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Transcript

COMPUTER MODELING OF LASER SYSTEMS Dejan Škrabelj Advisers: Prof. Dr. Irena Drevenšek - Olenik Dr. Marko Marinček __________________________________________ OUTLINE 1. 2. 3. 4. 5. Tatoo removal application - motivation Revision of a basic laser physics Laser model for a Q – switched solid state laser Simulations of a ruby laser system Conclusion __________________________________________ Motivation – tatoo removal application • • • 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 application • • 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. __________________________________________ Basic laser physics – laser system • 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. __________________________________________ Basic laser physics – QS 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: E ~ 1J t ~ 10ns P ~ 100MW __________________________________________ Basic laser physics – unstable resonator • 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. R R0e 2 ( wr ) ord __________________________________________ Model – introduction i ( r ,t ) E (r , t ) AE (r , t )e i ( r , t ) (r , t ) A (r , t )e | AE | | A | • 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. • 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. __________________________________________ Model – free space propagation • For the propagation a method based on the 2D FT is used. et ( s x , s y ; z ) E ( x, y , z ) e 2i ( s x x s y y ) dxdy, E ( x, y , z ) e ( s , s ; z )e t sx, y kx,y 2 x y 2i ( s x x s y y ) ds x ds y , __________________________________________ Model – free space propagation • Propagating field must obey the wave equation. 2 2 E (r ) k E (r ) 0, d 2 et ( s x , s y ; z ) dz 2 ( 2 ) 2 (1 2 s x2 2 s y2 )et ( s x , s y ; z ) 0, et ( s x , s y ; z 2 ) et ( s x , s y ; z1 )e i 2 1 2 s x2 2 s 2y d . • The EM field transveral spectrum propagation is performed by a simple multiplication with the phase factor! real space: Fourier space: d E( x, y, z1 ) FT et ( s x , s y ; z1 ) e E ( x, y, z2 ) IFT i 2 12 s x2 2 s 2y d et ( s x , s y ; z 2 ) • In the numerical calculation we cover the EM field with n x n mesh points. __________________________________________ Model – propagation through a lens • Lens is characterized with its focal length f: 1 f (n 1)( r11 r12 ) • 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: ( x, y) nk0 d ( x, y) k0 [d 0 d ( x, y)] nk0 d0 (n 1)k0 d ( x, y). __________________________________________ Model – propagation through a lens d ( x, y ) d 0 {R [ R 2 ( x 2 y 2 )]1/ 2 } x 2 y 2 R 2 d ( x, y ) d 0 x2 y2 2R . f R /( n 1), ( x, y ) const. k0 ( x 2 y 2 ) 2f Transmitivity of a lens is equal to: ik0 ( x2 y 2 ) Etransmitted tL ei ( x , y ) e 2 f . Eincident In the model the transmitivity of a lens is present with n x n matrix. __________________________________________ Model – thermally induced laser rod lensing • 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. T (r ) T (r0 ) 4QD (r02 r 2 ), dn n(r ) [T (r ) T (r 0)] dT 4QD dn dT r 2. (r ) k0 [n0 n(r )]l • The transmitivity factor of the rod introduced by the heating is thr e ik ( x2 y 2 ) 2f rod , f rod 2K 1 dn Q dT __________________________________________ Model – effect of a mirror 1. Back resonator mirror R 100% ik0 ( x2 y 2 ) only the phase of the EM field plane is modified: rM e rb . 2. Front resonator mirror R 100% * Reflected part of the EM field rreflected e ik0 ( x2 y 2 ) rf , Areflected R Aincident. * Transmitted part of the EM field: ttransmitted e ik0 ( x 2 y 2 ) 2 f fron t , Atransmitted 1 R Aincident. Reflectance R, r, and t – factors are present in the model with n x n matrices. __________________________________________ Model – QS element, gain QS element is approximated with a nearly step function. Laser flux density addition represents gain mechanism. QS technique: population inversion density photon flux density n n t cn t (cn ll' tmin ) R ruby 2 • The initial population inversion density is the simulation input parameter. • Spontaneous emission is the origin of the lasing process. | i | a niu (1 e t / ), ' niu n0 , t' l' cro d . n / 21, n / 21 n / 2, n / 21 n / 21,n / 2 n / 2,n / 2 __________________________________________ Model – simulation course n / 21, n / 21 n / 2, n / 21 • At each resonator plane the photon flux matrix n / 21,n / 2 n / 2,n / 2 is modified. • At each roundtrip time t part of the photon flux is transmitted F through the outcoupling mirror. The pulse intensity is a sum of all individual contributions. j0 I ( t j ) t F t , I ( t ) j 0 j t j j t F , effective radius I ( x , y ) x dxdy 2 rx 2 I ( x , y ) dxdy effective pulse width j 1,2,3, __________________________________________ Simulations – 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 f rod 12m and begin simulations. • After many simulations we chose a cavity and a mirror, for which the simulation gave the present NF intensity profile __________________________________________ Simulations – ruby laser and the pulse shape: We ordered the optics and waited ... __________________________________________ 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 f rod 40m instead of f rod 12m. f rod 40m f rod 30m f rod 20m __________________________________________ Simulations – ruby laser • We tested our system with higher repetition rate pulses. During the initial tests an optical damage in the laser rod occured. f rod 1 / Q • The simulation predicted spiking behaviour at f rod 20m. __________________________________________ Conclusion • 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.