Optics & Laser Technology 44 (2012) 1095–1100

Contents lists available at SciVerse ScienceDirect

Optics & Laser Technology

0030-39

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/optlastec

Theoretical study on thermal behavior of passively Q-switchedmicrochip Nd:YAG laser

Zahra Mohammadzahery, Maryam Jandaghi, Samira Alipour, Siamak Dadras n, Shahram Kazemi,Jamshid Sabbaghzadeh

Iranian National Centre for Laser Science and Technology, P.O. Box 14665-576, Tehran, Iran

a r t i c l e i n f o

Article history:

Received 15 August 2011

Received in revised form

19 September 2011

Accepted 5 October 2011Available online 26 October 2011

Keywords:

Passively Q-switched microchip Nd:YAG

laser

Crystal temperature

Theoretical parametric study

92/$ - see front matter & 2011 Elsevier Ltd. A

016/j.optlastec.2011.10.004

esponding author.

ail address: dadras@inlc.ir (S. Dadras).

a b s t r a c t

This study deals with the thermal characterization of a continuous wave (CW-) and end-pumped

passively Q-switched microchip Nd:YAG laser crystal by solving the rate and heat transfer equations in

the laser cavity. In this approach, a parametric study has been performed to investigate the influence of

the pumping parameters, cooling metal dimension and also the crystal dimension and doping

concentration on the thermal behavior of the laser crystal. Obtained results reveal a closed correlation

between the mentioned parameters and the thermal behavior of the crystal indicating that a

proper selection of the laser parameters is essential to control the crystal’s temperature and improve

the performance of the laser accordingly.

& 2011 Elsevier Ltd. All rights reserved.

1. Introduction

The CW- and end-pumped solid state lasers, passivelyQ-switched by an intra-cavity saturable absorber, are the sourcesof highly repetitive powerful ultra-short laser pulses with highoutput beam quality. Such exceptional properties, enclosed in aminiature-sized laser have provided a nontrivial position for thistype of lasers in numerous technologies including nonlinear optics,range finding, remote sensing, etc.

One of the crucial problems in solid state lasers is the heatgeneration due to absorption of the pump beam in the lasercrystal, which makes a temperature gradient in the gain mediumleading to undesirable phenomena such as thermal lensing andstress birefringence. These effects can subsequently result insignificant distortions on the output beam quality and the overallconversion efficiency [1–5]. Therefore, study on the behavior oftransient temperature, induced by the time-dependent thermalload in laser crystal, seems essential to control these adversephenomena and their subsequent effects on the laser beamquality and pulse parameters.

In Q-switched lasers, the absorption of the pump beam changesin time due to the variation of population inversion density duringthe pulse generation. Distribution of this density can be obtained bysolving the coupled rate equations [6,7]. In this approach, a number

ll rights reserved.

of studies have been reported on the temperature profile of the gaincrystals in different Q-switched lasers. Li et al. have proposed ageneral theory which describes the temporal behavior of tempera-ture in the crystal of a CW- and end-pumped passively Q-switchedYb:YAG laser. Their calculations have been performed by taking aTEC heat sink into consideration for cooling the crystal of thismicrochip laser [8]. Transient temperature profile is also investi-gated by Li et al. for actively Q-switched lasers by solving anumerical model coupling the rate equations and the transient heatconduction equation. They have derived this profile as a function ofpump power, repetition rate and thermal time constant to predictthe thermal behavior of the laser crystal for a large variety ofoperating parameters [9]. There are some other research worksfocusing mainly on in the thermal profile in the Q-switched lasersrealized by the active or passive Q-switching technique. However, asfar as our knowledge no comprehensive parametric study has beenperformed up until now which takes insight into the thermal andthermodynamic behavior of the passively Q-switched Nd:YAG lasercrystal.

In this paper, we numerically solve the rate and heat transferequations to simulate the thermal behavior of a Nd:YAG/Crþ4:YAG (gain/saturable absorber) crystal in a CW- and end-pumped passively Q-switched microchip laser. This simulation isemployed to investigate the correlation of various parameters(such as pumping, cooling jacket and gain crystal characteristics)with laser crystal’s thermal features, which is essential in deter-mining the appropriate parameters to optimize the performanceof this laser.

Fig. 1. Configuration of a passively Q-switched microchip laser cavity with heat

conductive cooling metal shown in (a) front view and (b) side view.

Z. Mohammadzahery et al. / Optics & Laser Technology 44 (2012) 1095–11001096

2. Theoretical model

Dynamics of a passively Q-switched laser can be described bya set of rate equations for temporal behavior of laser radiationintensity inside the laser resonator (I), population inversiondensity inside the active medium (n) and the excited statepopulation density of the saturable absorber (ns1) [7,10]:

dI1

dt¼

I1

tr2snlg�2s24ns1ls�2s13ðns0�ns1Þls�ln

1

R

� ��Lloss

� �dn

dt¼ Rin�

snI1

hn�

n

tdns1

dt¼½ðns0�ns1Þs13�s24ns1�I1

hn �ns1

ts: ð1Þ

where I1 is the intensity of oscillating laser, ts is s is the stimulatedemission cross section of the laser crystal, and s13 and s24 arerespectively the absorption cross-sections of ground state andexcited state of saturable absorber. n and ns0 are the populationinversion density of the gain crystal and total density of thesaturable absorber. lg and ls are respectively the length of gainmedium and the thickness of saturable absorber and tr and t are thecavity round-trip time and emission lifetime of laser crystal. c is thelight velocity in the vacuum space, hu is the photon energy and Rin isthe volume pumping rate given by [7,11]:

Rin ¼ZPin

po2phuplg

ð2Þ

In this equation, Pin is the incident pumping power, Z is thepumping efficiency and op and up are, respectively, the effectiveradius and radiation frequency of the pump light. Specifications of

Q ðr,z,tÞ ¼

BPin

po2ps Nt�nðtÞ½ � expð�s Nt�nðtÞ½ �zÞþexpð�s Nt�nðtÞ½ � 2lg�z

� �Þ

� �exp � r

op

� 2� �

,0ozo lg

PðtÞpop

2 lsexp � r

op

� 2� �

,lg ozo lgþ ls

8>>><>>>:

ð5Þ

both gain and saturable absorber crystals used in the currentsimulation have been summarized in Table 1.

The maximal achievable inversion value, defined by thepumping and gain medium parameters, can be extracted fromthe second equation of Eq. (1) assuming I1E0 [11]:

nmax ¼ZPint

po2phuplg

ð3Þ

Fig. 1 shows the configuration of a typical passivelyQ-switched microchip laser cavity comprising a short piece ofgain crystal (Nd:YAG) and a saturable absorber (Crþ4:YAG) whichare bonded to each other and surrounded by a copper coolingjacket. The pump side face of the gain medium is supposed to becoated to highly transmit the pump light and totally reflect theoscillating wavelength. Also the interface facets between the gainand saturable absorber crystals are coated such that the interfaceis totally transmitting at the oscillating frequency and highlyreflecting at the pump light frequency. Coating of the output face

Table 1Gain and saturable absorber crystals specifications employed in the present

simulation.

s 6.6�10-19 cm2 [12] s13 4.3�10-18 cm2 [12]

t 230 ms [12] s24 8.2�10-19 cm2 [12]

lg 1 mm ns0 4.51�1017 cm-3 [12]

ls 0.25 mm ns1 4.2�1016 cm-3 [12]

Lloss 0

of the saturable absorber is also assumed to be partially (85%)reflecting at the oscillating frequency.

During the laser operation, a portion of the pump powerdeposits in laser medium resulting in the temperature distribu-tion T(r,z,t) which is defined on a cylinder of radius r (0ororcu)and length z (0ozo lgþ ls). This temperature distribution satisfiesthe partial differential equation [1,2]:

ðrCÞ@T

@t�Kr2T ¼ Q ðr,z,tÞ ð4Þ

where K, r and C are, respectively, the heat conductivity, densityand specific heat capacity of the laser material. Q representsthe thermal power density of the heat source, which is givenby [8,13]:

in which, Nt is the total doping concentration of active ions in thelaser crystal, B is the fractional thermal load, r and z are the radialand axial coordinates of the points in the microchip crystal, lg andls are respectively the gain and saturable absorber media lengthsand the function P(t) determines the time dependence of Q(r,z,t)in the saturable absorber that is defined as [13]:

PðtÞ ¼Pmax during laser pulsegeneration

0 in the intervals between laser pulses

(ð6Þ

Since the thermal energy emerged in the saturable absorberduring the laser pulse generation is in the same order as theenergy in the laser pulse [14], one can estimate Pmax by obtainingthe pulse maximum power from the laser output parameters. Inaddition, the population inversion density n can be obtained as afunction of time by employing the Runga–Kutta method to solvethe rate equations as described elsewhere [8].

The heat flux normal to each surface of the laser crystal isproportional to the temperature rise of that surface (T) over theambient temperature. The general form of this condition is thenexpressed as:

Kn:rTþhðT�TeÞ ¼ 0 ð7Þ

where, h is the heat transfer coefficient through the surface theoutward normal of which is n and Te is the ambient temperature(300 K) QUOTE QUOTE . Eq. (7) is Newton’s law of cooling,showing that the heat flux removed by convection must be equalto the flux provided by the conduction. When expressed specifi-cally for three surfaces of the structure containing the crystal and

Table 2Parameters employed in corresponding thermal equations.

Nd:YAG Cr4þ:YAG Cu

Thermal conductivity at 300 K W m�1 K�1 13 [5] 12.13 [17] 401 [17]

Heat capacity (J kg�1 K�1) 607 [5] 620 [17] 385 [17]

Density (g cm-3) 4.55 [5] 4.56 [17] 8.96 [17]

Refractive index 1.82 [5] 1.82 –

B 0.1 [5] – –

Pump wavelength (nm) 808 – –

Laser wavelength (nm) 1064 1064 –

Fig. 2. Typical temperature profile of the gain and absorber crystals (1 mm radius)

after 1 s pumping with 1 W power and 100 mm radius.

Z. Mohammadzahery et al. / Optics & Laser Technology 44 (2012) 1095–1100 1097

the metal jacket, these boundary conditions become:

@T@z ¼ þ

hoK ðT�TeÞ, z¼ 0

@T@z ¼�

hL

K ðT�TeÞ, z¼ L

@T@r ¼�

hrcu

K ðT�TeÞ, r¼ rcu

8>><>>: ð8Þ

It is anticipated that for a practical laser operation, all thementioned surfaces of the crystal–metal structure are cooled viathe convection, the coefficients of which are determined by thecoolant (air) flow rate and the physical and geometrical featuresof this structure. The crystal’s front surface (z¼0) is also assumedto be cooled via the radiative heat transfer from the crystal’spumping spot. However this parameter is usually neglected inliterature because of its trivial contribution in cooling the crystalin comparison with that of the convection.

After obtaining the population inversion density, the parabolicheat equation was solved using PDE MATLAB tools environmentand taking into account the boundary conditions and requiredconstants mentioned in Table 2.

During the thermal deposition of the pump power in lasercrystal, the temperature increases in a short time until it reaches aquasi-steady-state by balancing the radial heat flow and the heatinput in the crystal and thereafter it and keeps oscillating aroundan equilibrium temperature. The equilibrium temperature (Te)and the essential time to reach steady-state conditions (Td) varywith laser parameters and crystals properties. Thermodynamicsof the laser crystal depends on the axial and radial thermal timeconstants which can be defined as [15]:

tz ¼CrK

l2 ð9Þ

and

tr ¼CrK

r2 ð10Þ

The temperature gradient caused by the thermal energydeposition through the absorption of the pump light results in aradial refractive index gradient within the laser crystal. Thisconsequence is equivalent to the generation of a spherical lenswithin the laser cavity. The focal length of such a lens-likemedium is given by [16]:

f TL ¼�kr2

2DjðrÞTð11Þ

in which, k is the wave number and Dj(r)T is the phasedifference along the crystal axis. Table 2 illustrates the requiredvalues for the parameters exploited in the mentioned thermalequations.

Fig. 3. Temperature of the gain medium’s hot spot versus pumping radius.

3. Results and discussions

Effects of various parameters, including pumping beam char-acteristics, dimension of crystal’s cooling jacket and the featuresof the gain crystal on thermal and thermodynamic behavior of the

laser crystal have been analyzed in the following sections. Thisanalysis is performed by considering the variation of the gaincrystal’s hottest point temperature versus the mentioned para-meters. Fig. 2 represents the temperature profile of the gain andabsorber crystals in a typical CW- and end-pumped passivelyQ-switched solid state laser. This maximum temperature isattributed to the gain crystal’s hot spot located near to r¼0 andz¼0 point from which the generated heat dissipates throughconvection into the air.

3.1. Pumping beam radius

Fig. 3 illustrates the variation of hot spot’s temperature versusthe pumping beam radius (op) at 1 W pumping power. It can beseen in this figure that this temperature increases by enlarging op

up to 100 mm and thereafter keeps reducing by further enlarge-ment in the pumping beam radius. Such dissimilar manners canbe justified by taking a pair of competitive terms of Q(0.0,t) in Eq.(5) into consideration:

Nt�nðtÞ½ � and1

op

� �2

Herein the initial population inversion (n(t)) is supposed to beequal to nmax at which the output energy achieves its maximumvalue. At small values of op (enhancing region of temperature–pumping radius diagram), since the pumping power density isremarkably high, the initial population inversion (n(t)) is in thesame order of the total doping concentration (Nt). So increasingthe pumping radius will considerably result in enhancement of[Nt–nmax (p 1/op

2)] value and this term will be more effective in Q

variations by overwhelming the decreasing effect of the 1/op2

term. While by increasing the pumping radius over 100 mm, the

Fig. 6. Variation of copper jacket’s temperature as a function of jacket radius.

Fig. 7. Temporal evolution of the gain crystal’s hot spot temperature for gain

crystal radii of 1 (a), 1.25 (b), 1.5 (c) and 1.75 mm (d).

Z. Mohammadzahery et al. / Optics & Laser Technology 44 (2012) 1095–11001098

initial population inversion density is orders of magnitude smal-ler than Nt and thus, variations in op cannot significantly changethis parameter in comparison with Nt. Consequently, the firstterm in Q acts as a constant and the term 1/op

2 will effectivelyreduce the heat deposition in laser crystal by further increase inthe pumping radius.

3.2. Pumping power

Variation of the gain crystal’s hot spot temperature versus thepumping radius is shown in Fig. 4 for different pumping powersabove the threshold (0.4 W). It is clearly seen that the curves holdlarger slopes by increasing the pumping power, revealing that thecrystal’s temperature undergoes a larger variation by a smallchange in pumping beam radius at higher pumping powers.

3.3. Cooling jacket dimension

Fig. 5 illustrates the dependence of the gain crystal’s hot spottemperature to the radius of copper cooling jacket (rcu) typically at3 W pumping power. It can be inferred from this figure that thecrystal’s temperature reduces nonlinearly by increasing the coolingmetal radius until it reaches a minimum value at adequately largercu values (Z25 mm) and thereafter it remains constant showing nomore sensitivity to increasing the radius of the cooling jacket. Fig. 6,on the other hand, represents the temperature of the copper jacketas a function of its radius. This temperature is supposed to be thesame all over the jacket due to high heat conductivity of the coppermetal. According to this figure, the temperature of the jacket alsoremains constant (300 K; ambient temperature) at sufficiently largercu values (Z25 mm). This means that the temperature remainsunchanged at the surface of the laser crystal, which is surrounded bycopper metal and the jacket acts as a heat sink.

Fig. 4. Variation of the crystal’s hot spot temperature versus the pumping radius

at different pumping powers of 1 (a), 5 (b) and 10 W (c).

Fig. 5. Variation of the gain crystal’s hot spot temperature versus the radius of

copper cooling jacket.

3.4. Gain crystal dimension and doping concentration

Numerical models based on finite element analysis can besuitably exploited to investigate the thermodynamics of the lasercrystal as a function of the gain medium characteristics. In thisapproach, dynamic temperature profile of the gain crystal’s hotspot is investigated versus the gain crystal radius and dopingconcentration.

3.5. Gain crystal radius

Fig. 7 shows the temporal evolution of the hot spot’s tempera-ture for different gain crystal radii typically simulated for apumping with 3 W power and 100 mm radius. It can be seen inthis figure that for all considered radii, the temperature of thegain medium increases by initiating the crystal pumping and thenit reaches a quasi-steady-state in tens of milliseconds and there-after it keeps oscillating with certain amplitude in this state (insetin Fig. 7). However, this equilibrium temperature decreases andthe time required to reach this condition increases with enlargingthe crystal radius. For instance, these parameters change respec-tively from 320 to 312 K and 212 to 650 ms by increasing thecrystal radius from 1 to 1.75 mm. One can justify such discre-pancy in equilibrium temperatures by considering the enlarge-ment of the crystal–metal interface with increasing the crystalradius which results in the enhancement of heat dissipation andthus the decline of equilibrium temperature. On the other hand,according to Eq. (10), the radial thermal time constant (tr) isproportional to the square of crystal radius. It means that the timerequired for dissipating the induced thermal load enhances withthe crystal radius and therefore achieving the thermal equili-brium condition prolongs with the enlargement in this parameter.

Dissimilarity in the thermal behavior of the laser crystal due tothe difference in gain crystal dimension emerges as the discrepancyin the thermal lensing features of the laser crystal. Generally, thetemperature gradient, induced by the pump power in solid state

Z. Mohammadzahery et al. / Optics & Laser Technology 44 (2012) 1095–1100 1099

lasers, results in the variation of the refractive index throughout thecrystal (radial direction in the present case). The lens formed due tothis refractive index gradient is known as thermal lens which candestructively affect the laser beam quality. In order to study thedependence of the crystal thermal lensing to the gain crystal radius,radial temperature gradient of this medium has been calculated fordifferent crystal radii at a constant z (hot spot’s z) and then the focallength of each thermally-induced lens has been determined usingEq. (11). Fig. 8 represents the results of this analysis as the variationof the corresponding focal length versus the gain crystal radius.These results apparently demonstrate the enlargement of the focallength with the crystal radius revealing the improvement of thelaser beam quality due to decreasing the thermal distortions in thelaser crystal.

3.6. Gain crystal doping concentration

Variation of the gain crystal’s hot spot temperature is illu-strated in Fig. 9 as a function of its doping concentration whenpumping power is 3 W. A conspicuous enhancement in thetemperature of the gain medium is observed in this figure withincreasing the Nd3þ doping concentration. As it is seen, for atypical range of Nd doping (0.3–1%), this temperature varies overa range of 11 K. This effect can be attributed to the enlargement ofthe gain crystal absorption coefficient with increasing the dopingconcentration which finally results in the enhancement of thefractional thermal load in the crystal. It is worthwhile to mentionthat a greater fractional thermal load can create a higher tem-perature gradient within the crystal which increases the crystalstress and consequently reduces the pumping efficiency [18,19].

Fig. 8. Focal length variation of the thermally-induced lens versus the gain crystal

radius.

Fig. 9. Variation of the gain crystal’s hot spot temperature as a function of Nd3þ

doping concentration.

Increasing the temperature gradient also decreases the value ofthermal shock parameter which determines the permissiblethermal load in the crystal before the fracture occurs.

4. Conclusions

Thermal characterization of a CW- and end-pumped passivelyQ-switched microchip Nd:YAG laser is performed by solving of therate and heat transfer equations in the laser cavity. Correlationbetween the thermal characteristics of the laser crystal (and itscooling jacket) and various laser parameters has been investigated,the results of which are briefly explained in the following summary:

1.

The pumping beam radius conspicuously affects the lasercrystal’s temperature. The present model predicts two dis-tinct regions in which the crystal temperature enhances withthe pumping radius until it reaches its maximum value in acertain radius and then reduces by further increase in thisparameter.

2.

Study on the thermal effects of the cooling jacket radiusindicates that both the gain medium and the jacket tempera-tures reduce with this parameter and the jacket acts as a heatsink at sufficiently high radii.

3.

In order to decline the crystal equilibrium temperature andthus the thermal lensing effects, one can increase the radiusof the gain crystal. However, prolonging the time required forachieving the equilibrium conditions limits the further enlar-gement of the crystal radius. Therefore attaining the optimumoperating conditions strongly depends on an appropriateselection of the gain crystal radius.

4.

The laser crystal temperature has also a closed correlation withthe doping concentration of the gain crystal. Simulation resultsindicate that this temperature rises remarkably with increasingthe Nd3þ doping concentration in the gain medium.

As a final point, since the performance of a passively Q-switchedmicrochip laser is generally recognized to be in closed relation to thecrystal thermal characteristics, an appropriate design of the laserparameters seems essential to control the laser thermal conditions.This goal can be achieved by proper selection of the pumpingparameters, cooling metal geometry and crystals dimension anddoping concentration by considering the results obtained in thisstudy.

References

[1] Farrukh UO, Buoncristiani AM, Byvik CE. An analysis of the temperaturedistribution in finite solid-state laser rods. IEEE Journal of Quantum Electro-nics 1988;24(11):2253–63.

[2] Kalaycioglu H, Sennaroglu A. Influence of doping concentration on powerperformance of diode pumped continuous wave Tm3þ:YAlO3 lasers. IEEEJournal of Selected Topics in Quantum Electronics 2005;11(3):667–73.

[3] Peng X, Xu L, Asundi A. Power scaling of diode pumped Nd:YVO4 lasers. IEEEJournal of Quantum Electronics 2002;38(9):1291–9.

[4] Kemp AJ, Maclean AJ, Hastie JE, Smith SA, Hopkins JM, Valentine GJ, et al.Thermal lensing, thermal management and transverse mode control inmicrochip VECSELs. Applied Physics B: Lasers and Optics 2006;83(2):189–94.

[5] Frauchiger J, Albers P, Weber HP. Modeling of thermal lensing and higherorder ring mode oscillation in end pumped CW Nd:YAG lasers. IEEE Journal ofQuantum Electronics 1992;28(4):1046–56.

[6] Dascalu T, Philipps G, Weber H. Investigation of a Cr4þ:YAG passiveQ-switched in CW pumped ND:YAG lasers. Optics and Laser Technology1997;29(3):145–9.

[7] Zhao S, Chen L, Zhao H, Li G, Zhang L, Yang K. Laser diode pumped passivelyQ-switched Nd3þ:NaY(WO4)2 laser with GaAs saturable absorber. Optics andLaser Technology 2005;37(3):187–91.

[8] Li J, Dong J, Mitsurua M, Shirakawa A, Ueda K. Transient temperature profilein the gain medium of CW- and end-pumped passively Q-switched microchiplaser. Optics Communications 2007;270(1):63–7.

Z. Mohammadzahery et al. / Optics & Laser Technology 44 (2012) 1095–11001100

[9] Li T, Zhang S, Zhao S, Yang K, Zhuo Z. Thermal modeling of the continuous-waveend-pumped Q-switched lasers. Optics Communications 2010;283(15):3070–5.

[10] Zhao S, Zhang X, Zheng J, Chen L, Cheng Z, Cheng H. Passively Q-switched selffrequency doubling Nd3þ:GdCa4O(BO3)3 laser with GaAs saturable absorber.Optical Engineering 2002;41:559–60.

[11] Buryy OA, Ubiaszkii SB, Melnyk SS, Matkovskii AO. The Q-Switched Nd:YAGand Yb:YAG microchip lasers optimization and comparative analysis. AppliedPhysics B Lasers and Optics 2004;78(3–4):291–7.

[12] Zhang X, Zhao S, Wang Q, Zhang Q, Sun L. Optimization of Cr4þ-Dopedsaturable-absorber Q-switched lasers. IEEE Journal of Quantum Electronics1997;33(12):2286–94.

[13] Buryy, OA, Izhnin, OI, Syvorotka, II, Syvorotka, IM, Izhnin, II, Sugak, DY, et al.The temperature distribution and thermomechanical strains in passivelyQ-switched YAG:Nd3þ/YAG:Cr4þ and GGG:Nd3þ/GGG:Cr4þ microchiplasers. 9th International Conference on Laser and Fiber-Optical NetworksModeling, LFNM 2008, Alushta, Crimea, Ukraine: p. 54–6.

[14] Buryy, OA, Ubiaszkii, SB, Melnyk, SS, Matkovskii, AO The temperaturedistribution and the thermomechanical effects in the Cr:YAG quality mod-ulator. Proceedings of LFNM 2003, 5th International Workshop on Laser andFiber-Optical Networks Modeling, Alushta, Crimea, Ukraine, p. 84–6.

[15] Dong J. Numerical modeling of cw pumped repetitively passively Q-SwitchedYb:YAG laser with Cr:YAG as saturable absorber. Optics Communications2003;226(1–6):337–44.

[16] Fan S, Zhang X, Wang Q, Li S, Ding S, Su F. More precise determination ofthermal lens focal length for end-pumped solid-state lasers. Optics Commu-nications 2006;266(2):620–6.

[17] Weber MJ. Handbook of optical materials. Boca Raton: CRC Press LLC;2003.

[18] Koechner W. Solid state laser engineering.6th Ed. New York: Springer; 2006.[19] Miao J, Wang B, Peng J, Tan H, Bian H. Efficient diode-pumped passively

Q-switched laser with Nd:YAg/Cr:YAG composite crystal. Optics and LaserTechnology 2008;40(1):137–41.