theoretical and experimental study of a diode-pumped actively q-switched nd:yvo4 green laser with...

Laser Phys. Lett. 2, No. 9, 423–428 (2005) / DOI 10.1002/lapl.200510020 423

Abstract: A diode-pumped acively Q-switched Nd:YdVO4

green laser with periodically poled KTP (PPKTP) has been re-alized. The dependences of pulse width, pulse energy and peakpower on incident pump power are measured for the generated-green-light pulses. A rate equation model is introduced to theo-retically analyze the results obtained in the experiment, in whichthe spatial distributions of the intracavity photon density, thepump beam and the population-inversion density are taken intoaccount. These rate equations are solved numerically and the the-oretical calculations are in agreement with the experimental re-sults. 0 50 100 150 200 250

Time, ns

0

0.2

0.4

0.6

0.8

1.0

Inte

nsity

, a.u

.

Temporal profile of single-pulse

c© 2005 by Astro Ltd.Published exclusively by WILEY-VCH Verlag GmbH & Co. KGaA

Theoretical and experimental study of a diode-pumpedactively Q-switched Nd:YVO4 green laser withperiodically poled KTPG. Li, ∗ S. Zhao, K. Yang, and W. Wu

School of Information Science and Engineering, Shandong University, Jinan 250100, China

Received: 11 April 2005, Accepted: 15 April 2005Published online: 2 May 2005

Key words: diode-pumped; actively Q-switched; PPKTP; spatial distribution; numerical solution

PACS: 42.55.Ah, 42.55.Xi, 42.60.Gd, 42.70.Mp

1. Introduction

Due to the wide applications in the fields of remote sens-ing, information storage, coherent telecommunications,medicine and so on, all-solid-state Q-switched lasers haveattracted a great deal of attention in recent years. Fre-quency doubling of diode-pumped Q-switched lasers isan attractive approach to realizing the solid-state lasers inthe blue-green wavelength range. One of the key steps insuccessful efficient second harmonic generation is to ob-tain good phase matching, which has traditionally beenachieved by taking advantage of the birefringent propertiesof the nonlinear crystals. However, as far back as in 1962,Armstrong et al. [1] proposed the quasi-phase-matching(QPM). QPM permits access to the highest nonlinear co-efficients of a material, and hence can provide greater con-version efficiency than possible with traditional birefingentphase matching. Congruent lithium niobate (LiNbO3) is

the most extensively poled nonlinear material. The driv-ing force for use of this material is its high nonlinear co-efficient, d33 = 27.2 pm/V, the large size of the wafers,large degree of homogeneity and good optical quality [2].Besides periodically poled lithium niobate (PPLN), pe-riodically poled KTiOPO4 (PPKTP) has also been suc-cessfully developed by using millimeter-thick samples [3].The PPKTP crystal possesses a high damage threshold(> 900 MW/cm2 for 5 ns pulse) and a high resistanceto photorefractive damage [4], although its nonlinear co-efficient is 2/3 that of PPLN crystal. The diode-pumpedcw green lasers with PPKTP has been studied during thepast few years [5–6], nevertheless, the actively Q-switchedNd:YVO4/PPKTP green laser has not yet been reported asfar as we know. In addition, the theoretical investigationsof this type of laser have not been carried out.

In this paper, we present the performance of a diode-pumped acively Q-switched Nd:YdVO4/PPKTP green

∗ Corresponding author: e-mail: [email protected]


424 G. Li, S. Zhao, et al.: Theoretical and experimental study

Laser-diode Focusing optics

M1 M2

M3

Nd:YVO4AO

Filter

PPKTP

Figure 1 Schematic of the experimental setup

10 kHz 20 kHz 40 kHz

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

Pump power, W

Out

put p

ower

, W

Figure 2 Average output power versus pump power

laser. The dependences of pulse width, pulse energy andpeak power on incident pump power are measured forthe generated-green-light pulses. To understand the resultsobtained in the experiment, we introduce a rate equationmodel in which the spatial distributions of the intracav-ity photon density, the pump beam and the population-inversion density are taken into account. These rate equa-tions are solved numerically and the theoretical calcula-tions are consistent with the experimental results.

2. Experimental setup and results

The experimental setup is shown in Fig. 1. The pumpsource is a fiber-coupled laser-diode (made by Semi-conductor Institute, Chinese Academic, maximum outputpower 5 W) which works at the maximum absorptionwavelength (808 nm) of the Nd:YVO4 crystal. The outputpump beam from the fiber bundle end, which is 800 µm indiameter, is focused into the laser crystal with a spot sizeof about 440 µm at the focal plane and far-field half-angleof 18◦ by a focusing optics. The mirror M1 with 150-mm

curvature radius is high antireflection coated at 808 nm andhigh reflection coated at 1064 nm. The Nd:YVO4 crystaldoped with 1.0 at.% Nd3+ ions is 4× 4× 5 mm3. Its frontsurface is antireflection coated at 808 nm and its rear sur-face is high antireflection coated at 1064 nm. It is nearM1. The mirror M2 with 100-mm curvature radius is alsoused as the output mirror of the generated green light andthe distance between M1 and M2 is about 21.5 cm. Theacoustic-optic (AO) crystal is a piece of fused glass andits rear surface is 11 cm from the mirror M2. The PPKTPcrystal (made by RAICOL Crystal Ltd, ISRAEL) is 10 mmlong, 1 mm thick, and 2 mm high, and has a 9 µm gratingperiod with antireflection coating at 1064 nm and 532 nmon both surfaces. The temperatures of the Nd:YVO4 crys-tal and the PPKTP crystal are controlled at 20◦C and 30◦Cby means of a temperature controller, respectively. Theplane mirror M3 is about 7.5 cm from M2 and its surfaceis high reflection coated at 1064 nm and 532 nm. The PP-KTP crystal is near M3 and its 10-mm long size belongsto the direction along the axis between the mirrors M2 andM3. The filter is used for separating 532-nm green laserfrom the remainder 1064-nm fundamental wave leakingout from the resonator. A LPE-1B power meter (Instituteof Physics, Chinese Academy of Science) is used to mea-sure the generated-green-laser power and a TED620B dig-ital oscilloscope (Tektronix Inc., USA) is used to measurethe generated-green-laser pulse width.

The average output power and pulse width in the Q-switched operation are measured as functions of incidentpump power. The pulse energy is determined from the av-erage output power and repetition rate. The peak power isdetermined from the pulse energy and pulse width. Fig. 2shows the average output power as a function of the inci-dent pump power for different repetition rate. The averageoutput power increases almost linearly with the incidentpump power. The highest average output power of 1.57 Wis obtained at a maximum incident pump power of 4.1 Wand a repetition rate of 40 kHz, and the corresponding op-tical conversion efficiency is about 38.3%.

The scattered marks in Figs. 3–5 show the pulse width,the pulse energy and the peak power as functions of theincident pump power for different repetition rate. We cansee from Figs. 3–5 that regardless of the repetition rate, thepulse energy and the peak power increase, while the pulsewidth decreases with the increasing incident pump power.The solid line in Fig. 6 shows a single-pulse temporal pro-file of an oscilloscope trace with a pulse width of 35.3 nsat a maximum incident pump power of 4.1 W and a pulserepetition rate of 10 kHz.

The peak power of the output pulse is mainly deter-mined by the population accumulated at the upper laserlevel during the period when the Q-switch is shut down. Sothe pulse peak power is directly influenced by the lifetimeof Nd:YVO4 upper level. When the period of the modu-lation pulses approaches the lifetime of Nd:YVO4 upperlevel (the corresponding repetition rate is about 10 kHz),the population accumulated at the upper laser level duringthe period when the Q-switch is shut down approaches the


Laser Phys. Lett. 2, No. 9 (2005) / www.lphys.org 425

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

Pump power, W

0

50

100

150

200

250

300

350

Pul

se w

idth

, ns


Figure 3 Pulse width versus pump power


1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

Pump power, W

0

20

40

60

80

100

120

Ene

rgy,

µJ

Figure 4 Single-pulse energy versus pump power

maximum. Under the condition that the AO modulationvoltage does not change, the pulse energy and the peakpower of the output pulse are the highest. When the modu-lation frequency is more than 10 kHz, the population accu-mulated at the upper level is only dependent on the modu-lation frequency, and the pulse energy and the peak powerdecrease with the rise of the modulation frequency. Theanalysis is consistent with the experimental results, whichare shown in Figs. 4 and 5.

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

Pump power, W

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Pea

k po

wer

, kW


Figure 5 Pulse peak power versus pump power

0 50 100 150 200 250

Time, ns

0

0.2

0.4

0.6

0.8

1.0

Inte

nsity

, a.u

.

Figure 6 Temporal profile of single-pulse. Solid line – oscillo-scope trace, dotted line – calculated result

3. Theoretical calculations

3.1. The spatial distribution of the photondensity

We consider a diode-pumped passively Q-switchedNd:YVO4/PPKTP green laser depicted in Fig. 1, in whichNd:YVO4 works as gain medium, GaAs saturable ab-sorber works as passive Q-switch, and PPKTP works asfrequency-doubling crystal. If the intracavity photon den-sity is assumed to be a Gaussian spatial distribution dur-ing the entire formatting process of the diode-pumped pas-sively Q-switched laser pulse, the intracavity photon den-sity φ(r, t) for the TEM00 mode can be expressed as:

φ(r, t) = φ(0, t) exp(−2r2

w2l

), (1)



0 1 2 3 4 5

0.40

0.35

0.30

0.25

0.20

0.15

0.10

0.05

Pump power, W

Spo

t siz

e, m

m

Wg

Wl

Wa

Wk

Figure 7 Beam size versus pump power

where r is the radial coordinate; wl is the average radiusof the TEM00 mode, which is mainly determined by thegeometry of the resonator; φ(0, t) is the photon density inthe laser axis.

If the longitudinal distribution of the intracavity pho-ton density along the cavity axis is considered, the pho-ton densities φg(r, t), φa(r, t), and φk(r, t) at the positionsof Nd:YVO4 crystal, AO crystal, and PPKTP can respec-tively be expressed as [7]:

φi(r, t) =w2

l

w2i

φ(0, t) exp(−2r2

w2i

), (i = g, a, k) . (2)

where wg , wa, and wk are the radii of the TEM00 mode atthe above-mentioned three positions, respectively.

In our experiment, however, the pump power is fo-cused into the gain medium with a spot size of a fewhundred microns, so the phase difference of it becomesuneven due to the un-uniformity of the temperature fielddistribution in the gain medium. The phase difference isdistributed as a parabola profile and the gain medium hasthermal lens effect, and the thermal focal length is [8]:

fT =2πKc

dndT + αT n1

w2p

ξPinη, (3)

where wp is the average radius of the pump light in thegain medium; η = 1 − exp(−αl) is the absorptivityof the gain medium, in which α is the absorption coef-ficient and l is the length of the gain medium; Pin isthe incident pump power; n1 is the refractive index ofthe gain medium; and for our a-cut Nd:YVO4 crystal:Kc = 5.23×10−3 Wmm−1K−1, dn/dT = 3×10−6 K−1,ξ = 0.24, αT = 4.43 × 10−6 K−1.

On the basis of the paraxial approximation, the radiusof the pump light in the gain medium wp(z) may be givenas:

wp(z) = wp0 + θp|z − z0| , (4)

where wp0 is the radius at the pump beam waist; θp andz0 are the far-field half-angle and the distance between thefocal plane of the pump beam in the gain medium and thepumped end of the laser crystal. If the absorption factorof the gain medium in the laser axis exp(−αz) is consid-ered, we obtain the dependence of the average pump beamradius wp in the gain medium on z0, and the minimumwp = 216.6 µm is at z0 = 1.0 mm, where the maximumgenerated-green-laser power can be obtained at a certainpump power.

For our experimental configuration shown in Fig. 1, us-ing the well-known ABCD matrix method and consideringthe thermal lens effect of the gain medium, we have sim-ulated wl, wg , wa, and wk as functions of incident pumppower with wp = 216.6 µm, and the results are shown inFig. 7.

3.2. Nonlinear loss due to harmonic conversion

For a Q-switched intracavity-frequency-doubling laser, theharmonic conversion is always considered as a nonlinearloss of the fundamental wave. The single-pass conversionefficiency En is related to the effective nonlinear coeffi-cient deff through:

En = d2eff

2ω2

n2ωn2ωc3ε0

|J2ω|2Ak

, (5)

where ω is the angle frequency of the fundamental wave;nω and n2ω are the refractive indices of the fundamentalwave and the second-harmonic wave; c is the light velocityin vacuum; ε0 is the dielectric permeability of vacuum; Ak

is the area of fundamental wave at the position of PPKTP;J2ω describes second harmonic generation, and when a fo-cused Gaussian beam is used, it can be given as [9]:

J2ω =

lk∫0

exp (i∆kz)(1 + 2iz

b

) dz , (6)

where lk is the length of PPKTP; b = πnωw2k/λ is the

confocal parameter, in which λ is the wavelength of thefundamental wave; ∆k = ∆k′ − kg is the total phase mis-matching factor, where kg = 2π/Λg is the wavevector de-fined by the grating period Λg , ∆k′ = 4π/λ(n2ω − nω) isa particular (non-zero) wavevector mismatch.

For QPM materials the relation between effectivenonlinear coefficient deff and the nonlinear coefficientd33 along the optical axis is defined by deff =(2d33/πm) sin πmD [9]. Our material is designated foroptimum second harmonic generation, i.e., m = 1 and aduty cycle D = 0.5.

According to the relationship of power and photondensity, the fundamental power at the position of PPKTPis:

P (ω, r, t) =12Akh̄ωcφk (r, t) , (7)


Laser Phys. Lett. 2, No. 9 (2005) / www.lphys.org 427

where h̄ω is the single photon energy of the fundamentalwave.

So the nonlinear loss due to harmonic conversion canbe expressed as:

δn =P (2ω, r, t)P (ω, r, t)

= EnP (ω, r, t) = δkφk (r, t) , (8)

where

δk =12EnAkh̄ωc . (9)

3.3. Rate equations and solutions

For laser-diode end-pumped lasers, the pump light canbe approximated by a Gaussian profile. The normalizedfunction that describes the spatial distribution of the pumppower can be expressed as [10]:

rp (r, z) =2α

πw2p (z) η

exp(− 2r2

w2p (z)

)exp (−αz) . (10)

So for this laser, if neglecting the spontaneous radia-tion during the pulse formation, we can obtain the couplingrate equations [11]:∞∫0

dφ(r, t)dt

2πrdr = (11)

=

∞∫0

1tr

⎧⎨⎩2σ

⎛⎝ l∫

0

n(r, z, t)dz

⎞⎠φg(r, t) −

− δa(t)φa(r, t) − δkφ2k(r, t) − Lφ(r, t)

⎫⎬⎭ 2πrdr ,

dn (r, z, t)dt

= (12)

= Wprp (r, z) − σcn (r, z, t)φg (r, t) − n (r, z, t)τ

,

where n(r, z, t) is the spatial distribution of thepopulation-inversion density; σ and l are the stimulated-emission cross section and length of Nd:YVO4 gainmedium, respectively; tr is the round-trip time of light inthe resonator {tr = [2n1l + 2n2la + 2nωlk + 2(Le −l − la − lk)]/c; n1 and n2 are the refractive indices ofNd:YVO4 gain medium and AO crystal, respectively; la isthe length of AO crystal; Le is the cavity length; L is theintrinsic loss; τ is the stimulated-radiation lifetime of thegain medium; Wp = Pinη/hγp is the pump rate, wherehγp is the single-photon energy of the pump light; δa(t) isthe loss function of the AO Q-switch, which is defined as[11]:

δa (t) = δa exp

[−

(t

ts

)2]

, (13)

where δa is the intrinsic diffraction loss of the AO Q-switch; ts is the turnoff time of the AO Q-switch.

Substituting Eq. (2) into Eq. (12) and integrating theresult over time, we obtain:

n (r, z, t) = (14)

= exp

⎡⎣−σc

w2l

w2g

ψ

t∫0

φ (0, t) dt − t

τ

⎤⎦×

×⎧⎨⎩Wprp(r, z)

t∫0

exp

⎡⎣σc

w2l

w2g

ψ

t∫0

φ (0, t) dt +t

τ

⎤⎦dt +

+ n(0, 0, 0) exp(− 2r2

w2p (z)

)exp (−αz)

⎫⎬⎭ ,

where ψ = exp[−(2r2)/(w2g)], n(0, 0, 0) is the ini-

tial population-inversion density in the laser axis; FromEq. (12), we can deduce n(0, 0, 0) accumulated during amodulation period of the AO modulator:

n (0, 0, 0) =2αWp

πw2p (0) ηfp

, (15)

where fp is the modulation frequency of the AO modula-tor; wp(0) is the pump beam radius at z = 0.

Substituting Eqs. (1) and (2) into Eq. (11), we obtain:

dφ(0, t)dt

=4φ(0, t)w2

l tr× (16)

×∞∫0

{2σ

w2l

w2g

exp(−2r2

w2g

)− δa(t)

w2l

w2a

exp(−2r2

w2a

)−

− δkφ(0, t)w4

l

w4k

exp(−4r2

w2k

)− L exp

(−2r2

w2l

)}rdr ,

where n(r, z, t) is given in Eq. (14). Eq. (16) is the ba-sic differential equation describing φ(0, t) as a function oftime t for a diode-pumped actively Q-switched Nd:YVO4

green laser with PPKTP.By numerically solving Eq. (16), we can obtain the re-

lation between φ2k(0, t) and t, from which we can obtain

the pulse width (FWHM) W of the generated-green-lightpulses. The pulse peak power P and the single-pulse en-ergy E can be given as:

P =14ξEn (Akh̄ωc)2 φ2

km , (17)

E =14ξEn (Akh̄ωc)2 φint , (18)

where ξ is the fraction that coupled out the resonator; φkm

is the maximum value of φk(0, t); φint is the integral ofφ2

k(0, t) over t from the beginning time t1 to ending timet2 of the single pulse.



Parameters Values Parameters Valuesσ 3.42 × 10−18 cm2 la 2.4 cmτ 98 µs lk 1.0 cmα 5.32 cm−1 Λg 9 µmn1 2.183 d33 16.9 pm/vn2 1.6 ts 14 nsnω 1.83 δa 0.85n2ω 1.889 L 0.15l 0.5 cm ξ 0.85

Table 1 The parameters of the theoretical calculation

The corresponding parameters values of the theoreticalcalculation are shown in Table 1. The solid lines in Figs. 3to 5 are the theoretical calculation curves for pulse width,pulse energy, and peak power versus pump power, respec-tively. The dotted line in Fig. 6 shows the theoretical pulseshape with a pulse width of 34.4 ns at a maximum inci-dent pump power of 4.1 W and a pulse repetition rate of10 kHz.

From Figs. 3 to 6, we can see that the theoretical cal-culations are in agreement with the experimental results.

4. Conclusions

We have successfully demonstrated the performance ofa diode-pumped acively Q-switched Nd:YdVO4/PPKTPgreen laser. The dependences of pulse width, pulse energyand peak power on incident pump power are obtained forthe generated-green-light pulses. A rate equation modelis introduced to theoretically analyze the results ob-tained in the experiment, in which the spatial distributions

of the intracavity photon density, the pump beam and thepopulation-inversion density are taken into account. Theserate equations are solved numerically and the theoreticalcalculations agree with the experimental results.

Acknowledgements This work is partially supported by theScience and Technology Development Program of ShandongProvince and the Research Fund for the Doctoral Program ofHigher Education.

References

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[2] M. Peltz, U. Bader, A. Borsitzky, et al., Appl. Phys. B 73,663–670 (2001).

[3] A. Arie, G. Rosenman, A. Korenfeld, et al., Opt. Lett. 23,28–30 (1998).

[4] G.M. Gibson, G.A. Turnbull, M. Ebrahimzadeh, et al., Appl.Phys. B 67, 675–677 (1998).

[5] J. Zhang, H. Ma, Y. Luo, et al., Chin. J. Lasers A29, 1057–1060 (2002) (in Chinese).

[6] J. Yu, W. Ni, T. Xue, et al., Acta Opt. Sin. 23, 793–795(2003) (in Chinese).

[7] G. Li, S. Zhao, H. Zhao, et al., Opt. Commun. 234, 321–328(2004).

[8] J. Zheng, S. Zhao, Q. Wang, et al., Acta Photon. Sin. 30,724–729 (2001) (in Chinese).

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theoretical and experimental study of a diode-pumped actively q-switched nd:yvo4 green laser with...

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