Biomedical Engineering Reference
In-Depth Information
n
i
A
1
B
61
0.8
31
n
A
d
A
A
θ
A
0.6
a
15
d
B
n
B
B
θ
B
0.4
5
A
0.2
B
0.5
0.55
0.6
Wavelength(μm)
0.65
0.7
n
t
(a)
(b)
Figure 9.3
Coniguration.and.relectivity.of.an.ideal.multilayer..(a).Arrangement.of.constructive.interference.with.an.ideal.
multilayer..Layers.A.and.B.have.a.distinct.refractive.index.(
n
A
.and.
n
B
),.thickness.(
d
A
.and.
d
B
),.and.angle.of.refrac-
tion.(θ
A
.and.θ
B
)..(b).Relectivity.from.a.multilayer.with.various.numbers.of.layers.of.5,.15,.31,.and.61.(
n
A
.=.1.55.and.
n
B
.=.1.60)..(Kinoshita,.S..and.Yoshioka,.S.:.Structural.colors.in.nature:.The.role.of.regularity.and.irregularity.in.
the.structure..
ChemPhysChem
..2005..6..1442-1459..Copyright.Wiley-VCH.Verlag.Gmbh.&.Co..KGaA..Reproduced.
with.modiication.with.permission.)
Rayleigh. presented. a. paper. on. the. intense. relectivity. caused. by. an. ideal. multilayer.
(Rayleigh.1917)..Kinoshita.and.Yoshioka.drew.the.schematics.to.depict.the.arrangement.
of.constructive.interference.within.a.multilayer.to.enhance.the.relected.light.as.shown.
in. Figure. 9.3a. (Kinoshita. and. Yoshioka. 2005).. A. multilayer. could. be. formed. by. a. pair.
of. thin. layers. that. pile. upon. each. other. periodically. to. enhance. the. relected. light.. If.
we. represent. two. layers. as. A. and. B. and. deine. their. thickness. as.
d
A
. and.
d
B
,. and. their.
refractive.indices.as.
N
A
.and.
N
B
,.the.desired.qualities.of.thickness.can.cause.constructive.
interference. assuming. that.
N
A
. >.
N
B
.. Depending. on. the. thickness,. angle. of. incidence,.
and.refractive.index,.the.relected.light.that.crosses.through.layer.A.twice.can.undergo.
constructive.interference.with.the.relected.light.from.layer.B..If.Equation.9.1.satisies.the.
phase.difference.necessary.for.constructive.interference,.then.the.relectivity.will.rapidly.
increase.. According. to. Rayleigh,. as. the. number. of. layers. increases. in. the. multilayer,.
the.relectivity.increases.rapidly.and.the.bandwidth.of.the.relected.light's.wavelength.
decreases.(see.Figure.9.3b).
1
2
(
)
=
(
)
+
(
)
2
N d
cos
θ
N d
cos
θ
m
+
λ
.
(9.1)
A A
A
B B
B
.
The. hierarchical. structure. of.
Morpho
. cover. scales. and. optical. relations. of. the. ideal.
multilayer.come.together.to.explain.the.structural.color.phenomenon.in.
Morpho
.butterlies..
Figure.9.4.displays.how.the.extensive.structure.induces.the.optical.phenomenon.(Kinoshita.
and. Yoshioka. 2005).. The. irst. optical. phenomenon. shown. in. Figure. 9.4. is. the. lamellar.
structure..It.is.responsible.for.the.primary.function.of.increasing.relectivity.by.the.already.
mentioned. quasi-multilayer. interference.. From. SEM. images. of. these. nanostructures.
(Figure.9.2),.the.heights.of.the.lamellae.are.varied.across.the.scale..The.varied.height.and.
narrow. width. produce. the. other. optical. feature. called. diffraction,. which. changes. the.
intensity. of. the. relected. light. based. on. the. viewer's. angle. of. incidence.. There. is. a. large.
difference.of.index.of.refraction.between.lamellar.ridges,.which.produces.high.relectivity.
