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PULSED LASERS:Q-SWITCHINGAND MODE LOCKING
Pulsed lasers are valuable when PEAK(or instantaneous) POWER rather thanaverage power is most important.
Examples: Nonlinear photochemicalprocesses where
RATE In ( integer > 1)
PEAK POWER
P
t (FWHM)
time
If E = pulse energy (J), then
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Peak Power tE
Average Power =
E/pulse
(PRF)frequencyrepetitionpulse
pulses/sec#
EXAMPLE
A KrF laser ( = 248 nm) producespulses having energies of 250 mJ
and temporal widths of 20 ns at aPRF of 80 Hz.
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Peak Power =ns20
mJ250
= 12.5 MW
Average Power =
41
J 80 s1 = 20 W !
Pulsing a laser may also be anecessity if the threshold pumping
power (specific power loading:W-cm3) cannot be long sustained.
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EXAMPLE: KrF Again
SE = 2.6 2
TH = 3 103 cm1
NTH = 1.2 1013 cm3
SP = (A21)1 = 5 109 s
Formation efficiency for upper laserlevel = 15%
Threshold Pump Power
!cmkW14~hN 3formSP
TH =
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Approaches to Pulsing Lasers
1. Pulsing the excitation itself;requires high power electronics;typically high peak power but lowPRF (and low average power).
2. Q-switching
3. Mode-locking Operate laserCW but, with optics, can inducelaser to produce a train of short
pulses; active or passive mode-locking.
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Q-SWITCHING
The idea is simple: Spoil the Q of anoptical cavity, allowing N to risewell above NTH.
Then, restore Q suddenly Giant Pulse!
EXAMPLE: Spinning Mirror
Gain
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Although Q-switching does notproduce the shortest pulses available(mode-locking does that), it hasseveral advantages:
1. Its inexpensive!
2. Easy to implement3. Efficient in extracting energy
stored in upper laser level.
Gain
Fast Shutter
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1. Pump at low rate with shutterclosed to prevent lasing.
2. N rises to > NTH
3. Open shutter, laser oscillation
builds up rapidly.
4. 2 1 stimulated transitionsdeplete N quickly andefficiently.
Shutter Pump
Laser medium
A
R1 R2L
l
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5. N can go below NTH beforepulse terminates.
6. Close shutter.
Shutteropens
Time
109-106s103-1s
NTH
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Analysis of Q-SwitchingL
l
0,
R1 R2
Immediately after the shutter opens,the intensity I grows from the
noise as
I(z) = I0ez
dt
dI= I
and Inc
dtdz
dzdI
dtdI
==
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Letting
total number of photonscirculating in the optical cavity, then
mirrorsandto
duelosses
p
)(sconstant
growthtemporal
Ln
c
dt
d
1
=
l
Only this fraction is
amplified at any given
time.
wherep = photon lifetime
=
1
221 eRR1cnL2
l
Define
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=p
t (dimensionless time)
and so
=
1
Ln
c
d
dp
l
But1
pL
cn
when0dd ==
l
TH
=
=
1N
N1
d
d
THTH
(1)
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Note, however, that for each 2 1stimulated transition that occurs, Nchanges by 2.
THN
N2
d
)N(d
=
(2)
# of photonsgenerated by inducedemission per unit of
normalized time
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ni = N (t = 0)
nf= N (t )
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PULSED LASERS: Q-Switching &Mode Locking
I. METHODSTO PRODUCE SHORT LASERPULSES
A. Pulsed lasers typically have
higher peak power (thoughperhaps lower average power)than continuous wave CWlasers.
1. Pulse lasers having highpeak power are useful fora. Nonlinear processes
(such as multiphoton
ionization) which scaleas En, n > 1.
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b. Processes which areintensity (as opposedto fluence) driven suchas photochemistry.
2. Pulsed system are typicallyrequired if the laser has a
high threshold gain.3. EXAMPLE: KrF Laser at 247
nm. (5 eV)
Stimulated emission cross section:2.6 1016 cm2.
Threshold gain: 0.003 cm1
Threshold inversion:1.2 1013 cm3
Radiative lifetime: 5 109 sFormation efficiency of upper level:
15%
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Threshold pump power:
P = 3forms
upper
cm
kW14hN
B. Methods to produce pulsedlasers1. Pulsed application of pump
a. Requires high powerelectronics
b. Typically high peakpower, low rep rate
2. Q-Switcha. Store energy in laser
medium while cavity isblocked
b. Unblock cavity; extractpower
3. Mode locking
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a. Actually operate laser asa CW device, but tricklaser into outputting
power in a series of shortpulses.
b. Active or passive.
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Q-SWITCHING
I. INTRODUCTION
A. Q-switching is a techniquewhereby one controls the Q
or feedback of the opticalcavity.
1. Generate short pulses of
high peak power.
2. Pump the laser and build upan inversion over long
periods; extract over shortperiods.
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laser is then turned on, andpower is rapidly extracted.
D. Typical sequence of events.
Mirror Mirror
Gainmedium
Shutter
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j Pump at low rate with cavity
blocked to prevent laser oscillation.
k Generate N > (N)TH. Unblock cavity to allow laser
oscillation.
m Laser pulse extracts power from
inversion, driving N < (N)TH(absorption).n Laser pulse terminates.
o Close shutter.
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Time
109-106s103-1s
(N)TH (N)I
j
k
m
jno
II. DERIVATIONOF Q-SWITCHINGBEHAVIOR
A. We have a laser cavity withoutput mirror reflectivity R,length L. The average photonlifetime in the cavity is
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)d2exp(RRTT1cnL2
)RoundTrip/LossFractional(cnL2
2122
21
c
=Laser medium
R1 R2
L
dT1 T2
n = index of refraction
B. Since most Q-switched laserpulses are very short, we canignore any additional pumpingor loss from laser levels during
the laser pulse other than bysaturation. When the Q-switchis opened,
Inc
dtdz
dzdI
dtdIlaser ==
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The total number of photons inthe cavity changes as
=
c
1
L
d
n
c
dt
d
Only this fraction isamplified at any given time.
cower
h
P
=