q switching and mode locking

7/31/2019 Q Switching and Mode Locking

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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

=

q switching and mode locking

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