Optical Parametric Generators and Oscillators

Pump (p) partially depleted

Signal (s) amplified

Idler (i) generated

p = s + i

Parametric Amplifier

(2)

Parametric Oscillator

(2)

mirrors

- Signal and idler generated from noise

- Tune wavelength (k) via temperature or incidence angle

2400 nmA single 266 nm pumped BBO OPO

Kr-ion LaserAr-ion Laser

He-Ne LasersHe-CdLasers

N Laser GaAlAs Lasers

Ti:Sapphire

Alexandrite Laser InGaAsP Diode Lasers

Ruby Laser & 2nd Harmonic

Nd YAG Laser and 2nd and 3rd Harmonics

XeF Excimer LasersXeCl

Dye Lasers (7-10 different dyes) Color Center Lasers

13001100900700300Wavelength (nm)

Early 1990s

The strong “pump” beam at c is undepleted.

i.e.

The weak “signal beam at a is amplified.

An “idler” beam at b is generated bacbac kk k ω ω ω

A pump beam photon breaks up into a signal photon and idler photon

)( ),()( bac III

kziab

kziaceff

b

bb

kziba

kzibceff

a

aa

eziezdcn(ω

ωiz

dz

d

eziezdcn

izdz

d

),(~),(),0(~

)),(

),(~),(),0(~

)(),(

**)2(

**)2(

EEEE

EEEE

OPA: Undepleted Pump Approximation

bbaacb

effbbc

a

effaa nnnn

cn

d

cn

d )( )( ),0(

~~ ),0(

~~ :Define

)2()2(

EE

kziabb

kzibaa eziz

dz

deziz

dz

d ),(~),( ),(~),( ** EEEE

solve and derivative take},2

Δ{exp ),(),( substitute d/dz

kz-izz ii EE

),(}4

~~{),( ),( and ),(for ngSubstituti

),(~),(2

),( ),(for

2

2

2*

*2

2

abaaba

baaaa

zk

zdz

dz

dz

dz

dz

d

zdz

diz

dz

dkiz

dz

dz

EEEE

EEEE

4~~ with ]exp[ form theof solutions

22 k

z ba

)in ()in (

)/in ()/in (~

1726.0)in (

1)(

)(0,~

)()(

4)(0,

~~~1 define

22/1)2(1

c)2(

2

c)2(

2OPA

mmnnn

cmMWIVpmd

cmcm

dnn

dcnn

bapba

peff

OPA

effbvacavacba

effba

baba

EE

Clearly the functional behavior depends on the sign of 2.1. The behavior near and on phase match (2>0) is exponential growth2. When 2<0, the behavior is oscillatory.3. Using the boundary condition )(0, aE

)sinh(

),0(~),( ;)sinh(2

)cosh(),0(),(

0

2*2

2

kzi

abb

kzi

aa ez

izezk

izz

EEEE

)(0, aE

z

|),(| bz E

|),(| az E

OPA,OPA exp),( sinh) (andcosh for

zzz baE

)(intensity 2

)(amplitude t coefficiengain 1

1

OPA

OPA

0 0|| 2 k

4

11

2

1At

22/1

22/1k

kOPAOPA

OPA

k

3 2/1

For this difference frequency process,the larger the intensity gain coefficient 2, the broader the gain bandwidth!

This is contrast to SHG (i.e. sum frequency case) in which the bandwidth narrows with increasing intensity

Exponential Gain Coefficient

0k

Solutionsy Oscillator:0~~4/22 bak

z

),( azI

),( bzI

2/

),0( aI

No gain!

2*2 )sin(),0(~),( )sin(

2)cos()(0,),(

kzi

abb

zk

i

aa ez

izezk

izz

EEEE

),0(

),0(),()G( :Gain Signal General,In

a

aaa I

ILIL,ω

Notes:

1. For large , low level oscillations still

exist, but are too small to be seen

2. The zero level is different for .

3. For there is no signal gain, just

energy exchange with the idler as shown above.

OPAL /

1/ OPAL

bak ~~2

OPA Numerical Example

cmLMW/cmIVpmddn

mm

ceff

ba

1 5),0( /95.5~

24.2

06.1 53.0amplifier parametric LiNbO

215

)2(c3

)(sinh4

1)G(L, 22

2L

ka

Assume k=0

34.0)(4

1)(sinh),G(

0.64

)in ,,0()in ()in (

)in (~

172.0

)in (

1

)I(0,

~22

|)(0,~21

264.064.02

1-

2)2(

c0

)2(

c)2(

eeLL

cm

MW/cmIμmμmnnn

pm/Vd

cm

cnnn

dd

nn

a

cbacba

eff

OPA

bacba

effeff

babaOPA

E|

Single pass gain is 34%

OPA Solutions with Pump Depletion

.)0()0(

)0(],)[0(1)0()( 0

2

ac

cccc NN

NNsnNN

)0()0(

)0(],)[0(1)0()0()( 0

2

ac

cccaa NN

NNsnNNN

.)0()0(

)0(],)[0(1)0()( 0

2

ac

cccb NN

NNsnNN

function of period 1/2

0at maximum is

that so requiredoffset

nintegratio ofconstant 0

sn

sn

1~ ,10)0( ,1)0( .. 4 ac NNge

Note:1. This amplifier response is periodic in distance and pump power.2. Therefore there is no saturation as with other amplifiers.3. The gain is exponential, but only over a finite range of length.4. For small distances the signal growth is not exponential although the idler growth is!

Optical Parametric Oscillators (OPOs)

OPOs are the most powerful devices for generating tunable radiation efficiently.

Put a nonlinear gain medium in a cavity, “noise” at a and b is amplified.

By using a cavity, the pump is depleted more efficiently. Using a doubly resonant cavity (resonant at both the idler and the signal), the threshold for net gain is reduced substantially.Triply resonant cavities (also resonant at the pump frequency) have been reported, but their stability problems have limited their utility and commercial availability

Assume that pump is essentially undepleted on a single pass through the cavity

0

0

%100

c

b

a

R

R

R

Singly Resonant Oscillator

0

0

%100

'

'

'

c

b

a

R

R

R

Have to deal with cavitymodes at signal frequency

Doubly Resonant Oscillator

0

%100

%100

c

b

a

R

R

R

0

%100

%100

'

'

'

c

b

a

R

R

R

Cavity modes at both signal and idler frequency need to be considered

(2)c b

a iRiR

Doubly Resonant Cavity Threshold Condition

- Idler (b) and signal (a) beams experience gain in one direction only,

i.e. interact with (c) pump beam only in forward direction)Forward Backward

-Cavity “turn-on” and “turn-off” dynamics is complicated we deal only with steady state (cw)- Assume lossless (2) medium- Only loss is due to transmission through mirrors- Steady state occurs when double pass loss equals single pass gain!

)(huge! 2 cbac kkkkk

0 bac kkkk

After interacting in forward pass with pump beam inside the cavity

),( aL E),( bL E),0( bE

),0( cE ),0(),( ccL EE ),0( aE (2)

- In addition, since the mirrors are coated for high reflectivities at b and a, they accumulate

phase shifts of 2kbL and 2kaL respectively after a single round trip inside the cavity.

Linear phase accumulation

Linear phase accumulation

'aRaR

Reflection Reflection

tscoefficien reflection amplitude field are and aa RR

,),0()sinh(~

),0(sinh2

cosh),( 2*kL

i

ba

aa eLiLk

iLL

EEE

.),0(sinh2

cosh),0()sinh(~

),( 2

kLi

bab

b eLk

iLLiL

** EEE

. ),(),02(

, ),(),02(

'2

'2

bbLik

bb

aaLik

aa

RReLzL

RReLzL

b

a

EE

EE

Steady state afterone round trip

matrix transfer - M

For minimum threshold, 2kbL =2mb and 2kaL=2ma

)(

)1)(1(2)(

)(

1cosh 2/1

bbaa

bbaa

OPA

L

bbaa

baba

OPA RRRR

RRRRL

RRRR

RRRRL OPA

)(

)1)(1(

)]in (~

[)]in ([

)in ()in (2.67)in ,,0(

)(

)1)(1(

4),0(for ngSubstituti

2)2(22

2)2(22

0/1OPA

bbaa

bbaa

eff

bacbacth

bbaa

bbaa

eff

bacbacth

L

RRRR

RRRR

pm/VdcmL

μmμmnnnMW/cmI

RRRR

RRRR

dL

cnnnIOPA

0sinh1cosh1cosh )(2222

Lkki

OPAbaba

Lik

OPAbb

Lik

OPAaa

baba eL

RRRReL

RReL

RR

Gain threshold: 0|| IM

}{)( c

n

c

nkkkk ba

acba fixed by pumpdepends on cavity modes

OPO Instabilities: Doubly Resonant CavityMechanical instabilities (vibrations, mount creep and relaxation..) and thermal drift cause cavity length changes and hence output frequency changes

abbaaabac ωωωω in changeany fixed, is

bab

bba

aa mmLn

cm

Ln

cm

Non-degenerate integers

→ Discrete cavity mode frequencies with separations

bbb

aaa Ln

cm

Ln

cm

1 1i

How many cavity modes exist within the gain bandwidth?

Cavity resonances on whichthreshold is minimum

Signal and idler are both standing waves in cavity

integers are 22 22 ,babbaa mmLkmLk

baaa

aa

baaba

a

nnnLn

c

nnL

cnn

cLk

since δ

)(

2)(

2

Many cavity modes within gain bandwidth

Gai

n C

oeff

icie

nt

a

OPO oscillates when cavity modes coincide

If length or changes, the next operating point when cavity modes coincidecan cause a large shift (called a “mode hop”) in output frequency

c

“Mode hop”

Note that when

a drifts up in

frequency, b

drifts down in frequency!

n 1n a

b1mm

e.g. Type I birefringent phase matched LiNbO3 d31=5.95pm/V, L=1cm

c=0.53m a=b =1.06m (near degeneracy) nanbnc2.24, Ra=Rb=0.98 2 4.8)( KW/cmI cth quite a modest intensity!

Singly Resonant OPO (SRO)

Cavity is resonant at only one frequency, usually the desired signal (a) Ra 1 Rb0

aa

aa

eff

bacbaSROcth

bbaa

bbaa

eff

bacbaDROcth

RR

RR

pm/VdcmL

μmμmnnnMW/cmI

RRRR

RRRR

pm/VdcmL

μmμmnnnMW/cmI

)1(

)]in (~

[)]in ([

)in ()in (2.67)in ,,0(

)(

)1)(1(

)]in (~

[)]in ([

)in ()in (2.67)in ,,0(

2)2(22

2)2(22

100)(

)( %98for

)1(

2

)(

)(

DROI

SROIR

RDROI

SROI

th

thb

bth

th Threshold much higherfor SRO than for DRO

e.g. The threshold for the previously discussed LiNbO3 case is 1 MW/cm2

Stability of Singly Resonant OPO

a

a

If the cavity drifts, the outputfrequency drifts with it, no largemode hops occur. Frequencyhops will be just the modeseparation.

OPO Output

At threshold, gain=loss.

If I(c) > Ith(c), input photons in excess of threshold are converted into output

signal and idler photonsOne pump photon is converted into one signal and one idler photon.

How much comes out of OPO depends on the mirror transmission coefficients

b

b

a

a

c

cthc IIII

)()()()(

)]()([)( cthcc

aa III

)( cI )( cthI

)( aI “slope efficiency” 1

c

a

Frequency Tuning of OPO

Two approaches: (1) angle tuning (2) temperature tuning (relatively small – useful for fine tuning

Angle Tuning (uniaxial crystal)

xz

y

e.g. ),( cen

)( aon

)( bon

bbaacc

bac

nnn

usly simultaneo

satisfy toneed

b

bb

a

aaba

PMcoce

ceca

nnnn

nnn

)(

)2sin()(

1

)(

1

),(2

1 changes angle smallFor

223

In general requires numerical calculations

Examples of OPOs

Example of Angle Tuning

LiNbO3 (birefringence phase-matched)

Example of Temperature Tuning

Mid-infrared OPA and OPO Parametric Devices

Atmospheric transmission and the molecules responsible for the absorption

Need broadly tunable sources for pollution sensing applications

Materials

NPP: N-(4-nitrophenyl)-L-propinolDMNP: 3,5-dimethyl-1-(4-nitrophenyl) pyrazoleDAST: Dimethyl-amino-4-N-methylstilbazolium tosylate