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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 8 — Apr. 11, 2011
  • pp: 7153–7160
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Non-invasive characterization of the domain boundary and structure properties of periodically poled ferroelectrics

Shan-Chuang Pei, Tuan-Shu Ho, Chien-Chung Tsai, Ting-Hao Chen, Yi Ho, Pi-Ling Huang, A. H. Kung, and Sheng-Lung Huang  »View Author Affiliations


Optics Express, Vol. 19, Issue 8, pp. 7153-7160 (2011)
http://dx.doi.org/10.1364/OE.19.007153


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Abstract

Shaping the ferroelectric domains as waveguide, grating, lens, and prism are key to the successful penetration of periodically-poled ferroelectrics on various wavelength conversion applications. The complicated structures are, however, difficult to be fully characterized, especially the unexpected index contrast at the anti-parallel domain boundaries are typical in the order of 10−4 or less. An ultrahigh resolution optical coherence tomography was employed to fully characterize the domain boundary and structure properties of a periodically-poled lithium niobate (PPLN) waveguide with an axial resolution of 0.68 μm, an transversal resolution of 3.2 μm, and an index contrast sensitivity of 4x10−7. The anti-parallel domain uniformity can clearly be seen non-invasively. Dispersion of the ferroelectric material was also obtained from 500 to 750 nm.

© 2011 OSA

1. Introduction

In this study, we use an ultrahigh resolution optical coherence tomography (OCT) technique to non-invasively profile the extraordinary index (ne) of periodically poled congruent LiNbO3 (CLN) near the domain boundary in three dimensions and the refractive index difference was estimated [15

15. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991). [CrossRef] [PubMed]

17

17. K. Wiesauer, M. Pircher, E. Goetzinger, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Gruetzner, and D. Stifter, “Transversal ultrahigh-resolution polarizationsensitive optical coherence tomography for strain mapping in materials,” Opt. Express 14(13), 5945–5953 (2006). [CrossRef] [PubMed]

]. The 3D information shows the uniformity of domain boundary and the poled completeness of domain in whole cross section. In addition, the dispersion of a MgO-doped congruent LiNbO3 (MgO:CLN) was characterized from the broadband OCT signal. The axial resolution down to submicron order in high refractive index (n~2.2) material makes it suitable for nondestructive examination on poled periods with microstructures, such as waveguide, grating, lens, and prism.

2. Experimental setup

The OCT system light source was based on a Ce3+:YAG double-clad fiber (DCF) fabricated by a co-drawing laser-heated pedestal growth (CDLHPG) method. The core and inner-clad sizes were accordingly 10 and 100 μm. The DCF was pumped by a 300-mW, 446-nm blue laser diode and the excited visible amplified spontaneous emission (ASE) power was 500 μW. The central wavelength λ0 and the FWHM Δλ of Ce3+:YAG were 560 and 98 nm, respectively. Due to the near Gaussian spectral shape, low image pixel cross talk was expected. To probe the birefringence, the OCT system was configured as polarization-analytic detection. The axial and transversal resolutions were 0.68 and 3.2 μm in the PPLN crystal, and the depth of focus was about 126 μm.

3. Experimental results and discussions

3.1 Etched surface morphology

As a preliminary test on the system resolutions, HF was used to etch the crystalline surface. The periodical domains were distinguished by different etching speeds at the + z and -z faces. The etched surface was scanned by both the OCT and an atomic force microscope (AFM) to compare the etched width and depth as shown in Fig. 1
Fig. 1 Profiles of z-face etched patterns of a PPLN bulk crystal by (a) OCT and (b) AFM. Top: 3D images, Bottom: Line scan profiles.
. The etched depth between domain boundaries was 307 ± 63 nm by the OCT and 310.6 ± 9.3 nm by the AFM. Compared with AFM, the advantage of OCT comes from the capability of interior probing non-invasively.

3.2 Domain boundaries analysis

Figure 2
Fig. 2 Axial scan of a periodically poled congruent LiNbO3 crystal without etching. Inset shows the surface etched pattern by an optical microscope.
shows an axial scan by the OCT without any HF etching treatment. A series of peaks after Hilbert transformation can be observed inside the crystal due to the changes of refractive index at the domain boundaries. The signal reflected from the first domain boundary (peak 2) was merged with the wide signal envelope of peak 1, which was generated from the air-crystal interface. The inset shows the etched pattern from the z-face, which indicates the corresponding relation to the interferometric signals. With the current system’s signal-to-noise ratio, such a result can only be obtained when the polarization of light is set along the c-axis (E-field parallel to the c-axis). The cross-sectional image was scanned as shown in Fig. 3
Fig. 3 The cross-section scan with polarization-analytic OCT. The fine lines in axial position from 300 to 400 μm cannot be seen when the light polarization is normal to the c-axis.
.

The magnitude of refractive index difference can be estimated according to a multiple reflection scheme. Assuming the absorption of LiNbO3 is negligible because of the short-range scanning, the peak value of each interference signal is proportional to the square of the reflected light intensity from the sample arm.

Considering an incident light (I0) from the air (n0 ~1), the refractive index difference (Δn) between the poled and non-poled regions can be estimated using the reflected light from each boundaries,

Ii=I0T12T2i-4R.(for i>1, i: integer)T1=4nn0(n+n0)2,T=4n(n+Δn)(2n+Δn)2,R=(Δn2n+Δn)2,I1=I0(nn0n+n0)2.
(1)

Ii is intensity of the reflected light from the ith boundary. T and R are the transmittance and reflectance at the domain boundaries, respectively. Noting that Δn is much smaller than the bulk index, so R is nearly independent of the sign of Δn.

At a signal to noise ratio of 77 dB for the present polarization sensitive system, the index contrast sensitivity can readily be determined to be about 4x10−7 from the reflectance equation above. I1 and I5~I9 were taken individually into account to calculate the refraction index to avoid the side lobe problem. The refraction index difference Δne is estimated to be 4.2x10−4. Figure 4
Fig. 4 3D image of domain boundary layers of a PPLN bulk crystal. The domain uniformity can clearly be seen in Media 1.
shows a 3D image of the domain boundary with 200 μm x 200 μm cross-section. The 3D image shows uniformity of the domain boundary and reveals that the domains were completely poled in the whole cross section.

3.3 Dispersion characterization

The broadening of the peaks in the axial scan resulted from dispersion of the device under test. Using Wiener-Khinchin theorem on the peaks, the dispersion of extraordinary wave of a 5-mol.% MgO-doped congruent LiNbO3 was characterized as shown in Fig. 5
Fig. 5 Dispersion of extraordinary wave of a 5 mol.% MgO-doped CLN by peaks 1 and 3.
. The dispersion was estimated by two adjacent peaks. The result agrees quite well with the Sellmeier equation [18

18. O. Paul, A. Quosig, T. Bauer, M. Nittmann, J. Bartschke, G. Anstett, and J. A. L’Huillier, “Temperature-dependent Sellmeier equation in the MIR for the extraordinary refractive index of 5% MgO doped congruent LiNbO3,” Appl. Phys. B 86(1), 111–115 (2006). [CrossRef]

,19

19. D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, n(e), in congruent lithium niobate,” Opt. Lett. 22(20), 1553–1555 (1997). [CrossRef]

]. Due to the broadband nature of the light source, the dispersion in a wavelength range from 0.5 to 0.7 μm was obtained.

3.4 Axial scan on other ferroelectrics

The axial scan was also attempted on periodically poled LiTaO3 crystals as shown in Fig. 6
Fig. 6 Axial scans of periodically poled congruent LiTaO3 and periodically poled near-stoichiometric LiTaO3 crystals.
. However, the interference peaks from the congruent LiTaO3 were much smaller than those of congruent LiNbO3, which can be attributed to the smaller refractive index difference between anti-parallel domains due to material property [10

10. V. Gopalan, V. Dierolf, and D. A. Scrymgeour, “Defect-domain wall interactions in trigonal ferroelectrics,” Annu. Rev. Mater. Res. 37(1), 449–489 (2007). [CrossRef]

]. Thus, the deeper signals in domain boundary were difficult to detect. The refraction index difference can be only roughly estimated to be around 5.5x10−4. Besides, there are numerous polarization reversal properties (e.g. optical birefringence, coercive fields, domain stabilization time, domain back-switching and internal fields) that are different in congruent and near-stoichiometric crystals [12

12. T. J. Yang, V. Gopalan, P. Swart, and U. Mohideen, “Experimental study of internal fields and movement of single ferroelectric domain walls,” J. Phys. Chem. Solids 61(2), 275–282 (2000). [CrossRef]

]. Similar result occurred in the periodically poled near-stoichiometric LiTaO3. The interference peaks come from the anti-parallel domain boundary is very weak, and only one peak can be observed as shown in Fig. 6.

3.5 Planar ridge PPLN waveguide analysis

For a ridge-type waveguide, only the ridge width and length can be well defined by mask design. However, the waveguide thickness uniformity is crucial for the performance of the device [20

20. S. M. Zhang, K. M. Wang, X. Liu, Z. Bi, and X. H. Liu, “Planar and ridge waveguides formed in LiNbO3 by proton exchange combined with oxygen ion implantation,” Opt. Express 18(15), 15609–15617 (2010). [CrossRef] [PubMed]

,21

21. M. A. Webster, R. M. Pafchek, G. Sukumaran, and T. L. Koch, “Low-loss quasi-planar ridge waveguides formed on thin silicon-on-insulator,” Appl. Phys. Lett. 87(23), 231108 (2005). [CrossRef]

]. Figure 7
Fig. 7 Optical microscope images show the structure of a triple-layer planar ridge PPLN waveguide, WG-1, with a length of 1 mm. (a) end view and (b) top view. The yellow arrows in (a) indicate the OCT axial scan locations shown in Fig. 8. The red circle shows the scan area in Fig. 9.
shows the end view and top view of a planar ridge waveguide by an optical microscope. A cleaved face is shown in Fig. 7(a). The top layer is a periodically poled MgO:LiNbO3 ridge waveguide with a 6.75-μm poling pitch and a polished surface (1); the middle layer is epoxy and the bottom layer is an undoped LiNbO3 single crystal substrate. In Fig. 7(b), the waveguide width and the poled period can be indistinctively observed from the etched pattern. Due to the etched surfaces (2) and (3) are facing downward and buried in epoxy.

To probe the waveguide, an OCT incident light (solid yellow line in Fig. 7(a)) enters the polished surface (1) and passes through the ridge for an axial scan. As shown in Fig. 8(a)
Fig. 8 Depth position of axial scan (a) with and (b) without through the ridge waveguide.
, a ridge thickness of 4.73 μm is precisely defined by peaks (1) and (3). The thickness of the thin PPLN layer nearby the ridge waveguide can also be measured (dotted yellow line in Fig. 7(a)). The thickness is only 1.3 μm as shown in Fig. 8(b).

A series of axial scans were performed to measure the waveguide thickness. Table 1

Table 1. Waveguide thickness measurement

table-icon
View This Table
summarizes the measurement of thickness and standard deviation of WG-1. We also measure another waveguide (WG-2) on the same substrate with the same fabrication process. Slight variation of thickness toward the rear region was detected from the measurement.

A 3D tomography of WG-1 was obtained as shown in Fig. 9
Fig. 9 3D tomographic images of a planar ridge PPLN waveguide. (a) The scan area is shown in Fig. 7(a). Markers (1) to (4) correspond to the interfaces (1) to (4) in Fig. 7(a). (b) A different viewing angle shows the poled pitches in the waveguiding region.
. The periodic height variation of interface (4) is due to accumulated optical path length of the top layers. The uniformity of layer thickness and roughness of each interface can be observed. As shown in Fig. 9(b), the periodical patterns from (2) and (3) in Fig. 7(a) are enhanced by image processing and the 6.75-μm poled period can clearly be seen. With the non-invasive 3D profiling technique, the poling quality in the waveguiding region as well as the mode matching design at the input and output ports were verified.

4. Conclusion

It is demonstrated that the complex structure, dispersion, and small index contrast of periodically poled ferroelectric waveguide can be non-invasively characterized. An axial resolution of 0.68 μm, an transversal resolution of 3.2 μm, and an index contrast sensitivity of 4x10−7 were achieved. The index difference between the + z and –z domains in a MgO-doped congruent LiNbO3 was estimated to be 4.2x10−4, which is an important indicator for the quality of the poled ferroelectrics. The high spatial resolution and high index contrast sensitivity technique can facilitate the development of quasi-phased nonlinear waveguide devices for improving wavelength conversion efficiency as well as reducing insertion loss by mode-matched coupling.

Acknowledgments

This work is partially supported by the National Science Council, Taiwan.

References and links

1.

L. E. Myers, G. D. Miller, R. C. Eckardt, M. M. Fejer, R. L. Byer, and W. R. Bosenberg, “Quasi-phase-matched 1.064-μm-pumped optical parametric oscillator in bulk periodically poled LiNbO3,” Opt. Lett. 20(1), 52–54 (1995). [CrossRef] [PubMed]

2.

G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, and R. L. Byer, “42%-efficient single-pass cw second-harmonic generation in periodically poled lithium niobate,” Opt. Lett. 22(24), 1834–1836 (1997). [CrossRef]

3.

L. M. Lee, S. C. Pei, D. F. Lin, P. C. Chiu, M. C. Tsai, T. M. Tai, D. H. Sun, A. H. Kung, and S. L. Huang, “Generation of tunable blue-green light using ZnO periodically poled lithium niobate crystal fiber by self-cascaded second-order nonlinearity,” J. Opt. Soc. Am. B 24(8), 1909–1915 (2007). [CrossRef]

4.

J. Wang, J. Sun, C. Lou, and Q. Sun, “Experimental demonstration of wavelength conversion between ps-pulses based on cascaded sum- and difference frequency generation (SFG+DFG) in LiNbO3 waveguides,” Opt. Express 13(19), 7405–7414 (2005). [CrossRef] [PubMed]

5.

K. T. Gahagan, V. Gopalan, J. M. Robinson, Q. X. Jia, T. E. Mitchell, M. J. Kawas, T. E. Schlesinger, and D. D. Stancil, “Integrated electro-optic lens/scanner in a LiTaO3 single crystal,” Appl. Opt. 38(7), 1186–1190 (1999). [CrossRef]

6.

J. Harris, G. Norris, and G. McConnell, “Characterisation of periodically poled materials using nonlinear microscopy,” Opt. Express 16(8), 5667–5672 (2008). [CrossRef] [PubMed]

7.

Y. Sheng, A. Best, H. J. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Cerenkov-type second harmonic generation,” Opt. Express 18(16), 16539–16545 (2010). [CrossRef] [PubMed]

8.

S. Kim, V. Gopalan, and B. Steiner, “Direct x-ray synchrotron imaging of strains at 180° domain walls in congruent LiNbO3 and LiTaO3 crystals,” Appl. Phys. Lett. 77(13), 2051–2053 (2000). [CrossRef]

9.

V. Gopalan and M. C. Gupta, “Origin and characteristics of internal fields in LiNbO3 crystals,” Ferroelectrics 198(1), 49–59 (1997). [CrossRef]

10.

V. Gopalan, V. Dierolf, and D. A. Scrymgeour, “Defect-domain wall interactions in trigonal ferroelectrics,” Annu. Rev. Mater. Res. 37(1), 449–489 (2007). [CrossRef]

11.

S. Kim and V. Gopalan, “Optical index profile at an antiparallel ferroelectric domain wall in lithium niobate,” Mater. Sci. Eng. B 120(1-3), 91–94 (2005). [CrossRef]

12.

T. J. Yang, V. Gopalan, P. Swart, and U. Mohideen, “Experimental study of internal fields and movement of single ferroelectric domain walls,” J. Phys. Chem. Solids 61(2), 275–282 (2000). [CrossRef]

13.

T. Jach, S. Kim, V. Gopalan, S. Durbin, and D. Bright, “Long-range strains and the effects of applied field at 180° ferroelectric domain walls in lithium niobate,” Phys. Rev. B 69(6), 064113 (2004). [CrossRef]

14.

S. Kim, V. Gopalan, K. Kitamura, and Y. Furukawa, “Domain reversal and nonstoichiometry in lithium tantalate,” J. Appl. Phys. 90(6), 2949–2963 (2001). [CrossRef]

15.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991). [CrossRef] [PubMed]

16.

C. C. Tsai, T. H. Chen, Y. S. Lin, Y. T. Wang, W. Chang, K. Y. Hsu, Y. H. Chang, P. K. Hsu, D. Y. Jheng, K. Y. Huang, E. Sun, and S. L. Huang, “Ce3+:YAG double-clad crystal-fiber-based optical coherence tomography on fish cornea,” Opt. Lett. 35(6), 811–813 (2010). [CrossRef] [PubMed]

17.

K. Wiesauer, M. Pircher, E. Goetzinger, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Gruetzner, and D. Stifter, “Transversal ultrahigh-resolution polarizationsensitive optical coherence tomography for strain mapping in materials,” Opt. Express 14(13), 5945–5953 (2006). [CrossRef] [PubMed]

18.

O. Paul, A. Quosig, T. Bauer, M. Nittmann, J. Bartschke, G. Anstett, and J. A. L’Huillier, “Temperature-dependent Sellmeier equation in the MIR for the extraordinary refractive index of 5% MgO doped congruent LiNbO3,” Appl. Phys. B 86(1), 111–115 (2006). [CrossRef]

19.

D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, n(e), in congruent lithium niobate,” Opt. Lett. 22(20), 1553–1555 (1997). [CrossRef]

20.

S. M. Zhang, K. M. Wang, X. Liu, Z. Bi, and X. H. Liu, “Planar and ridge waveguides formed in LiNbO3 by proton exchange combined with oxygen ion implantation,” Opt. Express 18(15), 15609–15617 (2010). [CrossRef] [PubMed]

21.

M. A. Webster, R. M. Pafchek, G. Sukumaran, and T. L. Koch, “Low-loss quasi-planar ridge waveguides formed on thin silicon-on-insulator,” Appl. Phys. Lett. 87(23), 231108 (2005). [CrossRef]

OCIS Codes
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(130.3730) Integrated optics : Lithium niobate
(160.2260) Materials : Ferroelectrics
(230.7370) Optical devices : Waveguides

ToC Category:
Materials

History
Original Manuscript: November 11, 2010
Manuscript Accepted: February 17, 2011
Published: March 30, 2011

Citation
Shan-Chuang Pei, Tuan-Shu Ho, Chien-Chung Tsai, Ting-Hao Chen, Yi Ho, Pi-Ling Huang, A. H. Kung, and Sheng-Lung Huang, "Non-invasive characterization of the domain boundary and structure properties of periodically poled ferroelectrics," Opt. Express 19, 7153-7160 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-8-7153


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References

  1. L. E. Myers, G. D. Miller, R. C. Eckardt, M. M. Fejer, R. L. Byer, and W. R. Bosenberg, “Quasi-phase-matched 1.064-μm-pumped optical parametric oscillator in bulk periodically poled LiNbO3,” Opt. Lett. 20(1), 52–54 (1995). [CrossRef] [PubMed]
  2. G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, and R. L. Byer, “42%-efficient single-pass cw second-harmonic generation in periodically poled lithium niobate,” Opt. Lett. 22(24), 1834–1836 (1997). [CrossRef]
  3. L. M. Lee, S. C. Pei, D. F. Lin, P. C. Chiu, M. C. Tsai, T. M. Tai, D. H. Sun, A. H. Kung, and S. L. Huang, “Generation of tunable blue-green light using ZnO periodically poled lithium niobate crystal fiber by self-cascaded second-order nonlinearity,” J. Opt. Soc. Am. B 24(8), 1909–1915 (2007). [CrossRef]
  4. J. Wang, J. Sun, C. Lou, and Q. Sun, “Experimental demonstration of wavelength conversion between ps-pulses based on cascaded sum- and difference frequency generation (SFG+DFG) in LiNbO3 waveguides,” Opt. Express 13(19), 7405–7414 (2005). [CrossRef] [PubMed]
  5. K. T. Gahagan, V. Gopalan, J. M. Robinson, Q. X. Jia, T. E. Mitchell, M. J. Kawas, T. E. Schlesinger, and D. D. Stancil, “Integrated electro-optic lens/scanner in a LiTaO3 single crystal,” Appl. Opt. 38(7), 1186–1190 (1999). [CrossRef]
  6. J. Harris, G. Norris, and G. McConnell, “Characterisation of periodically poled materials using nonlinear microscopy,” Opt. Express 16(8), 5667–5672 (2008). [CrossRef] [PubMed]
  7. Y. Sheng, A. Best, H. J. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Cerenkov-type second harmonic generation,” Opt. Express 18(16), 16539–16545 (2010). [CrossRef] [PubMed]
  8. S. Kim, V. Gopalan, and B. Steiner, “Direct x-ray synchrotron imaging of strains at 180° domain walls in congruent LiNbO3 and LiTaO3 crystals,” Appl. Phys. Lett. 77(13), 2051–2053 (2000). [CrossRef]
  9. V. Gopalan and M. C. Gupta, “Origin and characteristics of internal fields in LiNbO3 crystals,” Ferroelectrics 198(1), 49–59 (1997). [CrossRef]
  10. V. Gopalan, V. Dierolf, and D. A. Scrymgeour, “Defect-domain wall interactions in trigonal ferroelectrics,” Annu. Rev. Mater. Res. 37(1), 449–489 (2007). [CrossRef]
  11. S. Kim and V. Gopalan, “Optical index profile at an antiparallel ferroelectric domain wall in lithium niobate,” Mater. Sci. Eng. B 120(1-3), 91–94 (2005). [CrossRef]
  12. T. J. Yang, V. Gopalan, P. Swart, and U. Mohideen, “Experimental study of internal fields and movement of single ferroelectric domain walls,” J. Phys. Chem. Solids 61(2), 275–282 (2000). [CrossRef]
  13. T. Jach, S. Kim, V. Gopalan, S. Durbin, and D. Bright, “Long-range strains and the effects of applied field at 180° ferroelectric domain walls in lithium niobate,” Phys. Rev. B 69(6), 064113 (2004). [CrossRef]
  14. S. Kim, V. Gopalan, K. Kitamura, and Y. Furukawa, “Domain reversal and nonstoichiometry in lithium tantalate,” J. Appl. Phys. 90(6), 2949–2963 (2001). [CrossRef]
  15. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991). [CrossRef] [PubMed]
  16. C. C. Tsai, T. H. Chen, Y. S. Lin, Y. T. Wang, W. Chang, K. Y. Hsu, Y. H. Chang, P. K. Hsu, D. Y. Jheng, K. Y. Huang, E. Sun, and S. L. Huang, “Ce3+:YAG double-clad crystal-fiber-based optical coherence tomography on fish cornea,” Opt. Lett. 35(6), 811–813 (2010). [CrossRef] [PubMed]
  17. K. Wiesauer, M. Pircher, E. Goetzinger, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Gruetzner, and D. Stifter, “Transversal ultrahigh-resolution polarizationsensitive optical coherence tomography for strain mapping in materials,” Opt. Express 14(13), 5945–5953 (2006). [CrossRef] [PubMed]
  18. O. Paul, A. Quosig, T. Bauer, M. Nittmann, J. Bartschke, G. Anstett, and J. A. L’Huillier, “Temperature-dependent Sellmeier equation in the MIR for the extraordinary refractive index of 5% MgO doped congruent LiNbO3,” Appl. Phys. B 86(1), 111–115 (2006). [CrossRef]
  19. D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, n(e), in congruent lithium niobate,” Opt. Lett. 22(20), 1553–1555 (1997). [CrossRef]
  20. S. M. Zhang, K. M. Wang, X. Liu, Z. Bi, and X. H. Liu, “Planar and ridge waveguides formed in LiNbO3 by proton exchange combined with oxygen ion implantation,” Opt. Express 18(15), 15609–15617 (2010). [CrossRef] [PubMed]
  21. M. A. Webster, R. M. Pafchek, G. Sukumaran, and T. L. Koch, “Low-loss quasi-planar ridge waveguides formed on thin silicon-on-insulator,” Appl. Phys. Lett. 87(23), 231108 (2005). [CrossRef]

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