Modes of Laser Operation

8/11/2019 Modes of Laser Operation

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Laser Engineering

A.K. NathDate: 10-08-2011


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Modes of Operation of Laser

* Continuous Wave (CW)

* Pulsed Mode

*

* Mode-locked + Pulse Compression


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Time

Free Running Laser

Relaxation Oscillation

Pump duration is longerthan the Cavity Decay Time

Laser pulses= 10s s spikeson ms pulse envelop

Pump Pulse

Gain

LoseLine

LaserPulse

Total pulseduration= 0.1-20ms

dN/dt = .N0 I . .N /h N/t 2

dI/dt = I. .N .c I/t c


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Methods of Pulsed Laser OperationQ-Switched Laser

Q- Quality Factor of Optical Resonator High-Q: Low Cavity Loss Low Q: High Cavity Loss Switching from Low Q (High Cavity

Loss) to High-Q( Low Cavity Loss)

Q-switch involves* Preventing the laser from lasing until

pumping is over, and* Abruptly allowing the laser to lasewhen the population inversion is max.

Laser pulse rise time is limited by theswitching time and the peak powerdepends on the initial populationinversion N max .

Laser pulse fall time depends upon thecavity photon decay time, t c

Time

Q-SwitchedLaser Pulse

CavityLoss-

Curve

Q-Switched Laser Pulse: 1-100ns


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Electro-Optic Effect

Change in the optical properties of amaterial in response to an electric field

Refractive Index = f (E)

V /4

PlanePolarizedBeam

PlanePolarizedBeam

PlanePolarizedBeam

CircularlyPolarizedBeam

Two orthogonal polarized rays havedifferent velocities.Emerging rays have

phase difference Applied Voltage

V /4 /2 Phase differencePlane Polarized Beam Circularly Polarized Beam

V /2 Phase differencePlane Polarization rotates by 90 0

Round trip with V /4 VoltagePlane Polarization rotates by 90 0

Two Types of Electro-Optic Effects:

1. Pockels Effect: Change in refractiveindex n = n e no E Electric Field

Electro-optic MaterialsAmmonium dihydrogen phosphate (ADP)Potassium dihydrogen phosphate (KDP)Potassium dideuterium phosphate (KD *P)Lithium niobate (LN)


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2. Kerr effect : Change in refractive index n E2

Refractive Index in presence of Intense Laser Beam n = n 0 +n 2.I

where n 2 - the second-order nonlinear refractive index,

I Laser Beam Intensity

The refractive index change is proportional to the intensity of the light travelingthrough the medium.

I n FocusingEffect


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Acousto- Optic Effect

Sound wave (series ofcompressions and

rarefactions ) travelingthrough a transparentmaterial, causes

periodic variations ofthe index of refraction.

Light beam travelingthrough the periodicvarying refractiveindex gets diffracted:Acousto- Optic Effect

Piezoelectric

Intensity of undeflected beamreduces i.e. loss is introduced


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Cavity Dumping:Laser Pulse Rise time in Q-Switched Laser:Switching time of Q-Switch device &Initial Population Inversion

Fall Time ~ 5-6 t c ; Several 10s nstc =Cavity Photon Decay Time= 1/c[a-(1/2L)lnR 1.R 2]

Q-SwitchedLaser pulse

Time

L a s e r

P o w e r

A-OSwitch

Cavity Dumping Process:With high Q, Laser Power isallowed to build to the maximum.At the maximum laser power Q isreduced to almost zero bydeflecting the beam either by E-Oor A-O Switch out of the lasercavity.Entire laser energy inside cavitycomes out in nearly single round

trip time rt , a few ns.


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Laser Action on MultipleLongitudinal Modes:

Longitudinal Modes inrandom phases


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Out of phase Out of phaseIn phase

LOCKED phases for all the laser modes

Out of phase

RANDOM phase for all the laser modesIrradiance vs. Time

Mode Locking:


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M ode L ocking

( 1) /2 ( 1) /2

( 1) /2 ( 1) /2exp ( ) ( )

N N

n m ax n mn N m N A A j n m t j t t

( 1) /2 ( 1) /2 ( 1)/2

2

( 1)/2 ( 1)/2exp exp ( ) ( )

N N N

n n m ax n mn N m n n N

A A A j n m t j t t

Random phases

M ul timode lasing

( 1)/ 2

0( 1)/ 2

( ) exp ( ) N

n ax n N

E t A j n j t

2

2ax

rt FSR

A

2

( 1) /220

( 1) /2( ) ~ ( ) exp ( )

N

n ax n N

S t E t A j n t j t

0

2

nnS A S

( ) 0n m j t e S

t

S

=2 .f = 2 . c


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L ocked phases0 0

( 1)/ 2

( 1) /2( ) ( )n ax

N j t j t j jn t

n e N

E t e A e e E t e

( 1) /2

( 1) / 2( ) n ax

N

j jn t e n N

E t A e e Equal ampli tudes and phases , 0n n A A

( 1) / 2( 1) / 2

( 1) / 2

sin( / 2)1( )

1 sin( / 2)

ax

ax ax

ax

jN t N jn t j N t ax

e j t N ax

N t e E t A e Ae A

e t

222

sin ( / 2)( ) ~sin ( / 2)

ax

ax

N t S t At

,min12

1~ p

M inimum pul se length p

trt = 2L/c

M ax. no, of modes Nmax ~ 12. rt

Peak Power = N 2.A2

Average Power = N.A 2

N- No. of L asing modes


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Mode-Locked Laser Several Longitudinal modes each

separated by c= c/2L can lase Usually they are in random-phases Laser output is incoherent

superimposition of intensities ofseveral lasing modes.

Locking the phases of all laserlongitudinal modes yield a train ofUltra-short laser pulses

Laser pulse duration is limited bylaser emission / gain bandwidth,

p 1/ s Laser pulses are separation the

round-trip time of the cavity

Random Phases

Phase LockedRandomPhase

RandomPhase

Round-trip timert= 2nL/c

Laser PulseDuration =

p ~ 1/ s


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Requirement for generating Short-duration Laser Pulse:

Large Gain Bandwidth

Mechanism for Mode-locking

Gain bandwidth of Different Lasers:

CO 2 Laser: 50MHz

He-Ne Laser : 1.5GHz

Nd:YAG Laser: 1200GHz p~ ps

Dye Laser: 40THz p~ 25fs

Ti-Sapphire Laser: 100THz p~ 10fs

Typical Cavity mode separationc = c/2L =3x10 10/ 30 = 10 9Hz = 1GHz

Mode-locking Techniques :

1. Saturable Absorber

2. Electro-optic Modulator

3. Acousto-optic Modulator

Modulators provide low-loss ata frequency = 1/ rt

M 1

M 2Laser

SaturableAbsorber

Polarizer EOM/AOM


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Active mode-locking: the electro-optic modulator

V

If V = 0, the pulse polarizationdoesnt change.

Laser pulse builds up andoutput pulse comes out

If V = V /4, the pulse plane polarization switches to circular polarization & inreturn pass it becomes plane polarized, but 90 rotated.

Polarizer deflects the pulse out of optic axis- thus introduces loss

Applying a sinusoidal voltage yields sinusoidal modulation to cavity loss and whenvoltage is zero, loss is minimum and laser pulse comes out.

Modulation frequency, fm = 1/t rt , trt = Round trip time = 2nL/c, n = Av. refractive index

Pockels cell

Polarizer

, trt = Round trip

time = 2nL/c Lasermedium


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Active mode-locking: the acousto-optic modulator

Sinusoidally modulating the acoustic wave amplitude at round-tripfrequency yields mode-locked laser pulses.

Quartz DiffractedBeam (Loss)

Acoustictransducer

Pressure, density, and refractive-index variations due to acoustic wave

Output

beamLasermedium

, t rt = Round trip

time = 2nL/c


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Laser Mode Locking with Kerr Lens

Kerr Lens

Mode-locking

HR

PR

Laser Medium

Pump Aperture

WithoutMode-locking

With

Mode-locking


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GVD Compensation

GVD can be compensated if optical pathlength is different for blue and red components of the pulse.

0

R B

R b

If OR + RR > OB, GVD < 0

Diffraction grating compensator Prism compensator

Wavelengthtuning mask

Red component of the pulse propagates in glass more than theblue one and has longer optical

path (n x L).


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Pump

HR

GainOC

Mode-locking

Mechanism

Dispersion

Compensation

Components of ultrafast laser system

Kerr LensMode-locking

Ti-Sapphire:Kerr Medium

v

v


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Typical fs Oscillator

GVDC

Active medium(Also Kerr medium) From the pump

laser

Wavelengthtuning mask

Typical Ti: Sapphire fs Oscillator Layout Tuning range 690-1050 nm Pulse duration > 5 fs (typically

50 -100 fs) Pulse energy < 10 nJ Repetition rate 40 1000 MHz

(determined by the cavity length) Pump source:

Ar-ion laser (488+514 nm)DPSS CW YAG laser (532 nm)

Typical applications:

time-resolved emission studies,multi-photon absorption spectroscopyand imaging

O. Zvelto, Principles of lasers, Plenum, NY (2004)


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Amplification of fs Pulses

Oscillator Stretcher Amplifier Compressor

Stretch femtosecond oscillator pulse by ~100 times Pulse stretched exploiting frequency dispersion is called Chirped Pulse Amplify Recompress amplified pulse

Concept:

Issue-2: Shorter pulse High Peak power Damage of Laser Medium

Due to high intensity, fs pulses can not be amplified as is.


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Femtosceond Laser: Chirped pulse amplification

High Precision Alignment ofoptical componentsHigh cost

Expert for maintenance

Short Laserpulse: Oscillator

Energy=mJ/pulse10-100kHzA few Watts


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Summary:

*

* Mode-locking + Pulse Compression and Amplification

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Modes of Laser Operation

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