Simulation of Kerr Lens Behavior in a Ti:Sapphire Oscillator with Symmetric and Asymmetric Resenator

Transcription

1 *1 () (94/1/05 : 94/05/14 :) : Abstract Simulation of Kerr Lens Behavior in a Ti:Sapphire Oscillator with Symmetric and Asymmetric Resenator A. Malakzadeh*, M. J. Kamjoo, S. R. Zare Kalate Imam Hossein University (Received: 05/08/015, Accepted: 4/0/016) Femtosecond pulse lasers are one of the most widely used lasers. Femtosecond oscillator is first step to generate powerful femtosecond pulses. In this work, the laser beam propagation in an oscillator in symmetric and asymmetric designs without Kerr lens effect inside a Ti:Sa medium was simulated and the cavity stable operation conditions have been obtained. Then, Kerr lens modelocking behavior is simulated and the situation compensating the beam astigmatism is achieved. Split-step method has been used to obtain the beam intensity change in the Ti:Sa rod and shooting method has been utilized to calculate the beam spot size on the first cavity mirror. Assuming no Kerr lens effect, influence of the cavity length changes in laser beam characteristics is investigated and considering the Kerr lens effect in the laser rod, influence of the rod position in the beam characteristics and beam propagation is simulated. Finally, by considering the simulations results, conditions to achieve soft or hard aperture modelocking are discussed. Keywords: Femtosecond, Oscillator, Kerr Lens Effect, Astigmatism, Modelocking, Soft Aperture Modelocking, Hard Aperture Modelocking. * Corresponding Author afard77@googl .com Advanced Defence Sci.& Tech., 016, 6,

2 [1] [11,10] [13] [16] [15 14] [17]..[18]. 5].[19- ABCD [4 3] :.. [ 1].[3] 1.. [4-8]..1.[10 9] 3 Split-Step 4 Shooting 1 Profile Kerr lens modelocking (KLM)

3 ABCD : Mtt (1) ABCD..[7] AtDt l3=l k +l B +l3 k. 1/Ct 1/Ct [8] ) TEM 00. :[7] q(z) ( W(z) z R(z). L z d(z)= q(z). z 1.[9] Z=0 M1 q R(0)= : (1) ( ) (3)) : z z (4) 1.. (1)...[5].[6] ABCD.1.1- () ABCD.. * ri z)..( (5) ABCD..o i. 1 Sagittal Tangential

4 ( 6). m :. (7) ).( ( R fs=r/cos) (f=r/) (ft=rcos/). L ( B lb ). (1). ABCD : ( ) (8) fs=ft. (). ( l B ).1 ABCD. (W(z))..

5 (9). (1)..3-..[] M 3 M (L 1 =L 34 4).3.(p=0) (). (l 3 /). () (). : (15) : (16) (10) n E0L 0. n Lc00 0 IL E0L. c 0 n n. nlc00 : (TEM 00 ) (14) w w w w w n w. n n s I I0LL 0L s L : w (11).[30] ( 1) n IL n Lc 00 ( 13) t L 0L L w w t I n

6 (L 1 =3L 34 ).(p=0). (). () (). 4. d d(z)= [Ln()] 1/ w(z)...4 C t. : (17) (188 ) ) ( cm cm 800nm (cm) () () 1.7 Ti:Sapphire 800nm ) ni L. n BnL nlc00 ABCDA. (1) LB.3 (lk) () Ti:Sapphire (FWHM)( di. Z min d min Ct. 1/.1-3 ( n). 1.(54 3

7 L =44.5mm.7 (d min ) ( ) (W 01 ).(17 ) W 01.. W 01 l k I.5 : 17 W(z) (L 1 =L 34 ).P=*10 5 W (19)..6 : L =49 mm z(m).8.(5) (0) : ( 1)

8 (W) (7).. L = 44,5mm (8).. 49 mmm (9)... L k > Z min L k < Z min -L B. ( ) Z min =z+ll B +L :..... L (6) z....(i) l k.10 ( 5) ) z z min. ( L k = Z mi in-l B ).[11] (L k = Z m min L.9.(5)

9 (dmin) - -1 ).[31 19,5] ( 14. L k < Zmin-L B L k > Z min. (t=s/nl)( s t -. ).[31]( L k = Z m min-l B / ).( ) P= =*10-5W.( L L k L 3.(1 11 )..( (II ) l k.1 5 (17). II ( L 3min + L 3 L k (1 ) M 4 -. =Z m 3max/ L 3) min-l B L 3 /-L d min L B. l k k.11.(i) 5

10 ( -17)) ((4) ) ) I M 4 M 3.((15) ) L k = Z min. P= 10-5 W.(I ) l k (L 1 =L 34 ).14. ()..(II ) l k.13 (5)..(I ) l k L 3 =106.6m.15 mm (14) II (16). L k Z Z min M3 d min.( -17)

11 ABCD....(II I ). ( t = s /n L )... L k > Z m min L k < Z min -L B Z min.. II L 3min + L 3 ) ) M 4 (L 3max / L k = Z min -L B L 3 /-L B (11. d min.( -17) (4 ) M 4 M 3 I L k k=z min II.( 15 )..16.(II ) l k (14) () ( ) ).17 d- ().n L =1.76 n p =1.77 z 0 =mm d min =d- () d min =(1/)d minp = = () min =d= minp. minp =

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