OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 18 — Sep. 9, 2013
  • pp: 20641–20648
« Show journal navigation

Temperature-dependent Sellmeier equations of nonlinear optical crystal La2CaB10O19

Naixia Zhai, Yin Li, Guochun Zhang, Yicheng Wu, and Chuangtian Chen  »View Author Affiliations


Optics Express, Vol. 21, Issue 18, pp. 20641-20648 (2013)
http://dx.doi.org/10.1364/OE.21.020641


View Full Text Article

Acrobat PDF (1020 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The thermal dependence principal refractive indices of La2CaB10O19 (LCB) crystal at wavelengths of 0.254, 0.365, 0.405, 0.480, 0.546, 0.644, 0.852, 1.014, and 2.325 μm were accurately measured by using the vertical incidence method within the temperature range from 25 to 170 °C. We derived equations of thermal refractive index coefficients as a function of wavelength that could be used to calculate the principal thermal refractive indices at different wavelengths. The temperature-dependent Sellmeier equations were also derived and used to calculate the phase-matching angles for the third-harmonic generation of LCB crystal at different temperatures. Theoretical and experimental phase-matching angles for the type I third-harmonic generation of LCB crystal at different temperatures were in good agreement.

© 2013 OSA

1. Introduction

La2CaB10O19 (LCB) crystal is a competitive candidate nonlinear optical (NLO) crystal due to its high laser damage threshold (11.5 GW/cm2 for 8 ns pulses at 1064 nm), moderate birefringence (△n≈0.05), wide transparency range (170–3000 nm), relatively large effective NLO coefficient (1.05 pm/V for second harmonic generation of 1064 nm), superior chemical stability, and good mechanical properties [1

1. Y. C. Wu, J. G. Liu, P. Z. Fu, J. X. Wang, H. Y. Zhou, G. F. Wang, and C. T. Chen, “A new lanthanum and calcium borate La2CaB10O19,” Chem. Mater. 13(3), 753–755 (2001). [CrossRef]

3

3. G. L. Wang, J. H. Lu, D. F. Cui, Z. Y. Xu, Y. C. Wu, P. Z. Fu, X. G. Guan, and C. T. Chen, “Efficient second harmonic generation in a new nonlinear La2CaB10O19 crystal,” Opt. Commun. 209(4–6), 481–484 (2002). [CrossRef]

]. In particular, LCB crystal exhibits excellent third-harmonic generation (THG) performance and may be a promising THG crystal for use in all-solid-state lasers [4

4. J. X. Zhang, L. R. Wang, Y. Wu, G. L. Wang, P. Z. Fu, and Y. C. Wu, “High-efficiency third harmonic generation at 355nm based on La2CaB10O19.,” Opt. Express 19(18), 16722–16729 (2011). [CrossRef] [PubMed]

,5

5. L. R. Wang, Y. Wu, G. L. Wang, J. X. Zhang, Y. C. Wu, and C. T. Chen, “31.6-W, 355-nm generation with La2CaB10O19 crystals,” Appl. Phys. B 108(2), 307–311 (2012). [CrossRef]

].

In this work, we determine the principal refractive indices at different temperatures, and present the thermal refractive index coefficients and the temperature-dependent Sellmeier equations of LCB crystal for the first time. Based on the above investigation, a THG device of LCB crystal for use at 80 °C was fabricated, and a stable THG output with average power of 24.5 W within five hours has been successfully demonstrated.

2. Measurement of refractive indices

LCB is a biaxial crystal and belongs to the monoclinic system with space group C2 [1

1. Y. C. Wu, J. G. Liu, P. Z. Fu, J. X. Wang, H. Y. Zhou, G. F. Wang, and C. T. Chen, “A new lanthanum and calcium borate La2CaB10O19,” Chem. Mater. 13(3), 753–755 (2001). [CrossRef]

]. To measure its three independent principal refractive indices nx, ny, and nz, one LCB crystal was cut into two right-angle prisms with the sides of the right angle aligned with different crystalline axes, as shown in Fig. 1
Fig. 1 Schematic of prism 1 and prism 2.
. The apex angles of two prisms were approximately 30°. The flatness of the crystalline faces b and c as well as the slope of the prism were better than λ/4. In our experiment, the refractive index could be calculated by using n = sin(α + β)/sin(α), where n is the principal refractive index, α is the apex angle of the prism, and β is the deviation angle of refractive light. When the incident light travelled perpendicular to the b face of prism 1, refractive indices nx and nz could be measured. Refractive indices ny as well as na` could also be measured when the light travelled perpendicular to the c face of prism 2.

Our experimental system comprised two components: a refractive index measurement instrument (SpectroMaster UV-VIS-IR, Trioptics, Germany) with a high accuracy of 1 × 10−5 and a homemade temperature-stabilized reheating furnace with an accuracy of ± 0.1 °C,as shown in Fig. 2
Fig. 2 Experiment setup for refractive indices measurement.
. In the measurement, mercury lamp at wavelengths of 0.254, 0.365, 0.405, 0.546, 1.014, and 2.325 μm, Chromium lamp at wavelengths of 0.480 and 0.644 μm, and Cesium lamp at wavelength of 0.852 μm were used. The temperatures were maintained at 25, 40, 60, 80, 110, 140, and 170 °C, respectively. The prisms were placed in a temperature-stabilized furnace, and heated to the target temperature with 30 °C/h and allowed to reach thermal equilibrium. During the measurement process, the incident angle of the central collimator beam was defined as 0°. We firstly adjusted the sample table to be horizontal and measured the accurate apex angle of the prism, after that the sample would be adjust to be aligned square to the collimator as shown in Fig. 2, and then we would rotated the goniometer manually to find the refractive signal and measure the deviation angle using the measurement program of the instrument. At each target temperature, the deviation angle was usually measured four times with the previously mentioned different wavelengths, and the results were averaged to obtain a single determination of deviation. The measured results are listed in Table 1

Table 1. Principal Refractive Indices of LCB Crystal

table-icon
View This Table
| View All Tables
.

3. Thermal refractive index coefficients and temperature-dependent Sellmeier equations

As shown in Table 1, refractive indices nx, ny, and nz all increase slowly with the increased temperature at different wavelengths. For a specific wavelength, the index can be assumed as a linear variation with the increased temperature, which could be expressed as
n=n0+dndT(TT0).
(1)
where n is the refractive index at temperature T, n0 is the refractive index at T0 and dn/dT is the thermal refractive index coefficient.

According to the measured principal indices, the relationship between dn/dT of the principal refractive indices and the wavelength λ could be fitted [9

9. T. Mikami, T. Okamoto, and K. Kato, “Sellmeier and thermo-optic dispersion formulas for CsTiOAsO4,” J. Appl. Phys. 109(2), 023108 (2011). [CrossRef]

11

11. G. C. Zhang, S. S. Liu, L. X. Huang, G. Zhang, and Y. C. Wu, “Thermal refractive index coefficients of nonlinear optical crystal CsB3O5,” Opt. Lett. 38(10), 1594–1596 (2013). [CrossRef]

]. It is
dnxdT=(-0.1148λ3+1.8140λ2-4.2937λ+10.8278)×106,dnydT=(-0.3384λ3+3.1356λ2-5.5422λ+7.7771)×106,dnzdT=(-0.1511λ3+1.9754λ2-4.8200λ+6.5930)×106.
(2)
where λ is in micrometer and 0.254 μm ≤ λ ≤ 2.325 μm.

The thermal refractive index coefficients for nx, ny, and nz were calculated by monadic linear regression method and are given in Table 2

Table 2. Thermal Refractive Index Coefficients ( × 10−6) of LCB Crystal at Different Wavelengths

table-icon
View This Table
| View All Tables
. Table 2 shows that these constants are all positive with magnitude level of 10−6. The value of dnx/dT of different wavelengths is the largest, while that of dnz/dT is the smallest. Refractive indices corresponding to different wavelengths at different temperatures were calculated by using Eq. (1) and Eq. (2) (T0 is 25 °C, n0 is the experimental value of refractive index at 25 °C). Figures 3(a)
Fig. 3 Calculated (solid lines) and measured (open circles) LCB refractive indices as a function of temperature for nine different wavelengths: (a) nx, (b) ny, (c) nz.
-3(c) show theoretical and measured values of nx, ny, and nz. The difference between the measured and calculated values was less than 2 × 10−4. This verifies the reliability of Eq. (2).

The temperature-dependent Sellmeier equations of nx, ny, and nz were obtained by using the least-square-fit method with the same form as Ref. 11

11. G. C. Zhang, S. S. Liu, L. X. Huang, G. Zhang, and Y. C. Wu, “Thermal refractive index coefficients of nonlinear optical crystal CsB3O5,” Opt. Lett. 38(10), 1594–1596 (2013). [CrossRef]

, as shown in Eq. (3) and Table 3

Table 3. Constants in Eq. (3)

table-icon
View This Table
| View All Tables
, where i is x, y, or z, and λ is the wavelength in micrometer, A, B, C, D, E, F, G, and H are constants.

ni2(λ,T)=A+ET+B+FTλ2(C+GT)+(D+HT)×λ2.
(3)

Based on the above Sellmeier equations, type I PM angles in the yz plane for THG of LCB crystal (1064 nm + 532 nm→355 nm) at different temperatures were calculated and listed in Table 4

Table 4. Calculated and Experimental PM Angles for Type I THG with LCB Crystal at Different Temperatures

table-icon
View This Table
| View All Tables
. In order to check the reliability of the calculated results, PM angles at different temperatures were measured. The type I phase matching LCB was cut at θ = 48.7ο and φ = 90ο. During the measurement, the LCB crystal was kept in an oven with controlling precision of ± 0.1 οC and located on a motorized rotary stage table with a precision of 0.0025ο. The measured results are also listed in Table 4. It shows that the measured values agree well with the calculated values after considering thermal refractive index coefficients, which suggests the reliability of the obtained Sellmeier equations.

In addition, we performed a stability test of THG for LCB crystal. A type I THG device of LCB crystal for use at 80 °C was fabricated at θ = 49.1° and φ = 90° with dimensions of 4 × 4 × 14.85 mm3. A Q-switched Nd:YAG laser (IS161-E, Edgewave) which emits 10 ns pulses at 1064 nm with a pulse repetition rate of 10 kHz was employed as the fundamental light source. The maximum average output power is 150 W with square dimensions of 5 × 5 mm2, and the beam quality factor M2 < 2. An attenuation system was used to adjust its output power. A lens system was used to minimize the fundamental beam diameter by a ratio of three in order to get enough power density for second-harmonic generation (SHG). A type I noncritical PM LBO crystal cut at θ = 90° and φ = 0° was used to generate the 532 nm frequency-doubling light. The 1064 nm laser beam and the 532 nm laser beams were focused by a lens with focal length of 300 mm. LCB crystal was kept at 80 °C to obtain a stable temperature inside the crystal. When the input 1064 nm power was 110 W, the 355 nm output was around 24.5 W over a period of 5 hours. The power stability (RMS) was 1.64%, and the period power instability may result from the temperature resolution of our homemade oven, as shown in Fig. 4
Fig. 4 Stability of the 355 nm output power at 24.5 W within 5 hours.
. No surface or internal damage in LCB crystal was found after the test. The long-time stable 355 nm output indicates that LCB crystal is a competitive candidate for high-average-power THG.

4. Conclusions

In summary, the thermal refractive index coefficients of LCB crystal were measured for the first time. The temperature-dependent Sellmeier equations were fitted, and were used to calculate PM angles of THG for LCB crystal at different temperatures. The calculated results were well consistent with the experimental results, which indicated that the thermal refractive index coefficients and the temperature-dependent Sellmeier equations of LCB crystal were reliable and highly useful for designing a high average power frequency conversion system based on LCB crystal. The long-time stable 355 nm output indicated that LCB crystal is a competitive candidate for high-average-power THG.

Acknowledgments

This work was financially supported by the National Natural Science Foundation of China (nos: 51132008 and 50932005).

References and links

1.

Y. C. Wu, J. G. Liu, P. Z. Fu, J. X. Wang, H. Y. Zhou, G. F. Wang, and C. T. Chen, “A new lanthanum and calcium borate La2CaB10O19,” Chem. Mater. 13(3), 753–755 (2001). [CrossRef]

2.

F. L. Jing, P. Z. Fu, Y. C. Wu, Y. L. Zu, and X. Wang, “Growth and assessment of physical properties of a new nonlinear optical crystal: Lanthanum calcium borate,” Opt. Mater. 30(12), 1867–1872 (2008). [CrossRef]

3.

G. L. Wang, J. H. Lu, D. F. Cui, Z. Y. Xu, Y. C. Wu, P. Z. Fu, X. G. Guan, and C. T. Chen, “Efficient second harmonic generation in a new nonlinear La2CaB10O19 crystal,” Opt. Commun. 209(4–6), 481–484 (2002). [CrossRef]

4.

J. X. Zhang, L. R. Wang, Y. Wu, G. L. Wang, P. Z. Fu, and Y. C. Wu, “High-efficiency third harmonic generation at 355nm based on La2CaB10O19.,” Opt. Express 19(18), 16722–16729 (2011). [CrossRef] [PubMed]

5.

L. R. Wang, Y. Wu, G. L. Wang, J. X. Zhang, Y. C. Wu, and C. T. Chen, “31.6-W, 355-nm generation with La2CaB10O19 crystals,” Appl. Phys. B 108(2), 307–311 (2012). [CrossRef]

6.

P. A. Loiko, K. V. Yumashev, N. V. Kuleshov, G. E. Rachkovskaya, and A. A. Pavlyuk, “Thermo-optic dispersion formulas for monoclinic double tungstates KRe(WO4)2 where Re = Gd, Y, Lu, Yb,” Opt. Mater. 33(11), 1688–1694 (2011). [CrossRef]

7.

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]

8.

A. Bruner, D. Eger, M. B. Oron, P. Blau, M. Katz, and S. Ruschin, “Temperature-dependent Sellmeier equation for the refractive index of stoichiometric lithium tantalate,” Opt. Lett. 28(3), 194–196 (2003). [CrossRef] [PubMed]

9.

T. Mikami, T. Okamoto, and K. Kato, “Sellmeier and thermo-optic dispersion formulas for CsTiOAsO4,” J. Appl. Phys. 109(2), 023108 (2011). [CrossRef]

10.

L. J. Qin, X. L. Meng, H. Y. Shen, L. Zhu, B. C. Xu, L. X. Huang, H. R. Xia, P. Zhao, and G. Zheng, “Thermal conductivity and refractive indices of Nd:GdVO4 crystals,” Cryst. Res. Technol. 38(9), 793–797 (2003). [CrossRef]

11.

G. C. Zhang, S. S. Liu, L. X. Huang, G. Zhang, and Y. C. Wu, “Thermal refractive index coefficients of nonlinear optical crystal CsB3O5,” Opt. Lett. 38(10), 1594–1596 (2013). [CrossRef]

OCIS Codes
(160.4330) Materials : Nonlinear optical materials
(230.4320) Optical devices : Nonlinear optical devices

ToC Category:
Nonlinear Optics

History
Original Manuscript: May 13, 2013
Revised Manuscript: July 4, 2013
Manuscript Accepted: July 10, 2013
Published: August 27, 2013

Citation
Naixia Zhai, Yin Li, Guochun Zhang, Yicheng Wu, and Chuangtian Chen, "Temperature-dependent Sellmeier equations of nonlinear optical crystal La2CaB10O19," Opt. Express 21, 20641-20648 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-18-20641


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. Y. C. Wu, J. G. Liu, P. Z. Fu, J. X. Wang, H. Y. Zhou, G. F. Wang, and C. T. Chen, “A new lanthanum and calcium borate La2CaB10O19,” Chem. Mater.13(3), 753–755 (2001). [CrossRef]
  2. F. L. Jing, P. Z. Fu, Y. C. Wu, Y. L. Zu, and X. Wang, “Growth and assessment of physical properties of a new nonlinear optical crystal: Lanthanum calcium borate,” Opt. Mater.30(12), 1867–1872 (2008). [CrossRef]
  3. G. L. Wang, J. H. Lu, D. F. Cui, Z. Y. Xu, Y. C. Wu, P. Z. Fu, X. G. Guan, and C. T. Chen, “Efficient second harmonic generation in a new nonlinear La2CaB10O19 crystal,” Opt. Commun.209(4–6), 481–484 (2002). [CrossRef]
  4. J. X. Zhang, L. R. Wang, Y. Wu, G. L. Wang, P. Z. Fu, and Y. C. Wu, “High-efficiency third harmonic generation at 355nm based on La2CaB10O19.,” Opt. Express19(18), 16722–16729 (2011). [CrossRef] [PubMed]
  5. L. R. Wang, Y. Wu, G. L. Wang, J. X. Zhang, Y. C. Wu, and C. T. Chen, “31.6-W, 355-nm generation with La2CaB10O19 crystals,” Appl. Phys. B108(2), 307–311 (2012). [CrossRef]
  6. P. A. Loiko, K. V. Yumashev, N. V. Kuleshov, G. E. Rachkovskaya, and A. A. Pavlyuk, “Thermo-optic dispersion formulas for monoclinic double tungstates KRe(WO4)2 where Re = Gd, Y, Lu, Yb,” Opt. Mater.33(11), 1688–1694 (2011). [CrossRef]
  7. 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]
  8. A. Bruner, D. Eger, M. B. Oron, P. Blau, M. Katz, and S. Ruschin, “Temperature-dependent Sellmeier equation for the refractive index of stoichiometric lithium tantalate,” Opt. Lett.28(3), 194–196 (2003). [CrossRef] [PubMed]
  9. T. Mikami, T. Okamoto, and K. Kato, “Sellmeier and thermo-optic dispersion formulas for CsTiOAsO4,” J. Appl. Phys.109(2), 023108 (2011). [CrossRef]
  10. L. J. Qin, X. L. Meng, H. Y. Shen, L. Zhu, B. C. Xu, L. X. Huang, H. R. Xia, P. Zhao, and G. Zheng, “Thermal conductivity and refractive indices of Nd:GdVO4 crystals,” Cryst. Res. Technol.38(9), 793–797 (2003). [CrossRef]
  11. G. C. Zhang, S. S. Liu, L. X. Huang, G. Zhang, and Y. C. Wu, “Thermal refractive index coefficients of nonlinear optical crystal CsB3O5,” Opt. Lett.38(10), 1594–1596 (2013). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited