1
材料导论第十一章光学性质
Position
E
H
λ
光的传播
X-radiation Microwaves
γ-radiation
UV IR Radio waves
10
-6
10
-3
1 10
3
10
6
10
9
10
12
Wavelength(nm)
可见光光波谱系微波无线电波
00
1
με
=c
λν=c
μ
0
=4π×10
-7
H/m
ε
0
=8.85×10
12
F/m
h is Planck's constant
λ
ν
hc
hE ==
sJ1063.6
34
×=
h
θ
i
θ
r
Transmitted beam
Incident beam
θ
i
Reflected beam
I
0
Refraction
I
T
I
R
Absorption I
A
11.2 光与材料的相互作用透射反射折射吸收入射
2
RAT
IIII ++=
0
1=++ RAT
000
,,
I
I
R
I
I
A
I
I
T
RAT
===
电子极化能量吸收速度降低折射电子跃迁
11.2.1 作用机理
E
5
E
3
E
4
E
2
E
1
E
n
ergy
Electron
Excitation,
E = E
4
-E
2
= hν
42
电子跃迁频率为ν
42
的入射光子
E
Photon
emitted
E
Fermi
energy
Ene
r
gy
Fi
lle
d
s
t
at
es
Em
pty
s
t
at
es
Photon
absorbed
金属中的电子跃迁
E
Photon
emitted
Excited
(free)
electron
E
E
g
Photon
absorbed
Ene
r
gy
Conduc
t
i
on
ba
nd
Val
e
n
ce
ba
nd
B
a
nd
ga
p
Hole
非金属中的电子跃迁
E
Photon
absorbed
Ene
r
gy
Conduc
t
i
on
ba
nd
Val
e
n
ce
ba
nd
B
a
nd
ga
p
Impurity
level
3
E
1
Photon
emitted
E
2
Phonon
Generated
having
energy?E
1
ν
2
=
E
2
h
E
1
Photon
emitted
E
2
ν
2
=
E
2
h
Photon
emitted
ν
1
=
E
1
h
θ
i
θ
r
Transmitted beam
Incident beam
I
0
I
T
11.2.2 折射透射入射r
i
v
c
n
θ
θ
sin
sin
==
折光指数
εμ
1
=v
rr
v
c
n με
με
εμ
===
00
r
n ε?
绝大多数材料μ
r
≈ 1
故与极化有关
α
Maximum angle = 90 – α
α
β
β = 90°
(b)(a)
例题：将激光束引入折光指数为1.5的玻璃纤维，如何能使光线泄漏为最小？
(a) 设玻璃纤维处于空气(n=1)中,光子以60°的角度进入,
α = 90-60 = 30°:
Solution
°=
=×=
6.48
75.030sin5.1sin
β
β
ββ
α
sin
30sin
5.1
1
sin
sin
1
2
== or
n
n
60°
α = 30°
β
(b) 为防止光线泄漏，β角至少应为90°:
α
α
β
α
sin
90sin
sin
sin
sin
5.1
1
=
°
==
°== 8.416667.0sin αα or
如果入射光与纤维轴的夹角小于等于90 - 41.8 =
48.2°，光线就完全被反射。
Maximum angle
= 90 – α
α
β = 90°
4
(c) 如果纤维浸于水(n=1.333)中,则:
α
α
β
α
sin
90sin
sin
sin
sin
5.1
333.1
=
°
==
°== 7.62,8887.0sin αα
为避免发生透射，入射角必须小于90 - 62.7=27.3°。
θ
i
θ
r
Refraction beam
Glass
Vacuum (or air)
Incident beam
θ
i
Reflected beam
11.2.3 反射
2
0
1
1
+
==
s
sR
n
n
I
I
R
2
12
12
+
=
nn
nn
R
Fresnel’s formula
入射反射折射
Incident wave
Primary reflected wave
Secondary
reflected waveλ
1/4 λ
入射主反射二级反射空气
Substrate (n
2
>n
1
)
基材
Air (n=1)
Coating (n
1
>1)
涂层反射的最小化
Incident light
Specular reflection
Diffuse reflection
True surface
topography
Average surface
入射光特征反射弥散散射实际表面平均表面实际表面的反射入射光入射光
I
0 θ
I = I
0
cosθ
“光滑”表面粗糙表面
(a)
(b)
反射极图
θ
θ
cos
0
II =
constant
cos
cos
brightness
0
0
===
θ
θ
θ
θ
A
I
A
I
理想粗糙表面
5
(1) 电子极化
11.2.4 吸收与透射吸收机理
(2) 电子跃迁产生跃迁的条件：
gg
E
hc
orEh >>
λ
ν
例题,计算可见光谱中光子完全透射和完全吸收的临界能隙。
Solution
这说明能隙大于3.1 eV的非金属材料不能吸收光线，如果材料是纯的，则为无色透明。
eV1.3
m104
m/s)10s)(3eV10(4.13
(min)
(max)
7
815
=
×
×?×
=
=
λ
hc
E
g
可见光最短波长λ(min)约为0.4μm,则吸收可见光的最大能隙E
g
(max)为：
eV8.1
m107
m/s)10s)(3eV10(4.13
(max)
(min)
7
815
=
×
×?×
=
=
λ
hc
E
g
可见光最大波长λ(max)约为0.7μm，发生吸收的最小能隙E
g
(min)为：
x
T
eII
β?
=
0
''
吸收不仅与介质本质有关，也与路径长短有关
β为吸收系数（单位mm
-1
），由材料本质所决定
I
0
R
Incident beam
I
0
Transmitted beam
I
0
(1-R)
2
e
-βl
Reflected beam
Reflected beam
I
0
R(1-R) e
-βl
I
0
(1-R)
Absorption
I
0
(1-R)
2
e
-βl
EXAMPLE 设计一滤板，使能至少透过95% Zn的K
α
X光。
以铝为材料，其吸收系数为1.08 × 10
4
m
-1
，忽略反射。
Solution
由公式
x
T
eII
β?
=
0
mmmx
x
x
I
I
0047.0107.4
)1008.1(
051.0
1008.1051.0)95.0ln(
))(1008.1(
95.0
ln
6
4
4
4
0
0
=×=
×?
=
×?=?=
×?=
6
EXAMPLE 一材料的反射率为0.15，吸收系数为1 × 10
4
m
-1
,
设计一挡板使只有1%的光线透过.
Solution
mmx
x
x
x
xR
I
I
t
428.01028.4
1028.4)01384.0ln(
)10exp(01384.0
85.0
01.0
)101exp()15.01(01.0
)exp()1(
4
4
4
2
42
2
0
=×=
=?=
==
×=
=
β
入射光弥散反射特征反射弥散透射特征透射
Diffuse reflection
Specular reflection
Diffuse transmission
Specular transmission
透明与半透明
Incident light ray
Pore (n=1)
Glass or ceramic
(n>1)
Scattered
light ray
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
T
r
an
s
m
itta
n
ce (%
)
Violet
Blue
Green
Yellow
Orange
Red
Sappire
Rubby
Wavelength,λ (μm)
90
80
70
60
50
40
氧化铝的颜色
11.3 光学性质的应用
E
0
Incoming electron
E
1
+ E
2
+ E
3
+ E
4
+ E
5
= E
0
E
1
E
2
E
3
E
4
E
5
11.3.1 X-ray fluorescent analysis(X萤光分析）
7
K
α
λ = 0.154nm
E = 1.29 × 10
-15
J
K
β
λ = 0.139nm
E = 0.15 ×10
-15
J
L
α
λ = 1.336nm
E = 1.43 ×10
-15
J
where K = 1s
2
level
L = 2s
2
p
6
level
M = 2s
2
p
6
d
10
level
Copper
Characteristic
peaks
Continuous radiation
High-energy
stimulus
L
α
K
β
K
α
λ
swl
Int
e
nsit
y
o
f
e
m
it
t
e
d r
a
di
a
t
io
n
Low-energy
stimulus
Energy
Wavelength
Fluorescence(萤光)
reemission occurs for times much less than one second
Phosphorescence(磷光)
for longer times
11.3.2 LUMINESCENCE (发光)
再发射时间较长再发射时间短于1秒
Photon
Stimulus
Valence band
No E
g
λ very long
e
－
e
－
金属激励光子价带
fixed
E
hc
g
==λ
萤光材料
Stimulus
Photon
Conduction band
Valence band
e
－
e
－
E
g
激励光子价带
Trap E
d
E
g
fixed
EE
hc
dg
=
=λ
Stimulus
Conduction band
Valence band
e
－
e
－
e
－
磷光材料
τ
t
I
I
=
0
ln
激励光子价带
8
Electroluminescence
light-emitting diodes (LEDs)
I
silver contact
n-type
p-type
+
电致发光
Light Amplification by Stimulated Emission of Radiation,
Coherent
beam
Flash lamp
Ruby
Power source
11.3.3 激光激发态
E
Spontaneous
decay (nonradiative,
phonon emission)
M
亚稳态
Spontaneous and
stimulated
emission
激光
G
电子跃迁
E
n
erg
y
氙灯入射光基态
(Cr
3+
)
反射前晶体中部反射后基态Cr原子激发Cr原子
(a)
(b)
(c)
(d)
(e)
完全镀银部分镀银
g
E
hc
=λ
Holes
Excited electrons
Valence band
Photon emission
Conduction band
E
g
(a)
Valence band
Conduction band
Recombined excited
electron and hole
(b)
完全镀银部分镀银
9
Valence band
Conduction band
New excited
electron
New hole
(c)
Valence band
Conduction band
(d)
Valence band
Conduction band
(e)
Valence band
Conduction band
(f)
Incident photon
hν≥E
g
E
g
(bottom of
conduction band)
O (top of valence band)
11.3.4 光导性
n-type
p-type
Voltage
produced
e
－
h
+
太阳能电池
g
E
hc
=
max
λ
Input
Signal
Encoder
Electrical/
Optical
Converter
Repeater
Optical/
Electrical
Converter
Decoder
Output
Signal
Fiber Optic Cable
11.3.5 光导纤维
10
Digital encoding
I
n
ten
s
ity
Time
(a)
I
n
ten
s
ity
Time
(b)
Coaxial design of commercial optical fibers
Core
Cladding
Coating
同轴光缆
In
t
e
n
s
i
t
y
In
t
e
n
s
i
t
y
In
t
e
n
s
i
t
y
Time
Input
pulse
Time
Input
pulse
Time
Input
pulse
In
t
e
n
s
i
t
y
In
t
e
n
s
i
t
y
In
t
e
n
s
i
t
y
Time
Output
pulse
Time
Output
pulse
Time
Output
pulse(c)
(b)
(a)
完
材料导论第十一章光学性质
Position
E
H
λ
光的传播
X-radiation Microwaves
γ-radiation
UV IR Radio waves
10
-6
10
-3
1 10
3
10
6
10
9
10
12
Wavelength(nm)
可见光光波谱系微波无线电波
00
1
με
=c
λν=c
μ
0
=4π×10
-7
H/m
ε
0
=8.85×10
12
F/m
h is Planck's constant
λ
ν
hc
hE ==
sJ1063.6
34
×=
h
θ
i
θ
r
Transmitted beam
Incident beam
θ
i
Reflected beam
I
0
Refraction
I
T
I
R
Absorption I
A
11.2 光与材料的相互作用透射反射折射吸收入射
2
RAT
IIII ++=
0
1=++ RAT
000
,,
I
I
R
I
I
A
I
I
T
RAT
===
电子极化能量吸收速度降低折射电子跃迁
11.2.1 作用机理
E
5
E
3
E
4
E
2
E
1
E
n
ergy
Electron
Excitation,
E = E
4
-E
2
= hν
42
电子跃迁频率为ν
42
的入射光子
E
Photon
emitted
E
Fermi
energy
Ene
r
gy
Fi
lle
d
s
t
at
es
Em
pty
s
t
at
es
Photon
absorbed
金属中的电子跃迁
E
Photon
emitted
Excited
(free)
electron
E
E
g
Photon
absorbed
Ene
r
gy
Conduc
t
i
on
ba
nd
Val
e
n
ce
ba
nd
B
a
nd
ga
p
Hole
非金属中的电子跃迁
E
Photon
absorbed
Ene
r
gy
Conduc
t
i
on
ba
nd
Val
e
n
ce
ba
nd
B
a
nd
ga
p
Impurity
level
3
E
1
Photon
emitted
E
2
Phonon
Generated
having
energy?E
1
ν
2
=
E
2
h
E
1
Photon
emitted
E
2
ν
2
=
E
2
h
Photon
emitted
ν
1
=
E
1
h
θ
i
θ
r
Transmitted beam
Incident beam
I
0
I
T
11.2.2 折射透射入射r
i
v
c
n
θ
θ
sin
sin
==
折光指数
εμ
1
=v
rr
v
c
n με
με
εμ
===
00
r
n ε?
绝大多数材料μ
r
≈ 1
故与极化有关
α
Maximum angle = 90 – α
α
β
β = 90°
(b)(a)
例题：将激光束引入折光指数为1.5的玻璃纤维，如何能使光线泄漏为最小？
(a) 设玻璃纤维处于空气(n=1)中,光子以60°的角度进入,
α = 90-60 = 30°:
Solution
°=
=×=
6.48
75.030sin5.1sin
β
β
ββ
α
sin
30sin
5.1
1
sin
sin
1
2
== or
n
n
60°
α = 30°
β
(b) 为防止光线泄漏，β角至少应为90°:
α
α
β
α
sin
90sin
sin
sin
sin
5.1
1
=
°
==
°== 8.416667.0sin αα or
如果入射光与纤维轴的夹角小于等于90 - 41.8 =
48.2°，光线就完全被反射。
Maximum angle
= 90 – α
α
β = 90°
4
(c) 如果纤维浸于水(n=1.333)中,则:
α
α
β
α
sin
90sin
sin
sin
sin
5.1
333.1
=
°
==
°== 7.62,8887.0sin αα
为避免发生透射，入射角必须小于90 - 62.7=27.3°。
θ
i
θ
r
Refraction beam
Glass
Vacuum (or air)
Incident beam
θ
i
Reflected beam
11.2.3 反射
2
0
1
1
+
==
s
sR
n
n
I
I
R
2
12
12
+
=
nn
nn
R
Fresnel’s formula
入射反射折射
Incident wave
Primary reflected wave
Secondary
reflected waveλ
1/4 λ
入射主反射二级反射空气
Substrate (n
2
>n
1
)
基材
Air (n=1)
Coating (n
1
>1)
涂层反射的最小化
Incident light
Specular reflection
Diffuse reflection
True surface
topography
Average surface
入射光特征反射弥散散射实际表面平均表面实际表面的反射入射光入射光
I
0 θ
I = I
0
cosθ
“光滑”表面粗糙表面
(a)
(b)
反射极图
θ
θ
cos
0
II =
constant
cos
cos
brightness
0
0
===
θ
θ
θ
θ
A
I
A
I
理想粗糙表面
5
(1) 电子极化
11.2.4 吸收与透射吸收机理
(2) 电子跃迁产生跃迁的条件：
gg
E
hc
orEh >>
λ
ν
例题,计算可见光谱中光子完全透射和完全吸收的临界能隙。
Solution
这说明能隙大于3.1 eV的非金属材料不能吸收光线，如果材料是纯的，则为无色透明。
eV1.3
m104
m/s)10s)(3eV10(4.13
(min)
(max)
7
815
=
×
×?×
=
=
λ
hc
E
g
可见光最短波长λ(min)约为0.4μm,则吸收可见光的最大能隙E
g
(max)为：
eV8.1
m107
m/s)10s)(3eV10(4.13
(max)
(min)
7
815
=
×
×?×
=
=
λ
hc
E
g
可见光最大波长λ(max)约为0.7μm，发生吸收的最小能隙E
g
(min)为：
x
T
eII
β?
=
0
''
吸收不仅与介质本质有关，也与路径长短有关
β为吸收系数（单位mm
-1
），由材料本质所决定
I
0
R
Incident beam
I
0
Transmitted beam
I
0
(1-R)
2
e
-βl
Reflected beam
Reflected beam
I
0
R(1-R) e
-βl
I
0
(1-R)
Absorption
I
0
(1-R)
2
e
-βl
EXAMPLE 设计一滤板，使能至少透过95% Zn的K
α
X光。
以铝为材料，其吸收系数为1.08 × 10
4
m
-1
，忽略反射。
Solution
由公式
x
T
eII
β?
=
0
mmmx
x
x
I
I
0047.0107.4
)1008.1(
051.0
1008.1051.0)95.0ln(
))(1008.1(
95.0
ln
6
4
4
4
0
0
=×=
×?
=
×?=?=
×?=
6
EXAMPLE 一材料的反射率为0.15，吸收系数为1 × 10
4
m
-1
,
设计一挡板使只有1%的光线透过.
Solution
mmx
x
x
x
xR
I
I
t
428.01028.4
1028.4)01384.0ln(
)10exp(01384.0
85.0
01.0
)101exp()15.01(01.0
)exp()1(
4
4
4
2
42
2
0
=×=
=?=
==
×=
=
β
入射光弥散反射特征反射弥散透射特征透射
Diffuse reflection
Specular reflection
Diffuse transmission
Specular transmission
透明与半透明
Incident light ray
Pore (n=1)
Glass or ceramic
(n>1)
Scattered
light ray
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
T
r
an
s
m
itta
n
ce (%
)
Violet
Blue
Green
Yellow
Orange
Red
Sappire
Rubby
Wavelength,λ (μm)
90
80
70
60
50
40
氧化铝的颜色
11.3 光学性质的应用
E
0
Incoming electron
E
1
+ E
2
+ E
3
+ E
4
+ E
5
= E
0
E
1
E
2
E
3
E
4
E
5
11.3.1 X-ray fluorescent analysis(X萤光分析）
7
K
α
λ = 0.154nm
E = 1.29 × 10
-15
J
K
β
λ = 0.139nm
E = 0.15 ×10
-15
J
L
α
λ = 1.336nm
E = 1.43 ×10
-15
J
where K = 1s
2
level
L = 2s
2
p
6
level
M = 2s
2
p
6
d
10
level
Copper
Characteristic
peaks
Continuous radiation
High-energy
stimulus
L
α
K
β
K
α
λ
swl
Int
e
nsit
y
o
f
e
m
it
t
e
d r
a
di
a
t
io
n
Low-energy
stimulus
Energy
Wavelength
Fluorescence(萤光)
reemission occurs for times much less than one second
Phosphorescence(磷光)
for longer times
11.3.2 LUMINESCENCE (发光)
再发射时间较长再发射时间短于1秒
Photon
Stimulus
Valence band
No E
g
λ very long
e
－
e
－
金属激励光子价带
fixed
E
hc
g
==λ
萤光材料
Stimulus
Photon
Conduction band
Valence band
e
－
e
－
E
g
激励光子价带
Trap E
d
E
g
fixed
EE
hc
dg
=
=λ
Stimulus
Conduction band
Valence band
e
－
e
－
e
－
磷光材料
τ
t
I
I
=
0
ln
激励光子价带
8
Electroluminescence
light-emitting diodes (LEDs)
I
silver contact
n-type
p-type
+
电致发光
Light Amplification by Stimulated Emission of Radiation,
Coherent
beam
Flash lamp
Ruby
Power source
11.3.3 激光激发态
E
Spontaneous
decay (nonradiative,
phonon emission)
M
亚稳态
Spontaneous and
stimulated
emission
激光
G
电子跃迁
E
n
erg
y
氙灯入射光基态
(Cr
3+
)
反射前晶体中部反射后基态Cr原子激发Cr原子
(a)
(b)
(c)
(d)
(e)
完全镀银部分镀银
g
E
hc
=λ
Holes
Excited electrons
Valence band
Photon emission
Conduction band
E
g
(a)
Valence band
Conduction band
Recombined excited
electron and hole
(b)
完全镀银部分镀银
9
Valence band
Conduction band
New excited
electron
New hole
(c)
Valence band
Conduction band
(d)
Valence band
Conduction band
(e)
Valence band
Conduction band
(f)
Incident photon
hν≥E
g
E
g
(bottom of
conduction band)
O (top of valence band)
11.3.4 光导性
n-type
p-type
Voltage
produced
e
－
h
+
太阳能电池
g
E
hc
=
max
λ
Input
Signal
Encoder
Electrical/
Optical
Converter
Repeater
Optical/
Electrical
Converter
Decoder
Output
Signal
Fiber Optic Cable
11.3.5 光导纤维
10
Digital encoding
I
n
ten
s
ity
Time
(a)
I
n
ten
s
ity
Time
(b)
Coaxial design of commercial optical fibers
Core
Cladding
Coating
同轴光缆
In
t
e
n
s
i
t
y
In
t
e
n
s
i
t
y
In
t
e
n
s
i
t
y
Time
Input
pulse
Time
Input
pulse
Time
Input
pulse
In
t
e
n
s
i
t
y
In
t
e
n
s
i
t
y
In
t
e
n
s
i
t
y
Time
Output
pulse
Time
Output
pulse
Time
Output
pulse(c)
(b)
(a)
完
