optical parametric generators and oscillators pump ( p ) partially depleted signal ( s ) amplified...
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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