Optical Materials 34 (2012) 622–626

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Optical Materials

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Enhancement of stability and peak power in a diode-pumped doubly QMLYVO4/Nd:YVO4 laser with EO and Cr4+:YAG saturable absorber

Jia Zhao, Shengzhi Zhao ⇑, Kang Li, Fanmin Kong, Tao LiSchool of Information Science and Engineering, Shandong University, Jinan, Shandong 250100, China

a r t i c l e i n f o

Article history:Received 3 March 2011Received in revised form 19 July 2011Accepted 9 September 2011Available online 7 October 2011

Keywords:LD-pumpedYVO4/NdYVO4 composite crystalDoubly QML laser

0925-3467/$ - see front matter � 2011 Elsevier B.V. Adoi:10.1016/j.optmat.2011.09.006

⇑ Corresponding author. Tel.: +86 0531 88361736;E-mail address: Shengzhi_zhao@sdu.edu.cn (S. Zha

a b s t r a c t

A diode-pumped doubly Q-switched and mode-locked (QML) YVO4/NdYVO4 laser is realized with theelectro-optic (EO) modulator and Cr4+:YAG saturable absorber, in which the repetition rate of theQ-switched envelope is controlled by the active EO modulation while the mode-locked pulses insidethe Q-switched envelope depend on both the actively modulated loss and the passive saturable absorp-tion. The experimental results show that the doubly QML laser can generate more stable and shorterpulses with higher peak power when compared with the singly passively QML laser with Cr4+:YAG. Atthe pump power of 20 W and the repetition rate 1 kHz, a 21 ns Q-switched pulse envelope with a averagemode-locked peak power of 544 kW is obtained, which is the shortest Q-switched pulse envelope to myknowledge. In comparison to the singly passively QML laser with Cr4+:YAG, the doubly QML laser hascompressed the Q-switched envelope pulse width 70% and improved the mode-locked pulsed peakpower 27 times. By using a hyperbolic secant square function and considering the Gaussian distributionof the intracavity photon density, the coupled equations for diode-pumped dual-loss-modulated QMLlaser is given and the numerical solutions of the equations are in good agreement with the experimentalresults.

� 2011 Elsevier B.V. All rights reserved.

1. Introduction

Stable pulsed laser sources with picosecond order have beenwidely applied in the fields of laser medicine, information storage,material processing, and coherent telecommunications [1–7].These kinds of lasers can be easily obtained by means of the pas-sive Q-switching and mode-locking or the continuous-wave (cw)mode-locking techniques [8–10]. By using a saturable absorber,such as Cr4+:YAG [11,12], the singly passively Q-switched andmode-locked (QML) lasers can be realized. However, the singlypassively QML lasers have the poor shot-to-shot stability andreproducibility as well as the low controllability for the pulse rep-etition rate of Q-switched envelope [13]. Although the cw mode-locked laser can generate the stable picosecond pulse, its peakpower is low and the repetition rate is only determined by the cav-ity length. Generation of the stable QML pulses with the high en-ergy and the optional repetition rate can be obtained in thedoubly QML lasers by the integrations of the active acousto-opticmodulator and the passive saturable absorption [14–17]. In thoselasers, the repetition rate of the Q-switched envelope is controlledby the active acousto-optic switch while the mode-locked pulsesinside the Q-switched envelope depend on both the actively

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modulated loss and the saturable absorption. The experimental re-sults show that the dual-loss-modulated QML lasers can generatemore stable pulses with higher peak power than the singly pas-sively QML lasers. In comparison to the acousto-optic modulator,the electro-optic (EO) modulator is known to be advantageous inits faster switching and better hold-off ability [18–20]. However,as far as we know, the simultaneously Q-switched and mode-locked laser at 1.06 lm with the active electro-optic modulatorand the passive saturable absorption has not been reported.

Due to the advantages of high absorption coefficient, broadabsorption peak, large stimulated emission cross section, linearlypolarized output, Nd:YVO4 has been widely used as laser mediumin miniature solid state lasers [21,22]. However, its weak thermalconduction limits its application in high-power laser systems[23,24]. By using diffusion bonding of a doped laser crystalNd:YVO4 with a non-doped crystal YVO4, known as the compositecrystal, it had been shown that the temperature gradient and thethermal effect in the YVO4/Nd:YVO4 composite crystal can be re-duced at the same pump power in comparison to that of Nd:YVO4

crystal [25]. The employment of a composite crystal has been dem-onstrated to be a useful method in relieving the thermal lens effect[26].

In this paper, by simultaneously employing EO modulator andCr4+:YAG saturable absorber, a diode-pumped doubly QMLYVO4/NdYVO4 laser at 1.06 lm is realized for the first time. The

Fig. 2. TEM00 beam radii of gain medium (up) and Cr4+:YAG (down) versus thepump power.

J. Zhao et al. / Optical Materials 34 (2012) 622–626 623

experimental results show that the doubly QML laser can generatemore stable pulse trains, shorter pulse duration and higher peakpower than the singly passively QML laser with Cr4+:YAG saturableabsorber. Under Gaussian approximation, the coupled equationsfor diode-pumped dual-loss-modulated QML laser is given andthe numerical solutions of the equations are in good agreementwith the experimental results.

2. Experiment

2.1. Experimental setup and cavity design

The experimental setup is shown in Fig. 1. The laser host is an a-cut YVO4/Nd:YVO4 composite crystal which is fabricated by thethermal diffusion bonding technique with a dimensions of 3 � 3� (3 + 8) mm3. The Nd:YVO4 in composite crystal has a Nd3+ dopedconcentration of 0.5 at.%. One end facet of the Nd:YVO4 crystal isantireflective (AR) coated at 1064 nm, while the other facet ofYVO4 is AR coated at 808 nm and 1064 nm at the pump end. In orderto efficiently dissipate the heat deposition, the laser crystal iswrapped with a thin layer of indium foil and fitted into a copperholder cooled by a thermo-electric cooler. The pump source is a fi-ber-coupled diode laser emitting at 808 nm with the maximum out-put power of 30 W (FAP system, Coherent, Inc.). The core size of thefiber is 400 lm in radius, with a numerical aperture of 0.22. The EOmodulator (BBO crystal, the repetition rate 1–5 kHz, commercialproduct made in Quantum Technology Inc., USA) with a polarizerand k/4 plate is used as active Q-switch while a Cr4+:YAG wafer withsmall signal transmission of 70% is used as passive one. A MAX500AD laser power meter (Coherent, Inc., USA) is used to measurethe generated laser power. The laser pulse’s temporal behavior is re-corded by a fast photo-electronic diode (with response time of lessthan 1 ns) and a TDS620B digital oscilloscope (Tektronix, Inc., USA).

The folded laser cavity consisted of four mirrors. Flat mirror M1

AR coated at 808 nm and high-reflection (HR) coated at 1064 nm islocated near laser crystal, functioning as the input mirror. Concavemirror M2 and M3 with the radii of curvature (ROC) of 500 mm and150 mm are HR coated at 1064 nm, acting as the resonator mirror.Flat mirror M4 with a reflectivity of 70% acts as the output coupler.The lengths of the three arms, L1, L2 and L3 are chosen to be 520,710 and 86 mm, respectively, corresponding to a total cavity lengthof 131.6 cm. The gain medium has the thermal lens effectwith increasing pump power which can be described by the focallength of the thermal lens, resulting in the variation of beam radiuswith the pump power in the cavity. By considering the thermallens effect of the gain medium and using ABCD matrix method,the beam radii of the gain medium and Cr4+:YAG saturable absor-ber versus the pump power can be calculated. The calculated re-sults show that the thermal lens effect of laser crystal results inthe variations of the beam radii with the pump power, which is gi-ven in Fig. 2. From Fig. 2, we can see that when the pump powerincreases from 2 W to 20 W, the beam radius of the gain medium

Fig. 1. Experimental setup.

varies from 500 lm to 390 lm while the beam radius of Cr4+:YAGsaturable absorber varies from 46 lm to 90 lm. The ratio of themode area at the gain medium to that at the saturable absorberat the range of the pump power is always higher than 40 so as tosaturate the excited state absorption at Cr4+:YAG. In addition, thebeam radius of Cr4+:YAG saturable absorber decreases withincreasing pump power, preventing it from being damaged at highpump power.

2.2. Experimental results

Both the singly passively QML laser run and the doubly QML la-ser run depend on the operation case of the EO modulator. Whenthe EO modulator is inserted into the cavity, the laser is the doublyQML laser with EO and Cr4+:YAG while the laser is the singly pas-sively QML laser with Cr4+:YAG when the EO modulator is removedaway from the cavity. For the singly passively QML laser, the rep-etition rate of the Q-switched envelope depends on the pumppower and varies from 4 kHz to 28 kHz when the pump power in-creases from 2 W to 20 W. For the doubly QML laser, the repetitionrate of the Q-switch envelope is equal to the repetition rate of EOmodulator and smaller than that of the singly passively QML laser.

The threshold powers for the singly passively and doubly QMLlasers are 2 W and 4 W, respectively, in which higher thresholdpower for the doubly QML laser is induced by the additional lossof the inserted EO switch. Fig. 3 shows two QML laser pulse trainsin longer time scale at the incident pump power of 10 W. The sta-bility of QML laser can be described by the amplitude fluctuationwhich is defined as the ratio between the largest deviation andthe mean value of the pulse amplitude. The smaller the amplitudefluctuation, the better the stability of QML laser. The pulse to pulseamplitude fluctuation in the singly passively QML laser easily ex-cesses 30%, while in the doubly QML laser it is relatively stableand the amplitude fluctuation is about 5%. From Fig. 3, we cansee that the stability of pulse trains in the doubly QML laser is sig-nificantly improved in compared to that of singly passively QMLlaser.

Fig. 4 shows the average output power versus the pump powerfor two kinds of QML lasers. Because the singly passively QML laserhas higher repetition rate, its average output power is higher thanthat of the doubly QML laser. At the pump power of 20 W, a max-imum output power of 3.1 W with the optical conversion efficiencyof 15.5% is obtained for the singly passively QML laser, while the

Fig. 4. Average output power versus incident pump power.

0 2 4 6 8 10 12 14 16 18 20 220.00.10.20.30.40.50.60.70.80.91.01.1

Puls

e en

ergy

(mJ)

Incident pump power (W)

Cr:YAG EO/Cr:YAG at 1 kHz EO/Cr:YAG at 3 kHz EO/Cr:YAG at 5 kHz

Fig. 5. Pulse energy of the Q-switched envelope versus the incident pump power.

2 4 6 8 10 12 14 16 18 200

50

100

150

200

250

300

350

400

Q-s

witc

hed

puls

e w

idth

(ns)

Incident pump power (W)

Cr:YAG EO/Cr:YAG at 1 kHz EO/Cr:YAG at 3 kHz EO/Cr:YAG at 5 kHz

Fig. 6. Pulse width of the Q-switched envelope versus the incident pump power.

0.00.20.40.60.81.0

Inte

nsity

(a.u

.)

Cr4+:YAG

21.1 ns

-250 -200 -150 -100 -50 0 50 100 150 200 250

0.00.20.40.60.81.0

71.8 ns

EO/Cr4+:YAG

Time (ns)

Fig. 7. Oscilloscope profiles of the Q-switched pulse envelope for two QML lasers.

Fig. 3. Oscilloscope traces of the pulse trains for two QML lasers.

624 J. Zhao et al. / Optical Materials 34 (2012) 622–626

maximum output power of 2.2 W with the optical conversion effi-ciency of 11% is obtained for the doubly QML laser at 5 kHz.

According to the repetition rate and the average output power,the pulse energy of the single Q-switched envelope can be calcu-lated. Fig. 5 gives the pulse energy of the Q-switched envelope ver-sus the incident pump power with the scattered points for twokinds of QML lasers. From Fig. 5, we can see that the pulse energyof the Q-switched envelope almost increases linearly with pump

power and is much higher in the doubly QML laser than that in thesingly passively QML laser. At the pump power of 20 W, the obtainedmaximum pulse energies are 140 lJ for the singly passively QML la-ser and 950 lJ for the doubly QML laser at 1 kHz, respectively, corre-sponding to a pulse energy improvement seven times.

Fig. 6 gives the pulse width of the Q-switched envelope versusthe pump power for two kinds of QML lasers. From Fig. 6, we cansee that the pulse width always decreases with the increase ofthe incident pump power and is obviously compressed in the dou-bly QML laser when compared with that in the singly passivelyQML laser. At pump power 20 W and the repetition rate 1 kHz ofEO, the temporal shape of the Q-switched envelope is shown inFig. 7. It can be seen that the modulation depth in the doublyQML laser is deeper than that in the singly passively QML laser.In addition, the repetition rate inside the Q-switched envelope is114 MHz, matching exactly with the cavity roundtrip transmittime. Meanwhile it can be also seen that the pulse width of theQ-switched envelope is 71.8 ns for singly passively QML laserand 21.2 ns for the doubly QML laser, respectively, correspondingto a pulse width compression 70%.

For QML laser, it is very difficult to directly measure the mode-locked pulse width. According to the expanded oscilloscope tracesof the mode-locked pulse within the Q-switched envelope, themode-locked pulse width can be approximately estimated by theformula [20,27]

treal ¼ ðt2measure � t2

probe � t2oscilloscopeÞ

1=2; ð1Þ

here, treal is the real rise time of the pulse, tmeasure is the measuredrise time, tprobe is the rise time of the probe and toscilloscope is the rise

J. Zhao et al. / Optical Materials 34 (2012) 622–626 625

time of the oscilloscope. In our experiment, the average rise time ofthe mode-locked pulse in two QML lasers are measured to be1.23 ns and 1.3 ns, respectively. The rise time of oscilloscope is0.7 ns, and the rise time of the GaAs probe is about 1 ns. Assumingthat the pulse width is approximately 1.25 time more than the risetime, it can be calculated that two kinds of QML pulse widths areabout 582 ps and 757 ps, respectively. According to the evaluatedpulse width of mode-locked pulse sm, the average mode-lockedpulse peak power can be written as:

Pp ¼Pa

fp � N � smð2Þ

where Pa is the average output power, N is the number of pulses in aQ-switched envelope, fp is the repetition rate of the Q-switchedenvelope. At the pump power of 20 W, the obtained maximum peakpowers are 19.6 kW for the singly passively QML laser and 544 kWfor the doubly QML laser at 1 kHz, respectively, corresponding to apeak power increase 27 times.

3. Theoretical analysis

The fluctuation mechanism has been proposed to explain thegeneration of picosecond pulses in simultaneously Q-switchedand mode-locked laser with saturable absorber [27–30]. Based onthis mechanism, both the linear stage and the nonlinear stage playthe key role during the ultra-short pulse formation. In the formerstage, the fluctuations of intensity arise due to the interference ofa great number of modes having a random phase distribution sothat the radiation consists of a chaotic collection of ultra-shortpeaks. In the latter stage, because the absorber is bleached, themost intensive fluctuation peaks are compressed and amplifiedfaster than the weaker ones. Once the pulse intensity rises beyondthe saturation intensity range of the absorber, the preferred pulseswill not be much further shortened on sequent roundtrips. Basedon the rate equation model describing the mode-locking process,considering the Gaussian distribution of the intracavity photondensity and the influence of the EO Q-switch, the rate equationsdescribing diode-pumped dual-loss-modulated Q-switched andmode-locked Nd:YVO4 laser with EO and Cr4+:YAG can be writtenas follows [27]:

/k ¼ /k�1 exp2

pw2l

Z 1

02rnðr; tkÞl

w2l

w2g

exp �2r2

w2g

!" #( );

� 2rgsns1ðr; tkÞlsw2

l

w2s

exp �2r2

w2g

!

� 2res ns0 � ns1ðr; tkÞ½ �lsw2

l

w2s

exp �2r2

w2s

� �;

� Lþ de þ ln1R

� �� �exp �2r2

w2l

� ��2prdr ð3Þ

dnðr; tÞdt

¼ RinðrÞ � rcnðr; tÞ/gðr; tÞ �nðr; tÞ

s; ð4Þ

dns1ðr; tÞdt

¼ ns0 � ns1ðr; tÞss

� rgscns1ðr; tÞ/sðr; tÞ: ð5Þ

Here, /k is the relative amplitude of the mode-locked pulses at thekth round trip, n(r,t) is the inversion population density in the gainmedium, r is the stimulated emission section of the gain medium;ns0 and ns1(r,t) are the total and the ground state population densityin absorber, respectively; ls is the length of the absorber, rgs and res

are the ground-state and excited-state absorption cross section ofthe absorber, c is the speed of light, Rin is the pump rate and canbe written as:

Rinðr; z; tÞ ¼2aPin

hmppw2pl

exp �2r2

w2P

� �½1� expð�alÞ�; ð6Þ

where Pin is the incident pump power, a is the absorption coefficientat the pump wavelength, h is the Planck constant, mP is the fre-quency of the pump power, wP is the radius of the pump beams, lis the length of the laser crystal; s is the upper state lifetime ofthe gain medium, ss is the excited-state lifetime of the saturable ab-sorber, R is the reflectivity of the output mirror, L is the intrinsicloss, deðtÞ ¼ cos2½pVðtÞ=2Vk=4� is the loss function of EO Q-switcher,in which V k=4 is the quarter wave voltage,

VðtÞ ¼0 t 6 0Vk=4 t > 0

�

is the voltage at the EO modulator, /g and /s are the photon inten-sity of the mode-locked pulse at the position of gain medium andsaturable absorber, respectively, which can be given by [27]:

/iðr; tÞ ¼w2

l

w2i

/ð0; tÞ exp �2r2

w2i

� �

¼ w2l

w2i

exp �2r2

w2i

� �Xk¼0

/kf ðt � tkÞ ði ¼ g; sÞ; ð7Þ

here wg and ws are the radii of the TEM00 mode at the position oflaser medium and saturable absorber, wl is the average radius ofTEM00 mode oscillating, f(t) is the mode-locked pulse evolving fromthe noise and satisfies

R1�1 crf ðtÞdt ¼ 1. Because f(t) can be consid-

ered to be a hyperbolic secant function, it can be written as [27,28]:

f ðtÞ ¼ 12rcsp

sech2 1sp

� �; ð8Þ

in which, sp is related to the FWHM mode-locked pulse duration sat fundamental wavelength by s = 1.76 sp.

Under a Gaussian profile approximation, the initial inversionn(r,0) at the operating pulse repetition rate fe is given by:

nðr;0Þ ¼ nð0;0Þ exp �2r2

w2P

� �; ð9Þ

ns1 ¼ ns0 ð10Þ

here n(0,0) is the initial inversion population density in the laseraxis. During a modulation period of the EO switcher, the photondensity in laser medium is /g = 0, so n(0,0) can be deduced fromEq. (4) as:

nð0;0Þ ¼ 2aPinspw2

PlghvP½1� expð�alÞ� 1� exp � 1

fes

� �� �: ð11Þ

Then /k can be numerically obtained by solving Eqs. (3)–(5) with agiven initial value /0 and the average power of the fundamentalwave can be also obtained:

Pt ¼hvpw2

l

8rspln

1R

X1k¼0

/ksech2 t � tk

sp

� �; ð12Þ

The output energy of the QML pulse can be written by:

E ¼Z 1

0Ptdt ¼ hvpw2

l

8rln

1R

X1k¼0

/k: ð13Þ

With the parameters shown in Table 1 [19,30], the calculated tem-poral Q-switched pulse shape at the pump power of 20 W is shownin Fig. 8, which reproduces the experimental pulse shape well inFig. 7. The calculated pulse widths 70 ns and 20 ns agree fundamen-tally with the experimental values 71.8 ns and 21.2 ns. According tothe Eq. (13), the dependence of the total Q-switched pulse energyon the incident pump power can be also obtained, which is shownas solid line in Fig. 5. From Figs. 5, 7 and 8, it can be seen that the

Table 1The parameters of the theoretical calculation.

Parameters Values Parameters Values

l 0.8 cm r 1.56 � 10�18 cm2

a 5.32 cm�1 re 8.2 � 10�19 cm2

ls 0.11 cm rg 4.3 � 10�18 cm2

le 5 cm ns0 2.0 � 1017 cm�3

L 0.02 k 1064 nmxl 200 lm xP 320 lmxg 300 lm c 3 � 1010 cm�s�1

xs 80 lm s 98 lsVk=4 4.8 kV

-250 -200 -150 -100 -50 0 50 100 150 200 250

0.00.20.40.60.81.0

EO/Cr4+:YAG at 1 kHz

Time (ns)

0.00.20.40.60.81.0

Inte

nsity

(a.u

.)

Cr4+:YAG

Fig. 8. Calculated QML pulse shape at the pump power of 20 W.

626 J. Zhao et al. / Optical Materials 34 (2012) 622–626

numerical simulations are in agreement with the experimentalresults.

4. Conclusion

In conclusion, we have successfully realized a doubly QMLYVO4/Nd:YVO4 laser by simultaneously using the EO modulatorand Cr4+:YAG saturable. As expected, this laser can generate morestable QML pulses with shorter pulse width and higher peakpower. At the pump power of 20 W and the repetition rate of1 kHz, a peak power of about 27 times is significantly improvedwhen compared with that of the singly passively QML laser withCr4+:YAG. Using a hyperbolic secant function method, a fluctuationrate equation model has been proposed to describe the mode-lock-ing characteristics, and the theoretical calculations reproduce the

laser characteristics well. It is believed that with the advantagesof the excellent stability and the easy controllability over the rep-etition rate, the doubly QML lasers will be a promising means toobtain laser source with short pulse duration and high peakpower.

Acknowledgments

This work is supported by the National Science Foundation ofChina (61078031 and 60978024) and the Natural Science Founda-tion of Shandong Province (ZR2011 FM012).

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