Biomedical Engineering Reference
In-Depth Information
25.1 SimpleStructures,One-DimensionalPeriodicity
The.simplest.and.most.widely.observable.photonic.structures.are.those.based.on.a.varia-
tion. in. refractive. index. in. one. dimension,. typically. produced. by. multiple. alternating.
layers.of.material..The.most.basic.form.is.that.observed.in.the.epicuticle.of.a.number.of.
beetle.families,.including.the.scarabs.and.buprestid.jewel.beetles,.such.as.
Chrysochroa raja
..
Variations.are.also.largely.present.in.iridescent.butterlies.and.moths,.from.a.simple.mul-
tilayer.within.the.wing.scales.of.moths.in.the.
Urania
.family,
3,4
.to.discontinuous.layers.in.
the.supericial.structures.on.the.scales.of.
Morpho
.butterlies.
5
25.1.1
Chrysochroa raja
Chrysochroa raja
.is.an.excellent.example.of.the.multilayers.observed.in.iridescent.beetles..
At.normal.incidence.it.appears.a.metallic.green.with.a.red.stripe.along.the.center.of.the.
elytral.wings.(Figure 25.1a)..The.inner.surface.of.the.elytra.also.displays.a.metallic.green.
color,. although. observation. of. the. cross. section. by. optical. microscopy. demonstrates. no.
discernible.iridescence.(Figure 25.1b)..Examination.by.transmission.electron.microscopy.
(TEM).reveals.that.there.is.a.uniform.multilayer.structure.within.the.top.2.μm.of.the.epi-
cuticle..It.has.long.been.known.that.for.a.semi-ideal.multilayer.stack,.where.the.structure.
is.a.repeating.stack.of.identical.layer.pairs,.the.peak.wavelength.can.be.calculated.using.a.
relatively.simple.formula:
λ
max
.=.2(
n
a
d
a
.cos(θ
a
)+.
n
b
d
b
.cos(θ
b
)).
(25.1)
where.
n
.is.the.refractive.index,.
d
.is.the.thickness,.and.θ.is.the.angle.of.incidence.for.the.
different.layers,.
a
.and.
b
,.with.θ
related.to.θ
by.Snell's.law.
While. the. variations. between. the. alternating. layer. pairs. in.
C. raja
. are. approximately.
consistent,.they.make.it.impossible.to.treat.the.structure.as.an.ideal.multilayer.structure,.
and.thereby.prevent.the.reduction.of.the.complexity.of.the.optical.model.
6,7
Furthermore,.the.surface.of.the.cuticle.is.highly.irregular.and.incapable.of.specular.relec-
tion..This.makes.it.impossible.to.measure.the.absolute.relection.spectra.of.the.system.at.a.
(a)
(b)
(c)
(d)
FIGURE 25.1
(a).Picture.of.
Chrysochroa raja
..The.red.regions.on.
C. raja
.are.visible.on.both.elytral.wings,.with.the.majority.of.
the.wing.being.green..It.is.also.possible.to.see.the.variation.in.hue.toward.the.edge.of.the.wings,.as.they.tilt.
away. from. the. camera.. (b-d). Cross-sectional. images. from. the. elytra. from.
C. raja
.. (b). Optical. image. of. cross.
section.showing.the.surface.contour..High-resolution.TEM.image.showing.the.structure.in.the.green.region.(c).
and.red.region.(d)..Typical.layer.thicknesses.are.around.100.nm,.although.there.is.signiicant.variation.between.
50. and. 110. nm. in. the. layer. thicknesses. observed. throughout. the. structure.. Scale. bars:. 20. mm. (a),. 50. μm. (b),.
500.nm.(c,.d).
