rods) and orientations in the structure, and compute the emitted fields, expanded in terms of the photonic crystal eigenmodes. Radiation rate enhancements or inhibitions are predicted, according to the frequency and to the direction of the emission.