1 August 2001
Optics Communications 195 (2001) 233±240
www.elsevier.com/locate/optcom
Diode end-pumped passively Q-switched Nd:YAG laser intra-cavity frequency doubled by LBO crystal Nicolaie Pavel a,b,*, Jiro Saikawa a, Takunori Taira a a
b
Laser Research Center, Institute for Molecular Science, 38 Nishigonaka, Myodaiji, Okazaki 444-8585, Japan Solid-State Quantum Electronics Laboratory, Institute of Atomic Physics, National Institute for Lasers, Plasma and Radiation Physics, R-76900 Bucharest, Romania Received 20 March 2001; accepted 16 May 2001
Abstract A diode end-pumped Nd:YAG laser, passively Q-switched by a Cr4 :YAG medium as saturable absorber and intracavity frequency doubled employing a LBO crystal is described. The device produces 532-nm wavelength pulses of 226lJ energy, 86-ns width and 4.2-kHz repetition rate, with a laser beam of M 2 1:8. Ó 2001 Published by Elsevier Science B.V. PACS: 42.60.By; 42.65.Ky; 42.60.Gd; 42.60.Da Keywords: Nd:YAG laser; Diode pumping; Passive Q-switching; Second-harmonic generation
1. Introduction For scienti®c and industrial applications that do not require accurate repetition rates the passive Qswitching is a very attractive tool: this technique can improve the eciency, the reliability and the compactness, and also simplify the operation and reduce the laser production costs. As saturable absorber (SA) the Cr4 :YAG crystal was used, at the beginning, in passively Q-switched microchip Nd:YAG lasers that generate pulses of kilowatt * Corresponding author. Address: Solid-State Quantum Electronics Laboratory, Institute of Atomic Physics, National Institute for Lasers, Plasma and Radiation Physics, R-76900 Bucharest, Romania. Fax: +40-1-423-1650. E-mail addresses:
[email protected]®m.ro, npavel@alpha2. in®m.ro (N. Pavel),
[email protected] (T. Taira).
peak power and sub-nanosecond duration [1,2]. Later, Agnesi et al. [3] demonstrated ®rst highaverage power diode end-pumped continuous wave (CW) Nd:YAG laser, passively Q-switched by Cr4 :YAG SA: the system delivered a polarized light of 1.5 W average power at 1064 nm with a beam quality of M 2 1:5. A record average power of 12.3 W in TEM00 transversal mode was reported by Song et al. [4], employing a 142 W diode CW side-pumped Nd:YAG laser passively Qswitched by a Cr:YAG SA; moreover, they demonstrated that at this power level the thermal eect of the SA could become an important issue in the resonator design. A scheme that uses a composite Nd:YAG crystal, made by diusion bonding of doped and undoped YAG pieces, was employed to modify the con®guration of the thermal ®eld induced by pumping in the gain media, thereby
0030-4018/01/$ - see front matter Ó 2001 Published by Elsevier Science B.V. PII: S 0 0 3 0 - 4 0 1 8 ( 0 1 ) 0 1 3 0 7 - 4
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demonstrating improved output performances in high-average power Q-switched regime with Cr4 : YAG SA [5]. Cr4 :YAG SA was also considered as passive Q-switch medium for a variety of laser materials, such as Nd:YVO4 [6], Nd:KGW [7], Nd:LSB [8], or Nd:SVAP [9]. Nonlinear frequency conversion of a Q-switched, diode-pumped laser is a convenient method of extending the wavelengths to mid-infrared range: when pumping a PPLN chip with a Nd:YAG passively Q-switched laser, conversion eciencies between 35% and 50% were demonstrated for the 1±4 lm region [10,11]. Frequency doubling, which could be realized either inside or outside of the laser oscillator, enables the construction of pulsed sources in the blue-green region. The external-cavity frequency doubling has the advantages of simple laser cavity design and the green pulses are shorter than those of the Qswitched laser. Employing a KTP crystal (type II phase matching), placed outside of a high-averagepower Nd:YAG laser, 1.25 W diraction-limited 532-nm wavelength radiation with 50% conversion eciency was demonstrated [10]; the laser operated at 25 kHz repetition rate and the pulse width was 15 ns. Since the intra-cavity frequency doubling uses the high peak power present inside the cavity, a proper resonator design that gives an optimal compromise between second harmonic generation (SHG) and the SA initial transmission enables higher conversion eciency. Ostroumov et al. [8] reported a low average power system consisting of a Nd:LSB active media, a Cr4 :YAG SA and a KTP frequency doubling crystal placed together in a sandwich-type cavity. The output average power at 532 nm was 190 mW (pulses of 2.5-lJ energy and 30-ns width) with a conversion eciency of 39%, as compared with the optimally coupled laser at 1064 nm. The strong thermal lensing eect in Nd:LSB, which has thermal conductivity approximately ®ve times lower than Nd:YAG, was used to operate this system. However, this eect could be the major limitation for the system power scaling. Almost at the same time Kajava and Gaeta [12] developed a V-type diodepumped Nd:YAG laser passively Q-switched by a GaAs semiconductor SA and intra-cavity frequency doubled by a KTP, and obtained a high
beam quality 250 mW average power at 532 nm (pulses of 20.5-lJ energy and 25-ns width). A disadvantage of the intra-cavity frequency doubling could be the longer pulses than those produced by a comparable Q-switched laser that operates at 1064 nm and is externally frequency doubled. However, if the accurate pulse width were not critical for application, the intra-cavity option would reduce the possibility of various types of optical damages. In this work we report what seems to be ®rst demonstration of a diode-pumped Nd:YAG laser passively Q-switched by a Cr4 :YAG SA and intra-cavity frequency doubled by a LBO crystal. With a Cr4 :YAG SA of initial transmission T0 90% the laser produces 532-nm pulses of 226lJ energy and 86-ns width at a repetition rate of 4.2 kHz and beam quality characterized by the M 2 factor of 1.8. The maximum average power of 1.0 W at 532 nm resulted with a Cr4 :YAG SA of 85% initial transmission; the pulse energy and width were 131 lJ and 97 ns, respectively. The theoretical calculations based on a model of the rate of equations, show satisfactory agreement with the experimental data. 2. Experimental set-up and results Fig. 1 presents the scheme of the diode endpumped passively Q-switched and intra-cavity frequency doubled Nd:YAG laser. A 1.55-mm diameter, 0.11 NA ®ber-bundled diode (OPCB030-mmm-FC, OptoPower) with a CW maximum output 808 nm power of 26 W at the ®ber end was used for pump. The Nd:YAG medium (1.3-at.% doping level, 10-mm length) has both sides antire¯ection (AR) coated at 1064 nm and the pumping face high-transmission (HT) coated at 808 nm. The resonator rear plane mirror M1, coated as HR for 1064 nm and HT for 808 nm, was placed very close to the active medium. The CW performance of the laser was optimized following the design procedure reported elsewhere [13]. A collimating lens of a 120-mm focal length (NA 0:17) and a focusing lens of a 50-mm focal length (NA 0:4) were used to image the end face of the ®ber bundle into the Nd:YAG, resulting a
N. Pavel et al. / Optics Communications 195 (2001) 233±240
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Fig. 1. Schematic of the diode end-pumped Nd:YAG laser, passively Q-switched by a Cr4 :YAG SA and intra-cavity frequency doubled by a LBO crystal.
radius of 400 lm; the focusing point was inside of the active medium, at 2.0 mm below the entering surface. Employing a linear resonator of 40-mm length with a ¯at output mirror of 95% re¯ectivity at 1064 nm the laser delivered a maximum CW power of 8.7 W with an optical eciency of 41.2% in a beam characterized by a M 2 factor (measured by a Meles Griot WaveAlyzer) of 2.2. The slope eciency was 45.2% with respect to the absorbed pump power. From a Findlay±Clay analysis [14] the round-trip residual losses L were evaluated to 2% and the coecient K that relates the medium small-signal gain to the absorbed power was 0.066 W 1 . The focal length of the Nd:YAG medium thermal lens, under lasing conditions, was determined by changing the resonator length and investigating its stability as a function of the absorbed pump power [15]. A least-squares ®t to these data gives the focal lens f (m) as a function of absorbed power Pabs (W): f 6:214 Pabs1:44 . For CW green generation a V-type cavity, as shown in Fig. 1, with the plane mirror M2 coated as HR at 1064 nm and HT at 532 nm was employed. A glass plate positioned at the Brewster angle (BP) was used in order to achieve polarized beam. The concave M3 mirror has a radius of 50 cm and HR coatings at 1064 and 532 nm. The distances between mirrors M1 and M2, and M2 and M3 were 80 and 90 mm, respectively. Although KTP has very good nonlinear properties
for frequency doubling, such as a high nonlinear coecient (deff 3.2pm/V), small walk-o angle and high angular acceptance, a major drawback is the gray-tracing eect that comes from the photorefractive eect. This disadvantage is usually eliminated by operating the crystal at 80°C. Because of this we choose as frequency converter a LBO crystal (10-mm length) designed for type I critical phase-matching condition (h 90°, / 11:4°) and operated at 25°C. The crystal surfaces were AR coated at both 1064 and 532-nm wavelengths. Fig. 2 shows the CW performances of the V-type
Fig. 2. CW 1064 and 532-nm power and the M 2 factor as a function of absorbed power.
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N. Pavel et al. / Optics Communications 195 (2001) 233±240
cavity. The maximum green power was 3.2 W for an absorbed pump power of 18.6 W with a laser beam M 2 factor of 1.5. The infrared beam characteristics are also presented in Fig. 2: in this case the LBO crystal was removed from the cavity and the mirror M3 was replaced by one of the same radius and coated as 95% re¯ectivity at 1064 nm. Thereby, a maximum power of 3.8 W with a M 2 factor of 1.14 was achieved, indicating an overall green-conversion eciency of 84%. It is worthwhile to mention that inserting a quarter-wave plate between the Nd:YAG medium and the Brewster polarizer increased the maximum infrared power to 5.6 W, with M 2 2:8, but reduced the maximum green emission to 1.2 W: this was attributed to additional losses introduced by the plate and to a lower laser mode quality. Nevertheless, these results suggest that with a modi®ed resonator higher performances at 532 nm could be achieved. Cr4 :YAG SA crystals (supplied by FEE, Germany) with unsaturated (or initial) transmissions T0 of 90%, 85% and 80%, and AR coated at 1064 nm were considered for Q-switch operation. The output properties of the diode-pumped Nd:YAG laser passively Q-switched by Cr4 :SA and intracavity frequency doubled by LBO crystal are presented in Fig. 3. For the Cr4 :YAG SA with T0 90% the maximum pulse energy of 226 lJ was obtained for an absorbed pump power of 13.1 W. When increasing the pump power beyond this value the green output decreases rapidly to zero, indicating that the resonator reaches the boundary of its stability zone. The laser runs at a frequency of 4.2 kHz with a pulse width (FWHM) of 86 ns. A fast photo-diode and a Tektronics TDS 3012 100MHz digital oscilloscope were used to investigate the pulse stability, repetitively collecting few tens of pulses. While near threshold both pulse amplitude stability and time width ¯uctuations were within 2%, at the maximum pump level 5% and 7% changes were recorded for the pulse amplitude and width, respectively. The pulses characteristics for the maximum absorbed pump power are summarized in Table 1. A slightly higher average power of 1.0 W was obtained with the SA of 85% initial transmission; however, the pulse energy was reduced to 131 lJ while the pulse width was increased to 96 ns.
Fig. 3. Green passive Q-switching characteristics function of the absorbed pump power: (a) average output power and M 2 factor; (b) pulse width and pulse repetition rate; (c) pulse energy and pulse peak power.
For comparative data on 1064 nm passive Qswitching operation, the LBO crystal was removed from the resonator and the mirror M3 was replaced by one with the same radius of curvature and coated as 90% re¯ectivity for 1064 nm. The 1064 nm pulses performances are summarized in Table 2. An average output power of 1.1 W in a beam of M 2 1:4 resulted for the SA of T0 90%,
N. Pavel et al. / Optics Communications 195 (2001) 233±240 Table 1 Summary of green pulses performances for the 13.1 W absorbed pump power T0 (%)
Energy (lJ)
Repetition rate (kHz)
Pulse width (ns)
Average power (W)
90 85 80
226 131 203
4.2 7.6 3.7
86 96 86
0.95 1.0 0.75
Table 2 Summary of 1064 nm pulses characteristics for the 13.1 W absorbed pump power and 90% re¯ectivity output coupler T0 (%)
Energy (lJ)
Repetition rate (kHz)
Pulse width (ns)
Average power (W)
90 85 80
282 268 242
3.9 4.1 3.3
41.5 37.8 28
1.1 1.1 0.8
which is 13% more than the average green power obtained with the same Cr4 :YAG sample under the same pumping level. The laser runs at 3.9 kHz and the pulse energy and width were 282 lJ and 41.5 ns, respectively. For the Cr4 :YAG sample with T0 80% the infrared average power was 0.8 W, 6% larger than the corresponding 532 nm average power. Good frequency conversion was then obtained. However, the green pulses were longer than those obtained at 1064 nm operation: it was theoretically demonstrated earlier [16] that this ``pulse lengthening'' eect is a results of the intensity-dependent loss that prevents fast buildup of the green pulse. 3. Modeling Starting from the coupled rate equations of Szabo and Stein [17], Degnan has developed an analytical method for optimizing the passively Qswitched laser [18]. During the Q-switched pulse duration the optical pumping and the relaxation term in both gain and the SA population dynamics can be neglected. The rate equations [18] for the photon density inside the resonator /, for the population inversion density in the active medium ng , and for the population density of the SA absorbing state nSA , were then modi®ed to include the excited state absorption (ESA) eect for Cr4 :YAG and the intra-cavity frequency doubling:
237
d/ / 2rg ng `g 2rSA nSA `SA dt tr 2rESA
nSAi nSA `SA L dng dt
k/2 ;
cg rg c/ng ;
dnSA dt
cSA rSA c/nSA
1
2
Ag : ASA
3
Here rg and rSA are the laser stimulated emission and the SA absorption cross-section respectively, rESA is the ESA cross-section of SA, `g and `SA are the lengths of the gain and SA media respectively, cg and cSA are the population reduction factors, c is the light speed, and Ag and ASA are the eective areas of resonator mode in the gain and SA, respectively. The term k/2 re¯ects the out-coupling of the cavity ®eld by frequency conversion. The resonator is characterized by the round-trip transit time tr and L is the two-way residual loss. Dividing Eq. (2) by Eq. (3) and integrating resulted [18]:
ng ngi
a
nSA ; nSAi
4
where the lower index i denotes the initial values of population inversion and of SA inversion, and a is a parameter that depends of the gain and SA properties, but accounts also for the ratio of the laser-beam area in medium gain to that in SA as a
cSA rSA =
cg rg Ag =ASA . The SA initial inversion nSAi can be expressed by nSAi ln
T02 =
2rSA `SA . The laser action begins at the moment the population inversion density crosses a speci®ed value ngi ; then, setting Eq. (1) equals to zero yields the condition for ngi : ngi
L
ln T02 : 2rg `g
5
Dividing Eq. (1) by Eq. (2) and using Eq. (4) gives: d/ dng
a `g
1 d ln T02 ng 1 cg ` c 2rg `g ng ngi 2 L d ln T0 2`g k / 2rg `g ng ccg 2rg `g ng
6
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N. Pavel et al. / Optics Communications 195 (2001) 233±240
with d rESA =rSA and where `c is the optical length of the resonator. The last equation was integrated to obtain a relation between photon, / and population inversion density, ng as: ( 1 L ln T02 1 d ng 1 /
ng cg `c d d 1 ngi 2rg d 1 a
1 d ln T02 ng d 1 d a L ln T02 ngi a )
1 d ln T02 d ng 1 ; d a ngi L ln T02
7 where the adimensional parameter d was de®ned by d k=
ccg rg . Then, by setting Eq. (7) to zero, the next transcendental equation concerning the ®nal inversion density, ngf was found: " d #
1 d ln T02 ngf 1 1 2 ngi L ln T0 " d # d ngf ngf d 1 ngi ngi " d # a
1 d ln T02 d ngf ngf :
8 ngi ngi L ln T02 d a An expression for the energy of the green Q-switched pulse, E2x R was next obtained considering that E2x hmA`c k /2
t dt. Then, using Eqs. (1), (2) and (7) the green pulse energy resulted as: ( hm
1 d ln T02 2 A
L ln T0 1 E2x 2cg rg L ln T02 ngf d ngf 1 ln d 1 ngi ngi a 2 d
1 d ln T0 ngf 1 a
d a L ln T02 ngi 1 a
1 d ln T02 d
d 1 d
d a L ln T02 " d #) ngf 1
9 ngi with A the green beam eective area and hm the photon energy at 532 nm. The maximum photon density, /max occurs when d/=dng 0; thus, from
Eq. (6) the inversion of population at the point of maximum power, ngt could be easily obtained, allowing analytical expression for peak power and duration of the green pulse. Fig. 4 presents the expected energy of the green pulse, at various values of losses L, for the Cr4 :YAG SA of 90% initial transmission. For Nd:YAG at 300 K the Maxwell±Boltzmann equilibrium fractional population of the upper laser level fa , and that of the lower laser level fb are 0.41 and 0.19, respectively. In calculation we assumed cg fa fb [18] and the stimulated emission crosssection rg as 4:6 10 19 cm2 . If we consider the four-level model of Cr:YAG and if the rSA and rESA are determined as in Ref. [19], then cSA 1, rSA 3:5 10 18 cm2 , and rESA 2:5 10 19 cm2 . The coecient k was estimated from the theory of SHG as [20,21]: 2 4 5:46deff 10 9 `LBO hm1:06 c2 xrod k q
2 ; k1:06 n3=2 2`c xLBO
10 where `LBO is the LBO crystal length, deff (pm/V) is the eective SHG coecient of LBO (0.8 pm/V), the fundamental laser wavelength k1:06 is expressed in lm, and c 3 1010 cm/s. The enhanced photon density in LBO is taken into account by the xrod =xLBO factor, and q
2 is the coherence parameter, being equal to 2 for the multiaxial mode operation. The laser beam size in the gain crystal, xrod in the Cr:YAG SA and in the LBO crystal, xLBO were evaluated by the P A R A X I A software package (Sciopt Enterprises, San Jose, CA): the active medium was described as a thin lens with a focal length as determined in Section 2. The expected pulse energy of the passively Qswitched laser at 1064 nm was next calculated. Generally the fundamental wave pulse energy Ex is [18]: hmAg 1 ngi Ex ln ln
11 R 2rg cg ngf with hm the photon energy at 1064 nm and R the output mirror re¯ectivity. The initial inversion of population was written as ngi
ln R L ln T02 =
2rg `g while considering Eq. (1) with k 0 and changing L to
ln R L, the ®nal popula-
N. Pavel et al. / Optics Communications 195 (2001) 233±240
Fig. 4. The green pulse energy versus absorbed power for the Cr4 :YAG SA with T0 90%: signs for experiments and theory by continuous curves.
239
Fig. 5. The infrared pulse energy versus absorbed power for the Cr4 :YAG SA with T0 90%: signs for experiments and theory by continuous curves.
4. Conclusion tion inversion ngf was described by the next transcendental relation [5]: 1
ngf 1 ngi
1 a
1 d ln T02 ngf ln ln R L ln T02 ngi ! nagf
1 d ln T02 1 0: 2 ln R L ln T0 nagi
12
Fig. 5 compares the experimental pulse energy at 1064 nm for the Cr4 :YAG SA of T0 90% with the theoretical curves resulted from Eq. (11). A good agreement between the experimental data and theory is observed for L 4%, while the experimental data at 532 nm are satisfactorily described by the curve with L 6%. In this analysis a homogeneous distribution of the fundamental and green beam densities in the laser cavity was considered. Moreover, the active media refractive power could slightly dier from that determined under ecient laser emission (because of the lower power extracted from medium as well as some dierences in laser beam to pump beam overlap eciency for the V-type and linear cavities), and the Cr4 :YAG SA thermal eect was neglected.
In conclusion, we report what is to our knowledge ®rst diode end-pumped Nd:YAG laser, passively Q-switched by a Cr4 :YAG medium as SA and intra-cavity frequency-doubled by a LBO crystal. With a SA sample of 90% initial transmission the device produces green pulses of 226-lJ energy, 86-ns width and 4.2-kHz repetition rate. The maximum green average power of 1.0 W resulted for a Cr4 :YAG SA with T0 85%: the corresponding pulse energy and width were 131 lJ and 97 ns, respectively. The output characteristics were satisfactory described by introducing a nonlinear term caused be the frequency conversion in the coupled rate equations.
Acknowledgements The authors acknowledge the support of the Ministries of Education, Science, Sports, and Culture of Japan (the Grant-in-Aid for Scienti®c Research B, no. 12792003) and Japanese Society for the Promotion of Science (Grant-in-Aid for JSPS Fellow, project no. 10-98381).
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