Numerical Analysis of a Q-switched Er:YAG Laser to Determine the Operational Parameter Effect of a Pockels Cell
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1 New Physics: Sae Mulli, Vol. 64, No. 2, February 2014, pp DOI: /NPSM Numerical Analysis of a Q-switched Er:YAG Laser to Determine the Operational Parameter Effect of a Pockels Cell Sang Ho Lee Department of Liberal Arts & Teacher Training, Kumoh National Institute of Technology, Gumi , Korea Han Tae Choo Gyu Ug Kim Department of Optical Engineering, Kumoh National Institute of Technology, Gumi , Korea (Received 13 December 2013 : revised 5 January 2014 : accepted 12 February 2014) We have numerically analyzed the rate equations to investigate the effect of the operational parameters of a LiNbO 3 Pockels cell on the pulse energy and the pulse width of a Q-switched Er:YAG laser. We have calculated the output energy to be 10.6 mj when the reflectivity of the output coupler is 90% and the shape factor of Pockels cell voltage is 17. The maximum output energy is obtained when the delay time between the flashlamp and the Pockels cell is 395 µs, which is in good agreement with the previous experimental result [30]. PACS numbers: Gd, Tp Keywords: Er:YAG laser, Q-switching, Numerical calculation, Pockels cell Er:YAG Q-switching, כ, ( , , ) LiNbO 3 Q-switching Er:YAG. 90% mj. 395 µs. [30]. PACS numbers: Gd, Tp Keywords: Er:YAG, Q-switching,, gukim@kumoh.ac.kr 217 This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
2 218 New Physics: Sae Mulli, Vol. 64, No. 2, February 2014 I., 3 µm. CO 2 Er:YAG Er:YAG [1,2] µm Er:YAG µm Er:YAG [3 5]. Er:YAG 200 µs. [6,7]. Q-switching. Q-switching [8], InAs [9], GaAs [10] Cr 2+ :ZnSe [11], U 2+ :SrF2 [12], Co 2+ :MgAl 2 O 4 [13], Co 2+ :ZnSe [14], Fe 2+ :ZnSe [15]. Q-switching [16 21], FTIR (Frustrated Total Internal Reflection) [22], [23], [24], PLZT (Lead- Lanthanum Zirconate Titanate) [25]. Er:YAG Q- switching LiNbO 3. Salvestrini [26] LiNbO 3 Q-switching Q-switching. Georgescu [27] FTIR Er:YAG Q-switching Q- switching. Q-switch [28]. LiNbO 3 Er:YAG Q-switching [29 31]. Q-switching Er:YAG.. Fig. 1. (Color online) Diagram for the energy levels of Er 3+ ion. The transitions show the up-conversion for (a) and (b); the cross-relaxation for (c). II. Er:YAG Q-switching Figure 1 Er:YAG Er 3+ כ, 4 I 11/2 4 I 13/ µm. Er:YAG Fig. 1 (a) 4 I 13/2 4 I 9/2 (upconversion, 4 I 13/2 4 I 9/2 ), (b) 4 I 11/2 4 I 7/2 (up-conversion, 4 I 11/2 4 I 7/2 ) (c) 4 I 15/2 4 I 13/2 4 I 7/2 4 I 9/2 (cross-relaxation) [32]. (a) (b) ω 1 ω 2., כ כ.,,, [31,32]. dn 1 dt dn 2 dt = n 1 T 1 + n 2 T 2 2ω 1 N 1 n 1 +ω 2 N 2 n 2 +σ(αn 2 βn 1 )φ+p 1 (1) = n 2 T 2 + ω 1 N 1 n 1 ω 2 N 2 n 2 σ(αn 2 βn 1 )φ + P 2 (2)
3 Numerical Analysis of a Q-switched Er:YAG Laser to Determine the Operational Sang Ho Lee et al. 219 Table 1. Parameters for the rate equation of the Q- switched Er:YAG laser [27]. Parameter Value Unit ω cm 3 /s ω cm 3 /s T µs T µs σ cm 2 κ α β dφ dt = νφ[σ(αn 2 βn 1 ) Ω] + κ n 2 T 2 (3) N 1 ( 4 I 13/2 ), N 2 ( 4 I 11/2 ). n 1 = N 1 /N 0, n 2 = N 2 /N 0, N 0 4 I 15/2. T 1 T 2 4 I 13/2 4 I 11/2 (fluorescent lifetime). α β 4 I 11/2 4 I 13/2 (Stark sublevel), σ, κ, φ. υ = cl P /(L + (n 1)L a ), L a, L p, L,,. P 1 Fig. 1 4 I 15/2 1 5 כ, P 2 4 I 15/2 2, 3, 4, 5 כ. Ω [27]. Ω = ln(r 1R 2 T 2 Q ) 2L + Ω 0 (4) R 1, R 2, L, Ω 0. T Q LiNbO 3 [27]. T Q (t) = T low Q +(T low Q (T high Q ) [(cos(2π (t t))) m 1] τ Q (5) TQ low high, TQ, t, τ Q, m כ (shape factor) (6). T Q (t) V (t) [27,33]. V (t) = 4 π V λ/4 sin 1 ( ) T Q (t) TQ low (6) V λ/4 λ/4. Q- switching [27]. (5) m כ (6), כ Q-switching. (1) (3) 4 Runge-Kutta Matlab. Q-switching. E pulse = hνcaln(1/r 2) φ(t)dt (7) 1 + (n 1)(L/L c ) hν, R 2, n, L, A,,, L c. (FWHM). τ pulse = 1 φ(t)dt (8) φ max φ max כ. III. Er:YAG Q-switching [31]. Crytur LM71R, 2.94 µm 98% LiNbO 3, 7 8 mm 2, 26 mm, (Brewster angle). ( ) כ, 1.4 kv 3.2 kv.
4 220 New Physics: Sae Mulli, Vol. 64, No. 2, February 2014 Fig. 2. (Color online) Electrical signals of Q-switched laser pulse and applied voltage to the Pockels cell. Figure 2 LiNbO 3 Q-switching Er:YAG כ [30]. 0 V Q-switching. 1.5 kv, 4 µs, 50 ns, 50 µs. Fig ns 140 ns Q-switching.,. Q-switching. Figure 3 (5) (6) m כ Q-switching (1) (3). Fig. 3 Fig. 2. m כ ns Q-switching כ. m כ Fig kv. Fig. 3 כ m כ, Q-switching כ Q-switching כ. Fig. 3. (Color online) Calculated Pockels cell voltage and Q-switched laser pulse for various values of shape factor m. Figure 4 m כ Q-switching. Fig. 4 (a), (b), (c) 90%, 85%, 80%. (d), (e), (f) 90%, 85%, 80%. Fig. 4 m כ. Fig. 3 כ m כ. כ., כ Q-switching כ. Q-switching [31]. Fig. 5 Q-switching כ, m 17. Fig. 5 (a) (b), (c) (d). Q-switching, 395 µs 10.6 mj
5 Numerical Analysis of a Q-switched Er:YAG Laser to Determine the Operational Sang Ho Lee et al. 221 Fig. 4. (Color online) Calculated pulse energy as a function of shape factor m for (a) R = 90%, (b) R = 85%, (c) R = 80% and pulse width for (d) R = 90%, (e) R = 85%, (f) R = 80%.. כ, כ., כ.., כ Q-switching כ... Fig. 5. (Color online) The pulse energy and the pulse width as a function of delay time between flashlamp and Pockels cell for a shape factor m of 17. In the figure, (a) and (d) are calculated; (b) and (c) are experimental. כ.., 395 µs 110 ns כ כ.. Fig. 5 Q-switching כ. IV. LiNbO 3 Er:YAG Q-switching REFERENCES [1] T. M. Marraccini, L. Bachmann, H. A. Wigdor, J. T. Walsh Jr and M. L. Turbino et al., Laser Phys. Lett. 3, 96 (2006). [2] T. M. Marraccini, L. Bachmann, H. A. Wigdor, A. Stabholtz and D. M. Zezell, Laser Phys. Lett. 2, 551 (2005). [3] H. Jelinkova, T. Dostalova, M. Nemec, P. Koranda and P. S. Miyagi et al., Laser Phys. Lett. 3, 43 (2006). [4] H. Jelinkova, T. Dostalova, M. Nemec, P. Koranda and P. S. Miyagi et al., Laser Phys. Lett. 1, 1 (2004). [5] J. Kampmeier, S. Schafer, G. E. Lang and G. K. Lang, J. Refractive Surgery 15, 563 (1999). [6] V. Semshichen, R. H. Funk and T. Seier, J. Refractive Surgery 16, 51 (2000). [7] R. K.Shori, A. A. Waiston, O. M. Stafsuudd, D. Fried and J. T. Walsh, IEEE J. Sel. Top. Quantum Electron. 7, 959 (2001).
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