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Optical Materials Express

Optical Materials Express

  • Editor: David Hagan
  • Vol. 4, Iss. 5 — May. 1, 2014
  • pp: 876–888
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Highly accurate interferometric evaluation of thermal expansion and dn/dT of optical materials

Yoichi Sato and Takunori Taira  »View Author Affiliations


Optical Materials Express, Vol. 4, Issue 5, pp. 876-888 (2014)
http://dx.doi.org/10.1364/OME.4.000876


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Abstract

Thermo-mechanical and -optical properties of Y3Al5O12 (YAG), YVO4, and GdVO4 were evaluated with less than 2% of evaluation error. Measured thermal expansion coefficient for YAG, [100]-YVO4, [001]-YVO4, [001]-GdVO4, and [001]-GdVO4 were 6.13, 1.76, 8.24, 1.19, and 7.26 × 10−6/K at room temperature. Temperature coefficients of refractive index for YAG, YVO4 in ordinary and extraordinary polarization, and GdVO4 in ordinary and extraordinary polarization at room temperature for the wavelength of 1.06 μm were 12.1, 15.5, 8.41, 15.2, and 9.92 × 10−6/K, respectively.

© 2014 Optical Society of America

1. Introduction

Recent advance in giant micro-photonics has enabled drastic power-scaling in various photon sources based on microchip lasers [1

1. T. Taira, “Domain-controlled laser ceramics toward giant micro-photonics,” Opt. Mater. Express 1(5), 1040–1050 (2011). [CrossRef]

]. Although many benefits have been realized by the miniaturization of highly bright solid-state lasers [2

2. N. Pavel, M. Tsunekane, and T. Taira, “Composite, all-ceramics, high-peak power Nd:YAG/Cr4+:YAG monolithic micro-laser with multiple-beam output for engine ignition,” Opt. Express 19(10), 9378–9384 (2011). [CrossRef] [PubMed]

, 3

3. R. Bhandari and T. Taira, “Megawatt level UV output from [110] Cr⁴⁺:YAG passively Q-switched microchip laser,” Opt. Express 19(23), 22510–22514 (2011). [CrossRef] [PubMed]

], the excessive heat generated by densification of the excitation limits the averaged-power from miniature lasers. The temperature increase in laser gain media due to this heat causes not only thermal expansion but also influences on the optical gain and the heat capacity [4

4. Y. Sato and T. Taira, “The studies of thermal conductivity in GdVO4, YVO4, and Y3Al5O12 measured by quasi-one-dimensional flash method,” Opt. Express 14(22), 10528–10536 (2006). [CrossRef] [PubMed]

, 5

5. Y. Sato and T. Taira, “Temperature dependencies of stimulated emission cross section for Nd-doped solid-state laser materials,” Opt. Mater. Express 2(8), 1076–1087 (2012). [CrossRef]

]. As a result of high power pumping, lensing and birefringence induced by the severe temperature distribution in laser gain media degrades the laser performance of destructs laser gain media itself.

In order to extend the scalability in both of brightness and average power, heat management in laser cavity according to precise thermo-mechanical and -optical parameters of laser gain media is the most critical. However, there are significant discrepancies in the reported value of material parameters. Especially reported values of the linear thermal expansion coefficient, α and temperature coefficient of refractive index, dndT are different more than one order. For examples, reported values of dn/dT at 1.06 μm for π-polarization in YVO4 varies from 0.3 to 13.5 × 10−6 K−1 [6

6. P. A. Loiko, K. V. Yumashev, V. N. Matrosov, and N. V. Kuleshov, “Dispersion and anisotropy of thermo-optic coefficients in tetragonal GdVO4 and YVO4 laser host crystals,” Appl. Opt. 52(4), 698–705 (2013). [CrossRef] [PubMed]

, 7

7. Z. Huang, J. Feng, and W. Pan, “Theoretical investigations of the physical properties of zircon-type YVO4,” J. Solid State Chem. 185, 42–48 (2012). [CrossRef]

], and still now there seems to be no hope that this difference will converge in near future.

The variation of reported α is within a several-fold range to the utmost: for example, reported values of α in Y3Al5O12 (YAG) varies from 2.5 to 8.2 × 10 −6 K−1 [8

8. X. Xu, Z. Zhao, H. Wang, P. Song, G. Zhou, J. Xu, and P. Deng, “Spectroscopic and thermal properties of Cr,Yb:YAG crystal,” J. Cryst. Growth 262(1-4), 317–321 (2004). [CrossRef]

, 9

9. K. Wu, L. Hao, H. Zhang, H. Yu, Y. Wang, J. Wang, X. Tian, Z. Zhou, J. Liu, and R. I. Boughton, “Lu3Ga5O12 crystal: exploration of new laser host material for the ytterbium ion,” J. Opt. Soc. Am. B 29(9), 2320 (2012). [CrossRef]

]. Our research started from a consultation that Nd:YVO4 crystal in the laser component with high brightness output designed for industrial application by use of the previously reported α [10

10. Private communications

]. Therefore, our report should be useful not only for scientific filed but also many real applications in industrial field urgently.

Moreover, α includes another important problem. Even though many researchers believe that YAG crystal has anisotropic thermal expansion [11

11. A. A. Kaminskii, Laser Crystals (Springer-Verlag, Berlin, 1981), p. 320.

, 12

12. W. Koechner, Solid-State Laser Engineering 6th ed. (Springer Science + Business Media, Inc., New York, 2006), p. 55.

], it should be wrong physically. Thermal expansion can be described as a coordinate transformation per unit temperature, thus α is a second order tensor. From Onsager reciprocal relations, YAG (cubic) and vanadate (tetragonal) have one and two independent components of thermal expansion coefficient, respectively. Authors consider that the reported anisotropy in thermal expansion of YAG was contributed by experimental error, which should be re-evaluated with high accuracy. One of objectives in this work is an experimental confirmation by evaluation of dependence on crystal axes in α of YAG.

We already provided the evaluation procedure for α and dn/dT of GdVO4 [13

13. Y. Sato and T. Taira, “Thermo-optical and -mechanical parameters of Nd:GdVO4 and Nd:YVO4,” CLEO’07, paper JWA87 (2007).

], however those were not proved by the evaluation of experimental errors. In this work, we tried to summarize these thermal properties of YAG, YVO4, and GdVO4 with high accuracy based on the careful treatment of experimental errors.

2. Methods

2.1 Thermal expansion coefficient

Thermal expansion was measured using a push-rod type dilatometer (DIL 402C, NETZSCH). Measurements were carried out under the dynamic helium atmosphere with gas flow rate was 50 ml/min, and heating rate is 4K/min within the range from 0 to 300 °C in temperature, T. The contact force of the push-rod was 0.25 N, and measured data was calibrated by an fused silica standard.

Measured samples were (111)-cut YAG single crystal (Scientific Materials Co.), (100)-cut and (001)-cut YVO4 single crystals (ITI Electro Optics Co.), and (100)-cut and (001)-cut GdVO4 single crystals (Shandong Newphotons Science and Technology Co., Ltd.) with the size of 8 mm in diameter and 25 mm in thickness.

2.2 Refractive index

The absolute value of refractive index, n was calculated from the angle of minimum deviation of the triangular prisms that have bases of isosceles right triangles [14

14. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon Press, 1975) sec. 4.7.

]. The height of prisms and the length of long side in bases were 10 mm. We evaluated undoped and 1.0at.% Nd3+-doped YAG single crystal (Scientific Materials Co.), YVO4 single crystals (ITI Electro Optics Co.), and GdVO4 single crystals (Shandong Newphotons Science and Technology Co.,LTD). Bases of the YAG prism were parallel to (111)-plane, on the contrary, bases of vanadates were parallel to (001)-plane.

The minimum deviation angle, Amin of these prisms and prism angles, Ap were measured within the wavelength range between 420 nm and 1600 nm, where light was analyzed by the spectrometer (V-30D, Shimadzu Rika Co.). Values of Amin and Ap were detected by the CCD camera (CCD-41R, Shimadzu Rika Co.) with the resolution of 30 seconds, as shown in Fig. 1.
Fig. 1 Schematic diagram of experimental setup for refractive index measurement (a) and the definition of Ap and Amin (b). The incident angle to the prism is equals to the output angle.
Temperature in the environment of experimental setup was 23 °C.

From these measured angles n can be calculated by
n=sin(Amin+Ap2)/sinAp2,
(1)
and evaluation error δn due to detection errors of angles δA can be defined by

δn=δA2+n23n2sin2Ap22ncosAp21n2sin2Ap2/2sinAp2.
(2)

2.3 The detection of the shift of the fringes in transmission

For evaluating temperature coefficient of refractive index, dn/dT, we measured phase shifts of interference fringes in transmittance of laser materials. The transmission T0 of thin laser material with a thickness of L is ideally modulated to Tr by multiple reflections by
Tr=T01+R2[12R1+R2cosφ]1.
(3)
where R and φ are the Fresnel reflectance and the phase of modulation. φ is dependent on wavelength, λ and is given by 4πnL/λ. Although this modulation can become smaller due to imperfectness in flatness of the sample, phase shift Δφ from the phase φ = 4πnL/λ in this modulation can be easily detected, which is expressed by
Δφφ=(1ndndT+α)ΔT,
(4)
where ΔT is the temperature change.
Fig. 2 The concept of multiple reflection. Ein, r, and t are the amplitude of electric field, reflectance, and transmittance of probe light, respectively. |t|4 equals to T0, and |r|2 equals to R.
Figure 2 shows the concept of multiple reflection expressed by Eq. (3) .

Fig. 3 Schematic diagram of experimental setup for evaluation of phase shift Δφ.
Experimental setup for measurement of Tr is shown in Fig. 3. The light emitted from halogen lamp (PHL-150, Mejiro Precision Inc.) was collimated and focused to the sample that was sandwiched by temperature controlled copper plates within the range from 15 °C to 65 °C. The temperature was stabilized by a peltier device and its driver (LDT-5948, ILX Lightwave Co.) with the resolution of 0.1 °C. Transmitted light from the sample was collected into a monochrometer (TRIAX-550, HORIBA Jobin Yvon S.A.S.) and detected by an InGaAs array sensor (IGA512-1-1, HORIBA Jobin Yvon S.A.S.) with the spectral resolution of 0.12 nm. Δφ can be obtained by the least square fitting of Tr to Eqs. (3-4).

2.4 Temperature coefficient of refractive index

We evaluated the modulation in Tr of (111)-, (100)-, and (110)-cut 1.0at.% Nd:YAG plates (Fujian Castech Crystals, Inc), (100)-cut 1.0at.% Nd:YVO4 (ITI Electro Optics Co.), and (100)-cut 1.0at.% Nd:GdVO4 (Shandong Newphotons Science and Technology Co.,LTD) plates. The thickness of YAG and YVO4 samples were ca. 0.2 mm, and GdVO4 sample has thickness of ca. 0.1 mm. These thicknesses were measured by a micrometer (BMD-25DM, Mitutoyo) with the resolution of 1 μm.

Temperature coefficient of refractive index dn/dT can be estimated from measured Δφ and α by
dndT=λ4πLΔφΔTnα.
(5)
From Eq. (6), the evaluation error of dn/dT is given from the differentiation of Eq. (5) by
δ(dndT)=n(1ΔTΔφφ)2[2(δφΔφ)2+2(δTΔT)2+(δλλ)2+(δLL)2]+α2[(δαα)2+(δnn)2],
(6)
where δφ, δT, δλ, δL, δα, and δn are the evaluation errors of Δφ, ΔT, λ, α and n, respectively. Factors of “2” in Eq. (6) are come from the subtraction in determining of Δφ and ΔT.

3. Results

3.1 Thermal expansion coefficient and refractive index

Fig. 4 Thermal expansion coefficients of YAG, YVO4, and GdVO4 single crystals.
Figure 4 shows measured α, and calculated n are shown in Fig. 5.
Fig. 5 Refractive indices of YAG, YVO4, and GdVO4 single crystals. (o) and (3) indicate ordinary and extraordinary polarization, respectively.
The difference in n of YAG between doped sample and undoped sample is within 0.0006, and markers for Nd-doped samples were situated at the same position as markers for doped samples in Fig. 5. Therefore there is a certain difference (3 times of δn) between n of 1.0at.% Nd:YAG and undoped YAG. On the contrary, differences in n of vanadates are below 0.0002, and those are lower than the evaluation error.

3.2 Interferometric fringes in transmission

Fig. 6 Temperature dependent Tr. (a) 1at.% Nd:YAG, (111)-cut. (b) 1.0at.% YVO4, (100)-cut in ordinary polarization. (c) 1.0at.% GdVO4, (100)-cut in extraordinary polarization.
Figure 6 shows Tr of various samples depending on the temperature, T. The ratio of the modulation depth in transmission, ΔTr is larger than 3% of transmission. We were able to evaluate φ with the estimation error of less than 0.02 rad by use of Eq. (3). The additional peaks at 1064 nm in transmittance are considered to be due to the fluorescence from Nd3+ excited by probe light.

3.3 Phase shift in the fringes and temperature coefficient of refractive index

Fig. 7 Relation between Δφ/φ and temperature in YAG, YVO4, and GdVO4 single crystals. (a) Δφ/φ at 0.9 μm. (b) Δφ/φ at 1.1 μm. (c) Δφ/φ at 1.3 μm 1.0at.%. (ord) and (ext) indicate ordinary and extraordinary polarization, respectively.
As shown in Eq. (4), the value of Δφ/φ depends not on thickness but on α, dn/dT, and ΔT. Δφ/φ of various samples at several important wavelengths are shown in Fig. 7, where 0.9 μm means 946 nm for Nd:YAG, 914 nm for Nd:YVO4, and 912 nm for Nd:GdVO4. Similarly 1.1 μm means 1064 nm for Nd:YAG and Nd:YVO4, and 1063 nm for Nd:GdVO4. Also 1.3 μm means 1319 nm for Nd:YAG, 1342 nm for Nd:YVO4, and 1341 nm for Nd:GdVO4. Lines in Fig. 7 are fitted by the least square method. dn/dT estimated from measured Δφ and α at room temperature are shown in Table 1.

Table 1. α and dn/dT of YAG, YVO4, and GdVO4 single crystals at room temperature

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In this work room temperature means the temperature range between 15 °C and 65 °C. The high linearity in our fringe-shifts of transmittance in Fig. 7 is an evidence of high temperature-controllability in our measurements.

4. Discussions

4.1 Sellmeier equations for YAG, YVO4, and GdVO4 single crystals

In order to quantize the relationship between n and λ, we can use Sellmeier equations. We can fit n of YAG crystals to Sellmeier equations given by
n2(λ)=1+Aλ2λ2B2+Cλ2λ2D2,
(7)
where A, B, C, and D are fitting parameters. In the case of vanadates, we can use
n2(λ)=A+Bλ2λ2C2Dλ2.
(8)

Table 2. Parameters in sellmeier equation for YAG, YVO4, and GdVO4 single crystals

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These fitting parameters for refractive indices in Fig. 5 are summarized in Table 2, where λ should be expressed with the unit of “λm.” In addition, the difference of n between Nd-doped and undoped YAG is too small to produce a significant mistake in the evaluation of dn/dT.

4.2 Thermal expansion coefficient along various planes in YAG single crystal

The correct measurement of α should provide a certain answer to the conflict between Onsager reciprocal relations and the common sense of anisotropic α of YAG in the solid-state laser researchers [11

11. A. A. Kaminskii, Laser Crystals (Springer-Verlag, Berlin, 1981), p. 320.

,12

12. W. Koechner, Solid-State Laser Engineering 6th ed. (Springer Science + Business Media, Inc., New York, 2006), p. 55.

]. Authors consider that the reported anisotropy in thermal expansion of YAG should be re-evaluated with high accuracy by use of our evaluation procedure.

Similarly to Eq. 54), we can estimate α by Δφ/φ and dn/dT by
α=1ΔTΔφφ1ndndT,
(9)
and α along [100]- and [110]-axes in YAG crystal evaluated by use of Eq. (9) at various wavelengths are shown in Table 3.

Table 3. α of YAG crystal estimated from Δφ/φ and dn/dT

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The standard deviation of measured α is only 0.12 × 10−6/K, and this value is smaller than the evaluation error given by
δα2=(1ΔTΔφφ)2[2(δφΔφ)2+2(δTΔT)2+(δλλ)2+(δLL)2].+1n2[(δdndT)2+(dndT)2(δnn)2]
(10)
Because α is not dependent on the wavelength of probe lights, we can reduce the estimation error in α as follows:
α=α0.9μm+α1.1μm+α1.3μm3,
(11)
and
δα=(δα0.9μm3)2+(δα1.1μm3)2+(δα1.3μm3)2,
(12)
where <α> is the mean value of α. The estimated α and errors along each planes from Eqs. (11), (12) are also shown in Table 3, where differences in α between crystal orientations of YAG single crystal is less than the evaluation error of 0.1 × 10−6/K ( = 1.6%) at the room temperature. Therefore, we can conclude that no anisotropy of thermal expansion in YAG crystal detected. The detailed evaluation of experimental errors are discussed in Appendix-1.

Fig. 8 Temperature changes of Δφ/φ in Nd:YAG plates. Lines are fitted by the least square method.
Figure 8 shows clearly that the dependence of Δφ/φ on crystal direction is quite small. This is the reason why the difference in calculated α along various orientations.

5. Summary

We evaluated thermo-mechanical and -optical properties of YAG, YVO4, and GdVO4 by with less than 2% of evaluation error, and it was also revealed that thermal expansion of YAG is independent on the crystal orientation against conventional knowledge. We tabulated thermal parameters of YAG, YVO4, and GdVO4, and it will be the reliable data table for thermal design and heat management not only of microchip lasers but also of a plenty of solid-state lasers.

Appendix-1 Evaluation errors for α and dn/dT

Three runs of measurements by the dilatometer brought no difference larger than 1.0 nm, and the evaluation error of measured thermal expansion was 10−9 m /10K / 0.025m = 4×10−9/K. Thus the experimental error in α is below 1% due to the resolution of the dilatometer.

30 seconds of resolution of our spectrometer was enough large to bring no difference in reading of the value of angles, thus it was considered to be δA.

0.02 rad of δφ is the maximum of errors during least square fitting. Since small δλ [5

5. Y. Sato and T. Taira, “Temperature dependencies of stimulated emission cross section for Nd-doped solid-state laser materials,” Opt. Mater. Express 2(8), 1076–1087 (2012). [CrossRef]

] and δn, δλ/λ and δn/n can be ignored.

Major part of evaluation error is due to Δφ and ΔT, and those depend on the effective data interval. Under the assumption that dn/dT is constant within the measured temperature range, ΔT become 50°C.

Table 4. Parameters for error evaluation

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and 5

Table 5. Experimental errors in α and dn/dT of YAG, YVO4, and GdVO4 single crystals

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Parameters for error calculation in Eq. (6) and calculated errors are summarized in Table 4, respectively.

The superiority of the evaluation method for dn/dT by the measurement of the temperature shift in the fringes on transmission is high reproducibility. In 1991, authors demonstrated the frequency tuning of Nd:YVO4 microchip laser [15

15. T. Taira, A. Mukai, Y. Nozawa, and T. Kobayashi, “Single-mode oscillation of laser-diode-pumped Nd:YVO4 microchip lasers,” Opt. Lett. 16(24), 1955–1957 (1991). [CrossRef] [PubMed]

], where the ratio of the oscillation frequency and the frequency tuning range, Δν/ν is the same as the ratio of the optical path of a microchip and it’s temperature deviation: this is definitively equal to Δφ/φ in this work.
Fig. 9 Temperature dependence of Δν/ν in Nd:YVO4 microchip laser compared with calculated shift based on the value in this work.
Figure 9 comparatively shows the Δν/ν evaluated in 1991 and the simulated value from Δφ/φ in this work (because temperature range in these two experiments were different). The accordance with these two lines in Fig. 9 directly proves the small reproducible error of evaluation methods that use fringes in transmissions due to multiple-reflections inside samples. From our error evaluations, we can conclude that α and dn/dT reported in this work is highly accurate compared with other traditional works.

Appendix-2 Comparison to past reports on α and dn/dT

We summarize the comparison between this work to past reports on α and dn/dT in Table 6.

Table 6. Maximum and minimum values of previously reported α and dn/dT

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α of YAG in this work is similar to [16

16. R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y3Al5O12, Lu3Al5O12, YAlO3, LiYF4, LiLuF4, BaY2F8, KGd(WO4)2, and KY(WO4)2 laser crystals in the 80–300 K temperature range,” J. Appl. Phys. 98, 103514 (2005). [CrossRef]

], while dn/dT is almost the same as the maximum of previously reported value [17

17. P. R. Stoddart, P. E. Ngoepe, P. M. Mjwara, J. D. Comins, and G. A. Saunders, “Hightemperature elastic constants of yttrium aluminum garne,” J. Appl. Phys. 73(11), 7298–7301 (1993). [CrossRef]

]. α and dn/dT of YVO4 in this work are close to [18

18. D. Rand, D. Miller, D. J. Ripin, and T. Y. Fan, “Cryogenic Yb3+-doped materials for pulsed solid-state laser applications,” Opt. Mater. Express 1(3), 434–450 (2011). [CrossRef]

] and [19

19. H. C. Liang, K. Y. Lin, Y. C. Lee, and Y. F. Chen, “Precise measurement of group refractive indices and temperature dependence of refractive index for Nd-doped yttrium orthovanadate by intracavity spontaneous mode locking,” Opt. Lett. 36(19), 3741–3743 (2011). [CrossRef] [PubMed]

], respectively. In the case of GdVO4, α in this work is proximate to [20

20. H. Zhang, J. Liu, J. Wang, C. Wang, L. Zhu, Z. Shao, X. Meng, X. Hu, and M. Jiang, “Characterization of the laser crystal Nd:GdVO4,” J. Opt. Soc. Am. B 19(1), 18–27 (2002).

] and dn/dT is larger than any other reported value.

Appendix-3 Relations between thermal effect and thermal parameters

As well as thermal conductivity κ [4

4. Y. Sato and T. Taira, “The studies of thermal conductivity in GdVO4, YVO4, and Y3Al5O12 measured by quasi-one-dimensional flash method,” Opt. Express 14(22), 10528–10536 (2006). [CrossRef] [PubMed]

], α and dn/dT of laser gain media are quite important thermal parameters for describing thermal effects in the laser cavity. For example, thermal lensing is severely depends on these parameters. Lens-effects inside a gain medium are caused by three kinds of changes of optical path: thermal expansion, refractive index change induced by thermal strain, and temperature dependent refractive index. The curvature of thermal lens is the summation of curvatures formed by these optical path changes. Optical path changes caused by thermal expansion and refractive index change induced by thermal strain are proportional to α, while optical path changes caused by temperature dependent refractive index are proportional to dn/dT. The focal length of thermal lens is the inverse of amount of these curvatures, and proportional to thermal conductivity. In the case of end-pumped solid-state rod lasers, the focal length of thermal lens f can be expressed by
f=πwp2κηaηhP[αr(n1)l+αn3C+12dndT]1,
(13)
where wp, ηa, ηh, P, r, l, and C are the radius of pump beam, the pump absorption efficiency, the thermal load, the induced pump power, the radius and length of rod, and photo-elastic coefficient for desired polarizations, respectively [29

29. W. Koechner, Solid-State Laser Engineering 6th ed. (Springer Science + Business Media, Inc., 2006), chap. 7.

].

On the contrary, the evaluation of α and dn/dT from the pump-induced therml lensing of laser cavities requires the precise evaluations of mode-matching and thermal load which are dependent on the pump intensity. Therefore, in this case it should be important for the estimation of experimental errors to clarify the uncertainty against not only wp, ηa, ηh, P, r, l, and C but also measured focal lens including focusing aberrations and astigmatism.

Appendix-4 Derivation of Eq. (2)

The experimental error of the refractive index estimated from the minimum deviation angle is given by Eq. (2), which can be derived by the differentiation of Eq. (1). Differentiating by Ap gives
nAp=12cos(Amin+Ap2)/sinAp212cosAp2sin(Amin+Ap2)/sin2Ap2=1n2sin2Ap2ncosAp22sinAp2,
(14)
and differentiating by Amin gives
nAmin=12cos(Amin+Ap2)/sinAp2=1n2sin2Ap22sinAp2.
(15)
Therefore, we can estimate experimental error δn by

δn=(nAp)2δAp2+(nAmin)2δAmin2=(nAp)2+(nAmin)2δA=2+n23n2sin2Ap22ncosAp21n2sin2Ap22sinAp2δA.
(16)

Acknowledgement

Authors thank to Prof. G. Aka for his kind help in refractive index measurement, Netzsch-Gerätebau GmbH for measurements of thermal expansion. This work was partially supported by Genesis Research Institute, Inc., and by the Special Coordination Funds for Promoting Science and Technology of the Ministry of Education, Culture, Sports, Science, and Technology of Japan.

References and links

1.

T. Taira, “Domain-controlled laser ceramics toward giant micro-photonics,” Opt. Mater. Express 1(5), 1040–1050 (2011). [CrossRef]

2.

N. Pavel, M. Tsunekane, and T. Taira, “Composite, all-ceramics, high-peak power Nd:YAG/Cr4+:YAG monolithic micro-laser with multiple-beam output for engine ignition,” Opt. Express 19(10), 9378–9384 (2011). [CrossRef] [PubMed]

3.

R. Bhandari and T. Taira, “Megawatt level UV output from [110] Cr⁴⁺:YAG passively Q-switched microchip laser,” Opt. Express 19(23), 22510–22514 (2011). [CrossRef] [PubMed]

4.

Y. Sato and T. Taira, “The studies of thermal conductivity in GdVO4, YVO4, and Y3Al5O12 measured by quasi-one-dimensional flash method,” Opt. Express 14(22), 10528–10536 (2006). [CrossRef] [PubMed]

5.

Y. Sato and T. Taira, “Temperature dependencies of stimulated emission cross section for Nd-doped solid-state laser materials,” Opt. Mater. Express 2(8), 1076–1087 (2012). [CrossRef]

6.

P. A. Loiko, K. V. Yumashev, V. N. Matrosov, and N. V. Kuleshov, “Dispersion and anisotropy of thermo-optic coefficients in tetragonal GdVO4 and YVO4 laser host crystals,” Appl. Opt. 52(4), 698–705 (2013). [CrossRef] [PubMed]

7.

Z. Huang, J. Feng, and W. Pan, “Theoretical investigations of the physical properties of zircon-type YVO4,” J. Solid State Chem. 185, 42–48 (2012). [CrossRef]

8.

X. Xu, Z. Zhao, H. Wang, P. Song, G. Zhou, J. Xu, and P. Deng, “Spectroscopic and thermal properties of Cr,Yb:YAG crystal,” J. Cryst. Growth 262(1-4), 317–321 (2004). [CrossRef]

9.

K. Wu, L. Hao, H. Zhang, H. Yu, Y. Wang, J. Wang, X. Tian, Z. Zhou, J. Liu, and R. I. Boughton, “Lu3Ga5O12 crystal: exploration of new laser host material for the ytterbium ion,” J. Opt. Soc. Am. B 29(9), 2320 (2012). [CrossRef]

10.

Private communications

11.

A. A. Kaminskii, Laser Crystals (Springer-Verlag, Berlin, 1981), p. 320.

12.

W. Koechner, Solid-State Laser Engineering 6th ed. (Springer Science + Business Media, Inc., New York, 2006), p. 55.

13.

Y. Sato and T. Taira, “Thermo-optical and -mechanical parameters of Nd:GdVO4 and Nd:YVO4,” CLEO’07, paper JWA87 (2007).

14.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon Press, 1975) sec. 4.7.

15.

T. Taira, A. Mukai, Y. Nozawa, and T. Kobayashi, “Single-mode oscillation of laser-diode-pumped Nd:YVO4 microchip lasers,” Opt. Lett. 16(24), 1955–1957 (1991). [CrossRef] [PubMed]

16.

R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y3Al5O12, Lu3Al5O12, YAlO3, LiYF4, LiLuF4, BaY2F8, KGd(WO4)2, and KY(WO4)2 laser crystals in the 80–300 K temperature range,” J. Appl. Phys. 98, 103514 (2005). [CrossRef]

17.

P. R. Stoddart, P. E. Ngoepe, P. M. Mjwara, J. D. Comins, and G. A. Saunders, “Hightemperature elastic constants of yttrium aluminum garne,” J. Appl. Phys. 73(11), 7298–7301 (1993). [CrossRef]

18.

D. Rand, D. Miller, D. J. Ripin, and T. Y. Fan, “Cryogenic Yb3+-doped materials for pulsed solid-state laser applications,” Opt. Mater. Express 1(3), 434–450 (2011). [CrossRef]

19.

H. C. Liang, K. Y. Lin, Y. C. Lee, and Y. F. Chen, “Precise measurement of group refractive indices and temperature dependence of refractive index for Nd-doped yttrium orthovanadate by intracavity spontaneous mode locking,” Opt. Lett. 36(19), 3741–3743 (2011). [CrossRef] [PubMed]

20.

H. Zhang, J. Liu, J. Wang, C. Wang, L. Zhu, Z. Shao, X. Meng, X. Hu, and M. Jiang, “Characterization of the laser crystal Nd:GdVO4,” J. Opt. Soc. Am. B 19(1), 18–27 (2002).

21.

N. R. Reddy and K. S. Murthy, “Thermal expansion of yttrium vanadate,” J. Mater. Sci. Lett. 2(4), 139–140 (1983). [CrossRef]

22.

X. Peng, A. Asundi, Y. Chen, and Z. Xiong, “Study of the mechanical properties of Nd:YVO4 crystal by use of laser interferometry and finite-element analysis,” Appl. Opt. 40(9), 1396–1403 (2001). [CrossRef] [PubMed]

23.

C. V. V. Reddy, P. Kistaiah, and K. S. Murthy, “X-ray studies on the thermal expansion of gadolinium vanadate,” J. Phys. D Appl. Phys. 18(6), L27–L30 (1985). [CrossRef]

24.

J. Petit, B. Viana, P. Goldner, J.-P. Roger, and D. Fournier, “Thermomechanical properties of Yb3+ doped laser crystals: Experiment and modeling,” J. Appl. Phys. 108(12), 123108 (2010). [CrossRef]

25.

T. M. Pollak, W. Wing, R. J. Grasso, E. P. Chicklis, and H. Jenssen, “CW laser operation of Nd:YLF,” J. Quant. Electron. 18(2), 159–163 (1982). [CrossRef]

26.

D. E. Zelmon, J. J. Lee, K. M. Currin, J. M. Northridge, and D. Perlov, “Revisiting the optical properties of Nd doped yttrium orthovanadate,” Appl. Opt. 49(4), 644–647 (2010). [CrossRef] [PubMed]

27.

R. Soulard, A. Zinoviev, J. L. Doualan, E. Ivakin, O. Antipov, and R. Moncorgé, “Detailed characterization of pump-induced refractive index changes observed in Nd:YVO4, Nd:GdVO4 and Nd:KGW,” Opt. Express 18(2), 1553–1568 (2010). [CrossRef] [PubMed]

28.

H. Y. Shen, X. L. Meng, G. Zhang, J. J. Qin, W. Liu, L. Zhu, C. H. Huang, L. X. Huang, and M. Wei, “Sellmeier’s equation and the expression of the thermal refractive-index coefficient for a Nd0.007Gd0.993VO4 crystal,” Appl. Opt. 43(4), 955–960 (2004). [CrossRef] [PubMed]

29.

W. Koechner, Solid-State Laser Engineering 6th ed. (Springer Science + Business Media, Inc., 2006), chap. 7.

OCIS Codes
(160.1190) Materials : Anisotropic optical materials
(160.3380) Materials : Laser materials
(160.5690) Materials : Rare-earth-doped materials

ToC Category:
Crystalline Materials

History
Original Manuscript: January 22, 2014
Revised Manuscript: March 15, 2014
Manuscript Accepted: March 24, 2014
Published: April 1, 2014

Virtual Issues
2013 Advanced Solid State Lasers (2013) Optics Express

Citation
Yoichi Sato and Takunori Taira, "Highly accurate interferometric evaluation of thermal expansion and dn/dT of optical materials," Opt. Mater. Express 4, 876-888 (2014)
http://www.opticsinfobase.org/ome/abstract.cfm?URI=ome-4-5-876


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References

  1. T. Taira, “Domain-controlled laser ceramics toward giant micro-photonics,” Opt. Mater. Express1(5), 1040–1050 (2011). [CrossRef]
  2. N. Pavel, M. Tsunekane, and T. Taira, “Composite, all-ceramics, high-peak power Nd:YAG/Cr4+:YAG monolithic micro-laser with multiple-beam output for engine ignition,” Opt. Express19(10), 9378–9384 (2011). [CrossRef] [PubMed]
  3. R. Bhandari and T. Taira, “Megawatt level UV output from [110] Cr⁴⁺:YAG passively Q-switched microchip laser,” Opt. Express19(23), 22510–22514 (2011). [CrossRef] [PubMed]
  4. Y. Sato and T. Taira, “The studies of thermal conductivity in GdVO4, YVO4, and Y3Al5O12 measured by quasi-one-dimensional flash method,” Opt. Express14(22), 10528–10536 (2006). [CrossRef] [PubMed]
  5. Y. Sato and T. Taira, “Temperature dependencies of stimulated emission cross section for Nd-doped solid-state laser materials,” Opt. Mater. Express2(8), 1076–1087 (2012). [CrossRef]
  6. P. A. Loiko, K. V. Yumashev, V. N. Matrosov, and N. V. Kuleshov, “Dispersion and anisotropy of thermo-optic coefficients in tetragonal GdVO4 and YVO4 laser host crystals,” Appl. Opt.52(4), 698–705 (2013). [CrossRef] [PubMed]
  7. Z. Huang, J. Feng, and W. Pan, “Theoretical investigations of the physical properties of zircon-type YVO4,” J. Solid State Chem.185, 42–48 (2012). [CrossRef]
  8. X. Xu, Z. Zhao, H. Wang, P. Song, G. Zhou, J. Xu, and P. Deng, “Spectroscopic and thermal properties of Cr,Yb:YAG crystal,” J. Cryst. Growth262(1-4), 317–321 (2004). [CrossRef]
  9. K. Wu, L. Hao, H. Zhang, H. Yu, Y. Wang, J. Wang, X. Tian, Z. Zhou, J. Liu, and R. I. Boughton, “Lu3Ga5O12 crystal: exploration of new laser host material for the ytterbium ion,” J. Opt. Soc. Am. B29(9), 2320 (2012). [CrossRef]
  10. Private communications
  11. A. A. Kaminskii, Laser Crystals (Springer-Verlag, Berlin, 1981), p. 320.
  12. W. Koechner, Solid-State Laser Engineering 6th ed. (Springer Science + Business Media, Inc., New York, 2006), p. 55.
  13. Y. Sato and T. Taira, “Thermo-optical and -mechanical parameters of Nd:GdVO4 and Nd:YVO4,” CLEO’07, paper JWA87 (2007).
  14. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon Press, 1975) sec. 4.7.
  15. T. Taira, A. Mukai, Y. Nozawa, and T. Kobayashi, “Single-mode oscillation of laser-diode-pumped Nd:YVO4 microchip lasers,” Opt. Lett.16(24), 1955–1957 (1991). [CrossRef] [PubMed]
  16. R. L. Aggarwal, D. J. Ripin, J. R. Ochoa, and T. Y. Fan, “Measurement of thermo-optic properties of Y3Al5O12, Lu3Al5O12, YAlO3, LiYF4, LiLuF4, BaY2F8, KGd(WO4)2, and KY(WO4)2 laser crystals in the 80–300 K temperature range,” J. Appl. Phys.98, 103514 (2005). [CrossRef]
  17. P. R. Stoddart, P. E. Ngoepe, P. M. Mjwara, J. D. Comins, and G. A. Saunders, “Hightemperature elastic constants of yttrium aluminum garne,” J. Appl. Phys.73(11), 7298–7301 (1993). [CrossRef]
  18. D. Rand, D. Miller, D. J. Ripin, and T. Y. Fan, “Cryogenic Yb3+-doped materials for pulsed solid-state laser applications,” Opt. Mater. Express1(3), 434–450 (2011). [CrossRef]
  19. H. C. Liang, K. Y. Lin, Y. C. Lee, and Y. F. Chen, “Precise measurement of group refractive indices and temperature dependence of refractive index for Nd-doped yttrium orthovanadate by intracavity spontaneous mode locking,” Opt. Lett.36(19), 3741–3743 (2011). [CrossRef] [PubMed]
  20. H. Zhang, J. Liu, J. Wang, C. Wang, L. Zhu, Z. Shao, X. Meng, X. Hu, and M. Jiang, “Characterization of the laser crystal Nd:GdVO4,” J. Opt. Soc. Am. B19(1), 18–27 (2002).
  21. N. R. Reddy and K. S. Murthy, “Thermal expansion of yttrium vanadate,” J. Mater. Sci. Lett.2(4), 139–140 (1983). [CrossRef]
  22. X. Peng, A. Asundi, Y. Chen, and Z. Xiong, “Study of the mechanical properties of Nd:YVO4 crystal by use of laser interferometry and finite-element analysis,” Appl. Opt.40(9), 1396–1403 (2001). [CrossRef] [PubMed]
  23. C. V. V. Reddy, P. Kistaiah, and K. S. Murthy, “X-ray studies on the thermal expansion of gadolinium vanadate,” J. Phys. D Appl. Phys.18(6), L27–L30 (1985). [CrossRef]
  24. J. Petit, B. Viana, P. Goldner, J.-P. Roger, and D. Fournier, “Thermomechanical properties of Yb3+ doped laser crystals: Experiment and modeling,” J. Appl. Phys.108(12), 123108 (2010). [CrossRef]
  25. T. M. Pollak, W. Wing, R. J. Grasso, E. P. Chicklis, and H. Jenssen, “CW laser operation of Nd:YLF,” J. Quant. Electron.18(2), 159–163 (1982). [CrossRef]
  26. D. E. Zelmon, J. J. Lee, K. M. Currin, J. M. Northridge, and D. Perlov, “Revisiting the optical properties of Nd doped yttrium orthovanadate,” Appl. Opt.49(4), 644–647 (2010). [CrossRef] [PubMed]
  27. R. Soulard, A. Zinoviev, J. L. Doualan, E. Ivakin, O. Antipov, and R. Moncorgé, “Detailed characterization of pump-induced refractive index changes observed in Nd:YVO4, Nd:GdVO4 and Nd:KGW,” Opt. Express18(2), 1553–1568 (2010). [CrossRef] [PubMed]
  28. H. Y. Shen, X. L. Meng, G. Zhang, J. J. Qin, W. Liu, L. Zhu, C. H. Huang, L. X. Huang, and M. Wei, “Sellmeier’s equation and the expression of the thermal refractive-index coefficient for a Nd0.007Gd0.993VO4 crystal,” Appl. Opt.43(4), 955–960 (2004). [CrossRef] [PubMed]
  29. W. Koechner, Solid-State Laser Engineering 6th ed. (Springer Science + Business Media, Inc., 2006), chap. 7.

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