Biomedical Engineering Reference
In-Depth Information
where.the.second.form.is.composed.of.two.factors,.the.sinusoidal.wave.at.the.mean.wavenumber,.vary-
ing.rapidly.in.space.at.
k
0
,.and.an.envelope.function,.varying.slowly.in.space.at.Δ
k
..he.rapid.sinusoids.
travel.at.the.phase.velocity
ω
0
0
c
n
.
v
p
=
=
k
whereas.the.envelope.travels.at.the.group.velocity
∆
∆
ω
∆
(
ck n
k
/
)
c
n
ck
n
∆
∆
n
k
v
=
=
= −
g
k
∆
2
.
=
c
n
∆
∆
n n
k k
/
/
c
n
∆
∆
/
λ λ
n n
=
1
−
1
+
Referring.to.
Figure.1.2
.for.the.case.of.silica.lint.glass,.we.see.that
.
∆
λ
λ
100
450
λ
=
400 500
−
nm,
=
=
0 222
.
∆
n
n
=
−
0 03
1 645
.
n
=
1 63 1 66
.
−
.
,
= −
0 207
.
.
and.thus
v
=
0 918
.
v
g
p
.
c
n
v
=
=
0 61
.
c
p
So.in.this.case.of.normal.dispersion,.the.group.velocity.of.the.packet.is.slower.than.the.phase.front.
velocity,.and.both.are.less.than.the.speed.of.light.
1.3.2 Polarization
So.far.our.picture.of.the.electromagnetic.plane.wave.is.like.that.shown.in.
Figure.1.2
,.where.the.
E
.vector.
increases.and.decreases.along.a.single.direction.orthogonal.to.the.direction.of.propagation..his.wave.
is.considered.linearly.polarized,.with.the.line.of.polarization.deined.by.the.direction.of.the.
E
.vector..If.
we.add.a.second.wave.to.this.one,.with.the.same.wavenumber.and.propagation.direction.but.with.the.
E
.vector.in.the.orthogonal.direction.(orthogonal.to.the.original.
E
.and.also.to.the.direction.of.propa-
gation),. we. can. generate. a. family. of. wave. functions. depending. on. the. relative. phases. of. the. irst. and.
second.oscillations..If.these.waves.are.in.phase,.then.the.resulting.wave.is.also.linearly.polarized,.but.in.
the.direction.that.is.the.vector.sum.of.the.two.wave's.polarization.vectors..If.the.waves.are.not.matching.
in.phase,.then.the.
E
.vector.will.spin.around.the.propagation.axis,.tracing.out.a.helical.path..Circular.
polarization.is.the.particular.case.when.the.waves.are.π/2.out.of.phase.and.of.equal.amplitude..here.is.
a.right.circular.polarization.and.a.let.circular.polarization.case,.depending.on.if.the.phase.diference.is.
plus.or.minus.π/2.(
Figure.1.5
).
One.method.of.describing.the.polarization.state.is.through.the.Stokes.parameters..hese.parameters.
are.convenient.combinations.of.the.
E
.vector.components..Let
.
ˆ
E E
x
E (x
=
y
)e
(
i
ω
t kz
−
)
y
E
=
|
E
| e
δ
i
.
y
y
