清华激光原理第七讲
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• Physical basic for rate equations: Einstein relationship
Red ruby, Er3+ doped fiber
E
3
w13A3 S3
11
S3
E
2
2
A2 S2 w2 w1
111 2
E
1
S 3 1S 3 2A 3 1S 3 2
202S1/221/11 A21
铒离子能级图
3
§4.3 Rate equations examples (three, four levels system )
• Differential equations describing the dynamics of population and photon density of various levels
1
Two, three, four level lasers
2
2
pump 1
laser 1 0
3 2
1
2021/2/11
laser
3 2
laser
1 0
2
100ns
10ns
0.98nm
与管壁碰撞
He + e He* 21S0,23S1 He* + Ne Ne* + He + DE
2021/2/11
various physical processes
• Different expressions of rate equations for a same laser
dn2 dt
R2
n2
2
n2
f2 f1
n121n,n0)vNl
dn1 dt
R1
n1
1
n221n2
f2 f1
n121n,n0)vNl
E2
S32
E2
dn3 dt
n0W03
n3S32
A30)
(ignore S30)
w03 A30 S30 S21 A21 W21 W12
E1
dn2 dt
n3S32 n2 S21
) A21 n1W12
n2W21
E0
S10
n3S32n2S21 A21)n2
f2 f1
n1
A21 nn
g~n ,n0 )Nl
dn0 dt
n2W21n1W12
Nl
Rl
n2
f2 f1
n121n,n0)vNl
Nl
Rl
I1 I 0e
t
I t ) I 0 e L c
t
I 0 e Rl
Photon lifetime 光子寿命
Rl
L c
（2.1.14）
• Rate equations for practical laser are set up according to the
R2 E1
R1
2 21Ltraasnesrition 1
R1, R2 is atom density pumped per second into E1 and E2, respectively.
1, 2 is lifetime at E1, E2, respectively; 21 is202s1p/2o/1n1taneous emission (荧光 fluorescence）lifetime for E2 E1. 6
E3
S32
E2
w03 A30 S30 S21 A21 W21 W12
E1
S10
E0
ddn2tn3S32n2S21A21)n1W12n2W21 ddn1tn2S21A21)n1W12n2W21n1S10
E2
2
R2
21
E1
R1
1
Pump transitions
Laser
dn2 dt
R2
n2
2
n2
f2 f1
• Neglect the difference of diffraction
DnF n
n loss in the modes
矩形面积＝原谱线面积
Simplifications
Line shape function rectangle (矩形)
Same loss, same lifetime of photon for each mode
第7讲
• 四能级系统单模速率方程的建立 • 多模速率方程的建立 • 均匀加宽工作介质的增益系数
从速率方程出发推导小信号增益系数表达式 小信号增益曲线 增益线宽
• 均匀加宽工作介质的增益饱和
大信号增益系数、强光作用下的弱光增益系数
• 非均匀加宽工作介质增益系数
作业:4-7、4-13、4-20
2021/2/11
n121n,n0)vNl
transition
ddn1t R1
n1
1
n221n2
f2 f1
n121n,n0)vNl
2021/2/11
7
2) Rate equations for multimode oscillation
Serial number of mode ll1,l2ln
Frequency of mode nnl1,nl2 nln
n1S1 0 n0W0 3 n3 A3 0
ddN ltn2W21n1W12NRll
W21B21g~n,n0) Nl hn
Ann21g~n,n0)Nl 21n,n0)Nlv （4.4.13）
n0n1n2n3n
2021/2/11
没有包括A21引起的光子数?
5
Consider loss only
dNl dt
ddN ltn2ff1 2n121 n,n0)v
N lNl Rl
2021/2/11
dNl1 ,dNln
dt
dt
8
g(nn0) g'(nn0)
Reasons of simplification
g(nn0)
• Do not need to consider differences
g'(nn0)
of the modes for studying question
Photon number of serial mode N l N l1,N l2 N ln Method : 对应每个模式分别建立一个速率方程, 序数相应变化
21n,n0)8A 2h1vn202 g ~n,n0)
nn ) ) d d 2 n tn 3 S 3 2n 2A 2 1S 21 l n 2ff1 2n 1 21 l,0vlN
He -Ne, Nd: YAG
E3
S32
E2
w03 A30 S30 S21 A21 W21 W12
× ×wk.baidu.com1
S10
E0
S 3 ,A 0 3 0S 3 2S 2 1A 2 1
E1E0 KT S10 较大 4
1. Four levels system
E3
1) single mode oscillation (l th mode, n)
nn ) 21 l,0vl N2 v 1N l 2 v 1N
Red ruby, Er3+ doped fiber
E
3
w13A3 S3
11
S3
E
2
2
A2 S2 w2 w1
111 2
E
1
S 3 1S 3 2A 3 1S 3 2
202S1/221/11 A21
铒离子能级图
3
§4.3 Rate equations examples (three, four levels system )
• Differential equations describing the dynamics of population and photon density of various levels
1
Two, three, four level lasers
2
2
pump 1
laser 1 0
3 2
1
2021/2/11
laser
3 2
laser
1 0
2
100ns
10ns
0.98nm
与管壁碰撞
He + e He* 21S0,23S1 He* + Ne Ne* + He + DE
2021/2/11
various physical processes
• Different expressions of rate equations for a same laser
dn2 dt
R2
n2
2
n2
f2 f1
n121n,n0)vNl
dn1 dt
R1
n1
1
n221n2
f2 f1
n121n,n0)vNl
E2
S32
E2
dn3 dt
n0W03
n3S32
A30)
(ignore S30)
w03 A30 S30 S21 A21 W21 W12
E1
dn2 dt
n3S32 n2 S21
) A21 n1W12
n2W21
E0
S10
n3S32n2S21 A21)n2
f2 f1
n1
A21 nn
g~n ,n0 )Nl
dn0 dt
n2W21n1W12
Nl
Rl
n2
f2 f1
n121n,n0)vNl
Nl
Rl
I1 I 0e
t
I t ) I 0 e L c
t
I 0 e Rl
Photon lifetime 光子寿命
Rl
L c
（2.1.14）
• Rate equations for practical laser are set up according to the
R2 E1
R1
2 21Ltraasnesrition 1
R1, R2 is atom density pumped per second into E1 and E2, respectively.
1, 2 is lifetime at E1, E2, respectively; 21 is202s1p/2o/1n1taneous emission (荧光 fluorescence）lifetime for E2 E1. 6
E3
S32
E2
w03 A30 S30 S21 A21 W21 W12
E1
S10
E0
ddn2tn3S32n2S21A21)n1W12n2W21 ddn1tn2S21A21)n1W12n2W21n1S10
E2
2
R2
21
E1
R1
1
Pump transitions
Laser
dn2 dt
R2
n2
2
n2
f2 f1
• Neglect the difference of diffraction
DnF n
n loss in the modes
矩形面积＝原谱线面积
Simplifications
Line shape function rectangle (矩形)
Same loss, same lifetime of photon for each mode
第7讲
• 四能级系统单模速率方程的建立 • 多模速率方程的建立 • 均匀加宽工作介质的增益系数
从速率方程出发推导小信号增益系数表达式 小信号增益曲线 增益线宽
• 均匀加宽工作介质的增益饱和
大信号增益系数、强光作用下的弱光增益系数
• 非均匀加宽工作介质增益系数
作业:4-7、4-13、4-20
2021/2/11
n121n,n0)vNl
transition
ddn1t R1
n1
1
n221n2
f2 f1
n121n,n0)vNl
2021/2/11
7
2) Rate equations for multimode oscillation
Serial number of mode ll1,l2ln
Frequency of mode nnl1,nl2 nln
n1S1 0 n0W0 3 n3 A3 0
ddN ltn2W21n1W12NRll
W21B21g~n,n0) Nl hn
Ann21g~n,n0)Nl 21n,n0)Nlv （4.4.13）
n0n1n2n3n
2021/2/11
没有包括A21引起的光子数?
5
Consider loss only
dNl dt
ddN ltn2ff1 2n121 n,n0)v
N lNl Rl
2021/2/11
dNl1 ,dNln
dt
dt
8
g(nn0) g'(nn0)
Reasons of simplification
g(nn0)
• Do not need to consider differences
g'(nn0)
of the modes for studying question
Photon number of serial mode N l N l1,N l2 N ln Method : 对应每个模式分别建立一个速率方程, 序数相应变化
21n,n0)8A 2h1vn202 g ~n,n0)
nn ) ) d d 2 n tn 3 S 3 2n 2A 2 1S 21 l n 2ff1 2n 1 21 l,0vlN
He -Ne, Nd: YAG
E3
S32
E2
w03 A30 S30 S21 A21 W21 W12
× ×wk.baidu.com1
S10
E0
S 3 ,A 0 3 0S 3 2S 2 1A 2 1
E1E0 KT S10 较大 4
1. Four levels system
E3
1) single mode oscillation (l th mode, n)
nn ) 21 l,0vl N2 v 1N l 2 v 1N