Experimental and theoretical study of a laser-diode-pumped passively Q -switched intracavity-frequency-
doubled Nd:GdVO4=KTP red laser with V:YAGsaturable absorber
Chao Xu, Guiqiu Li,* Shengzhi Zhao, Xin Li, Guolong Du, and Lei YinSchool of Information Science and Engineering and Shandong Provincial Key Laboratory
of Laser Technology and Application, Shandong University, Jinan 250100, China
Laser-diode-(LD)-pumped solid-state Q-switched la-sers have attracted a good deal of attention in recentyears, and they have been widely used in scientificresearch, medical treatment, and industrial andmilitary systems. The reason of this phenomenonis that LD-pumped solid-state Q-switched lasershave the advantages of simplicity, compactness, highefficiency, and good frequency stability. Nd:GdVO4crystal has obtained much development in the pastfew years because of its excellent performance ofshort pulse width and high peak power in passivelyQ-switched lasers [1–3]. KTP crystal has high non-linear conversion coefficient, so it is easy to obtainhigh second-harmonic conversion efficiency for theLD-pumped Q-switched lasers [4–6]. V:YAG crystalhas been proved to be an effective passively
Q-switched crystal [7–9]. Its saturable absorptionspectrum is between 400 and 1500nm, and it hasa large ground-state absorption cross section, low ex-cited-state absorption loss, short recovery time, lowsaturable energy, and high damage threshold. Toour knowledge, the experimental and theoretical in-vestigations of the LD-pumped passively Q-switchedintracavity-frequency-doubled Nd:GdVO4=KTP redlaser with V:YAG saturable absorber in a V-type re-sonator have not been carried out previously.
In this paper, we have realized the LD-pumpedpassively Q-switched intracavity-frequency-doubledNd:GdVO4=KTP red laser with V:YAG saturableabsorber in a V-type cavity. The dependences of thepulse repetition rate, pulse width, single-pulse en-ergy, and peak power on the incident pump powerare measured. For theoretical analysis, we introducethe rate equations describing the Nd:GdVO4=KTPred laser realized in our experiments, in whichthe intracavity photon density and the initial
population-inversion density are assumed to beGaussian spatial distributions. The rate equationsare solved numerically, and the theoretical calcula-tions agree with the experimental results. Further-more, in order to help one designing a similar laser,we have simulated the variations of the pulse width,peak power, single-pulse energy, and laser efficiencywith the initial transmission of the saturable absor-ber and the ratio of the laser beam radius to thepump beam radius, respectively.
2. Experiments
A. Experimental Setup
The experimental arrangement is shown schemati-cally in Fig. 1. The passively Q-switched intracavity-frequency-doubled operation is carried out in aV-type resonator. The angle between mirrors M1M2and M2M3 is less than 10°. The different arm lengths(L1 and L2) are set as 190 and 65mm, respectively.The whole length of the folded cavity is 255mm. Thepump source of theQ-switched laser is a fiber-coupledLD (FAP-I system, Coherent, Inc., USA), which deli-vers a maximum output power of 30W at the centerwavelength of 808nm.TheNAof the focusing optics is0.25. M1 is a concave mirror with radius of curvatureof 150mm, antireflection (AR) coated at 808nm onthe entrance surface, high-reflection (HR) coated at1342nm, and high-transmission (HT) coated at808nm on the other surface. The a-cut Nd:GdVO4crystal is 0:5 at:% Nd3þ doped with dimensions of3mm × 3mm × 5mm,AR coated at 1342 and 1064nmon both sides, and HT coated at 808nm on the pumpsurface. The V:YAG crystal with two kinds of initialtransmission of 89% and 96% is used to switch thefundamental laser. It is also AR coated at 1342nmon both sides. M2 is a concave mirror with radius ofcurvature of 100mm, HR coated at 1342nm andHT coated at 671nmon the curved surface, AR coatedat 671nm on the other surface, and employed as theoutput coupler. The KTP crystal with dimensions of3mm × 3mm × 8mm is used for frequency doubling,being set close to M3, and is cut for type-II phasematching at 1342nm. Both of its surfaces are ARcoated at 1342nm and 671nm. M3 is a flat mirrorHR coated at both 1342 and 671nm. The tempera-tures of the laser crystal and the KTP crystal are con-trolled at 20 °C and 22 °C, by being wrapped withindium foil and held in a copper block cooled bywater,respectively. The average output power is measuredwith an EMP 2000 energy/power meter (MolectronDetector, Inc., USA). The temporal shape of the
output laser pulse is recordedwith aTED6208digitaloscilloscope (500MHz bandwidth, Tektronix, Inc.,USA) and a photodetector.
B. Experimental Results
Variation trends of the parameters including theaverage output power, pulse repetition rate, pulsewidth, single-pulse energy, and peak power areshown by scattered dots in Figs. 2–6.
Figure 2 shows the average output power(PA) characteristics of the passively Q-switchedintracavity-frequency-doubled Nd:GdVO4=KTP la-ser at 671nm when the initial transmissions (T0)of the V:YAG saturable absorber are 89% and 96%.The corresponding threshold pump powers are mea-sured to be 3.8 and 3:19W, respectively. It is shownthat the average output power increases with theaugment of the incident pump power, and the aver-age output power with T0 ¼ 96% is higher than thatwith T0 ¼ 89% under the same pump power.
The dependences of the pulse repetition rate (F)and pulse width (W) of the Q-switched pulses onthe incident pump power are shown in Figs. 3 and 4.The pulse repetition rate increases with the augmentof the incident pump power, while the pulse widthhas the opposite trend. Using the equations E ¼PA=F and P ¼ E=W, we can obtain the single-pulseenergy (E) and the peak power (P), which are shownin Figs. 5 and 6. We can find that the single-pulseenergy and peak power both increase with theaugment of the incident pump power. Through con-trasting, we find that the passivelyQ-switched intra-cavity-frequency-doubled Nd:GdVO4=KTP red laserwith initial transmission of 89% can generatenarrower pulse and get higher single-pulse energyand peak power.
3. Theoretical Calculations
A. Nonlinear Loss Due to Harmonic Conversion
For a Q-switched intracavity-frequency-doubled la-ser, the second-harmonic conversion can be usually
Nd:GdVO4 V:YAG
Fiber-coupled
LDFocusing
Optics
M1 M3
KTP M2
L1
L2
671 nm
Fig. 1. Experimental setup.Fig. 2. Variation of average output power versus incident pumppower.
considered as the nonlinear loss of the fundamentalwave when the rate equations are used to analyzethe performance of the laser. The second-harmonicpower for type-II phase-matching KTP crystal is [10]
P2ω ¼ KNl2KAK
P2ω; ð1Þ
where KN ¼ ω2d2eff
c3ε0n2ωe nω
o nωe;
lK is the length of KTP crystal; AK ¼ ð1=2Þπw2K is
the area of fundamental wave at the position of KTP,where wK is the radius of the TEM00 mode at the po-sition of KTP. ω is the angle frequency of fundamen-tal wave; deff is the effective nonlinear coefficient; c isthe velocity of light in vacuum; ε0 is the dielectric per-meability of vacuum; n2ω
e , nωo , nω
e are the second-harmonic and fundamental wave refractive indices,respectively. According to the relationship of powerand photon density, Pω ¼ AKℏωcðϕK=2Þ, where ϕK isthe photon density at the position of KTP, ℏω is thesingle-photon energy of the fundamental wave, ℏ isPlanck’s constant, and the nonlinear loss resultingfrom harmonic conversion can be expressed as
δN ¼ P2ωtrℏωφKAKLc
¼ KN
2ℏωcl2KφK ¼ δKφK ; ð2Þ
where δK ¼ KN2 ℏωcl2K ;
Lc is the optical length of the resonator, tr ¼ 2Lc=cis the round-trip time of the resonator. The corre-sponding parameters for type-II phase-matchingKTP crystal are presented in Table 1, where no andne can be obtained through the Sellmeier equations(λ in micrometers):
n2o ¼ 3:3134þ 0:05694=ðλ2 − 0:05658Þ − 0:01682λ2;
n2e ¼ 3:0333þ 0:04154=ðλ2 − 0:04547Þ − 0:01408λ2:
B. Rate Equations and Solutions
We consider an LD-pumped passively Q-switchedintracavity-frequency-doubled Nd:GdVO4=KTP redlaser with V:YAG saturable absorber, in whichNd:GdVO4=KTP works as the gain medium, KTPworks as the frequency-doubled crystal, and V:YAGworks as the passive Q-switch. If the intracavity
Fig. 3. Variation of pulse repetition rate versus incident pumppower.
Fig. 4. Variation of pulse width versus incident pump power.
Fig. 5. Variation of single-pulse energy versus incident pumppower.
Fig. 6. Variation of peak power versus incident pump power.
photon density is assumed to be a Gaussian spatialdistribution during the entire formatting process ofthe LD-pumped passively Q-switched intracavity-frequency-doubled laser pulse, the intracavityphoton density ϕðr; tÞ for the TEM00 mode can be ex-pressed as
ϕðr; tÞ ¼ ϕð0; tÞ exp�−
2r2
w2l
�; ð3Þ
where r is the radial coordinate; wl is the average ra-dius of the TEM00 mode; and ϕð0; tÞ is the photondensity in the laser axis.
If the longitudinal distribution of the intracavityphoton density along the cavity axis is considered,the photon densities ϕgðr; tÞ, ϕsðr; tÞ, and ϕKðr; tÞ atthe positions of Nd:GdVO4 crystal, V:YAG, andKTP can be expressed as [11]
ϕiðr; tÞ ¼w2
l
w2i
ϕð0; tÞ exp�−
2r2
w2i
�; ði ¼ g; s;KÞ; ð4Þ
where wg, ws, and wK are the radii of the TEM00mode at the three positions of Nd:GdVO4 crystal,V:YAG saturable absorber, and KTP crystal,respectively.
For our experimental configuration shown inFig. 1,using the well-known ABCDmatrix method and con-sidering the thermal lens effect of the gain medium,we can obtain wl, wg, ws, and wK , which are the func-tions of the incident pump power. The transforma-tional matrix of the resonator can be expressed as
T ¼�1 0
0 1
��1 Lc2
0 1
��1 0
−2=R2 1
��1 Lc1
0 1
�
�
1 0
−1=f T 1
��1 0
−2=R1 1
�
�
1 0
−1=f T 1
��1 Lc1
0 1
�
�
1 0
−2=R2 1
��1 Lc2
0 1
�¼
�A B
C D
�; ð5Þ
where f T ¼ 2πKcdn=dTþαTng
w2p
ζPinη is the thermal focal length;R1 and R2 are the radii of curvature of M1 and M2,respectively; Lc1 ¼ nglþ nsls þ ðLe1 − l − lsÞ is the op-tical length of the straight arm of resonator; Lc1 ¼
nKlK þ ðLe2 − lKÞ is the optical length of the foldedarm of resonator; Le1 and Le2 are the length of thestraight arm and folded arm of resonator, respec-tively; ng, ns, and nK are the refractive indices of theNd:GdVO4 gain medium, V:YAG saturable absorber,and KTP crystal, respectively; l is the length of theNd:GdVO4 gain medium; ls is the length of V:YAGsaturable absorber; Kc is the thermal conductivityof the gain medium; dn=dT and αT are the thermalchromatic dispersion coefficient and thermal expan-sion coefficient of the gain medium, respectively; wp
is the average radius of the pump beam in the gainmedium; ζ is the thermal load ratio, viz., the ratio ofthe pump energy that the laser crystal absorbs con-verted to the thermal energy; Pin is the incidentpump power; η ¼ 1 − expð−αlÞ is the absorptivity ofthe gain medium, in which α is the absorption coeffi-cient of the gain medium.
Because M3 is a flat mirror, the laser waist in thefolded arm of resonator is located at the position ofM3. According to the ABCDmatrix theory, the radiusof the TEM00 mode at M3 can be expressed as
w0 ¼�λπ
�12 jBj12h1 −
�AþD2
�2i14
: ð6Þ
If ignoring the distance between KTP crystal andM3, we can think that the radius of the TEM00 modeat KTP crystal is w0.
According to the ABCDmatrix theory and ignoringthe astigmatism, we can obtain the radius of theTEM00 mode at the laser waist in the straight armof resonator and the distance between this laserwaist and M2:
w1 ¼ R2w0
2h�
Lc2 −R22
�2 þ
�πw2
0λ
�2i12
; ð7Þ
L ¼ R2
2þ
R22
�Lc2 −
R22
�
4h�
Lc2 −R22
�2 þ
�πw2
0λ
�2i : ð8Þ
Then the radii of the TEM00 mode at the positionsof the Nd:GdVO4 crystal, V:YAG saturable absorber,and M2 can be expressed as
wi ¼ w1
�1þ
� λziπw2
1
�2�1
2 ði ¼ g; s; 2Þ; ð9Þ
where zg, zs, and z2 are the distances between thelaser waist in the straight arm of resonator andNd:GdVO4 crystal, V:YAG saturable absorber, andM2, respectively.
Table 1. Parameters of the Type-II Phase-MatchingKTP Crystal [11]
Figure 7 shows the variation trends of wg, wK , ws,and wl versus the incident pump power when the in-itial transmission of V:YAG is 89%, and we can seethat wg decreases with the augment of the incidentpump power and wg=wp is between 2 and 0.5when wp ¼ 0:02 cm.
For diode-pumped lasers, the pump light can be ap-proximated by a Gaussian profile. So for this laser, ifneglecting the spontaneous radiation during thepulse formation, we can obtain the coupling rateequations [11]
where nðr; tÞ is the average population-inversion den-sity; ns1ðr; tÞ and ns0 are the ground-state and totalpopulation densities of V:YAG saturable absorber, re-spectively; σ is the stimulated-emission cross sectionof Nd:GdVO4 gain medium; σg and σe are the ground-state and excited-state absorption cross sections ofthe saturable absorber, respectively; tr ¼ ½2nglþ2nsls þ 2nKlK þ 2ðLe − l − ls − lKÞ�=c is the round-triptime of light in the resonator; Le is the cavity length;
δk is given in Eq. (2); L is the intrinsic loss; RinðrÞ ¼Pin expð−2r2=w2
pÞ½1 − expð−αlÞ�=hγpπw2pl is the pump
rate, where hγp is the single-photon energy of thepump light; τ is the stimulated-radiation lifetimeof the gain medium; τs is the excited-state lifetimeof the saturable absorber.
Substituting Eq. (4) into Eqs. (12) and (13) andintegrating the results over time, we obtain
nðr;tÞ¼ exp�−σcw
2l
w2gexp
�−
2r2
w2g
�Zt
0ϕð0; tÞdt− t
τ
�
×�RinðrÞ
Zt
0exp
�σcw
2l
w2gexp
�−
2r2
w2g
�
×Z
t
0ϕð0;tÞdtþ t
τ
�dtþnð0;0Þexp
�−
2r2
w2p
��;ð14Þ
ns1ðr; tÞ ¼ exp�−σgc
w2l
w2sexp
�−
2r2
w2s
�Zt
0ϕð0; tÞdt − t
τs
�
�ns0
τs
Zt
0exp
�σgc
w2l
w2sexp
�−
2r2
w2s
�
×Z
t
0ϕð0; tÞdtþ t
τs
�dtþ ns0
�; ð15Þ
where nð0; 0Þ is the initial population-inversiondensity in the laser axis, i.e.,
nð0; 0Þ ¼ln�
1T2
0
�þ L
2σl
�1þ w2
g
w2p
�; ð16Þ
where T0 is the initial transmission of the saturableabsorber,
T0 ¼ expð−σgns0lsÞ: ð17Þ
Substituting Eqs. (3) and (4) into Eq. (11), weobtain
dϕð0; tÞdt
¼ 4ϕð0; tÞw2
l tr
Z∞
0
�2σnðr; tÞl w
2l
w2gexp
�−
2r2
w2g
�
− 2σgns1ðr; tÞlsw2
l
w2sexp
�−
2r2
w2s
�
− 2σe½ns0 − ns1ðr; tÞ�lsw2
l
w2sexp
�−
2r2
w2s
�
− δKϕð0; tÞw4
l
w4K
exp�−
4r2
w2K
�
− L exp�−
2r2
w2l
��rdr; ð18Þ
where nðr; tÞ and ns1ðr; tÞ are given in Eqs. (14) and(15), respectively. Equation (18) is the basic differen-tial equation describing ϕð0; tÞ as a function of t. Theinitial photons come from spontaneous-emissionFig. 7. Variation of laser beam size versus incident pump power.
noise. When Eq. (18) is solved numerically, the initialphoton density ϕð0; 0Þ can be set at a value muchsmaller than the peak value of the photon densityϕmð0; tÞ. We can estimate ϕmð0; tÞ by consulting theresults obtained under the plane-wave approxima-tion or by preliminarily solving the equations.
By numerically solving Eq. (18), we can obtain therelation between ϕð0; tÞ and t, and from Eq. (4), wecan obtain the relation between ϕKð0; tÞ and t. Fromthe relation between ϕ2
Kð0; tÞ and t, we can obtain thepulse width (W) and the pulse repetition rate (F) ofthe generated light pulses. In addition, the peakpower (P) and the single-pulse energy (E) can beexpressed as [11]
P ¼ 14ξKNAKl2KðℏωcÞ2ϕ2
Km; ð19Þ
E ¼ 14ξKNAKl2KðℏωcÞ2ϕint; ð20Þ
where ξ is the fraction that coupled out the resonator,KN is given in Eq. (1), ϕKm is the maximum value ofϕKð0; tÞ, ϕint is the integral of ϕ2
Kð0; tÞ to t in thesingle-pulse interval.
The corresponding parameter values of the theore-tical calculation are shown in Table 2. The initialtransmissions of V:YAG saturable absorber are T0 ¼89% and T0 ¼ 96%, respectively. According to theseparameters, we simulate the curves for the pulse re-petition rate, pulse width, single-pulse energy, andpeak power of the LD-pumped passively Q-switchedNd:GdVO4=KTP red laser with V:YAG saturable ab-sorber, which are shown in Figs. 3–6 as solid lines,respectively. From Figs. 3–6, we can find that thetheoretical calculations are in agreement with theexperimental results.
C. Analysis
Zhang et al. have proved wp=wl is a unique para-meter for the research of an LD-pumped passivelyQ-switched laser [12]. In this paper, from Eqs. (16)and (18)–(20) we can find that the pulse width, peakpower, and single-pulse energy are all dependent ontwo parameters: T0 and wg=wp. T0 is the initialtransmission of the saturable absorber. wg=wp isan important parameter when the spatial variationof the pumping and intracavity laser intensity is con-sidered, and it is dependent on the incident pumppower. In order to optimize the described systemand help others designing a similar laser, we havecalculated the variations of the pulse width, peakpower, and single-pulse energy versus T0 and wg=wp,respectively.
Figure 8 shows the variation of the pulse widthversus wg=wp when the initial transmissions of thesaturable absorber are 89% and 96%, respectively.It can be seen that the pulse width increases drama-tically with the augment of wg=wp. So the variationof output pulse width is induced by the change ofwg=wp. In our experiments, wp is constant, and wgdecreases with the augment of the incident pumppower, which is shown in Fig. 7. So we can obtain thatthe pulse width decreases sharply with the augmentof the incident pump power, and this result agreeswith the experimental phenomenon given in Fig. 4.Variations of the peak power and the single-pulseenergy versus wg=wp are shown in Figs. 9 and 10,and we can find that they both decrease with theaugment of wg=wp.
Besides wg=wp, the output parameters of the laserare also affected by the value of T0. Variations of thepulse width, peak power, and single-pulse energyversus T0 when the values of wg=wp are 0.5, 1, and2 are shown in Figs. 11–13. We can find that the
Table 2. Parameters of the Theoretical Calculation [5,8]
Parameter Value
σ Stimulated-emission cross section of Nd:GdVO4 1:8 × 10−19 cm2
ns0 Total population density of V:YAG 2:0 × 1017 cm−3
τ Stimulated-radiation lifetime of Nd:GdVO4 90 μsτs Excited-state lifetime of V:YAG 22� 6nsξ Coupled coefficient of the resonator 0.85ng Refractive index of Nd:GdVO4 2.19ns Refractive index of V:YAG 1.8nK Refractive index of KTP 1.821lK Length of KTP 0:8 cml Length of Nd:GdVO4 0:5 cmls Length of V:YAG (T0 ¼ 89%) 0:081 cm
Length of V:YAG (T0 ¼ 96%) 0:028 cmwp Average radius of the pump beam in the gain medium 0:02 cmL Intrinsic loss of the resonator 0.1Kc Thermal conductivity of the gain medium 11:7 × 10−3 Wmm−1 K−1
dn=dT Thermal chromatic dispersion coefficient of the gain medium 4:7 × 10−6 K−1
αT Thermal expansion coefficient of the gain medium 3:5 × 10−6 K−1
ζ Thermal load ratio 0.24α Absorption coefficient of the gain medium 5:69 cm−1
pulse width increases with the augment of T0, andthe peak power and the single-pulse energy both de-crease with the augment of T0.
The laser efficiency is an important parameter foran LD-pumped laser. If the efficiency η is defined asthe ratio of the frequency-doubled population to theinitial inversion population, η can be expressed as
η ¼ E
hνR∞
0
Rl0 nð0; 0Þ exp
�−
2r2
w2p
�2πrdrdz
; ð21Þ
where hν is the single-photon energy of the generatedlight pulses, and nð0; 0Þ is given in Eq. (16).
From Eq. (21) it can be seen that the laser effi-ciency is also dependent on the parameters T0 andwg=wp. By numerically solving Eq. (21), we can ob-tain η for different T0 and different wg=wp. Figure 14shows the laser efficiency η versus wg=wp when theinitial transmissions of the saturable absorber are89% and 96%, respectively. It can be seen that bothη decrease with the augment of wg=wp at different
transmissions. Figure 15 shows the laser efficiencyη versus T0 when the values of wg=wp are 0.5, 1,and 2, respectively. It is shown that η increases withthe augment of T0. So we can find that the higherinitial transmission saturable absorber will resultin a higher efficiency. The reason of this phenomenonis that the loss of the resonator is smaller when theinitial transmission of the saturable absorber is high-er. That is why the 96% initial transmission satur-able absorber gives a higher average output powerat 671nm than the one with T0 ¼ 89% althoughthe higher initial transmission saturable absorbergenerates a higher repetition rate but lower peakpower pulses, which are shown in Figs. 2, 3, and 6,respectively.
The stimulated-emission cross section σ of the gainmedium is another important factor that affects thelaser efficiency. Equation (16) indicates that nð0; 0Þ isinversely proportional to σ. So from Eq. (21) we canconclude that the gain medium with a larger stimu-lated-emission cross section will generate a higherefficiency. Thus, the small value of σ in our system
Fig. 8. Variation of pulse width versus wg=wp in the cases ofT0 ¼ 89% and T0 ¼ 96%.
Fig. 9. Variation of peak power versus wg=wp in the cases ofT0 ¼ 89% and T0 ¼ 96%.
Fig. 10. Variation of single-pulse energy versus wg=wp in thecases of T0 ¼ 89% and T0 ¼ 96%.
Fig. 11. Variation of pulse width versus T0 in the cases ofwg=wp ¼ 0:5, wg=wp ¼ 1, and wg=wp ¼ 2.
is the main limitation that induces the maximumefficiency of only 1.2%. This result can be verifiedby [12], in which the maximum efficiency and thestimulated-emission cross section are 10 and 18times larger than those in this paper, respectively.
4. Conclusions
Throughexperimentsandtheoretical calculations, theperformance of the LD-pumped passively Q-switchedintracavity-frequency-doubled Nd:GdVO4=KTP redlaserwithV:YAGsaturableabsorberhasbeenstudied.We have assumed the intracavity photon density andthe initial population-inversion density to be Gaus-sian spatial distributions in the rate equations of thislaser. These space-dependent rate equations aresolved numerically. From the numerical solutions,weobtainthedependencesof thepulse repetitionrate,pulse width, single-pulse energy, and peak power onthe incident pump power for the generated pulses.Thetheoreticalcalculationsof thenumericalsolutionsare consistentwith theexperimental results.Throughanalysis, we find that the laser-pulse characteristicsare all dependent on two important parameters: T0and wg=wp. The variations of the pulse width, peakpower, single-pulse energy, and laser efficiency withthese two parameters are given so that one can findtheoptimal condition fromthe resultswhendesigninga similar laser.
This work is supported by the National NaturalScience Foundation of China (NSFC) (60678015).
References1. J. Liu, C. Wang, C. Wang, X. Meng, H. Zhang, L. Zhu, J. Wang,
Z. Shao, and M. Jiang, “Diode end-pumped Q-switched high-power intracavity frequency-doubled Nd:GdVO4=KTP greenlaser,” Appl. Phys. B 72, 171–174 (2001).
2. J. Yang, J. Liu, and J. He, “High efficiency continuous-waveoperation of a diode-pumped Nd:GdVO4 laser at 1:06 μm,”Laser Phys. Lett. 2, 171–173 (2005).
3. S. Ng, D. Tang, J. Kong, Z. Xiong, T. Chen, L. Qin, andX. Meng, “Quasi-cw diode-pumped Nd:GdVO4 laser passively
Fig. 12. Variation of peak power versus T0 in the cases ofwg=wp ¼ 0:5, wg=wp ¼ 1, and wg=wp ¼ 2.
Fig. 13. Variation of single-pulse energy versus T0 in the cases ofwg=wp ¼ 0:5, wg=wp ¼ 1, and wg=wp ¼ 2.
Fig. 14. Variation of laser efficiency versus wg=wp in the cases ofT0 ¼ 89% and T0 ¼ 96%.
Fig. 15. Variation of laser efficiency versus T0 in the cases ofwg=wp ¼ 0:5, wg=wp ¼ 1, and wg=wp ¼ 2.
Q-switched and mode-locked by Cr4þ:YAG saturableabsorber,” Opt. Commun. 250, 168–173 (2005).
4. J. Bai and G. Chen, “Continuous-wave diode-laser end-pumped Nd:GdVO4=KTP high-power solid-state green laser,”Opt. Laser Technol. 34, 333–336 (2002).
5. G. Li, S. Zhao, K. Yang, and P. Song, “Control of the pulse widthin a diode-pumped passively Q-switched Nd:GdVO4=KTPgreen laser with a Cr4þ:YAG saturable absorber,” Appl. Opt.44, 5990–5995 (2005).
6. H. Huang, J. He, C. Zuo, B. Zhang, X. Dong, S. Zhao, and Y.Wang, “Highly efficient and compact laser-diode end-pumpedQ-switched Nd:GdVO4=KTP red laser,” Opt. Commun. 281,803–807 (2008).
7. Q. Xue, Q. Zheng, Y. Bu, and L. Qian, “LD-pumped passivelyQ-switched Nd:YVO4=LBO red laser with V:YAG,” Opt. LaserTechnol. 38, 540–543 (2006).
8. J. Ma, Y. Li, Y. Sun, H. Qi, R. Lan, and X. Hou, “PassivelyQ-switched 1:34 μm Nd:GdVO4 laser with V:YAG saturableabsorber,” Laser Phys. Lett. 5, 593–596 (2008).
9. H. Huang, J. He, B. Zhang, K. Yang, C. Zuo, J. Xu, X. Dong, andS. Zhao, “Intermittent oscillation of 1064nm and 1342nm ob-tained in a diode-pumped doubly passively Q-switchedNd:YVO4 laser,” Appl. Phys. B 96, 815–820 (2009).
10. J. Zheng, S. Zhao, Q. Wang, X. Zhang, and L. Chen, “Influenceof thermal effect on KTP type-II phase-matching second-harmonic generation,” Opt. Commun. 199, 207–214 (2001).
11. G.Li,S.Zhao,H.Zhao,K.Yang,andS.Ding,“Rateequationsandsolutions of a laser-diode end-pumped passively Q-switchedintracavity doubling laser by taking into account intracavitylaser spatial distribution,”Opt.Commun.234, 321–328 (2004).
12. X. Zhang, S. Zhao, and Q. Wang, “Modeling of passivelyQ-switched lasers,” J. Opt. Soc. Am. B 17, 1166–1175 (2000).
