COMPUTER MODELING OF LASER SYSTEMS

Dejan Škrabelj

Advisers: Prof. Dr. Irena Drevenšek - Olenik Dr. Marko Marinček

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1. Tatoo removal application - motivation2. Revision of a basic laser physics3. Laser model for a Q – switched solid state laser4. Simulations of a ruby laser system5. Conclusion

OUTLINEOUTLINE

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• Non-destructive method for tatoo removal is a laser treatment.

• High power pulses P ~ 10 MW are required to achieve pigment break down.

• Particular pigment color requires particular wavelength of the light. Blue pigment – ruby laser wavelength, 694 nm.

Motivation – tatoo removal Motivation – tatoo removal application application

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• desirable property of a laser beam: “top hat” profile. • We would like to construct a Q-switched ruby laser with a

supergaussian mirror output coupler. Good computer simulation model can enormously reduce development time and development expenses.

Motivation – tatoo removal Motivation – tatoo removal applicationapplication

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Basic laser physics – laser Basic laser physics – laser systemsystem

• Laser is an optical oscillator.

• Front mirror is partially transmitive.

• Resonator losses are compensated by amplification process based on the stimulated emission, which takes place in the laser rod. For the stimulated emission we have to attain the population inversion with an external pump source.

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Basic laser physics – QS Basic laser physics – QS technique technique • Additional element is put in

the resonator, which mediates the resonator losses. •QS element is constituted from a polarizer and an electrooptic modulator. The generated laser light is consequently linearly polarized.• Produced pulses: Nd –YAG system:

MWP

nst

JE

100~

10~

1~

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Basic laser physics – unstable Basic laser physics – unstable resonatorresonator • In the stable resonator the light

rays are confined between the resonator mirrors. In the unstable configuration, the light rays are no longer confined between mirrors.

• Radii of curvatures of the resonator mirrors and its length determine the type of the resonator.

• Energy extraction is greater with use of the unstable cavities.

• With an unstable cavity output coupled with a supergaussian mirror we can obtain “top–hat” profile of a laser beam.

• Supergaussian mirror has a non– uniform reflectance profile.

ordwr

eRR )(20

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Model – introductionModel – introduction

• Resonator is divided into effective planes, which present resonator elements.

• We have to determine:

1. how the flux plane is propagated between resonator elements,

2. the influence of the particular element inside of the resonator on the flux plane.

||||

),(),(

),(),(),(

),(

AA

etrAtr

etrAtrE

E

tri

triE

• For a given cavity configuration a good model should predict several parameters as: pulse energy, pulse width, intensity distribution in a plane perpendicular to the propagation direction, effective beam radii at different distances, etc.

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Model – free space propagationModel – free space propagation

• For the propagation a method based on the 2D FT is used.

2,

)(2

)(2

,

,);,(),,(

,),,();,(

yx

yx

yx

k

yx

yxysxsi

yxt

ysxsiyxt

s

dsdsezssezyxE

dxdyezyxEzsse

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Model – free space propagationModel – free space propagation• Propagating field must obey the wave equation.

.);,();,(

,0);,()1()(

,0)()(

22222

2

2

1

12

222222);,(

22

dssi

yxtyxt

yxtyxdz

zssed

yx

yxt

ezssezsse

zssess

rEkrE

• The EM field transveral spectrum propagation is performed by a simple multiplication with the phase factor!

d real space:

Fourier space:

FT

),,( 1zyxE ),,( 2zyxE

);,( 1zsse yxt

dssi yxe22222 1

);,( 2zsse yxt

IFT

• In the numerical calculation we cover the EM field with n x n mesh points.

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Model – propagation through a lensModel – propagation through a lens

• Lens is characterized with its focal length f:

))(1(21

111rrf n

• Curved partially transmitting mirror acts as a lens on the transmitted part of the wavefront. Laser rod acts like a lens, too.

• If the optical wave passes through the slice of a medium with refractive index n and a thickness d(x,y) its phase is changed:

)],([),(),( 000 yxddkyxdnkyx ).,()1( 000 yxdkndnk

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Model – propagation through a lensModel – propagation through a lens

.),(

})]([{),(

20

222

2/12220

22

Ryxdyxd

Ryx

yxRRdyxd

fyxkconstyx

nRf

2)( 22

0.),(

),1/(

Transmitivity of a lens is equal to:

.2)22(0

),( fyxik

eeE

Et yxi

incident

dtransmitteL

In the model the transmitivity of a lens is present with n x n matrix.

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Model – thermally induced laser rod Model – thermally induced laser rod lensinglensing• The heat produced by a flashlamp is absorbed inside the laser rod with a cylindrical shape. The radial temperature distribution in a cylinder with thermal conductivity D can be obtained from the heat conduction equation.

dTdn

DQ

rTrTrn

rrrTrT

)]0()([)(

),()()( 22040

.24 rdTdn

DQ

lrnnkr )]([)( 00

• The transmitivity factor of the rod introduced by the heating is

,2)22(

rodfyxik

ethr

dTdnQ

Krodf 12

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Model – effect of a mirrorModel – effect of a mirror

1. Back resonator mirror

%100Ronly the phase of the EM field plane is modified:

.)22(0

rbyxik

erM

2. Front resonator mirror

* Reflected part of the EM field

* Transmitted part of the EM field:

%100R

.

,)22(0

incidentreflected

reflected

ARA

er fryxik

.1

,2)22(0

incidentdtransmitte

dtransmitte

ARA

et frontfyxik

Reflectance R, r, and t – factors are present in the model with n x n matrices.

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Model – QS element, gainModel – QS element, gain

QS element is approximated with a nearly step function.

n population inversion density photon flux density2ruby

)( min

' Rtll

t

tn

cn

nc

Laser flux density addition represents gain mechanism. QS technique:

• The initial population inversion density is the simulation input parameter.

• Spontaneous emission is the origin of the lasing process.

.

,

),1(||

'

'

'

0

/

rodcl

iu

tiui

t

nn

ena

2/,2/12/,2/

2/,12/12/,12/

nnnn

nnnn

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Model – simulation courseModel – simulation course

• At each resonator plane the photon flux matrix is modified.

• At each roundtrip time part of the photon flux is transmitted through the outcoupling mirror. The pulse intensity is a sum of all individual contributions.

Ft

2/,2/12/,2/

2/,12/12/,12/

nnnn

nnnn

dxdyyxI

dxdyxyxI

xr),(

),( 2

2effective radius ,3,2,1

,

,0

0

)(

)(

j

tjt

t

Fj

tI

ttI

j j

j Fj

effective pulse width

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Simulations – ruby laserSimulations – ruby laser• Ruby laser system is planed to become a new product of Fotona.

• We constructed a test QS ruby laser with a stable cavity in order to estimate some model parameters. We estimated and begin simulations.

• After many simulations we chose a cavity and a mirror, for which the simulation gave the present NF intensity profile

mfrod 12

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Simulations – ruby laserSimulations – ruby laser

and the pulse shape:

We ordered the optics and waited ...

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Simulations – ruby laser Simulations – ruby laser

• Finally we mounted the supergaussian mirror in the resonator.

•It turned out that the lensing parameter of the rod was wrongly estimated. With the help of the model we found that instead of

mfrod 40 .12mfrod

mfrod 40 mfrod 20mfrod 30

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Simulations – ruby laserSimulations – ruby laser

• We tested our system with higher repetition rate pulses. During the initial tests an optical damage in the laser rod occured.

Qfrod /1

• The simulation predicted spiking behaviour at .20mfrod

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ConclusionConclusion

• We have present a laser model for a Q – switched solid state laser

• The model is used in the development of a new Fotona laser planned to be used in the tatoo removal application.

• We have compared simulations and experiment and have seen a good agreement.

• All obtained results will be considered in the next development iteration.