Characteristics of ruby passive Q switchingwith a Dy 21:CaF2 solid-state saturable absorber

Yen-Kuang Kuo and Milton Birnbaum

Characteristics of ruby passive Q switching with a Dy21:CaF2 solid-state saturable absorber areinvestigated with output couplers of various reflectivities and saturable absorbers of different thick-n e s s e s .Numerical simulation is used to investigate the behavior of ruby passive Q switching with a Dy21:CaF2saturable absorber and to interpret the experimental results.Key words: PassiveQ switching, ruby laser, saturable absorber. r 1995 Optical Society of America

1. Introduction

Passive Q switching of solid-state lasers with solid-state saturable absorbers is currently of interest, andseveral materials have been reported to work effec-tively as saturable-absorberQ switches for solid-statelasers in the visible and the near-infrared regions1see, for example, Refs. 1–122. In previous research8Dy21:CaF2 solid-state crystal was shown to be aneffective saturable absorber Q switch for the rubylaser at 694 nm. In this paper the characteristics ofruby passive Q switching with a Dy21:CaF2 saturableabsorber are investigated with output couplers ofvarious reflectivities and saturable absorbers of differ-ent thicknesses. A numerical simulation that usesthe Runge–Kutta–Fehlberg method to solve for thesolutions of the coupled rate equations is used toinvestigate the behavior of ruby passive Q switchingwith a Dy21:CaF2 saturable absorber and to interpretthe experimental results.

2. Theory

The coupled rate equations for ruby passiveQ switch-ing with a Dy21:CaF2 saturable absorber are8,11

dn

dt5 3KgNg 2 KaNa 2 bKa1Na0 2 Na2 2 gc4n, 112

dNg

dt5 Rp 2 ggNg 2 2KgNgn, 122

The authors are with the Center for Laser Studies, University ofSouthern California, DRB 17, LosAngeles, California 90089-1112.Received 11 May 1995.0003-6935@95@306829-05$06.00@0.

r 1995 Optical Society of America.

dNa

dt5 ga1Na02 Na2 2 KaNan. 132

The parameters used in these coupled rate equa-tions are defined as follows: n is the photon numberin the laser cavity, Ng is the population inversion ofthe laser, Na is the ground-state population of thesaturable absorber, Kg and Ka are coupling coeffi-cients, b is the ratio of the excited-state absorptioncross section to the ground-state absorption crosssection of the saturable absorber, Na0 is the initialvalue of Na, gc is the cavity decay rate, Rp is thepumping rate, gg is the decay rate of the upper laserlevel, and ga is the relaxation rate of the saturableabsorber.When the light intensity inside the laser cavity is

low, almost all the population of the saturable ab-sorber is in the ground state. Hence the initial laserpopulation inversion Ng0 that is required for the laseraction to occur can be derived from Eq. 112 by settingthe right-hand side of the equation to zero andassuming thatNa < Na0:

Ng0 <KaNa0 1 gc

Kg

. 142

When the light intensity is high, most of the popula-tion of the saturable absorber is promoted to theexcited state. Therefore the threshold populationinversion after the bleaching of the saturable ab-sorber, Nth, can be determined from Eq. 112 by settingthe right-hand side of the equation to zero andassuming thatNa < 0:

Nth <bKaNa0 1 gc

Kg

. 152

20 October 1995 @ Vol. 34, No. 30 @ APPLIED OPTICS 6829

When the method in Ref. 13 is followed, the final la-ser population inversion after the release of theQ-switched laser pulse, Nf, and the peak photonnumber inside the laser cavity, np, can be expressed:

Nf 2 Ng0 2 Nth ln1 Nf

Ng02 5 0, 162

np 5 21

2 3Nth 2 Ng0 2 Nth ln1Nth

Ng024 . 172

3. Experiments

Two Dy21:CaF2crystals 18- and 15-mm-thick, polishedflat–flat and uncoated2 were used in this passiveQ-switching experiment. The unpolarized absorp-tion spectra of the crystals, measured with a VarianCary spectrophotometer at room temperature, areshown in Fig. 1. Passive Q switching of the rubylaser with Dy21:CaF2 saturable absorber was demon-strated with a 27-cm-long laser resonator consistingof a flat high reflector and a flat output coupler. Theexperimental arrangement is shown in Fig. 2. Threeoutput couplers of 89%, 84%, and 78% reflectivity at694 nm were used for the passive Q-switching perfor-mancemeasurements. The results are shown in Fig.3.A typical Q-switched ruby laser pulse of approxi-

mately 100 ns in duration 1full-width at half-maxi-mum2 and 5.7 mJ was obtained at 95-J flash-lampinput energy with a 15-mm-thick Dy21:CaF2 satu-rable absorber and a 78%-reflective output coupler.With the 84%- and 89%-reflectivity output couplers,the laser thresholds were lower by a few joules;however, the energies of the Q-switched laser pulsesbecame smaller 1Fig. 32. The pulse width of theQ-switched laser output did not vary significantlywhen the output coupler was changed from one toanother.A typical Q-switched laser pulse of approximately

150 ns and 2.6 mJ was observed with the 8-mm-thickDy21:CaF2 saturable absorber and a 78%-reflectiveoutput coupler. The use of 84%- and 89%-reflectiv-ity output couplers resulted in lower laser thresholdsand lower Q-switched ruby laser output energies, asexpected. The pulse width of the Q-switched laser

Fig. 1. Room-temperature unpolarized absorption spectra ofDy21:CaF2 crystals.

6830 APPLIED OPTICS @ Vol. 34, No. 30 @ 20 October 1995

output did not vary significantly when the outputcoupler was changed.Figure 41a2 shows the relative timing of the

Q-switched laser pulse in relation to the free-runningtemporal profile for ruby Q-switching with a 15-mm-thick Dy21:CaF2 saturable absorber and a 78%-reflective output coupler. For both free-running andQ-switching laser pulses, the front edge of theflash-lamp pump pulse was used to trigger the Tektro-nix TDS 540 digitizing oscilloscope 1sampling rate1 GHz2. The temporal profile of theQ-switched laserpulse, which was recorded with a silicon detector of1.5-ns rise time, is shown with a greatly expandedscale in Fig. 41b2. Passive Q switching of the rubylaser with the 8-mm-thick Dy21:CaF2 saturable ab-sorber had a similar behavior and pulse shape tothose shown in Fig. 4, except that the Q-switched

Fig. 2. Experimental setup for ruby passive Q switching with aDy21:CaF2 solid-state saturable absorber.

Fig. 3. Ruby laser passive Q switching with Dy21:CaF2 saturableabsorbers: 1a2 flash-lamp input energy at laser threshold as afunction of the reflectivity of the output coupler, 1b2 Q-switchedlaser output energy as a function of the reflectivity of the outputcoupler.

laser pulse had a wider pulse width of approximately150 ns.

4. Numerical Simulation

Rate equations 112–132 were numerically solved withthe Runge–Kutta–Fehlberg method to investigatethe behavior of ruby passive Q switching with aDy21:CaF2 solid-state saturable absorber. The re-sults are shown in Fig. 5. The loss of the Q-switched

Fig. 4. Ruby laser passive Q switching with a 15-mm-thickDy21:CaF2 saturable absorber and a 78%-reflectivity output cou-pler: 1a2 timing of the Q-switched ruby laser output pulse 1lowertrace2 in relation to the ruby free-running temporal profile 1uppertrace2, 1b2 temporal profile of theQ-switched laser pulse.

Fig. 5. Numerical simulation of the ruby passive Q switchingwith a Dy21:CaF2 solid-state saturable absorber.

laser system is defined from Eq. 112 as

loss 5KaNa 1 bKa1Na0 2 Na2 1 gc

Kg

. 182

The parameters used in this simulation 1obtainedfrom the measurements2 are as follows: laser wave-length 694 nm, length of the laser cavity 27 cm,reflectivity of the output coupler 78%, effective laserbeam diameter 2 mm, thickness of the Dy21:CaF2 Qswitch 8 mm, ruby laser emission cross section 2.5 310220 cm2, Dy21:CaF2 ground-state absorption crosssection 1.2 3 10218 cm2, Kg 5 7.22 3 10210 s21, Ka 53.46 3 1028 s21, gc 5 3.42 3 108 s21, gg 5 333 s21, ga 56667 s21, b 5 0.75, Rp 5 1.7 3 1021 s21, and Na0 55.18 3 1015.When the phonon number is low, Na is close to Na0

and the loss of the laser system has an initial value of1KaNa0 1 gc2Kg. For the laser action to occur the laserhas to be pumped, through the xenon flash lamp inthis case, so that the gain is greater than the loss; i.e.,Ng . loss. When this condition is satisfied, thephoton number starts to build up from the noise bydepleting the laser population inversion and theDy21:CaF2 saturable absorber starts to saturate.As shown in Fig. 5, when the photon number insidethe laser cavity increases, the loss decreases becauseof the bleaching effect of the Dy21:CaF2 saturableabsorber. The photon number reaches a peak whenthe laser population inversin equals the cavity loss,i.e., whenNg 5 loss. Beyond this point the laser gainis smaller than the total loss of the laser system andthe Q-switched laser pulse dies out quickly, while thelaser population inversion decreases gradually to aconstant value.After the release of the Q-switched laser pulse,

presumably all the ground-state population of theDy21:CaF2 saturable absorber within the lasing vol-ume is promoted to the excited state and the loss ofthe laser system has a value of 1bKaNa0 1 gc2@Kg. Asshown in Fig. 5, loss remains constant after therelease of the laser pulse because the Dy21:CaF2saturable absorber has a relatively long relaxationtime.8A similar numerical simulation is executed for

several differentNa0, assuming that other parametersremain unchanged. The results are shown in Fig. 6.When Na0 increases, the pulse width decreasesand the output energy of the Q-switched laser pulseincreases. This indicates that better passiveQ-switching performance 1i.e., a shorter pulse with ahigher output energy2 can be obtained if a thickersaturable absorber or a saturable absorber of higherdoping concentration is used, as we have shown in theprevious passiveQ-switching experiments.Figure 71a2 shows the output energy of the simu-

lated Q-switched laser pulse as a function of theoutput-coupler reflectivity with Na0 held at 5.18 31015. Other parameters are assumed to be un-changed for this simulation. The energy of the simu-lated Q-switched laser pulse decreases when thereflectivity of the output coupler increases. The

20 October 1995 @ Vol. 34, No. 30 @ APPLIED OPTICS 6831

temporal profiles of the simulated Q-switched laseroutput for various output-coupler reflectivities areshown in Fig. 71b2. The pulse widths are all close to150 ns. Note that the peak photon number insidethe laser cavity is higher when an output coupler ofhigher reflectivity is used; however, the correspond-ing output energy is lower because the amount ofoutput coupling is smaller.

5. Discussion

As shown in Fig. 3, the ruby passive Q-switchingperformance has a strong dependence on the thick-

Fig. 6. Pulse width and output energy of the simulatedQ-switched laser pulse as a function of the initial ground-statepopulation of the saturable absorber,Na0.

Fig. 7. Results of the simulated Q-switched laser pulses as afunction of the output-coupler reflectivity: 1a2 pulse energy,1b2 temporal profiles.

6832 APPLIED OPTICS @ Vol. 34, No. 30 @ 20 October 1995

ness of the Dy21:CaF2 saturable absorbers. Betterruby passive Q-switching performance is obtainedwith the 15-mm-thick Dy21:CaF2 saturable absorber,which is attributed to the high initial populationinversion obtainable from a long saturable absorber.The pulse energy of the Q-switched ruby laser

output depends on the reflectivity of the outputcoupler because the output energy relates directly tothe amount of output coupling. Higher output en-ergy is obtained with an output coupler of lessreflectivity. However, the pulse width of theQ-switched laser output does not vary significantlywhen the output coupler is changed because thechange of output-coupler reflectivity from 78% to 89%causes only a small variation in the overall loss of thelaser cavity, which is dominated by the loss from theDy21:CaF2 saturable absorberQ switch.The initial laser population inversion required for

laser action that was calculated with Eq. 142 is approxi-mately 3% higher than that observed in the simula-tion because we neglect the effect of optical pumpingduring the development of the Q-switched laser pulsewhen deriving the equation. The accuracy of evalu-ating the final laser population inversion after therelease of the Q-switched laser pulse with Eq. 162 isalso within 4% when compared with the result of thenumerical simulation. If we use the initial popula-tion inversion and the final population inversionobtained from the numerical simulation, the peakphoton number calculatedwith Eq. 172 1np 5 6.4 3 10142is close to that observed in Fig. 5. The energy of thesimulated Q-switched laser output is calculated to beapproximately 3.0 mJ 1when the Q-switched laserpulse is integrated over a range covering the entirelaser pulse2, which is in good agreement with theresult obtained experimentally.

6. Conclusion

The characteristics of ruby passive Q switching withDy21:CaF2 solid-state saturable absorbers are investi-gated with output couplers of various reflectivitiesand saturable absorbers of different thicknesses.The energy of the Q-switched laser pulse is higherwhen the length of the Q switch is longer and thereflectivity of the output coupler is lower. The pulsewidth of theQ-switched laser output is narrower witha longer saturable absorber. BetterQ-switching per-formance can be obtained with a long saturableabsorber and an output coupler of low reflectivity.Numerical simulation is used to investigate the

behavior of ruby passive Q switching with Dy21:CaF2saturable absorber. The results of the numericalsimulation are in good agreement with theory and theresults observed experimentally.

The authors thank Robert Sparrow of Optovac,North Brookfield, Mass., for the Dy21:CaF2 crystalsand William R. Rapoport of the AlliedSignal Inc.,Morristown, N.J., for the mirrors used in this work.

References1. D. M. Andrauskas and C. Kennedy, ‘‘Tetravalent chromium

solid-state passive Q switch for Nd:YAG laser systems,’’ in

Advanced Solid-State Lasers, G. Dube and L. Chase, eds., Vol.10 of OSA Proceedings Series 1Optical Society of America,Washington, D.C., 19912, pp. 393–397.

2. I. J. Miller, A. J. Alcock, and J. E. Bernard, ‘‘Experimentalinvestigation of Cr41 in YAG as a passive Q-switch,’’ inAdvanced Solid-State Lasers, G. Dube and L. Chase, eds., Vol.10 of OSA Proceedings Series 1Optical Society of America,Washington, D.C., 19912, pp. 322–325.

3. M. I. Demchuk, V. P. Mikhailov, N. I. Zhavoronkov, N. V.Kuleshov, P. V. Prokoshin, K. V. Yumashev, M. G. Livshits, andB. I. Minkov, ‘‘Chromium-doped fosterite as a solid-statesaturable absorber,’’ Opt. Lett. 17, 929–930 119922.

4. V. P. Mikhailov, N. V. Kuleshov, N. I. Zhavoronkov, P. V.Prokohsin, K. V. Yumashev, and V. A. Sandulenko, ‘‘Opticalabsorption and nonlinear transmission of tetrahedral V31 1d22in yttrium aluminum garnet,’’ Opt. Mater. 2, 267–272 119932.

5. K. Spariosu, R. D. Stultz, and M. Birnbaum, ‘‘Er:Ca51PO423Fsaturable-absorberQ switch for the Er:glass laser at 1.53 µm,’’Appl. Phys. Lett. 62, 2763–2765 119932.

6. E. Munin, A. B. Villaverde, X. X. Zhang, and M. Bass,‘‘Broadband, intensity dependent absorption in tetravalent

chromium-doped crystals,’’ Appl. Phys. Lett. 63, 1739–1741119932.

7. R. D. Stultz, M. B. Camargo, S. T. Montgomery, M. Birnbaum,and K. Spariosu, ‘‘U41:SrF2 efficient saturable absorber Qswitch for the 1.54 µm erbium:glass laser,’’ Appl. Phys. Lett.64, 948–950 119942.

8. Y. K. Kuo, W. Chen, R. D. Stultz, and M. Birnbaum,‘‘Dy21:CaF2 saturable-absorber Q switch for the ruby laser,’’Appl. Opt. 33, 6348–6351 119942.

9. Y. K. Kuo, M. Birnbaum, and W. Chen, ‘‘Ho:YLiF4 saturableabsorber Q-switch for the 2-µm Tm,Cr:Y3Al5O12 laser,’’ Appl.Phys. Lett. 65, 3060–3062 119942.

10. M. B. Camargo, R. D. Stultz, M. Birnbaum, and M. Kokta,‘‘Co21:YSGG saturable absorber Q switch for infrared erbiumlasers,’’ Opt. Lett. 20, 339–341 119952.

11. Y. K. Kuo, M. F. Huang, and M. Birnbaum, ‘‘TunableCr41:YSO Q-switched Cr:LiCAF laser,’’ IEEE J. QuantumElectron. 31, 657–663 119952.

12. Y. K. Kuo and M. Birnbaum, ‘‘Passive Q-switching of thealexandrite laser with a Cr41:YSO solid-state saturable ab-sorber,’’Appl. Phys. Lett. 67, 173–175 119952.

13. A. E. Siegman, Lasers 1University Science, Mill Valley, Calif.,19862.

20 October 1995 @ Vol. 34, No. 30 @ APPLIED OPTICS 6833