High-sensitivity two-dimensionalthermal- and mechanical-stress-inducedbirefringence measurements in a Nd:YAG rod

Masato Ohmi, Masanori Akatsuka, Koji Ishikawa, Kenta Naito, Yoshiyuki Yonezawa,Yoshio Nishida, Masanobu Yamanaka, Yasukazu Izawa, and Sadao Nakai

A novel polarimeter for measuring the two-dimensional (2D) thermal- and mechanical-stress-inducedbirefringence in solid-state laser materials such as Nd:YAG is proposed. Using this device, we couldsensitively measure the direction of the principal birefringence axis as well as the phase shift 8 with signwhen S < iT/4. The 2D thermal- and mechanical-stress-induced birefringence in a laser-diode-pumpedNd:YAG rod was successfully measured with the proposed polarimeter. We also found an activequarter-wave Nd:YAG phase retarder.

1. Introduction

In a solid-state laser, such as a YAG laser, laseroscillation begins when energy from an excitationlight source, such as a lamp or a laser diode (LD), isapplied to a laser medium. A part of the light energyis converted into heat and accumulated in the lasermedium so that a temperature gradient or distortionis produced inside the laser medium. As is wellknown, this causes the laser medium to have opticalanisotropy, thereby permitting birefringence to ap-pear. In particular, when a temperature gradient isproduced inside the laser medium, the difference inthermal expansion between the surface and the cen-ter of the medium distorts the medium, thus generat-ing internal stresses. Similarly, mechanical stressesresulting from mounting the laser medium causeinternal stresses in the laser medium. The refrac-tive index of a medium for light depends on stress.

When this research was performed, M. Ohmi, M. Akatsuka, K.Ishikawa, K. Naito, M. Yamanaka, Y. Izawa, and S. Nakai werewith the Institute of Laser Engineering, Osaka University, 2-6Yamadaoka, Suita, Osaka 565, Japan; K. Naito is now with NissinElectric Co., Ltd., 47, Umezu-takase-cho, Ukyo-ku, Kyoto 615,Japan. Y. Yonezawa is with Fuji Electric Corporate Research andDevelopment, Ltd., 2-2-1, Nagasaka, Yokosuka, Kanagawa 240-01,Japan. Y. Nishida is with the Osaka Municipal Konohana HighSchool, 2-3-16, Torishima, Konohana-Ku, Osaka 554, Japan.

Received 1 November 1993; revised manuscript received 11 April1994.

0003-6935/94/27636805$06.00/0.© 1994 Optical Society of America.

As a result a distribution of refractive indices isproduced inside the medium (photoelastic effect).

In such a solid-state laser system, a laser beam isamplified when it is reflected back and forth betweentwo mirrors. When birefringence that is due tothe thermal or mechanical stress has occurred insidethe laser medium, therefore, the relative phase differ-ence between the two refracted beams causes thewave front to be disturbed, thereby presenting anobstacle to effective laser operation in cases in which alaser beam emitted from a laser is output as linearlypolarized light and then amplified for use.

From the standpoint of promoting the study ofbirefringence compensation to obtain a laser beamhaving a small wave-front distortion, there is need foran improved method for measuring the two-dimen-sional (2D) birefringence distribution quantitativelyand with high sensitivity.

It is commonly known that the birefringence effectsin pumped laser rods can be studied in a polariscopicarrangement in which the expanded and collimatedlight beam from a He-Ne laser serves as an illumina-tor for the observation of the rod between crossedpolarizers.1 Unfortunately, this method is insensi-tive to small birefringences such as those induced byLD end pumping. In a polarized cw laser, smallphase shifts lead to small losses, which are stillimportant. We have demonstrated highly sensitivemeasurements of small birefringences with a novelpolarimeter. In this method we could measure thedirection of the principal birefringence axis as well asthe phase shift with sign for each point. The 2Dthermal- and mechanical-stress-induced birefrin-

6368 APPLIED OPTICS / Vol. 33, No. 27 / 20 September 1994

gence in a LD-pumped Nd:YAG rod was successfullymeasured with the proposed polarimeter.

Furthermore, it is well known that the polarizationof a laser beam is changed when a mechanical stress isapplied to the laser material. This is a very seriousproblem in a LD-pumped microchip laser2 and infrequency-stabilized LD-pumped lasers.3 In the yt-terbium-doped fiber laser, quarter-wave retardationhas been induced by mechanical stress.4 A quarter-wave plate produced by mechanically stressing aNd:YAG laser rod has also been recently reported.5This is an active element because there is bothquarter-wave retardation and amplification of laserradiation simultaneously.

In this paper we describe high-sensitivity 2D ther-mal- and mechanical-stress-induced birefringencemeasurements in a Nd:YAG laser rod by the use ofthe new polarimeter. The quarter-wave retardationand the double-pass gain of 1.15 obtained in theLD-pumped mechanically stressed Nd:YAG rod arealso reported.

2. Two-Dimensional (21D) Thermal-Stress-InducedBirefringence Measurement in the Laser Rod

Figure 1 shows the schematic arrangement of ournewly constructed polarimeter. As is shown in Fig.1, a probe laser beam (632.8-nm He-Ne laser) ispassed through a linear polarizer and a quarter-waveplate to generate right-circularly polarized light, whichis then propagated through the birefringent materialto be tested, such as a LD-pumped or a mechanicallystressed laser rod. The image data are detected by a2D CCD camera while the analyzer is rotated aboutthe axis of the probe beam, in steps of a fixed rotationangle. A 2D CCD camera detects, as summarized inAppendix A, the signal I, given by

I = Io [1 + sin 2(( - )sin 8], (1)

where Io is the incident intensity of probe light at thequarter-wave plate, 4 is the angle of rotation of theanalyzer, and 0 is the angle of the fast axis ofbirefringence. According to Eq. (1), the relative phasedifference 8 is calculated from sin 8, together with thedetermination of the sign of 3. These calculationsare carried out automatically in a computer (NECPC9801BX) for each of the pixels of the image data, inour case for 4000 points (1 point = 4 pixels), wherebythe 2D distribution of birefringence in the sample andthe direction of the principal axis are obtained simul-taneously. Also, when the relative phase difference8 is very small, less than Tr/4 rad, the term sin is

V4

U)

C

a

0C

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 / , ,,,,z,. .,- . . . .. . .- ~~~~~ I

0 10 20 30 40Phase Shift (degrees)

50

Fig. 2. Relative intensity change versus relative phase shift 8 for aconventional conoscope (dotted curve) and for our polarimeter(solid curve).

approximated to 8, so that even a small relative phasedifference 8 can be measured with high sensitivity.

This novel polarimeter is superior to a conventionalconoscope, wherein the birefringent material is placedbetween a polarizer and an analyzer that are paralleland the transmitted intensity is given by'

I = Io - sin2(2qI)sin2( )| (2)

where i, is the angle between the polarizer and one ofthe principal birefringence axes and 8 is the polariza-tion phase shift. Equation (2) shows that the sign ofthe phase shift 8 cannot be measured; also, for 8 <Tr/4, sin2(6/2) is approximated as 82/4, which is muchsmaller than sin 3 8 of Eq. (1). Figure 2 shows therelative intensity change of the transmitted probebeam versus the relative phase change 8 (0° < <450) for a conventional conoscope (dotted curve) andfor our new polarimeter (solid curve). As can be seenfrom Fig. 2, our polarimeter is sensitive to phasedifferences smaller than 45°.

Figure 3 shows the experimental setup for 2Dthermal-stress-induced birefringence measurementsin a LD-pumped Nd:YAG laser rod. As shown in Fig.

Nd:YAG Rod

3-WLD808 nm

Analyzer

Babinet-SoleilCompensator

CCD Camera

(° BandpassFilter

V4 Plate

Polarizer Computer

He-Ne Laser

Fig. 1. Schematic arrangement of the newly constructed polarim-eter.

Fig. 3. Experimental setup for 2D thermal-stress-induced birefrin-gence measurements in a Nd:YAG rod. B. S., beam splitter.

20 September 1994 / Vol. 33, No. 27 / APPLIED OPTICS 6369

3, a probe laser beam (632.8-nm H4-Ne laser) ispassed through a polarizer and a quarter-wave plateto generate right-circularly polarized light, which isthen transmitted through the Nd:YAG rod to betested.

Figure 4(a) shows the 2D distribution of the phaseshift and the angle of the principal birefringenceaxis, 0, of the Nd:YAG rod (4 mm 4) x 5 mm) before

(degrees)

/ - - __

- - - - - - - -

1 - - - - -

\ I -a

(a)

0

pumping. The residual birefringence with 8 3 onthe outside of the rod is shown in Fig. 4(a). Figure4(b) shows the same rod when pumped with a cw 3-WLD (Spectra Diode Labs SDL2482). The pumpingregion was an elliptical area about the rod center.As shown in Fig. 4(b), the principal birefringence axiswas rotated and aligned along the length of thepumping region. Thermally induced birefringenceswith 8 = 100 were induced along the outer edge of thelaser rod, and there was practically no birefringencein the rod center. These results show the thermallyinduced stress distribution resulting from tempera-ture distribution in the LD-pumped Nd:YAG rod.In the case of this pumping configuration, one shoulduse the central region of the rod for the oscillator orthe amplifier because of the relatively small birefrin-gence.

3. Mechanical-Stress-Induced BirefringenceMeasurement in the Laser Rod

Birefringence is induced in a laser rod under mechani-cal stress.2 For example, quarter-wave or half-waveretardation can be obtained by changing the mechani-cal stress forces. In the measurements described inSection 3 we have ensured that the mechanical stressinduced a quarter-wave retardation in the Nd:YAGrod while the novel polarimeter was being used.This is an active element (active wave plate) becausethere is both quarter-wave retardation and amplifica-tion of laser radiation simultaneously.

As shown in Fig. 5, the uncoated laser rod(Nd:YAG, 4 mm 4) x 5 mm) was held in a brass heatsink and mechanically stressed by means of a pair ofscrews. To achieve uniform stress distribution overthe length of the rod, a copper wire (1 mm )) wasplaced on the top and bottom of the laser rod.

To estimate the mechanical force acting on thelaser rod, we assume a typical laser rod diamter d andthickness t. The stress components ax in the xdirection and ay in they direction are represented by6

a = 2Ffrrtd, (3)

(y = -6F/'wtd, (4)

respectively, where F is the force applied on the

(degrees)

Region

e

(b)

Fig. 4. 2D distribution of birefringence in a thermal-stressedNd:YAG rod (4 mm 4) at 632.8 nm (a) without LD pumping and (b)with cw 3-W LD pumping.

II_ ir Screw

t F

Holder (Brass)

Nd:YAG Rod(4 mm4 x 5 mm)

_______ Spacer (1 mm + Cu)

Fig. 5. Mechanical setup of the stress-induced Nd:YAG /4

retarder. F = 147 N for X = 632.8 nm andF = 246 N for X = 1064nm.

6370 APPLIED OPTICS / Vol. 33, No. 27 / 20 September 1994

-

- z

w =

outside of the rod. The phase shift 8 betweenp- ands-polarized light that is due to stress differences aboutthe x andy directions is represented by

8 = 27rC(ox -y)t/A\ (5)

where C is the constant of optical elasticity of thelaser material and is the wavelength of the probelaser. When a quarter-wave retardation is inducedin the laser rod, from Eqs. (3)-(5), the load force isobtained as

F(X/4) = Xd8/16C. (6)

For the Nd:YAG rod used in the experiment, X = 1064nm, d = 0.5 cm, C = 1.25 Brewster (Brewster = 10-12m2/N),7 and the load force F(X/4) is calculated to be245 N at 1064 nm and 147 N at 632.8 nm.

Figure 6(a) shows the 2D birefringence distributionin the mechanically stressed Nd:YAG rod. As shownin Fig. 6(a), three quarter-wave retardations wereinduced in the Nd:YAG rod, although it was possibleto obtain one quarter-wave retardation. The effec-tive size of the three-quarter-wave retardation regionwas 1 mm x 2 mm in the 4-mm-diameter Nd:YAGrod, as can be seen in Fig. 6(a). Figure 6(b) showsthe 2D birefringence distribution in the mechanicallystressed Nd:YAG rod under a cw 3-W LD pumping.As shown in Fig. 6(b), the effective quarter-wave areaof 1 mm x 2 mm at the center of the Nd:YAG rodremains virtually unchanged during LD pumping.

This laser rod was end pumped by a 2D LD array(Spectra Diode Labs SDL323OTD) at 808 nm. Thepulse peak power, pulse width, and repetition rate ofthe LD array that was used were set at 300 W, 200 Rs,and 50 Hz, respectively. Thus the average pumppower was equal to that of a cw 3-W LD. Underthese conditions a double-pass laser gain of 1.15 wasobtained. This mechanical-stress-induced Nd:YAGquarter-wave retarder was stable as long as themechanical force remained constant. This featurewill be useful in many optical applications, such aslaser amplification, stabilization of single-frequencylasers, and optical switches.

5. Conclusion

We have demonstrated highly sensitive 2D thermal-and mechanical-stress-induced birefringence measure-ments in a Nd:YAG laser rod with a newly con-structed polarimeter. A residual birefringence with8 3 on the outside of the rod was measured.When the rod was pumped with a cw 3-W LD,thermally induced birefringences with 10° weremeasured on the outside of the rod, and the principalbirefringence axis was found to be rotated along thelength of the pumping region. Also, mechanical-stress-induced birefringence in the Nd:YAG rod wassuccessfully measured with the proposed polarimeter.An effective quarter-wave retardation region of 1mm x 2 mm at the center of the 4-mm-diameterNd:YAG rod was measured. We then found that themechanically stressed laser rod behaved as an active

(degrees)(a)

(degrees)(b)

Fig. 6. Two-dimensional distribution of birefringence in mechani-cal-stressed Nd:YAG rod (4 mm +) at 632.8 nm under a load force of3 x 147 N (3X/4). (a) without LD pumping and (b) with cw 3-W LDpumping.

quarter-wave retarder when pumped with a LD withaverage power of 3 W. This feature can be exploitedin some laser applications that require a wave plate inthe system.

P QT

A

Fig. 7. Schematic arrangement of the polarimeter. P and A,main cross planes of the polarizer and the analyzer, respectively, Q,fast-axis direction of a quarter-wave plate; T, birefringent materialsuch as a LD-pumped or a mechanically stressed laser rod.

20 September 1994 / Vol. 33, No. 27 / APPLIED OPTICS 6371

Appendix A: Transmitted Intensity through a NovelPolarimeter

Figure 7 shows a schematic model of the proposedpolarimeter. P and A are the main cross planes ofthe polarizer and the analyzer, respectively. Q is thefast-axis direction of a quarter-wave plate, and T is abirefringent material, such as a LD-pumped or amechanically stressed laser rod.

The electric field of the circular polarized beam thatpasses through the birefringent material is given by

aX = - sin(ot + 8), (Al)

aY =- cos t, (A2)

where a is the amplitude of the light wave and 8 is thephase shift that is due to the birefringence. Theelectric field of the beam after it passes through theanalyzer A is given by

A =Xcos4 + Ysin4a

- [cos 4) sin(wt + 3) + sin 4) cos wt], (A3)

where 4) is the angle between the analyzer and one ofthe principal birefringence axes. Therefore the de-tected signal intensity I is represented by8

I = Io [(cos 4) sin 8 + sin 4)2 + COS2 ) COS

2 3]

= 2 (1 + sin 24 sin 8), (A4)

where Io is the incident intensity of the probe light atthe quarter-wave plate.

When the principal birefringence axis direction isinclined in a counterclockwise direction at an angle 0to the principal plane of the analyzer, Eq. (A4) iswritten as

I = 2I [1 + sin 2() - 0)sin ]. (A)

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2. J. J. Zayhowski and A. Mooradian, "Microchip lasers," inTunable Solid State Lasers, M. L. Shand and H. P. Jenssen,eds., Vol. 5 of OSA Proceedings Series (Optical Society ofAmerica, Washington, D.C., 1989), pp. 288-294.

3. B. Zhou, T. J. Kane, G. J. Dixon, and R. L. Byer, "Efficient,frequency-stable laser-diode-pumped Nd:YAG laser," Opt. Lett.10, 62-64 (1985).

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5. M. Ohmi, M. Akatsuka, K. Ishikawa, K. Naito, M. Yamanaka, Y.Izawa, S. Nakai, and Y. Yonezawa, "Two-dimensional thermaland mechanical stress-induced birefringence measurements inlaser-diode pumped solid-state laser materials," in Conferenceon Lasers and Electro-Optics, Vol. 11 of 1993 OSA TechnicalDigest Series (Optical Society of America, Washington, D.C.,1993), p. 306.

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