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Pii: s0925-3467(02)00003-4Y. Kalisky a,*, C. Labbe a, K. Waichman a,b, L. Kravchik a, U. Rachum a, a ‘‘Arava’’ Laser Laboratory, Rotem Industrial Park, D.N. Arava, Mishor Yamin 86800, Israel b Laser Department, NuclearResearch Centre Negev, P.O. Box 9001, Beer Sheva 89140, Israel c Crystal Laboratory, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Received 29 June 2001; received in revised form 15 October 2001; accepted 26 November 2001 We investigate the repetitive modulation in the kHz frequency domain of a passively Q-switched, diode-pumped Yb:YAG laser, by Cr4þ:YAG, Cr4þ:LuAG, and Cr4þ:GSGG saturable absorbers. The results presented here are fo-cused towards the design of a passively Q-switched Yb:YAG microlaser. The free-running performance of both rod anda diskYb:YAG is characterized and experimental parameters such as gain and loss are evaluated. These values, to-gether with the value of the stimulated emission cross-section, e.g. rem ¼ 3:3 Â 10À20 cm2 were found to ﬁt between ourexperimental results and an existing numerical model which relates the experimental and physical parameters to theminimal threshold pumping power. Q-switched pulses with maximum peakpower of %10.4 kW, with energy of %0.5mJ/pulse, were extracted with 30% extraction eﬃciency. Ó 2002 Elsevier Science B.V. All rights reserved.
Keywords: Diode pumped lasers; Passive Q-switching; Yb:YAG laser and microsurgery. Most commonly, systems pres-ently used are based on Nd:YAG or Nd:YVO4 Passively Q-switched, diode pumped solid state lasers, passively Q-switched by Cr4þ:YAG, where lasers are currently being used as miniature or the unique characteristics of Cr4þ garnets as sat- microlasers capable of delivering high peakoutput power at high repetition rates and short nanosec- Similarly to the Nd3þ/Cr4þ:YAG system, it is ond (ns) temporal pulsewidth. These lasers are of anticipated that the Yb3þ/Cr4þ laser system will great interest due to their potential applications in posses signiﬁcant advantages related to micro- micromachining, remote sensing, target ranging, lasers and their applications. During the last severalyears there are convincing indications pertain-ing the Yb3þ-based diode-pumped lasers and their possibility to replace the currently used Nd3þ- Corresponding author. Tel.: +972-7-655-6301; fax: +972-7- based systems, in particular the diode-pumped E-mail address: firstname.lastname@example.org (Y. Kalisky).
0925-3467/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 5 - 3 4 6 7 ( 0 2 ) 0 0 0 0 3 - 4 Y. Kalisky et al. / Optical Materials 19 (2002) 403–413 Solid state lasers based on Yb3þ doped solid nonradiative processes among excited states, hosts emit coherent radiation peaking at 1030 nm or quenching of excited state luminescence.
=2ðA1Þ ! 2F7=2ðZ3Þ, levels, where A1 and Z3 Pumping wavelengths of 940 or 970 nm––utiliza- are the J-Starkcomponents located at 10,327 and tion of the reliable Al-free InGaAs diode lasers 612 cmÀ1, respectively . Yb-based solid-state • Yb is capable of energy storage due to its long lasers have several advantages over Nd-doped la- lifetime––in the 0.95–1.2 ms temporal domain, sers. The advantages of Yb laser can be summa- • Finally, there is signiﬁcant advantage in using the YAG as laser host since both Yb and Nd • Low quantum defect e.g. 91% quantum eﬃ- ciency, hence low fractional heating (<11% as chanical properties of the hosting YAG.
compared to 37–43% in Nd3þ:YAG) , andsmaller thermal load on the crystal.
The main physical and optical characteristics of • Broad absorption bandwidth of about 10 nm Yb3þ:YAG are summarized in Table 1.
and 940 nm ð2F7=2 ! 2F5=2Þ, that implies more The main disadvantage of Yb doped host is its ﬂexibility on the pumping diode wavelength quasi-three-level nature due to the thermal popu- control within the absorption band of the gain lation of the highest J splitting of the 4F7=2 lower medium, and on the diode temperature. (This terminating lasing level, which is about 612 cmÀ1 absorption bandwidth is ﬁve times broader than above the ground level. This thermal population the 808-nm absorption transition in Nd:YAG.) has deleterious eﬀects of resonant re-absorption of • Broad emission bandwidth which results in the laser emission from the ground terminal Stark tunability and the ability to generate short state, which is thermally populated at 300 K by about 5% of the 4F7=2 population. Therefore, it is • High doping levels––up to 20 at.% and even diﬃcult to obtain population inversion at room higher levels, without concentration quenching temperature, and therefore, the lasing threshold is high and its eﬃciency is consequently low. Eﬃcient • Due to the simple 4f13 electronic conﬁguration population inversion is achieved by either pump- of Yb3þ ion, there are no relevant higher lying ing at high pump power densities at 300 K (1.5–10 excited states, and therefore, there is no excited kW/cm2) , or by depopulation of the highest state absorption, upconversion phenomena, Starkcomponents. The latter option is achieved by Table 1Main physical characteristics of Yb:YAG crystal Change of refraction index with temperature Y. Kalisky et al. / Optical Materials 19 (2002) 403–413 cooling down the system to low temperatures, used to study the repetitive modulation and where only the lowest Starklevels are thermally passively Q-switching of Yb laser. The Yb:YAG laser rod, (sample #1) supplied by VLOC (FL, For several applications, mainly industrial, Q- USA), was / ¼ 2 mm in diameter and l ¼ 4 mm switched nanosecond pulses are the preferred in length, and was doped with 10 at.% of Yb3þ.
choice over the high peakpower, sub picosec- ond mode-locked Yb:YAG laser system . It is sample #2 (/ ¼ 28 mm, thickness of 1.95 mm), therefore necessary to optimize the conditions, was supplied by Gospel. The Yb3þ concentration which allow the passively Q-switched operation of in the diskwas calculated from the absorption Yb:YAG laser towards applications that require spectra to be 8.5 at.%. Both laser crystals had mid-levels of average power or alternatively, me- ﬂat/ﬂat surfaces, where the laser rod was HT/HR dium peakpower level at 300 K, utilizing a com- @ 940/1030 nm, respectively, on the pump side and AR @1030 nm on the other side, and the The ytterbium laser is currently regarded as a diskhad an AR/AR coating @ 1030 nm on both suitable candidate to generate pulses having rela- tively high peakpower, due to the long lifetime of the excited level 2F5=2 of Yb3þ ion. This charac- Yb:YAG samples used are presented in Table 2.
teristics, coupled with the ability to obtain high The pumping transition peakat 940 nm is utilized Yb3þ doping levels (up to 20 at.% without con- for diode pumping using InGaAs diode arrays, centration quenching), make the ytterbium doped which are more robust than the AlGaAs diodes solids an ideal candidate as a microlaser in the 1030–1050 nm spectral range. This laser is pas- sively Q-switched by saturable absorbers such as pumped by two types of conductively cooled ﬁber Cr4þ:YAG and other quadrivalent chromium coupled diode array lasers. The ﬁrst one, an OPC- doped garnets, yielding repetitive modulation and B030-940-FC, with a nominal maximum ﬁber dia- meter of 1.55 mm, NA of 0.22 and an output In the present paper, we investigate the optimal power of 30 W, and a second diode model OPC- parameters of an eﬃcient operation of a micro- D060-940-FC, 1.5 mm, 0.1 NA, with a nominal laser based on a passively Q-switched diode-pumped output power of 60 W. The diode laser emission Yb:YAG laser, using several Cr4þ-doped garnets was centered at 940 nm at normal operating tem- perature of 20 °C with an emission spectralbandwidth (full width at half maximum, FWHM)of less than 4 nm. The temperature and hence the wavelength of the pumping diode were regulatedby a chiller (Neslab-CFT-33). The pump radiation The laser experimental set-up is presented was collimated and focused on the front surface of in Fig. 1. Two types of Yb:YAG crystals were the crystal with a focusing lens (OPC-ORU-03) to Fig. 1. Schematic of the passively Q-switched diode pumped Yb:YAG laser set-up.
Y. Kalisky et al. / Optical Materials 19 (2002) 403–413 Table 2Experimental parameters of Yb:YAG crystals used in this paper pumped at 300 K, and which aﬀects the laser crystalline rod was inserted inside a water-cooled For the CW operating mode, we used an Ophir controlled by a thermoelectric re-circulating solid- power meter, (Ophir 30A-SH) to monitor the state chiller (Melcor MLA 270). In order to obtain a good thermal contact between the crystal and the For the pulsed passively Q-switched operation, heat sink, the Yb:YAG crystal was wrapped by a we have inserted inside the cavity, perpendicular thin (0.1 mm) indium foil and then attached to the to the optical axis one of the crystalline samples either Cr4þ:YAG, Cr4þ:LuAG (Lu3Al5O12), or In the case of the Yb-crystal disk, it was sand- Cr4þ:GSGG, all with nominal concentration of the wiched between a water-cooled, ring-shaped, cir- chromium ion in the range 0.15–0.3 at.%. The cular heat sinkand a copper ring (5 mm aperture).
Cr4þ:YAG, Cr4þ:LuAG samples were kindly sup- The copper ring pressed the diskagainst an indium plied by Dr. M. Kokta of Bicron Crystals Products foil, to achieve a good thermal contact of the (USA), and that of Cr4þ:GSGG by Dr. Igor Iva- crystal disksurface to the copper heat sinkunit.
nov, of the Research of Material Science and We assume that the heat sinkand the crystal sur- Technology (Russia). Some important experi- face are always in thermal equilibrium.
mental parameters [1,6] of the Cr4þ doped satu- The laser resonator consisted of an output rable absorbers used in these experiments are presented in Table 3. The Q-switch crystal surfaces ROC ¼ 150 mm, with various reﬂectivities ranging were polished, without coating, and therefore their from R ¼ 85% to 98% @ 1030–1060 nm. A front transmission spectra are accounted for Fresnel ﬂat mirror, with high transmission coating at 940 nm and high-reﬂectivity (HR) coating at 1030 nm, The Q-switched output laser signal was detected was utilized with the diskcrystal. The length of the by a fast silicon photodiode (risetime <1 ns, col- diskand rod laser cavities, was lc ¼ 52 mm, which lected by a digital oscilloscope (Tektronix TDS yielded thermally undistorted waist xc % 150 lm, 724A), and further analyzed by commercial data where xc is the radius (1=e2) of the fundamental processing software. For laser pulse frequency mode size on the backmirror. This length ac- measurements, a detector with a slower risetime counts for the thermal lensing which results from (3.5–18 ls) was employed, followed by an FFT the high pumping power densities when the laser is Y. Kalisky et al. / Optical Materials 19 (2002) 403–413 Table 3Physical and optical parameters of Cr4þ:YAG samples used as saturable absorbers in diode-pumped Yb:YAG laser The thickness of the sample is l, a is the absorption coeﬃcient, and T0 is the small signal transmission.
and 15.7 at.%. The saturable absorbers used inthese cases was sample (a) (e.g. la ¼ 0:85 mm). The 3.1. Passively Q-switched operation––results and average output power for the 10 and 12 at.% was in the hundreds of mW, in the pumping rangeof 26–37 W. The pulsewidths (FWHM) in this pumping power regime were 46 and 34 ns and 184.108.40.206. Medium pump power level (up to 30 W).
the modulation frequency of 4.6 and 5.65 kHz, We passively Q-switched several Yb:YAG laser respectively. We did not test the diskwith CYb ¼ disks with two uncooled, polished Cr4þ:YAG sam- 15:7 at.% for passive Q-switching due to poor ples denoted by (a) and (b). See Table 3 for details.
free running laser performance especially above In these experiments an output coupling mirror Pin ¼ 40 W. This will be discussed further in Sec- with a reﬂectivity of R ¼ 95% was used. Also, in the ﬁrst set of Q-switching experiments we limitedthe input pumping power (pin) to levels of up to 220.127.116.11. High pump power level (up to 60 W). We tested both Yb:YAG rod (as will be described in The Q-switched Yb:YAG (8.5 at.%) laser per- the following section) and Yb:YAG diskfor Q- formance produced about 650 mW average output switching under higher pumping load. For that power at 30 W input pumping power. At this purpose we used a ﬁber coupled diode array of 60 pumping level, the Q-switching element surface W output power at 940 nm. The optimal output was damaged and the laser performance degraded coupling of the laser resonator was R ¼ 85%, and by 50%. The pulsewidth, s (denoted by the the Cr4þ:YAG was sample (a). The performance of FWHM), was of the value s % 30 ns both at low both Yb:YAG rod and diskwas degraded due to and maximum input pumping power, for samples damage at the Cr4þ:YAG surface. When the pas- (a) and (b) of the saturable absorbers.
sively Q-switched Yb:YAG disk(28 Â 1:95 mm) For Yb:YAG disklaser with the saturable ab- was pumped in the range of 20–51 W, it produced sorber sample (a), the modulation frequency of the an average output power of 3 W at 31 W pumping 1030–1048 nm laser emission varied from f % 4 to power. At that point the performance was de- 12 kHz at input pumping levels of Pin ¼ 21 and graded and the system was realigned, which re- Pin ¼ 31 W, respectively. Although there are slight sulted-in 4.2 W average output power @ 51 W diﬀerences between the two samples of the satu- rable absorbers, we cannot draw any comparative In a separate experiment at Pin ¼ 51:8 W, using conclusions pertaining their quality as passive Q- saturable absorber samples (a) and (b) we obtained switches, since the Cr4þ samples were not fabri- pulses of temporal widths of 43.4 and 54.4 ns (FWHM), respectively, and modulation frequency Q-switching operation was applied to Yb-disk of 9.6 and 16 kHz, respectively. All these mea- geometry with Yb3þ concentrations: CYb ¼ 10, 12, surements were carried out using output coupling Y. Kalisky et al. / Optical Materials 19 (2002) 403–413 reﬂectivity of R ¼ 95% and keeping the laser of Pin ¼ 28 W we observed damage to the saturable absorber and degradation in the performance by%25%. The maximum average output power after 3.1.2. Laser rod conﬁguration (sample #1) realignment was Pout ¼ 4:2 W @ Pin ¼ 43:5 W 18.104.22.168. Low pump power level (up to 30 W). Op- input power and the curve was slightly saturated.
erating passively Q-switched Yb:YAG laser rod In the pumping range of 20–51 W, the pulsewidths for both Cr4þ samples (a) and (b) at 30 W pumping ranged from 48 to 38 ns, respectively, and the laser power, produced pulses having temporal pulse- pulse frequency varied from 2 to 23.4 kHz, re- width (FWHM) of s % 16 ns, at an average mod- ulation frequency of f % 4 kHz. The average To improve the Q-switching performance, we output power of Yb:YAG laser rod was lower placed the Cr4þ:YAG inside a water cooled heat than the diskgeometry, namely Pout % 100 mW, sinkat 15 °C. In this conﬁguration (R ¼ 85%), the due to damage to the Q-switching surface. Signif- maximum average output power was Pout ¼ 4:5 W icant improvement in the Q-switched laser per- at an input pumping power of Pin ¼ 32:5 W. Fur- formance was obtained using an output coupler ther increase in the pumping power, up to 53 W, with a reﬂectivity of R ¼ 85%. We obtained max- led to saturation with maximum average output imum average output power of 1.32 W, with a power, namely, Pout % 4:8 W. Under the same slope eﬃciency of g ¼ 12:8%. For the 1.32 W experimental conditions, the free-running output average output power (@ 31 W input pumping power was %16 W, therefore the extraction eﬃ- power), the modulation frequency was f % 13 kHz, with an average pulsewidth of 22 ns. This switched pulsewidth and the modulation frequency implies that the pulse energy is %100 lJ/pulse and on the input pumping power is presented in Fig. 2.
the peakpower is %4.5 kW. At present the results From this ﬁgure we observe that in the pumping with R ¼ 85% are preliminary and no attempt was range of 16–33 W, the repetition rate changed made to optimize the Q-switched performance signiﬁcantly from 1.2 to 9.2 kHz, respectively. The with other output couplers. All the Q-switched change in the pulsewidth in this range was from measurements were performed with Cr4þ:YAG 54.3 to 48 ns, respectively. This conﬁguration sample (a). The maximum error in the pulsewidth yields pulse energy of 0.5 mJ/pulse and peakpower measurements is in the range of Æ10%. The free running average output power was Pout ¼ 5:3 Wunder pumping power and output coupling reﬂectivity,(31 W, Theat sink ¼ Tcrystal ¼ 15 °C, and R ¼ 85%,respectively). The fraction of the Q-switchedpower relative to the free-running output power isdeﬁned by g experimental conditions. We should note here thatdue to the surface damage on the Q-switching el-ement and consequently, the output power de-gradation at about Pin % 26–30 W, the pumpingpower did not exceed this value.
22.214.171.124. High pump power level (up to 60 W). Wealso tested for Q-switching the laser rod (2 Â 4mm) using Cr4þ:YAG sample (a) under higher Fig. 2. The repetition frequency and output pulsewidths versus pumping load similarly to what have been per- pumping power of a passively Q-switched, diode-pumped formed with Yb:YAG disk. The output coupler Yb:YAG/Cr4þ:YAG. The output coupling reﬂectivity is used was also R ¼ 85%. At input pumping power Y. Kalisky et al. / Optical Materials 19 (2002) 403–413 Finally, we used the relatively high peak Cr4þ:YAG when operated as saturable absorbers power to obtain frequency doubling at 525 nm by for Yb:YAG laser. With Cr4þ:LuAG (l ¼ 1:43 using KTP or BBO nonlinear crystals. Both crys- mm), we obtained an average output power of tals generated a modulated green light with a Pout % 235 mW, at Pin % 46 W. The modulation repetition rate in the kHz frequency regime, with frequency in the pumping range 30–46 W changed pulsewidths of about 20–40 ns (FWHM). At pre- from f % 0:6 to 1.7 kHz, respectively. The pulse- sent, the output power of the green laser emission width (FWHM) exhibited a small change namely, is low due to the optical system, which is not op- s % 26:2 to 24.7 ns, which is within the experi- mental error. For the Cr4þ:GSGG (l ¼ 0:2 mm),we obtained average output power of Pout % 220 3.2. Passive Q-switching with Cr4þ:LuAG and mW, with f % 2:7 k Hz and s % 16 ns at Pin % 60 W.
We have conducted preliminary experiments with two additional saturable absorbers based on In order to characterize the working parameters Cr4þ-doped garnets. For these preliminary testing and optimal conditions for passively Q-switched we used Yb:YAG disk(sample #1) with Yb3þ ytterbium laser, free-running operation mode has doping of 8.5 and 10 at.% The optimal output been studied extensively, as well. The free-running couplers used in all the experiments were of mode was operated ﬁrst, in order to characterize Rout ¼ 99% and 85% for both Cr4þ:LuAG and the working parameters and optimal conditions Cr4þ:GSGG, respectively. The Cr4þ:LuAG and for an eﬃcient passive Q-switching operation of Cr4þ:GSGG were polished, uncoated, with small Yb:YAG laser (using samples #1 and #2), in two signal transmission of T0 % 66% and 85%, respec- diﬀerent geometries and at several heat sinktem- tively. The Cr4þ:LuAG is of special interest due to peratures, ranging from 5 to 20 °C. The diode- its highest ratio of rgsa=resa values relative to other pumped Yb:YAG laser performance for Yb:YAG garnets, where rgsa and resa are the ground state rod and diskat 15 °C is presented in Fig. 3(a).
and the excited state absorption cross-sections, Since the experimental results at diﬀerent temper- atures behave similarly, we present only the per- formance at 15 °C. The Yb concentration in the much lower average output power relative to rod used is CYb ¼ 10 at.% (/ ¼ 2 mm, l ¼ 4 mm) Fig. 3. (a) Laser output power of a free-running CW Yb:YAG laser rod (CYb ¼ 10 at.%) and disk(CYb ¼ 8:5 at.%) versus incidentpumping power at 940 nm, at heat sinktemperature of 15 °C. (b) Laser output power of a free-running CW Yb:YAG laser rod(CYb ¼ 10 at.%) versus incident pumping power at 940 nm, at diﬀerent heat sinktemperatures. The various slope eﬃciencies are in-dicated in the ﬁgure.
Y. Kalisky et al. / Optical Materials 19 (2002) 403–413 and for the disk8.5 at.%. (The cavity character- was calculated to be T ðr ¼ r0Þ ¼ 15 °C. This per- istics of this set-up were similar to previous ex- formance is similar (although diﬀerent in beam periments, namely, cavity length of 52 mm, output quality) to the results of Giesen et al.  for Yb(8 coupling mirror of ROC ¼ 150 mm and a reﬂec- at.%):YAG, under similar pump power level, and tivity of R ¼ 95%.) Thermal gradients result in at ambient temperature. Under these experimental thermal lensing and eﬃciency reduction due to the conditions, Giesen et al. obtained free-running high temperature and subsequently, an increase in output power of about 18 W by using a thin disk the lower Starklevel population of the terminal laser (0.3 mm thickness) with four double-passes lasing level. In order to minimize the thermal load of the pump light. Furthermore, improvement in on the crystal we reduced the radial temperature the output power and in the total optical eﬃciency gradients by employing a diskshaped geometry for were obtained by Karszewski et al.  (to values of the laser medium. In this geometry, the thermal 47–45%), in the same temperature range, however, gradients are collinear with the laser beam and the with eightfold passes of the pumping light through axial heat removal is easier due the thinner di- the crystal. Our total optical eﬃciencies at 54 W mension of the disk. In the case of the disk con- pumping input power (single-pass) obtained at ﬁguration, the laser output power showed linear heat sinktemperatures of, T ¼ 5, 10, and 20 °C, dependence on the incident input power at same are 39%, 36.6%, and 34.7%, respectively.
heat sinktemperature range, while the laser rod The beam quality factor, M 2, of Yb:YAG was performance deviated from linearity.
measured in both the rod and diskgeometries. The The slope eﬃciency, g , was calculated from the values of M 2 yield further indication as to the in- linear dependence of the output power on the ﬂuence of the thermal gradients on the laser per- formance. The beam quality was measured byusing the knife-edge technique. The beam size DðzÞ was measured between 13.5% and 86.5% clip-level where Pout is the laser output power, Pin is the in- . The measured values of DðzÞ were ﬁtted to the put pumping power and Pth is the extrapolated threshold power. The maximum output power obtained at an operating temperature of T Tcrystal ¼ 5 °C in the above pumping scheme is where D0 is the width of the beam waist located at Pout ¼ 22:2 W, with a slope eﬃciency of g ¼ 56%.
a position z0, and h is the divergence angle. By When the crystal temperature was increased up using these parameters, the values of M 2 were to 20 °C, the Yb:YAG output power degraded slightly to Pout ¼ 19 W, with a slope eﬃciency, g ¼ 53:6%. The free-running performance of Yb:YAG rod at diﬀerent operating temperatures ispresented in Fig. 3(b). In all the experiments, the where k is the laser wavelength. For Yb:YAG rod laser was pumped around the maximum absorp- (CYb ¼ 10 at.%) and Yb:YAG disk(CYb ¼ 8:5 tion peak(941 nm), where most of the pump light at.%), the beam quality factors at 53 W input was absorbed. The temperature eﬀects on the laser power are 3.15 and 2.51, respectively. This con- performance are clearly observed at high pumping ﬁrms our assumption of better thermal manage- load, where deviation from linear ﬁtting in the input–output curves are observed. The radialtemperature gradient inside the laser rod (relative to the heat sinktemperature) was calculated usingthe formula of Innocenzi et al. . In the rod The concentration of Yb3þ active ion is a cru- center r ¼ 0, the relative temperature, T ðr ¼ 0Þ cial factor in the proper performance of Yb laser.
was calculated as 140 °C, while at the crystal sur- This stems from the quasi-three level nature of face, namely, at r ¼ r0 ¼ 1 mm, the temperature ytterbium laser and the reabsorption of the laser Y. Kalisky et al. / Optical Materials 19 (2002) 403–413 emission. We tested several samples of Yb:YAG Only the 10 at.% samples of this set performed with diﬀerent doping levels in order to establish a similarly to Yb:YAG rod (samples #3), in the relationship between the laser performance and output coupling range of R ¼ 99–95%, and with the active ion concentration. All the experiments were performed at crystal heat sinktemperature,Theat sink % Tcrystal ¼ 16 °C. The lengths of the 5 and 10 at.% laser rods were adjusted for %87% and%95% absorption of the pumping power, respec- The total round-trip losses in the Yb:YAG laser tively. The laser performance tests for samples #3 system were estimated by using the Findlay–Clay and #4 were made on samples from the same method. This is done by measuring the various vendor and under the same experimental condi- pumping input power at threshold versus the out- tions, which implies similar growth and coating put coupling mirror reﬂectivities . The follow- conditions. By using set samples #3 of Yb:YAG ing equation provides the relation between the rods with CYb ¼ 10 and 5 at.%, we obtained slope eﬃciencies of 37% and 25.5%, respectively.
The results were recorded for a variety of out- put couplers, ranging from R ¼ 92% to 99% (at where R is the reﬂectivity of the output mirror, Tcrystal ¼ 16 °C). We also used a mechanical chop- and K is the pumping coeﬃcient deﬁned as the per (duty cycle of 50%) to minimize thermal eﬀects product of all the coeﬃcients that lead to the and possible damage to the crystals. For the laser population of the upper lasing state. Eq. (1) is rods with CYb ¼ 10 and 5 at.%, the laser per- valid for only a four-level system. We use it for formed best with output coupler of R ¼ 95%. For Yb3þ assuming that under proper thermal man- CYb ¼ 5 at.% we observed a variation of %20% in agement the system is a quasi-three-level. This the maximum output power among diﬀerent point, will be veriﬁed later in the text. The incident samples from the same boule. Also we noticed pumping power at threshold is deﬁned by Pth, and instabilities in the output power above 20 W ab- L represents the total round-trip losses, deﬁned as: sorbed power, probably due to thermal eﬀects in- L ¼ 2dl þ LM. Here, l is the crystal length, and d side the Yb:YAG crystal. We should note here the are the passive losses per unit length. The value of eﬀect of pumping wavelength variation with the LM represents various losses , such as absorp- diode current on the Yb laser performance, for tion or scattering losses at the back(HR) mirror, both CYb ¼ 10 and 5 at.% While the optimal or diﬀraction losses of the resonator and is esti- wavelength at the maximum current is k ¼ 942 mated as LM % 1%. The laser was operated for nm, there is a signiﬁcant blue shift at lower diode optimal performance using diﬀerent output cou- currents, and this aﬀects the amount of the ab- pler reﬂectivities ranging from 85% to 98%. The sorbed power. With the CYb ¼ 10 at.% the insta- best performance obtained for both the Yb:YAG bilities of output power with time were much rod and the disk(samples #1 and #2) were at higher and in some cases led to 20% degradation of R ¼ 95%. The values of L and K can be extracted the initial power after 25 min of CW operation.
from the linear plot of À lnðRÞ vs. Pth according to We should mention here that unlike other re- Eq. (1). The values for the total round-trip losses ports, no lasing action was observed under the are, L ¼ 8% and the factor K ¼ 6:725 Â 10À3 WÀ1 same experimental conditions and at ambient for 10 at.% ytterbium laser rod. For the 8.5 at.% temperature with samples #4, namely, CYb ¼ 20 Yb3þ laser disk, the total round trip losses are, and 30 at.% (set samples #4), either when pumped L ¼ 9:3%, and the factor K is, K ¼ 7:15 Â 10À3 at the absorption peak(941 nm) or at the shoulder WÀ1. The experimental measurement error is of the absorption (935 nm). This is attributed to Æ10%. The passive losses per unit length extracted the strong ground state re-absorption at the lasing from our results (assuming that LM % 1%) are wavelength. All the samples were of diskshape 8.75% and 21% per cm for the ytterbium laser rod and adjusted for 60–63% absorption at 941 nm.
Y. Kalisky et al. / Optical Materials 19 (2002) 403–413 The small signal gain at threshold is calculated In the present paper, we report the results of optimizing the working parameters of an eﬃ- cient operation of a microlaser, based on a passiveQ-switched diode-pumped Yb:YAG laser. The From this expression, the small signal gain at resonator optimization accounts for the thermal threshold (with 95% reﬂectivity of the output lensing which results from the high pumping coupler) is obtained: gthðYb-rodÞ % 0:132 cmÀ1 power densities when the laser is pumped at 300 K, and gthðYb-diskÞ % 0:4 cmÀ1. From the values of and which aﬀects the laser performance and its gain at threshold and the known values of stimu- lated emission cross-section, the population in- The usefulness of tetravalent chromium-doped version at threshold can be estimated using the garnets as saturable absorbers is demonstrated by achieving repetitive modulation of a CW Yb:YAGlaser operation. By using Yb:YAG/Cr4þ:YAG crystals, it produces modulated light in the kHz frequency range with pulsewidths in the 16–48 ns temporal regime. Maximum peakpower of 10.4 2th ¼ N2ðj¼1Þth is the lowest Starkcompo- is reported. The optimization yields extraction of Q-switched pulses of %0.5 mJ/pulse, with j ¼ 3 Starkcomponent of the ground state (2F extraction eﬃciency of %30% relative to the free- cmÀ1 above the ground state. The stimulated conditions. Our experimental results of aver- age output power, modulation frequency, and pulsewidth in Yb:YAG/Cr4þ:YAG system are in that at threshold, the ground state population agreement with the recent results of Patel and depletion due to ground state absorption is small, Beach . The performance of Cr4þ:YAG as a saturable absorber is superior relative to that of 1 ( NT (N1 is the ground state ion density Cr4þ:LuAG or Cr4þ:GSGG. By utilizing the sig- niﬁcant advantages of Yb3þ ion, we are currentlydeveloping a compact diode-pumped Yb:YAG and it follows that gain at threshold is given by This workwas supported by the ‘‘MAGNET’’ th is the population inversion at thresh- program of the Chief Scientist Oﬃce at the Israeli 5:7 Â 1018 and 1:74 Â 1019 cmÀ3, for Yb:YAG rod Ministry of Industry and Trade, Consortium of and disk, respectively. The diﬀerences in gain, Diode Pumped Solid State Lasers (LESHED).
losses, and hence, in the population inversion atthreshold are attributed the diﬀerent crystal qual-ity and the presence of impurities which are pre- sent in small amounts in the Yb:YAG samples andwhich contributes to degradation in laser perfor-  Y. Kalisky, A. Ben Amar-Baranga, Y. Shimony, M.R.
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Institute for Theoretical Computer Science,is the first prototype implementation of non-standard inferences forDescription Logics that can be used via a graphical user interface. In addition tothat our implementation extends an earlier implementation of the least commonsubsumer and of the approximation inference service to more expressive Descrip-tion Logics, more precisely to Description Logics