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Optical Materials 29 (2007) 1271–1276
Thermally-induced-birefringence effects of highly Nd3+-dopedY3Al5O12 ceramic lasers
Ichiro Shoji a,*, Takunori Taira b, Akio Ikesue c
a Department of Electrical, Electronic, and Communication Engineering, Chuo University, Kasuga 1-13-27, Bunkyo-ku, Tokyo 112-8551, Japanb Laser Research Center, Institute for Molecular Science, 38 Nishigonaka, Myodaiji, Okazaki 444-8585, Japan
c Poly-Techno Co., Ltd., 2-4-1 Mutsuno, Atsuta-ku, Nagoya 456-8587, Japan
Received 17 October 2005; received in revised form 21 November 2005; accepted 12 December 2005Available online 7 September 2006
Abstract
Thermally-induced-birefringence effects of Nd:YAG ceramic lasers are accurately measured. Depolarization for the ceramics is foundto be nearly the same with that for (111)-cut single crystals if Nd3+ concentration is the same. Under non-lasing condition, the thermally-induced birefringence becomes larger as Nd3+ concentration increases due to severer quenching. Under lasing, however, depolarization ismeasured to be one-third of that under non-lasing because the stimulated emission reduces the nonradiative process, which decreases thethermal load. Moreover, direct pumping into the emitting level by use of a 885 nm pump source intrinsically reduces the heat generationcompared with the conventional 808 nm pumping; we have experimentally verified that the depolarization and the thermal load arereduced by 30% by the direct pumping.� 2006 Elsevier B.V. All rights reserved.
PACS: 42.70.Hj; 78.20.Fm; 78.20.Nv; 42.55.Rz; 78.55.Hx; 42.25.Ja; 42.25.Lc
Keywords: Ceramic laser; Thermally-induced birefringence; Depolarization; Direct pumping; Nd:YAG
1. Introduction
The ceramic laser has been intensively studied as a can-didate for the next-generation high-performance laser sincehighly transparent Nd3+:Y3Al5O12 (Nd:YAG) ceramicswere successfully grown and its laser oscillation was dem-onstrated [1]. We succeeded in oscillation of a microchipNd:YAG ceramic laser and constructed a green laser byintracavity frequency doubling [2]. The fundamental opti-cal properties were also investigated [3], and it was alsofound that Nd:YAG ceramics are suitable for direct pump-ing into the emitting level at 885 nm [4]. Furthermore, weachieved laser oscillation of Y3ScAl4O12 ceramics [5], andfemtosecond pulse operation with passively mode locking[6,7].
0925-3467/$ - see front matter � 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.optmat.2005.12.012
* Corresponding author. Fax: +81 3 3817 1847.E-mail address: [email protected] (I. Shoji).
One of the most significant advantages of Nd:YAGceramics is that Nd3+ can be highly doped into YAGceramics (up to �10%) without degradation of their homo-geneity and thermal conductivity [2]. This indicates thatNd:YAG ceramics can be highly efficient and high-powermicrochip laser materials because the pump absorptioncoefficient becomes larger in proportion to the Nd3+ con-centration [3]. In this paper, we report the thermally-induced-birefringence effects in Nd:YAG ceramics whichare important for their high-power operation.
2. Measurement of the thermally-induced-birefringence
effects
We developed a pump-probe method for accuratelymeasuring the depolarization caused by the thermally-induced birefringence [8], which is defined by the ratio ofthe depolarized power to the initially polarized power as
Fig. 1. Experimental setup for the measurement of depolarizationresulting from thermally-induced birefringence.
nr
X
YNd:YAG(111) Plane
(Analyzer)
(Polarizer)
InitialPolarization
nΦ
Φr
r0
wawp
Fig. 3. The principal axes and the thermally-induced birefringence nr andnU of the index ellipse which is formed in a (111) plane of a Nd:YAGsingle crystal. wp: the pump-beam radius; wa: the probe-beam radius.
0.03
0.02
0.01
0
Dep
olar
izat
ion
Dpo
l
543210
Nd Concentration (at.%)
Nd:YAG Ceramics
Nd:YAG Single Crystal
ηh = 0.24
ηh=0.69
0.58
0.41
0.38
Lasing
Fig. 4. Dependence of depolarization on Nd concentration under non-lasing at the absorbed pump power of 1 W. The solid line shows thecalculated depolarization, while the dotted line indicates the calculationunder the ideal lasing condition.
1272 I. Shoji et al. / Optical Materials 29 (2007) 1271–1276
Dpol = P?/Pinitial. The experimental setup is shown inFig. 1. A cw Ti:sapphire laser was used as the pump beam,which was focused onto the sample with the radius of35 lm. A linearly polarized He–Ne laser which was colli-mated to a 1 mm radius, was used as the probe. After pass-ing through the sample, the probe beam was reflected fromthe filter with high reflectivity at 633 nm, and went backthrough the sample again. We detected only the depolar-ized (i.e. X-polarized) component of the probe beam usingthe analyzer. In addition, we inserted plane mirrors to con-figure the cavity when we measured the depolarizationunder lasing conditions.
3. Depolarization under non-lasing conditions
First we measured the depolarization under non-lasingconditions. Fig. 2 shows the depolarized beam patternsfor the (111)-cut 1.0 at.% Nd:YAG single crystal and the3.5 at.% Nd:YAG ceramics, which were observed with aCCD camera. Since the thermally-induced birefringencein the (111) plane of a Nd:YAG single crystal is circularlysymmetric and occurs between the radial and the azimuthal
Fig. 2. Depolarized beam patterns under non-lasing. (a) (111)-cut1.0 at.% Nd:YAG single crystal; (b) 3.5 at.% Nd:YAG ceramics. Theabsorbed pump power, Pabs, were both 1.7 W.
directions as shown in Fig. 3, the depolarized beam forms afour-leaf-like pattern (Fig. 2(a)). Although the same pat-tern was observed for the 3.5 at.% Nd:YAG ceramics(Fig. 2(b)), its depolarization was enhanced compared withthat of the single crystal at the same absorbed pump power.Fig. 4 shows the dependence of the depolarization on theNd3+ concentration at the absorbed pump power of 1 W.It was found that the depolarization is nearly the samefor ceramic and single-crystal YAG when their Nd3+ con-centrations are the same. Because the YAG ceramics con-sist of many single-crystal grains (their sizes are in severaltens of micrometers) with random orientations, the ther-mally-induced birefringence effect is the average of thosegrains. Although the depolarization in the planes otherthan (111) significantly depends on the direction of polar-ization as shown in Fig. 5 [9], the average, and the depolar-ization for the ceramic YAG, are close to that for the (111)plane [10].
Moreover, it was found that the depolarization becamelarger in the samples with higher Nd3+ concentrations even
0.025
0.020
0.015
0.010
0.005
0
Dep
olar
izat
ion
Dpo
l
360270180900Polarization Angle θp (degree)
(111) (100) (110)Absorbed Pump Power: 1.5W
Fig. 5. Dependence of depolarization on the direction of polarization for(111), (100), and (110)-cut single crystals.
Table 1Parameters used for calculation of depolarization
wp: pump beam radius 35 lmwa: probe beam radius 1 mmk: probe wavelength 0.6328 lmn0: refractive index of Nd:YAG 1.83al: linear expansion coefficient 6.9 · 10�6 K�1
j: thermal conductivity 10 W/mKm: Poisson’s ratio 0.3pij: photoelastic coefficient p11 = �0.029
p12 = 0.009p44 = �0.062
I. Shoji et al. / Optical Materials 29 (2007) 1271–1276 1273
if the absorbed pump power was the same. This is mainlybecause the thermal load increases as Nd3+ concentrationincreases. The thermal load is given by the fraction of theabsorbed pump power that is converted into heat in thelaser medium as [11]
gh ¼ 1� gp½ð1� glÞgrðkp=kfÞ þ glðkp=klÞ�; ð1Þ
where gp is the pump quantum efficiency (�1), gl is the stim-ulated emission efficiency which is the fraction of excitedions that are extracted by stimulated emission, gr is the radi-ative quantum efficiency, kp is the pump wavelength, kf isthe average fluorescence wavelength (1038 nm), and kl isthe laser oscillation wavelength (1064 nm). Since gl = 0under non-lasing, Eq. (1) is simplified to gh = 1 � gr
(kp/kf). For a highly Nd3+-doped sample, in which the inter-action between Nd3+ ions is significant, the concentrationquenching decreases the value of gr. The thermal load, gh,then becomes larger as Nd3+ concentration increases,indicated in Fig. 4 [12]. We calculated the amount ofdepolarization at each Nd3+ concentration using these val-ues of gh.
The amount of depolarization is represented by [13]
Dpol ¼1
pw2a
Z wa
0
Z 2p
0
Dðr;UÞr dr dU; ð2Þ
which is the integration of the depolarization
Dðr;UÞ ¼ sin2 2U sin2 WðrÞ2
ð3Þ
at each point (r,U) in Fig. 3 over the whole probe beam.Here we assume that the thermally-induced-birefringenceeffect in ceramics is the same with that in a (111)-cut singlecrystal. W(r) is the phase difference caused by the ther-mally-induced birefringence, and written as
WðrÞ ¼ 2
Z t
0
2pk½nrðrÞ � nUðrÞ�dz ¼ XAðrÞS00; ð4Þ
where t is the thickness of the sample, the factor of 2 meansthat the probe beam makes the round trip through the sam-ple, and X, A(r), S00 are given by
X ¼ 1
3n3
0ð1þ mÞðp11 � p12 þ 4p44Þ; ð5Þ
AðrÞ ¼ 2 1� 2
r2
Z r
0
E1
2r02
w2p
!r0 dr0 þ E1
2r2
w2p
!" #; ð6Þ
S00 ¼ al
1� mghP abs
8jk; ð7Þ
respectively. The values of those parameters used for thecalculation are shown in Table 1. E1(z) is the exponentialintegral function. The solid line in Fig. 4 is the numericalcalculation of the depolarization, which agrees well withthe experimental data. It is not desirable that the depolar-ization becomes more significant as Nd3+ concentration in-creases. When lasing occurs, however, the stimulatedemission efficiency, gl, is ideally 1 in Eq. (1), which reducesthe thermal load to a small constant value gh = 1 � kp/kl = 0.24. The depolarization is then expected to remainsmall regardless of Nd3+ concentration as indicated bythe dotted line in Fig. 4.
4. Depolarization under lasing conditions
We measured reduction of depolarization under lasingconditions by use of the 3.5 at.% Nd:YAG ceramic andthe 1.0 at.% Nd:YAG single crystal samples. The pumpwavelengths for the ceramic and the single crystal were806 and 808 nm, respectively, in order for the absorptioncoefficients to be nearly the same. Fig. 6 shows the depen-dence of the output power on the absorbed pump power.The slope efficiency of 71% was obtained with the singlecrystal. On the other hand, the slope efficiency of the cera-mic was 47% presumably because the highly Nd3+-dopedYAG still generated more heat and suffered from largerthermal-lens effect than the lower concentrated YAG,reducing the mode-matching efficiency. However, theamount of depolarization was found to be greatly reducedto the value of 1/3 that under non-lasing, as shown inFig. 7.
The dotted lines in Fig. 7 are the calculation of depolar-ization under non-lasing, in which 0.69 and 0.38 were usedas the values of gh for the 3.5 and 1.0 at.% Nd:YAG,respectively. However, we have to experimentally obtainthe values of gh under lasing conditions because gl doesnot become 1 in practical cases. gl can be expressed by
0.10
0.08
0.06
0.04
0.02
0
Dep
olar
izat
ion
Dpo
l
210
Absorbed Pump Power Pabs (W)
Lasing
Lasing
1.0at.% Single Crystal ((111)-cut, λp=808nm)
Nd:YAG3.5at.% Ceramic (λp=806nm)
Fig. 7. Dependence of depolarization of the 1.0 at.% Nd:YAG singlecrystal ((111)-cut) and the 3.5 at.% Nd:YAG ceramic on the absorbedpump power under lasing and non-lasing conditions. The dotted curvesindicate the calculated depolarization under non-lasing conditions usingthe constant thermal load and the parameters shown in Table 1. On theother hand, the solid curves indicate the calculation under lasingconditions using the estimated values of the thermal load shown in Fig. 8.
1.0
0.8
0.6
0.4
0.2
0
The
rmal
Loa
d η h
210
Absorbed Pump Power Pabs (W)
1.0at.% Nd:YAG Single Crystal 3.5at.% Nd:YAG Ceramic
Lasing
ηl=1
ηl=0
ηl=0
3.5at.%Ndηr=0.39
1.0at.%Ndηr=0.80Lasing
Fig. 8. Dependence of the thermal load gh of the 1.0 at.% Nd:YAG singlecrystal and the 3.5 at.% Nd:YAG ceramic on the absorbed pump powerunder lasing condition, which was obtained by the values of gl shown inFig. 6. The constant values of gh under non-lasing (gl = 0) and the ideallasing (gl = 1) conditions are also shown by the dotted lines.
2.0
1.5
1.0
0.5
0
Out
put P
ower
Pou
t (W
)
210
Absorbed Pump Power Pabs (W)
1.0
0.8
0.6
0.4
0.2
0.0
Stim
ulated Em
ission Eff. η
l
ηs=71%
ηs=47%
3.5at.% Ceramic (λp=806nm)1.0at.% Single Crystal (λp=808nm)
Nd:YAG
Fig. 6. Dependence of the laser output power Pout of the 1.0 at.%Nd:YAG single crystal and the 3.5 at.% Nd:YAG ceramic on theabsorbed pump power Pabs. The stimulated emission efficiencies gl as afunction of the absorbed pump power, which were estimated by use of Eq.(8), are also shown.
1274 I. Shoji et al. / Optical Materials 29 (2007) 1271–1276
use of the output power, Pout, and the absorbed pumppower, Pabs, as
gl ¼nstimulated
nexcited
¼ 1
gcgp
nlaser
npump
¼ 1
gcgpgq
P out
P abs
; ð8Þ
where nlaser is the number of the output laser photons,npump is the number of the absorbed pump photons,gq = kp/kl, and gc is the coupling efficiency. The outputpower can also be represented by
P out ¼ gcgpgqgmðP abs � P thÞ; ð9Þ
where gm is the mode-matching efficiency and Pth is thethreshold absorbed pump power. Eqs. (8) and (9) givethe expression of gl as
gl ¼ gm
P abs � P th
P abs
: ð10Þ
It is obvious from Eq. (10) that gl cannot be 1 because thethreshold has a finite value and the mode-matching effi-ciency is usually smaller than 1. We then estimated the val-ues of gl under lasing at each absorbed pump power withEq. (8). Here gc is given by gc = ln(1/R)/[Li + ln(1/R)],and the reflectivity of the output mirror, R, the cavitylosses, Li, for the 3.5 at.% Nd:YAG ceramic and the1.0 at.% Nd:YAG single crystal, were 0.91, 0.029, and0.0096, respectively. gp was assumed to be 1. The opensquares and the open circles in Fig. 6 shows the estimatedvalues of gl for the ceramic and the single crystal, respec-tively, and Fig. 8 shows the dependence of the thermal loadon the absorbed pump power under lasing conditionswhich was obtained by the values of gl with Eq. (1).Although gh is large around the threshold, it becomes smal-ler as the pump and the output power increase. The solidlines in Fig. 7 are the calculated depolarization using the re-sults of Fig. 8, which agreed well with the experimentaldata. This means that we can approximately estimate theamount of the thermal load from the laser input–outputcharacteristics. Moreover, it was found that highly Nd3+-doped YAG ceramics are suitable for high-power cw orhigh-repetition-rate Q-switched operations because lasingreduces the thermally-induced-birefringence effect.
5. Reduction of the thermal load by the direct pumping of
highly Nd3+-doped YAG ceramics
The direct pumping is the scheme of pumping a Nd3+-doped material from the ground or the hot-band levels tothe emitting levels [4], reducing the quantum defect becausethe pump wavelength shifts from conventional 808 nm to�885 nm. This makes the upper limit of the efficiencyhigher; 80% slope efficiency was achieved by the directpumped Nd:YVO4 [14]. Although the diode pumping issuitable for direct pumping of Nd:YAG because theabsorption linewidth around the 885 nm band is as broadas 3 nm, the absorption coefficient for 1 at.% Nd:YAG is
68
0.001
2
4
68
0.01
2
4
68
0.1
Dep
olar
izat
ion
Dpo
l
210
Absorbed Pump Power Pabs (W)
Lasing
λp=806nm
λp=886nm
3.5at.% Nd:YAG Ceramic
(λp=806nm)
(λp=886nm)
ηl=1
ηl=1
} ηl=0
Fig. 11. Depolarization as a function of the absorbed pump power underlasing and non-lasing conditions for the direct and conventional pumping.The dashed and solid curves are the calculated result.
1.0
0.8
0.6oad
η h
λp=806nm
λp=886nmηl=0 (λp=806nm)ηl=0 (λp=886nm)
3.5at.% Nd:YAG Ceramic
I. Shoji et al. / Optical Materials 29 (2007) 1271–1276 1275
only 1.5 cm�1. Highly Nd3+-doped YAG ceramics whichhave large absorption coefficients are then appropriatefor highly efficient and high-power direct pumped lasermaterials.
In the case of 3.5 at.% Nd:YAG under non-lasing, thedifference of the thermal load between with the conven-tional (gh = 0.70) and with the direct pumping (gh = 0.67)is only 4%. Under lasing conditions, however, the thermalload is expected to be reduced by 30% from gh = 0.24 (con-ventional) to gh = 0.17 (direct pumping) if gl = 1 isassumed. We experimentally verified the reduction of thethermal load in the 3.5 at.% Nd:YAG ceramics by thedirect pumping.
Fig. 9 shows the dependence of the laser output poweron the absorbed pump power with the conventional(kp = 806 nm) and the direct (kp = 886 nm) pumping. Theslope efficiency increased to 66% by direct pumping, pre-sumably because less heat generation reduced the ther-mal-lens effect, improving the mode-matching. Thedepolarized beam patterns for the conventional and thedirect pumping are shown in Fig. 10, which shows thatthe depolarization with the direct pumping is smaller than
Fig. 10. Depolarized beam patterns under lasing for the 3.5 at.%Nd:YAG ceramics. The pumping wavelengths were (a) 806 and (b)886 nm. The absorbed pump power, Pabs, were both 1.7 W.
2.0
1.5
1.0
0.5
0
Out
put P
ower
Pou
t (W
)
210Absorbed Pump Power Pabs (W)
1.0
0.8
0.6
0.4
0.2
0.0
Stim
ulated Em
ission Eff.η
l
3.5at.% Nd:YAG Ceramic
ηs=47%
ηs=66%
λp=886nm
λp=806nm
TO.C.=9%
Fig. 9. Dependence of laser output power on the absorbed pump powerfor the conventional (filled square) and direct (filled circle) pumping. Theestimated stimulated emission efficiencies for the direct and conventionalpumping are also shown by open circles and squares, respectively.
0.4
0.2
0
The
rmal
L
210
Absorbed Pump Power Pabs (W)
Lasing
(λp=806nm)
ηl=1
ηl=1(λp=886nm)
Fig. 12. Dependence of the thermal load gh of the 3.5 at.% Nd:YAGceramic on the absorbed pump power under lasing by the conventionaland the direct pumping, which were obtained by the values of gl shown inFig. 9. The constant values of gh under non-lasing (gl = 0) and the ideallasing (gl = 1) conditions are also shown by the dotted lines.
with the conventional pumping even at the same absorbedpump power. This is quantitatively shown in Fig. 11, inwhich the depolarization is plotted in a log scale so thatthe difference can be clearly seen. While little differencewas measured under non-lasing conditions, the depolariza-tion with the direct pumping became 30% smaller than withthe conventional pumping under lasing conditions. Thecalculated depolarization, which was indicated by the dot-ted lines in Fig. 11, satisfactorily agreed with the experi-mental data. This result justifies the values of the thermalload shown in Fig. 12, which were used for the calculationof the depolarization, and Fig. 12 verifies that the heat gen-eration was reduced by 30% with the direct pumping.
6. Summary
We investigated the thermally-induced birefringence inNd:YAG ceramics. It was found that highly Nd3+-dopedYAG ceramics are promising for highly efficient, high-power cw or high-repetition-rate Q-switched microchiplaser materials. Highly Nd3+-doped ceramic YAG is also
1276 I. Shoji et al. / Optical Materials 29 (2007) 1271–1276
regarded as one of the best materials for the direct pumpingbecause 30% reduction of the thermal load is possible.
Acknowledgements
This work was partially supported by the Ministry ofEducation, Culture, Sports, Science and Technology,Grant-in-Aid for Scientific Research (A), 15206073, andthe Special Coordination Funds for Promoting Scienceand Technology.
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