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Laser Cavity

Laser Cavity

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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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Page 1: Laser Cavity

Laser Cavity

Page 2: 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

Page 3: Laser Cavity

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

Page 4: Laser Cavity

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

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eItIRRc

L

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RR

t

tI

RRtItIttII

c

t

tc

c

c

c

Page 5: Laser Cavity

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

LcF

RR

L

cRR

Lv

v

vQ

m

Page 6: Laser Cavity

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

E

ez

jkz

E

eE

Ekz

EE

EkE

ezyxEzyxE

t

t

jkz

jkz

jkztt

t

jkz

Page 7: Laser Cavity

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

2

2

0

1

2

20

0

00

wz

z

zz

z

wzzR

z

zw

w

zw zw

zR

rjk

z

zkzj

zw

r

zw

w

E

zkj

rr

r

Page 8: Laser Cavity

Amplitude of the Field

22

1

)(

2exp

)(2

1

2

1

const. a bemust z planearbitrary an passingpower totalThe

2

2 is beam theof angle divergence theand

,)( z, largeFor

1)(

.2 is waist theAt

0.z from off is z when decrease 0)(r axisat amplitude The

)()(exp

)(

0).(r uecenter val its of todrops at amplitude The

20

20

2

0 0 2

2

2

20

20

*

00

00

00

2

0

20

2

00

102

20

1

wErdrd

zw

r

zw

wEdA

EEP

wwdz

dw

w

z

z

zwzzw

z

zw zw

wz

ezw

w

zw

r

zw

w

ewr

Page 9: Laser Cavity

Phase Factors

TEM)(not plane. anot is surface equiphase The

thatimplieswhich ,)(2

isfactor phase Radial

tan2

1

tanfactor phase alLongitudin

2

0

10

1

0

1

zR

kr

zz

z

nc

wzv

z

zkz

p

Page 10: Laser Cavity

Radius

plannar. is wavefrontthe

and minimum is sizespot the0,zat

formula. beamGaussian in seen s what'is This

)2

exp( )exp(1

2

1

2

1)1(

When

where)exp(1

. wavefrontspherical a isit assume We

2

2221

2

22

R

krjjkz

RE

R

rz

z

rz

z

rzR

rzR

zrRjkRR

E

Page 11: Laser Cavity

factor phase radial )(2

exp

factor phase allongitudin tanexp

r with amplitude theofon variati )(

exp)(

0zat amplitude ),,(

2

0

1

2

20

0

zR

rjk

z

zkzj

zw

r

zw

w

EzyxE

Page 12: Laser Cavity

Higher Order Modes

)12(2

])(

exp[)(

),,(

2

])(

exp[)(

),,(

1

])(

exp[)(

),,(

)12(2)(

2)(

1)(

)(

2

)(

2]

)(exp[

)(),,(

2

2

220

0,00,2

2

20

0,10,1

2

220

0,00,0

22

1

0

2

220

,,

x

zw

yx

zw

wEzyxE

x

zw

x

zw

wEzyxE

zw

yx

zw

wEzyxE

uuH

uuH

uHwhere

zw

yH

zw

xH

zw

yx

zw

wEzyxE nmnmnm

TEM0,0

TEM1,0

TEM2,0

Page 13: Laser Cavity

Fig.17-15

Page 14: Laser Cavity

Gain Profile and Longitudinal Modes

Page 15: Laser Cavity

Spectrum

Page 16: Laser Cavity

laser beam and field

Fabry-perot(In-Plane)

P

n

Page 17: Laser Cavity

'2

'2

'22

'21

'12

'11

2221

1211

2

2

2221

1211

1

1

2222

2

2

2221

1211

1

1

2

1

2221

1211

2

1

,0

matrix T oftion multiplica Cascaded

;hint

B

A

TT

TT

TT

TT

B

A

TT

TT

B

A

BaAb

B

A

TT

TT

B

A

a

a

SS

SS

b

b

a

bS

jkaj

iij

k

T

A1 A2

B1 B2

T

A1 A2

B1 B2

T

A1’ A2’

B1’ B2’

S

a1 b2

b1 a2

Page 18: Laser Cavity

T

A1 A2

B1 B2

S

a1 b2

b1 a2

2112

2112

12

02

121

22

02

221

21

01

212

11

01

112

1

1

2

2

rt

tr

Sa

bt

Sa

br

Sa

bt

Sa

br

a

a

a

a

S

ST

T

det

11

det

1

11

22

21

1102

121

11

12

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221

1101

212

11

21

01

112

1

1

2

2

S

S

S

TB

Bt

T

T

B

Ar

TA

At

T

T

A

Br

A

A

B

B

Page 19: Laser Cavity

1

11

1

direction theNote

1

1

1

1

212112

12

1212

02

222

21

211

01

111

1

2

r

r

trt

tr

rtSS

nn

nnrr

a

bS

nn

nnr

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bS

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a

TS

a1 b2

b1 a2

11 rr

)0(

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)(

)(

1

1

Lb

La

Lj

Lj

Lj

Lj

e

e

e

e

0

0

0

0

T

S

Page 20: Laser Cavity

Building Block Components

Page 21: Laser Cavity

Fabry Perot Etalon

Lj

Lj

eba

eba

tarab

ratab

ratab

tarab

'1

'2

'2

'1

222'2

'2

222'22

1'111

'1

1'1111

Lj

Lj

a

Lj

Lj

a

Lj

Lj

a

Lj

Lj

a

err

ett

a

bS

err

ertr

a

bS

err

ett

a

bS

err

ertr

a

bS

221

21

02

112

221

21

22

2

02

222

221

21

01

221

221

22

21

1

01

111

1

1

1

1

1

1

2

2

Page 22: Laser Cavity

multiplymatrix 3.cascade

equationst coefficien thefrom solve 2.

toconvert 1.

by obtained becan matrix

T

TS

T

02

121

02

122

02

21112

01

11121

02

111

11

1

2

2

.2

AA

A

B

B

A

BT

A

BT

B

ATT

A

BTT

A

AT

S

Tdet

11 .1

11

22

21 S

S

S

1

11

0

0

1

11 .3

2

2

21

1

1 r

r

te

e

r

r

t Lj

Lj

T

Page 23: Laser Cavity

1

atoccur (extrema) points resonance The

L.2 of functions periodic are

spectra reflection andion transmissThe

sin41

1

sin41

sin4

;

sin41

11

sin41

sin4

21

212

22

22

21

22

22

11

21

221

22

222

212

21

22

222212

11

rr

rre

LRR

RS

LRR

LRS

rrIf

jerrRwhere

LRR

errS

LRR

LRerrS

L

iL

L

L

i

i

i

i

Page 24: Laser Cavity

Fabry Perot Laser

122

221

2

1

21

222

2

21

2

2

1

2

1

2'2

'1

2'22

1'11

21

221

1

2Im

, thresholdabove mode aFor

0

1. toequalsgain net tripround as same theiswhich

01

Therefore, .parameters Sin pole a toscorrespondit that impliesIt

input.hout output witphoton bemust therecondition, thresholdFor the

rt

rt

P

P

rre

ert

t

b

b

P

P

g

eraa

tab

tab

aa

err

o

oLg

Lg

o

o

ithxy

Lj

L

ithxy

ithxy

2

2

21

2121

11

22

2

121

21

1

22

2'2

21

2'1

2

111

22j

12

1

If

11

11

efficiencyout couplingphoton The

1r

lossy are mirrors theIf

r

tFF

ttr, trr

F

rrr

r

tF

rara

b

P

PF

t

mi

mid

m

o

j

Page 25: Laser Cavity

DBR

0

00

221102211

21

21

21

2211

21

2211

2

0

1

0212211

2211

222

22

2

2121

,0 loss no, parameter, detuning a Define

,2 islayer each ofdelay phase thefrequency, Bragg At the

2j and

2j is matrice in the termphase The

.grating, theconstantofn propagatio average theas defined is

) ( 0;

0;11

2

111

condition BraggAt

11

11

44 period and ,

2;

period one ofconstsnt n propagatiocomplex average The .0 condition, BraggAt

1

111

;

22

22

11

11

and

LLandLL

j

ifnn

nn

nn

nn

nnLLjLL

or

LLwhere

eret

eet

r

eet

rere

tere

ree

tere

ree

t

tttrrr

unit

jjjj

jjjj

LjLj

LjLj

LjLj

LjLj

unit

T

T

n2 n1 n2 n1

Page 26: Laser Cavity

211121

11

2111

11212111

221

21112212211

1122

1122

222112211

11

21

22

12

2221

1211g

unit

lntanh

0

1ln note ln

tanh ln

1 ; ;

condition, BraggAt

tanh

tanh

14

1

2

1ln

cosh1cosh1

cosh1cosh1

matrices, m of cascade aFor

TTmT

Tm

jπ-TTj

TTandTT

TTTTTT

mm

TT

TTj

TTTT

mjmmjmT

T

mjmT

Tmjm

TT

TT

eff

eff

effeff

effeffm

T

T

Page 27: Laser Cavity

DBR. theinto field theofdepth

npenetratio thedetermines ,by multipliedn which whe,tanh1

of valueaat saturates m offunction a as n,attenuatio largeFor .

periods, ofnumber small a and ,1Ren attenuatioeak For very w

aves.incident w by theseen periods ofnumber effective theis

0. condition, BraggAt

.tan ties,reflectivi smallFor condition. Bragg from

far how of measure a isIt parameter. detuning generlized theas defined is

band. stop a to

scorrespond This .by attenuated is amplitude wave thereal, pure is If

band. pass a toscorrespond This .shift phase a sexperiencebut constant

remains amplitude wave theimaginary, pure is If .by multiplied is

period one passing rseigenvecto Two constant.n propagatio discrete theis

Λξm

mm

ξ

m

δΛδΛΔ

e

e

eff

eff

eff

Page 28: Laser Cavity

ignored. are sorder termhigher where

2tanh2

1

1

1lntanh

2

1

21

1lnRe

12

21

1

1

lntanh

0

1ln note ln

tanh ln

1;;

condition, BraggAt

2

2

2

2

22

2

222

22

2

211121

11

2111

11212111

221

21112212211

mrrr

rm

r

rm

rr

r

t

r

t

rt

r

t

r

eret

eet

r

eet

rere

t

recall

TTmT

Tm

jπ-TTj

TTandTT

TTTTTT

eff

jjjj

jjjj

unit

eff

T

Page 29: Laser Cavity

nnn

nnn

nnn

where

n

nL

n

nmmrL

mrL

Lmr

nn

nnr

mrr

rmm

T

Tr

jm

jm

T

TTTSr

gg

g

g

m

m

g

effg

effeffgggg

2

11

4

2

2

2.0 sin

2r

period,each from reflectionFor weak

0)( 1

1

0)( 2tanh1

1lntanh

condition BraggAt

1

1

stack theofty reflectivi totalThe

0

21

0

12

12

g

221

221

11

21

11

21112111

Page 30: Laser Cavity

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

Page 31: Laser Cavity

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

Page 32: Laser Cavity

Etched Facet

Cleaved Facet

Broad-Area Etched-Facet Laser