Open Access
Add to BibSonomyAbstract
BaMgF4 single crystal is a promising candidate for many applications in the vacuum ultraviolet region. The electro-optic coefficient of BaMgF4 single crystal is measured by means of a symmetric metal-cladding waveguide, in which the effect refractive index is very sensitive to the change of the refractive index of the guiding layer. The resonance excitation angle shifts as the applied electric filed on the waveguide changes. Subsequently, the electro-optic coefficient γ13 = −36.2 pm/V of BaMgF4 single crystal is determined by measuring the variations of effective refractive index of the waveguide with different applied voltages. This considerable EO coefficient |γ13| is even larger than the largest one of LiNbO3 (γ51 = 32.6 pm/V) which offers an opportunity for the fabrication of vacuum ultraviolet electro-optic modulators and optical switches by BaMgF4 single crystal.
© 2017 Optical Society of America
1. Introduction
In the past several decades, all solid-state laser (ASSL) working in vacuum ultraviolet (VUV) region attracted much attention owing to its promising applications in VUV lithography, micromachining, photoelectron spectroscopy and so on [1–3]. The vital part of ASSLs is the nonlinear medium which producing VUV coherent radiation by frequency conversion. Conventional nonlinear optical crystals such as LiNbO3 (LN) [4], BBO [5], and LBO [6] cannot be used because of their rare transparency in VUV region. A series of newly found fluoride crystals may be the promising candidates to overcome the difficulty [7–9]. KBe2BO3F2 (KBBF) crystal was found to be one of them for its short cut-off wavelength at 155 nm [10]. Several frequency conversion experiments of KBBF crystal have been done in VUV region by birefringent phase matching [11–13]. Especially, the 149.8 nm wavelength laser is even obtained by Japanese researchers [14]. Unfortunately, the strong layering tendency of KBBF still limits the size of as-grown KBBF single crystal which leads to a low conversion efficiency [15]. Recently, BaMgF4 (BMF) crystal has been found widely transparent from 130 nm to 13 µm [16]. The ferroelectric [17, 18], second-order [19], and third-order nonlinear properties [20, 21] of BMF crystal have been studied by researchers. To the best of our knowledge, the electro-optic (EO) effects of BMF crystal which may be used in the fabrication of VUV EO modulators and optical switches have not been studied yet.
Nowadays a series of methods for measuring EO coefficients have been proposed, such as one-beam-ellipsometric technique [22, 23], two-beam-interferometric technique [24], Maker-fringe method [25], and attenuated-total-reflection (ATR) technique [26, 27]. At the beginning of this century, the symmetrical metal-cladding waveguide (SMCW) method was presented [28]. The ultrahigh order modes excited in SMCW show a high sensitivity to the change of refractive index of the guiding layer. Subsequently, more precise measurement and larger measurement range can be reached by using this method. In this work, we utilize these advantages to obtain the relation between the applied electric field and resonance excitation condition. As we know, the point group of BMF crystal is mm2 [19]. Thus, the EO coefficient tensor can be written as
The EO coefficients of BMF single crystal can be obtained by choosing the direction of the applied voltage and polarization of the incident light.
The BMF single crystal was grown by temperature gradient technique at the Institute of Ceramics, Shanghai, China [29]. The as-grown BMF single crystal was cut into rectangular-shaped sample along (0 0 1) orientation with a precision of better than 0.5° and then polished to optical level. The size of the sample is 8 × 15 × 1 mm3 and equivalence between crystallographic and optical axes is abc≡ xyz.
2. Theory
The schematic layout of SMCW is illustrated in Fig. 1. The BMF single crystal of 1mm thickness is sandwiched between two silver films which were deposited by thermal evaporation method under vacuum condition. The top thin silver film acts as the coupling layer and the bottom thick one acts as the substrate of the waveguide. Meanwhile, the two silver films are used as the electrodes to supply electric field. Owing to the symmetrical metal cladding structure, the incident light can be easily coupled into SMCW from free-space. This relatively thick waveguide can also accommodate thousands of guided modes. Then, dispersion equation of the ultrahigh order guided mode can be simply approximated as [30]
where the m th vertical propagation constant km can be expressed as n is the refractive index of BMF single crystal, Nm = βm/k0 is the effective refractive index of the guided modes with the propagation constant βm, and k0 = 2π/λ is the wave number with the wavelength in vacuum. The resonance excitation condition is where n0 is the refractive index of vacuum and θm is the incident angle of the m th order.According to differential principle and Eq. (3), the variation of the effective refractive index can be simply obtained as
where Δn is the change of the refractive index. When the light irradiate onto the sample at a sufficient small angle which means Nm is very small, we can see that Nm shows a very high sensitivity to Δn. In our experiments, Δn caused by EO effect can be simply written as where γ is the linear Pockels EO coefficient. Substituting Eq. (6) and Eq. (4) into Eq. (5), yields3. Experiment and result
The schematic diagram of the experiment is shown in Fig. 2. The laser source we used was a DPSS laser delivering 473 nm-wavelength continuum wave. The incident light was TE polarized controlled by a Glan-Taylor Prism. The sample was mounted on a θ/2θ goniometer which controlled by a computer and the reflected light was detected by a photodiode (PD). The electric field was applied onto the sample by a DC high voltage power. A series of resonance data which corresponding to the excited guided modes can be collected by a home-made software.
In our experiment, a series of resonance dips were scanned by the PD. The angle of incidence was set around one chosen ultrahigh order mode (θm = 5.6162°). The refractive index of BMF (n) is calculated to be 1.452 by theoretical calculation with the sellmeier equation reported several years ago [16]. The measured resonance dips as a function of the angle of incidence with different applied voltages is shown in Fig. 3(a). The resonance dip shifts to the right side of angle of incidence with the increase of the applied voltage. Then ΔNm can be determined by the relation of different positions of the resonance dips. The variation of the effective refractive index versus various applied voltages is shown in Fig. 4(a). The experimental data is fitted as a linear function by using the least square method. Substituting the fitting parameter A = 8.230 × 10−7 into Eq. (8), the EO coefficient γ13 = −36.2 pm/V is obtained. Under the same experimental condition, γ13 of LN was also measured. From Fig. 3(b) and Fig. 4(b), the parameter A in the experiment of LN single crystal is determined to be −1.004 × 10−6. By using Eq. (8), γ13 = 9.1 pm/V of LN single crystal is calculated and this result is in good agreement with γ13 = 9.6 pm/V reported previously [31]. Meanwhile, the experiment of LN single crystal can be regarded as an accuracy testing experiment to make sure our experiment setup was working normally. This |γ13| of BMF is even larger than γ51 = 32.6 pm/V of LN [31]. As we know, LN crystal now is widely used for the fabrication of many commercial products, such as EO modulators and switches [32–34]. We believe BMF single crystal could be one of the EO crystal candidates owing to its outstanding EO effect. Also, EO modulation in VUV region may be realized because of the very short absorption edge of BMF single crystal.
Fig. 3 The Resonance dips spectra for different applied voltages on (a) BMF crystal and (b) LN crystal.
Fig. 4 The variation of effect refractive index as a function of the voltage applied on (a) BMF crystal, (b) LN crystal. The blue line was obtained by fitting the experimental data to Eq. (6).
4. Conclusion
In conclusion, a simple method has been carried out to measure the EO coefficient of BMF single crystal. The high sensitivity to the refractive index of the guiding layer of the ultrahigh order modes in SMCW is the key point for the accurate measurement. By changing the applied electric field on the sample, the variation of the resonance dips can be detected conveniently. Finally, the EO coefficient of BMF single crystal (γ13) is achieved by simply linear fitting. Furthermore, due to its sufficiently large EO coefficient, BMF single crystal can be used as one promising material for key technical realization, such as EO modulators, switches, and highly dense memories, especially in VUV region.
Funding
National Natural Science Foundation of China under Grant No. 61235009.
References and links
1. K. Shimamura and E. G. Víllora, “Growth and characteristics of optical single crystals for UV/VUV applications,” J. Fluorine Chem. 132(12), 1040–1046 (2011). [CrossRef]
2. C. Chen, S. Watanabe, Z. Xu, and J. Wang, “Recent advances of deep and vacuum-UV harmonic generation with new borate crystals,” in Conference on Lasers and Electro-Optics, Technical Digest (Optical Society of America, 2003), paper CTuT3.
3. C. Chen, “Recent advances in deep and vacuum-UV harmonic generation with KBBF crystal,” Opt. Mater. 26(4), 425–429 (2004). [CrossRef]
4. G. Boyd, R. C. Miller, K. Nassau, W. Bond, and A. Savage, “LiNbO3: an efficient phase matchable nonlinear optical material,” Appl. Phys. Lett. 5(11), 234–236 (1964). [CrossRef]
5. C. Chen, B. Wu, A. Jiang, and G. You, “A new-type ultraviolet SHG crystal β-BaB2O4,” Sci. Sin. Ser. B 28(3), 235–243 (1985).
6. C. Chen, Y. Wu, A. Jiang, B. Wu, G. You, R. Li, and S. Lin, “New nonlinear-optical crystal: LiB3O5,” J. Opt. Soc. Am. B 6(4), 616–621 (1989). [CrossRef]
7. J. Bergman, G. Crane, and H. Guggenheim, “Linear and nonlinear optical properties of ferroelectric BaMgF4 and BaZnF4,” J. Appl. Phys. 46(11), 4645–4646 (1975). [CrossRef]
8. K. Shimamura, S. L. Baldochi, N. Mujilatu, K. Nakano, Z. Liu, N. Sarukura, and T. Fukuda, “Growth of Ce-doped LiCaAlF6 and LiSrAlF6 single crystals by the czochralski technique under CF4 atmosphere,” J. Cryst. Growth 211(1), 302–307 (2000). [CrossRef]
9. E. G. Víllora, K. Shimamura, K. Muramatsu, S. Takekawa, K. Kitamura, and N. Ichinose, “Refractive index of SrAlF5 and derived grating period for UV/VUV quasi-phase-matching SHG,” J. Cryst. Growth 280(1), 145–150 (2005). [CrossRef]
10. C. Chen, Y. Wang, Y. Xia, B. Wu, D. Tang, K. Wu, Z. Wenrong, L. Yu, and L. Mei, “New development of nonlinear optical crystals for the ultraviolet region with molecular engineering approach,” J. Appl. Phys. 77(6), 268–2272 (1995). [CrossRef]
11. H. Zhang, G. Wang, L. Guo, A. Geng, Y. Bo, D. Cui, Z. Xu, R. Li, Y. Zhu, and X. Wang, “175 to 210 nm widely tunable deep-ultraviolet light generation based on KBBF crystal,” Appl. Phys. B 93(2–3), 323–326 (2008). [CrossRef]
12. T. Kanai, X. Wang, S. Adachi, S. Watanabe, and C. Chen, “Watt-level tunable deep ultraviolet light source by a KBBF prism-coupled device,” Opt. Express 17(10), 8696–8703 (2009). [CrossRef] [PubMed]
13. S.-B. Dai, M. Chen, S.-J. Zhang, Z.-M. Wang, F.-F. Zhang, F. Yang, Z.-C. Wang, N. Zong, L.-J. Liu, and X.-Y. Wang, “2.14 mw deep-ultraviolet laser at 165 nm by eighth-harmonic generation of a 1319 nm Nd:YAG laser in KBBF,” Laser Phys. Lett. 13(3), 035401 (2016). [CrossRef]
14. T. Nakazato, I. Ito, Y. Kobayashi, X. Wang, C. Chen, and S. Watanabe, “Phase-matched frequency conversion below 150 nm in KBe2BO3F2,” Opt. Express 24(15), 17149–17158 (2016). [CrossRef] [PubMed]
15. C. Chen, J. Lu, T. Togashi, T. Suganuma, T. Sekikawa, S. Watanabe, Z. Xu, and J. Wang, “Second-harmonic generation from a KBe2BO3F2 crystal in the deep ultraviolet,” Opt. Letters 27(8), 637–639 (2002). [CrossRef]
16. E. G. VÝllora, K. Shimamura, K. Sumiya, and H. Ishibashi, “Birefringent-and quasi phase-matching with BaMgF4 for vacuum-UV/UV and mid-IR all solid-state lasers,” Opt. Express 17(15), 12362–12378 (2009). [CrossRef]
17. H. Zeng, K. Shimamura, C. Kannan, E. Villora, S. Takekawa, and K. Kitamura, “Ferroelectric domain phenomena and microdomain engineering in BaMgF4 single crystal,” Appl. Phys. A 85(2), 173–176 (2006). [CrossRef]
18. C. Kannan, K. Shimamura, H. Zeng, H. Kimura, E. Villora, and K. Kitamura, “Ferroelectric and anisotropic electrical properties of BaMgF4 single crystal for vacuum UV devices,” J. Appl. Phys. 104(11), 114113 (2008). [CrossRef]
19. J. Chen, X. Chen, Y. Ma, Y. Zheng, A. Wu, H. Li, L. Jiang, and J. Xu, “Measurement of second-order nonlinear optical coefficients of BaMgF4,” J. Opt. Soc. Am. B 29(4), 665–668 (2012). [CrossRef]
20. Y. Ma, J. Chen, Y. Zheng, and X. Chen, “Three-photon absorption and nonlinear refraction of BaMgF4 in the ultraviolet region,” Appl. Opt. 51(22), 5432–5437 (2012). [CrossRef] [PubMed]
21. L. Mateos, M. O. Ramírez, I. Carrasco, P. Molina, J. F. Galisteo-López, E. G. Víllora, C. de las Heras, K. Shimamura, C. Lopez, and L. E. Bausá, “BaMgF4: An ultra-transparent two-dimensional nonlinear photonic crystal with strong χ(3) response in the UV spectral region,” Adv. Funct. Mater. 24(11), 1509–1518 (2014). [CrossRef]
22. J. S. Schildkraut, “Determination of the electrooptic coefficient of a poled polymer film,” Appl. Opt. 29(19), 2839–2841 (1990). [CrossRef] [PubMed]
23. F. Wang, E. Furman, and G. H. Haertling, “Electro-optic measurements of thin-film materials by means of reflection differential ellipsometry,” J. Appl. Phys. 78(1), 9–15 (1995). [CrossRef]
24. P. Prêtre, L.-M. Wu, R. Hill, and A. Knoesen, “Characterization of electro-optic polymer films by use of decal-deposited reflection fabry perot microcavities,” J. Opt. Soc. Am. B 15(1), 379–392 (1998). [CrossRef]
25. B. Kang, B. K. Rhee, and G.-T. Joo, “Variation of electro-optic coefficients in MgO-doped LiNbO3 single crystals,” Mater. Lett. 60(17), 2306–2308 (2006). [CrossRef]
26. R. Helsten, L. Razzari, M. Ferrera, P. Ndione, M. Gaidi, C. Durand, M. Chaker, and R. Morandotti, “Pockels response in Calcium Barium Niobate thin films,” Appl. Phys. Lett. 91(26), 261101 (2007). [CrossRef]
27. Y. Jiang, Z. Cao, Q. Shen, X. Dou, Y. Chen, and Y. Ozaki, “Improved attenuated-total-reflection technique for measuring the electro-optic coefficients of nonlinear optical polymers,” J. Opt. Soc. Am. B 17(5), 805–808 (2000). [CrossRef]
28. H. Li, Z. Cao, H. Lu, and Q. Shen, “Free-space coupling of a light beam into a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett. 83(14), 2757–2759 (2003). [CrossRef]
29. A. Wu, Z. Wang, L. Su, D. Jiang, Y. Zou, J. Xu, J. Chen, Y. Ma, X. Chen, and Z. Hu, “Crystal growth and frequency conversion of BaMgF4 single crystal by temperature gradient technique,” Opt. Mater. 38, 238–241 (2014). [CrossRef]
30. H. Lu, Z. Cao, H. Li, and Q. Shen, “Study of ultrahigh-order modes in a symmetrical metal-cladding optical waveguide,” Appl. Phys. Lett. 85(14), 4579–4581 (2004). [CrossRef]
31. R. W. Boyd, Nonlinear optics (Academic press, 2003).
32. I. Kaminow, J. Carruthers, E. Turner, and L. Stulz, “Thin-film LiNbO3 electro-optic light modulator,” Appl. Phys. Lett. 22(10), 540–542 (1973). [CrossRef]
33. Y. Lu, Z. Wan, Q. Wang, Y. Xi, and N. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77(23), 3719–3721 (2000). [CrossRef]
34. S. Chang, C. Tsai, Y. Lin, J. Liu, and W. Wang, “Improved electrooptic modulator with ridge structure in x-cut LiNbO3,” J. Lightwave Technol. , 17(5), 843–847 (1999). [CrossRef]
