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Laser Cavity. M1 M2. 3D cavity. Fig.16-4. Photon Lifetime. Quality Factor and Cavity Finesse. Gaussian Beam. TEM 00 Mode. Amplitude of the Field. Phase Factors. Radius. TEM 0,0. TEM 1,0. TEM 2,0. Higher Order Modes. Fig.17-15. - PowerPoint PPT Presentation
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Laser Cavity
M1 M2
L
cv
nL
cm
ncv
mL
mL
L
mk
mLk
m
2 spacing mode
2 sfrequencie mode
2
222
22
node. a is this,0)cos(kx If
node. -antian is this,2
)cos(kx If
wave.standing a is This
)cos()cos(2
),(),(),(
)cos(),(
)cos(),(
:left andright towards
traveling waves travelingare there
s,frequencie resonance At the
0
0
0
n
wtkxE
txEtxEtxE
wtkxEtxE
wtkxEtxE
3D cavity
3
2
v
33
3
3
3
81)(
density mode spectral The
)2
( 3
8281
34
N
is sphere theinside modes ofnumber totalThe
z)y, x,scoordinate represents (
c
v
dv
dN
Vv
c
vkL
c
v
L
k
iL
mk ii
Fig.16-4
Photon Lifetime
.8.0for holds above The
width)(mode 2
)1(2
1
2
freq.angular theof FWHM theis where
1
relationy uncertaintBy
cos)(
)( and )1(
2
loss,mirror smallFor
)(1)(
)(2
1)(
]1)[()()(
is tripround oneafter changeintensity light The
21
2121
21
21
21
20
021
21
21
RRL
cRR
wv
w
τw
wteEtE
eItIRRc
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c
Quality Factor and Cavity Finesse
ty.reflectivion dependfactor quality and finesseboth while
length cavity oft independen is finesse that Note
2
2 that Recall
1
2
2
widthmode
spacing mode
as defined is finesseCavity
applied. be shouldty reflectivihigh andcavity long
time,coherence longmean time, in the and,factor quality high achieve To
)1(
4
)1(
)2)(2(
resonance offactor Quality
21
21
212121
mFLc
vFQ
L
cmv
RRF
v
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RR
L
cRR
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Gaussian Beam
TEM.near is beam The
therefore,Usually 2
smalleror 1cm becan D, beam,laser a of size The
)exp( isdirection zin ation major vari The
0 space freeIn
tz
ttz
tz
ttt
zz
ztt
EED
ED
ED
kE
D
EjkE
D
EE
jkEz
E
-jkzz
EEE
1)k (because 02
02
2
0
0equation Helmholtz
),,(),,(Let
2
2
22
2
22
2
2
22
22
22
22
0
zkj
zzkj
ezz
kjkz
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ez
jkz
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EE
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jkztt
t
jkz
TEM00 Mode
size.spot minimum heactually t isIt range.Rayleigh or sizespot called is
11)(
11)( where
phase radial )(2
exp
phase allongitudin tanexp
amplitude )(
exp)(
z)y,E(x,
is )(TEMsolution order lowest The
02r
1 coordinate lcylindrica Use
20
0
2
0
220
2
0
20
2
20
20
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2
0
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2
20
0
00
wz
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zz
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z
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Amplitude of the Field
22
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2
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)()(exp
)(
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20
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20
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*
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00
102
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ewr
Phase Factors
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thatimplieswhich ,)(2
isfactor phase Radial
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2
0
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kr
zz
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Radius
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and minimum is sizespot the0,zat
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)2
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When
where)exp(1
. wavefrontspherical a isit assume We
2
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22
R
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factor phase radial )(2
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w
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Higher Order Modes
)12(2
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),,(
2
])(
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),,(
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2)(
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)(
2
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0,00,2
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0,00,0
22
1
0
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x
zw
yx
zw
wEzyxE
x
zw
x
zw
wEzyxE
zw
yx
zw
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uuH
uuH
uHwhere
zw
yH
zw
xH
zw
yx
zw
wEzyxE nmnmnm
TEM0,0
TEM1,0
TEM2,0
Fig.17-15
Gain Profile and Longitudinal Modes
Spectrum
laser beam and field
Fabry-perot(In-Plane)
P
n
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Fabry Perot Laser
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1
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stack theofty reflectivi totalThe
0
21
0
12
12
g
221
221
11
21
11
21112111
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.220
10
20
30
40
50
60
70
Out
put P
ower
(mW
)
Current (A)
Facet Cleaved&
Cavity length 350 m
Mesa width 3 m
Mesa Width 22 m
0.00 0.02 0.04 0.06 0.08 0.10 0.120
5
10
15
20
25
30
35
Out
put P
ower
(mW
)
Current (A)
L380W2 L380W4
One Facet Etched&
Cavity length 380 m
Comparison of DQEs of Cleaved and Etched facet EE Lasers
DQE = 0.38 for w = 22 m
DQE = 0.38 for w = 3 m
DQE = 0.31 for w = 4 m
DQE = 0.26 for w = 2 m
Mesa width 4 m
Mesa width 2 m
Comparison of DQEs of Cleaved and Etched facet EE Lasers
(Broad area)
DQE = 0.4 for double-cleaved
DQE = 0.33 for etched facet
One facet etched the
other cleavedDouble Cleaving
Mesa width 22 m
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 55000
10
20
30
40
50
60
70
80
90
100
Ou
tpu
t P
ow
er
(mW
)
Current Density (A/cm2)
L340 L370 L400
Etched Facet
Cleaved Facet
Broad-Area Etched-Facet Laser