Numerical simulation and optimization of Q-switched 2 μm Tm,Ho:YLF laser Oleg A. Louchev1 and Yoshiharu Urata1. and Satoshi Wada2 1.
Megaopto Co. Ltd., RIKEN Cooperation Center W414, 2-1 Hirosawa, Wako, Saitama 351-0106, Japan 2. RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
[email protected]
Abstract: Numerical simulation suggests that for obtaining a giant (G) pulse from a 2.06 μm solid state Tm,Ho:YLF laser by the active Qswitching technique, the optimal Ho concentration will be higher than that used in normal operation. In simulations of 500 ns G-pulse generation maximal efficiency occurred at 6 % Tm and 1.0 % Ho, in contrast with 0.4% Ho found to be optimal for the normal pulse generation. Maximal energy output from Tm,Ho:YLF lasers can be achieved by incorporating a delay of about 0.7 ms between 0.5 ms 780 nm LD pulsed pumping and the start of Q-switched G-pulse operation. © 2007 Optical Society of America OCIS codes: (140.3480) Lasers, diode-pumped; (140.3540) Lasers, Q-switched; (140.3580) Lasers, solid-state.
References and links 1. J. K. Tyminski, D. M. Franich, and M. Kokta, “Gain dynamics of Tm,Ho:YAG pumped in near infrared,” J. Appl. Phys. 65, 3181-3188 (1989). 2. V. A. French, R. R. Petrin, R. C. Powell, and M. Kokta, “Energy-transfer processes in Y3Al5O12:Tm,Ho,” Phys. Rev. B 46, 8018-8026 (1992). 3. R. R. Petrin, M. G. Jani, R. C. Powell, and M. Kokta, “Spectral dynamics of laser-pumped Y3Al5O12:Tm,Ho lasers,” Opt. Mater. 1, 111-124 (1992). 4. M. G. Jani, R. J. Reeves, R. C. Powell, G. J. Quarles and L. Esterovitz, “Alexandrite-laser excitation of a Tm:Ho:Y3Al5O12 laser,” J. Opt. Soc. Am. B 8, 741-746 (1991). 5. M. G. Jani, F. L. Naranjo, N. P. Barnes, K. E. Murray, and G. E. Lockard, “Diode-pumped long-pulse-length Ho:Tm:YLiF4 laser at 10 Hz,” Opt. Lett. 20, 872-874 (1995). 6. J. Yu, U. N. Singh, P. Barnes and M. Petros, “125-mJ diode-pumped-injection-seeded HoTmYLF laser,” Opt. Lett. 23, 780-782 (1998). 7. A. N. Alpat'ev, V. A. Smirnov, and I. A. Shcherbakov, “Relaxation oscillations of the radiation from a 2- m holmium laser with a Cr,Tm,Ho:YSGG crystal,” Quantum Electron. 28, 143-146 (1998). 8. N. Alpat'ev, V. A. Smirnov, and I. A. Shcherbakov, “Model of an active medium based on YSGG Cr,Tm,Ho crystal,” Kvantovaya Elektron. 20, 1105-1110 (1993). 9. N. P. Barnes, E. D. Filer, C. A. Morison, and C. J. Lee, “Ho:Tm Lasers: Theoretical,” IEEE J. Quantum Electron. 32, 92-103 (1996). 10. C. J. Lee, G. Han, and N. P. Barnes, “Ho:Tm Lasers: Experiments,” IEEE J. Quantum Electron. 32, 104 111 (1996). 11. G. Rustad and K. Stenersen, “Modeling of laser-pumped Tm and Ho lasers accounting for upconversion and ground-state depletion,” IEEE J. Quantum Electron. 32, 1645 -1656 (1996). 12. D. Bruneau, S. Delmonte, and J. Pelon, “Modeling of Tm, Ho: YAG and Tm, Ho: YLF 2-μm lasers and calculation of extractable energies,” Appl. Opt. 37, 8406-8419 (1998). 13. G. L. Bourdet and G. Lescroart, “Theoretical modeling and design of a Tm, Ho: YLiF4 microchip laser,” Appl. Opt. 38, 3275-3281 (1999). 14. S. D. Jackson and T. A. King, “CW operation of a 1.064-μm pumped Tm-Ho-doped silica fiber laser,” IEEE J. Quantum Electron. 34, 1578-1587 (1998). 15. V. Sudesh and K. Asai, Spectroscopic and diode-pumped-laser properties of Tm,Ho:YLF; Tm,Ho:LuLF; and Tm,Ho:LuAG crystals: a comparative study,” J. Opt. Soc. Am. B 20, 1829-1837 (2003). 16. A. Sato, K. Asai and K. Mizutani, “Lasing characteristics and optimizations of diode-side-pumped Tm,Ho:GdVO4 laser,” Opt. Lett. 29, 836 –838 (2004). 17. B. M. Walsh, N. P. Barnes, M. Petros, J. Yu and U. N. Singh, “Spectroscopy and modeling of solid state lanthanide lasers: application to trivalent Tm3+ and Ho3+ in YLiF4 and LuLiF4,” J. Appl. Phys. 95, 32553271 (2004).
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18. G. Galzerano, E. Sani, A. Toncelli, G. Della Valle, S. Taccheo, M. Tonelli, and P. Laporta, “Widely tunable continuous-wave diode-pumped 2-µ m Tm-Ho:KYF4 laser,” Opt. Lett. 29, 715-717 (2004). 19. J. Izawa, H. Nakajima, H. Hara, and Y. Arimoto, “Comparison of lasing performance of Tm,Ho:YLF lasers by use of single and double cavities,” Appl. Opt. 39, 2418-2421 (2000). 20. J. Yu, B. C. Trieu, E. A. Modlin, U. N. Singh, M. J. Kavaya, S. Chen, Y. Bai, P. J. Petzar, and M. Petros, “1 J/pulse Q-switched 2 μm solid-state laser,” Opt. Lett. 31, 462-464 (2006). 21. X. Zhang, Y. Ju and Y. Wang, “Theoretical and experimental investigation of actively Q-switched Tm,Ho:YLF lasers,” Opt. Express 14, 7745-7750 (2006). 22. P. Černý and D. Burns, “Modeling and experimental investigation of a diode-pumped Tm:YAlO3 laser with a- and b- cut crystal orientations,” IEEE J. Sel. Top. Quantum Electron. 11, 674-681 (2005). 23. V. P. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am. B 5, 1412-1423 (1988).
1. Introduction The development of solid state 2 μm Tm, Ho lasers has remained a topic of particular interest for many years, due to a number of possible applications such as coherent laser radar, atmospheric sensing, a possible pump source for an optical parametric oscillator operating in the mid-infrared region, and medicine. In recent years significant progress in understanding the basic phenomena underlying Tm,Ho laser operation as well as in developing high power lasers has been achieved [1-21]. Nevertheless significant effort is still necessary for defining optimized parameters and achieving high lasing efficiency. In this communication we focus on computational simulation and optimization of a side pumped Tm,Ho:YLF laser for producing MW-power giant pulses with durations of several hundred nanoseconds. The results obtained suggest that the operation of such a laser can be significantly enhanced by (i) Ho doping optimization and (ii) adjustment of pumping pulse duration and Q-switch opening time. 2. Pulse generation model Our study is based on 8-level (see Fig. 1 for excited level scheme) rate dynamics model describing the population dynamics in Tm,Ho lasers by the following set of equations [17]: dn1 n = − R p (t , z, r ) + 2 + p 28 n2 n8 − p 71n7 n1 − p 41n 4 n1 + p 22 n 22 , dt τ2 + p 27 n 2 n7 − p51 n5 n1 − p61 n6 n1 + p 38 n3 n8 dn2 n n = − 2 + 3 − p 28 n 2 n8 + p 71n7 n1 + 2 p 41n4 n1 − 2 p 22 n22 , dt τ2 τ3 − p 27 n2 n7 + p51n5 n1 dn3 n n = − 3 + 4 + p61n6 n1 − p38 n3 n8 , τ3 τ4 dt dn4 n = R p (t , z , r ) − 4 − p41n4 n1 + p 22 n22 , τ4 dt dn5 n = − 5 + p 27 n7 n2 − p51n5 n1 , τ5 dt dn6 n n = − 6 + 5 − p61n6 n1 + p38 n8 n3 . τ6 τ5 dt
(1)
(2)
(3) (4) (5) (6)
For the upper laser state (5I7): dn7 n n cσ = − 7 + 6 + p28n2 n8 − p71n7 n1 − p27n2 n7 + p51n5n1 − se ( f 7 n7 − f8n8 )φ (t , r) . dt η τ7 τ6
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For the lower laser state (5I8): dn8 n7 cσ = − p28n2 n8 + p71n7 n1 + p61n6n1 − p38n3n8 + se ( f7 n7 − f8n8 )φ (t , r) , η dt τ 7
(8)
where ni are the state concentrations, pij are the probabilities of the optical transitions, τi are the state lifetimes, Rp(t,r,z) is the pumping source space and time distribution, σse is the stimulated emission cross-section, fi are the Boltzman level populations factors and φ (t , r ) is the local laser photon density with dimensionality of 1/m3. The local laser photon density is represented via the product of (i) the total number of photons depending on t and (ii) the normalized space distribution function as φ (t , r ) = Φ 0 (t )φ 0 (r , z ) . The resulting equation for total photon number, Φ 0 (t ) , inside the oscillator cavity is given by the differential equation [11,17, 22, 23]: dΦ 0 (t ) Φ 0 (t )cσ se = dt η
∫∫ ( f 7 n7
− f 8 n8 )φ 0 (r , z )dV −
Φ 0 (t )
τc
Vcr
+
ε τ7
∫∫ n7 dV
,
(9)
Vcr
which includes the integrals of the stimulated and spontaneous emissions over the crystal volume, Vcr, and where τc is the cavity time, and ε≈10-7-10-8 is the coefficient which takes into account the proportion of photons spontaneously emitted within the solid angle of resonator mirrors, thereby initiating the development of the laser beam. 3
4 P41
P22
H4
τ4
3
3 P38
P61
P28 P71 P41
P22
5
F4
5
H6
τ6
P61
7
I7
τ7
P28 P71
5
τ5
6
I6 P38
τ2 3
Tm
P27 P51
τ3
P27 P51
1
5
I5
H5
3
2
5
8
I8
3+
Ho
3+
Fig. 1. Energy transfer processes in Tm, Ho doped materials.
For the operating resonator the cavity time is given by:
τ c−1 =
c [− ln R1 − ln(1 − Tout )] , 2 Lopt
(10)
and for the locked resonator by:
τ c−1 =
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]
c − ln R1 − ln(1 − Tout ) + α qs l qs , 2 Lopt
(11)
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where Lopt = Lcav + (η − 1) Lcr is the characteristic optical length, Lcav is the cavity length and Lcr is the crystal length; R1=0.98 is the back mirror reflectance and Tout is the output mirror transmittance, αqslqs=102-103 is the absorption loss inside the locked Q-switch device. For the case of ≈500 ns pulse generation the cavity length Lcav >> Lcr and the laser beam radius inside the crystal may be considered to be constant. The spatial distribution of photons inside the operating crystal is simplified as:
φ (r , z ) =
⎛ − 2r 2 ⎞ 2 ⎟, ⎜ exp ⎜ w2 ⎟ πw 02 L cav 0 ⎠ ⎝
(12)
where w0 is the beam waist radius of TEM00 mode defined by the resonator parameters ( for instance, for the simplest case of the confocal spherical resonator one has w0 = Lcav λl 2π ). The solution of the rates equation together with main oscillator equation gives the value of the output energy fluence, (W), as: chν las 1 , (13) J (t ) = Φ 0 (t )
2 Lopt
ln
1 − Tout
2
and its radial distribution (W/m ) at the output mirror as: I 0 (t , r ) = Φ 0 (t )
⎛ − r 2 ⎞⎟ , chν las 1 1 × ln exp⎜ 2 2 * ⎜ 2 Lopt 1 − Tout 2πw0 2w0* ⎟⎠ ⎝
(14)
*
where the increased beam radius outside of the resonator, w0 , is taken into account. We consider Tm,Ho:YLF operation side pumped by 780 nm LD radiation. For 6 % Tm doped YLF one finds for the absorption coefficient α=σaNTm≈2.8 cm-1. Thus, a 2 mm diameter YLF crystal is able to absorb (1-exp(-2αd))≈0.67-fraction of the incident beam flux in the case of the double-pass pumping scheme providing high uniformity of the absorbed flux over the crystal volume. High incident fluxes are able, in fact, to deplete the 3H6-level in Tm3+ and to inhibit absorption [11, 22]. However, in the present study the concentration of the 3H6-level does not fall below 0.9 of the initial Tm-concentration, the related variations of absorption coefficient do not exceed 5 %, and in our simulation we use for Rp: ηηQ , (15) R p (t ) ≈ 2 p a p πd Lcr hν p Δt p where η a = ρ [1 − exp(−2αd )] is the absorption efficiency of the pumping radiation, ρ is the reflection loss of pumping radiation, Qp is the pumping pulse energy, Δtp is the pumping pulse duration, ηp≈1.3 is the pumping quantum efficiency for Tm,Ho:YLF. 3. Results and discussion Model parameters used for Tm,Ho:YLF in the simulations are fully specified in Ref. [17]. Other parameters used in the simulations reported below are: crystal length Lcr=2 cm, crystal diameter d=2 mm, cavity length Lcav=1 m, output transmittance T=0.05, reflectance R1=0.98, and beam waist radius w0=0.85 mm. The simulations reveal two main effects important for efficiency optimization in developing a laser for producing nanosecond G-pulses. Figure 2 shows a simulation results for 6 % Tm doping and two values of Ho doping, 0.4 and 1.0 %, for the case of normal pulse operation (without Q-switch) demonstrating a series of relaxation oscillations. The pumping (780 nm laser diode) time for both modes is 0.5 ms and the total absorbed energy η a Q p =1.8 J. Figure 2(a) shows the power oscillations for the cases of Ho = 0.4 and 1.0 % respectively, whereas Fig. 2(b) shows the output pulse energies
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versus time. The final pulse energy for the 0.4 % Ho case (≈0.9 J), is calculated to be higher than that of 1.0 % Ho case (≈0.8 J). However, Fig. 2(a) shows that the power of the first relaxation spike is higher for the case of 1.0 % Ho. Thus in G-pulse generation the 1.0 % Ho case is able to yield a higher output energy per pulse as compared with the 0.4 % Ho case. Figure 3 shows calculations of (a) G-pulse powers and (b) energies versus time for 0.4 % and 1.0 % Ho cases. The calculations assume Q-switch operation open by the end of the 0.5 ms pumping period. This figure shows that 1.0 % Ho doping can provide higher energy output per pulse as compared with 0.4 % Ho doping due to significantly larger level of the inverted population achieved after the pumping (See Fig. 4). Figure 5 compares the resulting pulse energy for the normal pulse and for the G-pulse as a function of Ho-concentration for the given 6 % Tm doping. These figures confirm that for the normal pulse 0.4 % Ho doping provides the highest output energy whereas for G-pulse 1.0-1.2 % looks to be optimal. 1.2
(a)
(b)
1.0
5000 pulse energy (J)
pulse power (W)
6000
4000 3000 6 % Tm, 0.4 % Ho 6 % Tm, 1.0 % Ho
2000 1000
0.8 0.6 0.4 6 % Tm, 0.4 % Ho 6 % Tm, 1.0 % Ho
0.2
0 0.0
0.5
1.0 time (s)
1.5
0.0 0.0
-3
2.0x10
0.5
1.0 time (s)
1.5
2.0x10
-3
Fig. 2. Pulse generation in normal mode: (a) pulse power versus time and (b) pulse energy versus time for two Tm, Ho concentrations.
6
1.0x10
0.16
0.8 0.6 0.4
G-pulse energy (J)
G-pulse power (W)
(a)
6 % Tm, 0.4 % Ho 6 % Tm, 1.0 % Ho
0.2 0.0 500.0 500.2 500.4 500.6 time (s)
-6
501.0x10
6 % Tm, 0.4 % Ho 6 % Tm, 1.0 % Ho
(b)
0.12 0.08 0.04 0.00 500.0 500.2 500.4 500.6 time (s)
-6
501.0x10
Fig. 3. G-pulse generation: (a) pulse power versus time and (b) pulse energy versus time.
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24
6x10
Δn (m
-3
)
4 2 0
6 % Tm, 0.4 % Ho 6 % Tm, 1.0 % Ho
-2 0
1
2
3 time (s)
4
-3
5x10
Fig. 4. Inversion population dynamics in G-pulse generation mode.
pulse energy (J)
1.0
normal pulse G - pulse
0.8 0.6 0.4 0.2 0.0 0.5
1.0
1.5 Ho (% at.)
2.0
2.5
Fig. 5. Comparison of output pulse energy in normal (solid) and G-pulse (dashed) mode.
Let us now focus on the time optimization of G-pulse operation. The above results on Gpulse generation assumed 0.5 ms pumping followed by immediate Q-switch opening. However, Fig. 4 suggests that such Q-switch opening is premature because the inverted population density does not achieve its maximum at the end of pumping. Now we provide more details to emphasize the importance of proper time control. In particular, Fig. 6(a) shows the dependence of G-pulse power as function of the time for three characteristic cases: (i) 0.5 ms pumping followed by Q-switch opening (green), giving a pulse energy of ≈0.08 J, (ii) 1.9 ms pumping followed by Q-switch opening (blue) giving a pulse energy of ≈0.11 J and (iii) 0.5 ms pumping followed by Q-switch opening at 1.2 ms (red) giving a pulse energy of ≈0.12 J. Figure 6(b) shows the behavior of Δn for all three cases considered and provides the background information for understanding time optimization issues. That is, in the first case the Q-switch is open prior to the moment when maximal population inversion in the Ho3+ is achieved and the resulting output G-pulse energy is small. After the pulse is finished and the Q-switch is closed, the excited Tm3+ state 3F4 continues to transfer excitation towards the Ho3+ 5I8. In this case a very significant part of the excitation “stored” initially in Tm3+ is transfered to Ho3+ after the G-pulse generation, and later on uselessly dissipated through spontaneous radiation and non-radiative transitions. In the second case of the significantly increased pumping time 1.9 ms with simultaneous opening of Q-switch a significantly higher generated pulse energy is achieved, 0.042 J, due to significantly higher electronic excitation energy stored on the Ho3+5I7 state by the end of the pumping pulse. The third case corresponds to the situation when a relatively short pumping time of 0.5 ms is used together with 0.7 ms delay in opening the Q-switch. This case gives maximal energy output of ≈0.12 J in G-pulse generation because the Q-switch opens exactly at the moment when the concentration on the lasing Ho3+5I7 state and the value of Δn reach their maximum, allowing maximal energy extraction by the laser pulse. #78561 - $15.00 USD
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3
24
5x10
(a)
(b) 4
)
600 -3
3
Δn (m
G-pulse power (W)
800x10
400
2 1
200
0
0 0
1
2 time (ms)
3
4x10
-1
-3
0
1
2 time (s)
-3
3
4x10
Fig. 6. Optimization of G-pulse generation: (a) G-pulse powers versus time and (b) corresponding population inversion densities versus time for three different scenarios.
0.25
(a)
0.20 0.15 0.10 0.05
6 % Tm, 0.4 % Ho 6 % Tm, 1.0 % Ho
0.00 2 4 6 8 10 pumping and Q-switch opening time (ms)
G-pulse energy (J)
G-pulse energy (J)
0.25
(b)
0.20 0.15 0.10 0.05 0.00 0.5
6 % Tm, 0.4 % Ho 6 % Tm, 1.0 % Ho 1.0 1.5 2.0 2.5 3.0 3.5 Q-switch opening time (ms)
4.0
Fig. 7. Optimization of operation times: (a) Q-switch is open by the end of pumping and (b) pumping time is 0.5 ms and Q-switch is open after a delay.
Figure 7 shows final results on G-pulse energy optimization: (a) for the case of extended LD pumping within the range 0.5 - 10 ms followed by immediate Q-switch opening and (b) 0.5 ms LD pumping with delayed Q-switch opening. Energy maxima exist in both cases: at ≈1.9 ms for (a) and at ≈1.2 ms for (b). However, case (b) provides the higher absolute maximum. It is worth noting that the delay between the pumping period and Q-switch opening shown above to optimize the energy pulse is associated with the characteristic time of the electronic transfer from the upper exited state 3H4 to 3F4 and, later on, towards 5I7. Our simulation based on the above model shows that the excitation transfer from the 3F4 state towards the 5I7 state happens without any significant deceleration whereas significant delay is associated with the 3 H4 → 3F4 radiation transfer process, i.e. the rise in concentration at the Tm3+3H4 state, defined by the pumping period used, and the depletion of this level, defined by the twophoton process p41n4n1 and requiring ≈0.7 ms. In the case of extended pumping of several ms this delay does not play a very significant role, in contrast with short pumping times. The decrease in the delivered G-pulse energy shown in both cases for long times is associated with the increasing role of spontaneous radiation loss from both 3F4 and5I7 states which have characteristic lifetimes of 16 and 15 ms respectively. To finalize the discussion we would like to note that a ≈0.7 ms delay between pumping and achieving the maximal population inversion density in a Tm,Ho:YLF laser found in this study is experimentally supported by the observation of the amplification signal in a Tm,Ho:YLF crystal pumped by a 780 nm radiation pulse of 65 μs duration [12]. Data recorded for the YLF case shows the amplification signal maximum at 0.6-0.7 ms after the #78561 - $15.00 USD
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start of the pumping. However, the data for Tm,Ho:YAG operation does not show any significant delay between pumping period and maximal amplification signal. 4. Conclusions This study, based on an 8-level rate equation model, shows two effects significant for giant pulse Tm,Ho:YLF laser optimization. The first one is associated with Ho doping. That is, in generating a G-pulse 1.0 % Ho concentration should provide a higher energy output as compared with normal pulse operation for which 0.4 % Ho concentration is confirmed to yield the highest energy output. The second effect is associated with the optimal time for opening the Q-switch. It is found that a delay of ≈0.7 ms between the 0.5 ms 780 nm LD pumping pulse and opening the Q-switch is able to provide a significant increase in the generated G-pulse energy. This is due to a ≈0.7 ms delay in the energy transfer from the initially excited Tm3+ ions to the upper lasing level of Ho3+ ions. This effect is captured by the 8-level rate equation model, which takes into account the possible deceleration of the electronic excitation transfer from the Tm3+ ions excited by the 780 nm pulse to the Tm3+3F4 state, and later on, towards the lasing Ho3+5I7 state. Acknowledgments This work is supported by the National Institute of Information and Communications Technology (Japan).
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