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Achieving the full-wavelength phase-matching for efficient nonlinear optical frequency conversion in C(NH2)3BF4

Abstract

Phase-matching of light waves is a critical condition for maximizing the efficiency of nonlinear frequency conversion processes in nonlinear optical crystals; however, phase-matching, commonly achieved by tuning birefringence, is often difficult to achieve over a wide wavelength range. Here, full-wavelength phase-matching crystals that can avoid phase-mismatching across the entire optical transparency range are proposed. The anisotropic strength of bonding in the dimension of energy is confirmed theoretically to be the key to the full-wavelength phase-matching ability. We demonstrate that a crystal of guanidinium tetrafluoroborate (C(NH2)3BF4) can be phase-matched throughout its entire optical transparency range and is able to generate harmonic light as short as ~193.2 nm, which is close to its deep-ultraviolet cut-off edge. Importantly, this crystal is stable, cheap and efficient compared with commercially available nonlinear optical crystals for generation of 266 nm light. This work lays the foundation for finding a new class of crystals in which the phase-matching wavelength fully covers its optical transparency range, and also provides a high-performance crystal for generating light at 266 nm—the fourth-harmonic of a commercial 1,064 nm laser.

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Fig. 1: Crystal structure, microstructural analysis and as-grown single crystal.
Fig. 2: Linear and nonlinear optical properties of GFB crystal.
Fig. 3: Comparison of ultraviolet cut-off edge, shortest phase-matching wavelength and phase-matching wavelength loss.
Fig. 4: Tunable harmonic light generation of GFB crystal.
Fig. 5: Second-order NLO coefficients and structure–property relationship analysis.

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Data availability

The data that support the findings of this study are available from the corresponding author on reasonable requests.

References

  1. Bloembergen, N. Nonlinear Optics (World Scientific, 1996).

  2. Boyd, R. W. Nonlinear Optics (Academic, 2008).

  3. Nielsen, M. P., Shi, X. Y., Dichtl, P., Maier, S. A. & Oulton, R. F. Giant nonlinear response at a plasmonic nanofocus drives efficient four-wave mixing. Science 358, 1179–1181 (2017).

    ADS  MathSciNet  MATH  Google Scholar 

  4. Klimmer, S. et al. All-optical polarization and amplitude modulation of second-harmonic generation in atomically thin semiconductors. Nat. Photon. 15, 837–842 (2021).

    ADS  Google Scholar 

  5. Beetar, J. E. et al. Sci. Adv. 6, eabb5375 (2020).

    ADS  Google Scholar 

  6. Armstrong, J. A., Bloembergen, N., Ducuing, J. & Pershan, P. S. Light waves at the boundary of nonlinear media. Phys. Rev. 127, 1918–1939 (1962).

    ADS  MathSciNet  Google Scholar 

  7. Suchowski, H. et al. Phase mismatch-free nonlinear propagation in optical zero-index materials. Science 342, 1223–1226 (2013).

    ADS  Google Scholar 

  8. Zhu, S. N., Zhu, Y. Y. & Ming, N. B. Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice. Science 278, 843–846 (1997).

    ADS  Google Scholar 

  9. Fiore, A., Berger, V., Rosencher, E., Bravetti, P. & Nagle, J. Phase matching using an isotropic nonlinear optical material. Nature 391, 463–466 (1998).

    ADS  Google Scholar 

  10. Lan, S. F. et al. Backward phase-matching for nonlinear optical generation in negative-index materials. Nat. Mater. 14, 807–811 (2015).

    ADS  Google Scholar 

  11. Shao, M. C., Liang, F., Yu, H. H. & Zhang, H. J. Pushing periodic-disorder-induced phase matching into the deep-ultraviolet spectral region: theory and demonstration. Light: Sci. Appl. 9, 45 (2020).

    ADS  Google Scholar 

  12. Bahabad, A., Cohen, O., Murnane, M. & Kapteyn, H. Quasi-periodic and random quasi-phase matching of high harmonic generation. Opt. Lett. 33, 1936–1938 (2008).

    ADS  Google Scholar 

  13. Zhang, W. G., Yu, H. W., Wu, H. P. & Halasyamani, P. S. Phase-matching in nonlinear optical compounds: a materials perspective. Chem. Mater. 29, 2655–2668 (2017).

    Google Scholar 

  14. Nikogosyan, D. N. Nonlinear Optical Crystals: A Complete Survey (Springer Science, 2009).

  15. Trabs, P., Noack, F., Aleksandrovsky, A. S., Zaitsev, A. I. & Petrov, V. Generation of coherent radiation in the vacuum ultraviolet using randomly quasi-phase-matched strontium tetraborate. Opt. Lett. 41, 618–621 (2016).

    ADS  Google Scholar 

  16. Wei, D. Z. et al. Efficient nonlinear beam shaping in three-dimensional lithium niobate nonlinear photonic crystals. Nat. Commun. 10, 4193 (2019).

    ADS  Google Scholar 

  17. Mutailipu, M. & Pan, S. L. Emergent deep-ultraviolet nonlinear optical candidates. Angew. Chem. Int. Ed. 59, 20302–20317 (2020).

    Google Scholar 

  18. Jin, C. C. et al. Guanidinium fluorooxoborates as efficient metal-free short-wavelength nonlinear optical crystals. Chem. Mater. 34, 440–450 (2022).

    Google Scholar 

  19. Chen, C. T. et al. Nonlinear Optical Borate Crystals: Principles and Applications (Wiley-VCH, 2012).

  20. Mutailipu, M., Poeppelmeier, K. R. & Pan, S. L. Borates: a rich source for optical materials. Chem. Rev. 121, 1130–1202 (2021).

    Google Scholar 

  21. Ok, K. M. Toward the rational design of novel noncentrosymmetric materials: factors influencing the framework structures. Acc. Chem. Res. 49, 2774–2785 (2016).

    Google Scholar 

  22. Luo, M., Ye, N., Zou, G. H., Lin, C. S. & Cheng, W. D. Na8Lu2(CO3)6F2 and Na3Lu(CO3)2F2: rare earth fluoride carbonates as deep-UV nonlinear optical materials. Chem. Mater. 25, 3147–3153 (2013).

    Google Scholar 

  23. Kang, L., Liang, F., Jiang, X. X., Lin, Z. S. & Chen, C. T. First-principles design and simulations promote the development of nonlinear optical crystals. Acc. Chem. Res. 53, 209–217 (2020).

    Google Scholar 

  24. Mutailipu, M. et al. L Strong nonlinearity induced by coaxial alignment of polar chain and dense [BO3] units in CaZn2(BO3)2. Angew. Chem. Int. Ed. 61, e202202096 (2022).

    Google Scholar 

  25. Kong, F., Huang, S. P., Sun, Z. M., Mao, J. G. & Cheng, W. D. Se2(B2O7): a new type of second-order NLO material. J. Am. Chem. Soc. 128, 7750–7751 (2006).

    Google Scholar 

  26. Aka, G. et al. Linear- and nonlinear-optical properties of a new gadolinium calcium oxoborate crystal, Ca4GdO(BO3)3. J. Opt. Soc. Am. B 14, 2238–2247 (1997).

    ADS  Google Scholar 

  27. Oganov, A. R., Pickard, C. J., Zhu, Q. & Needs, R. J. Structure prediction drives materials discovery. Nat. Rev. Mater. 4, 331–348 (2019).

    ADS  Google Scholar 

  28. Knyrim, J. S., Becker, P., Johrendt, D. & Huppertz, H. A new non-centrosymmetric modification of BiB3O6. Angew. Chem. Int. Ed. 45, 8239–8241 (2006).

    Google Scholar 

  29. Krumbe, W. & Haussühl, S. Crystal culture and determination of structure for guanidinium-hydrogen-selenite, guanidinium-hydrogen-phosphite, guanidinium-tetrafluoroborate, guanidinium-glutarate and guanidinium-acetate. Z. Kristallogr. 178, 132–134 (1987).

    Google Scholar 

  30. Haussühl, S. Pyroelectric, dielectric, piezoelectric, and elastic properties of trigonal guanidinium tetrafluoroborate, C(NH2)3BF4. Z. Kristallogr. 187, 153–158 (1989).

    Google Scholar 

  31. Nandhini, S., Sudhakar, K., Muniyappan, S. & Murugakoothan, P. Systematic discussions on structural, optical, mechanical, electrical and its application to NLO devices of a novel semi-organic single crystal: guanidinium tetrafluoroborate (GFB). Opt. Laser Technol. 105, 249–256 (2018).

    ADS  Google Scholar 

  32. Mulliken, R. S. Electronic population analysis on LCAO–MO molecular wave functions. J. Chem. Phys. 23, 1833–1840 (1955).

    ADS  Google Scholar 

  33. Nandhini, S., Muniyappan, S., Ramar, S. V., Balasubramanian, K. & Murugakoothan, P. Quantum chemical analysis on supramolecular assemblies of guanidinium tetrafluoroborate (GFB) crystal structure: emission and NLO behavior. J. Mol. Struct. 1198, 126859 (2019).

    Google Scholar 

  34. Halbout, J. M. & Tang, C. L. Nonlinear Optical Properties of Organic Molecules and Crystals (Academic, 1998)

  35. Chen, C. T., Wu, B. C., Jiang, A. D. & You, G. M. A new ultraviolet SHG crystal β-BaB2O4. Sci. Sin., Ser. B 28, 235–243 (1985).

    Google Scholar 

  36. Xu, Z. Y. et al. Advances in deep ultraviolet laser based high-resolution photoemission spectroscopy. Front. Inform. Technol. Electron. Eng. 20, 885–913 (2019).

    Google Scholar 

  37. Eimerl, D. Electro-optic, linear, and nonlinear optical properties of KDP and its isomorphs. Ferroelectrics 72, 95–139 (1987).

    ADS  Google Scholar 

  38. Mori, Y., Kuroda, I., Nakajima, S., Sasaki, T. & Nakai, S. New nonlinear optical crystal: cesium lithium borate. Appl. Phys. Lett. 67, 1818–1820 (1995).

    ADS  Google Scholar 

  39. Shoji, I. et al. Absolute measurement of second-harmonic nonlinear optical coefficients of CsLiB6O10 for visible-to-ultraviolet second-harmonic wavelengths. J. Opt. Soc. Am. B 18, 302–307 (2001).

    ADS  Google Scholar 

  40. Sasaki, T., Mori, Y., Yoshimura, M., Yap, Y. K. & Kamimura, T. Recent development of nonlinear optical borate crystals: key materials for generation of visible and UV light. Mater. Sci. Eng. R 30, 1–54 (2000).

    Google Scholar 

  41. Xu, K., Loiseau, P. & Aka, G. BaCaBO3F: a nonlinear optical crystal investigated for UV light generation. J. Cryst. Growth 311, 2508–2512 (2009).

    ADS  Google Scholar 

  42. Yang, L., Yue, Y. C., Yang, F., Hu, Z. G. & Xu, X. Y. 266 nm ultraviolet light generation in Ga-doped BaAlBO3F2 Crystals. Opt. Lett. 41, 1598–1600 (2016).

    ADS  Google Scholar 

  43. Xu, K. et al. Nonlinear optical properties of Ca5(BO3)3F crystal. Opt. Express 16, 17735–17744 (2016).

    ADS  Google Scholar 

  44. Fang, Z. et al. High-efficiency UV generation at 266 nm in a new nonlinear optical crystal NaSr3Be3B3O9F4. Opt. Express 25, 26500–26507 (2017).

    ADS  Google Scholar 

  45. Dhanaraj, G., Byrappa, K., Prasad V. & Dudley, M. Springer Handbook of Crystal Growth (Springer, 2010).

  46. Aversa, C. & Sipe, J. E. Nonlinear optical susceptibilities of semiconductors: results with a length-gauge analysis. Phys. Rev. B 52, 14636–14645 (1995).

    ADS  Google Scholar 

  47. Lin, J., Lee, M. H., Liu, Z. P., Chen, C. T. & Pickard, C. J. Mechanism for linear and nonlinear optical effects in β-BaB2O4 crystals. Phys. Rev. B 60, 13380–13389 (1999).

    ADS  Google Scholar 

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Acknowledgements

This work was financially supported by the National Key R&D Program of China (2021YFA0717800), National Natural Science Foundation of China (52002397, U2003131), West Light Foundation of CAS (XBZG-ZDSYS-202201, 2020-XBQNXZ-002), Young Elite Scientist Sponsorship Program by CAST (YESS20200068), Natural Science Foundation of Xinjiang (2022D01E087), Key Research and Development Program of Xinjiang (2022B01023-3), Key Research Program of Frontier Sciences, CAS (ZDBS-LY-SLH035), High-level Talent Project of Xinjiang Uygur Autonomous Region (2020000039), Xinjiang Tianshan Telent Program (2022TSYCCX0071), and CAS Project for Young Scientists in Basic Research (YSBR-024). We thank Z. Xu, S. Zhang and F. Zhang at Technical Institute of Physics and Chemistry, Chinese Academy of Sciences for their help with the tunable 193.2–200 nm light generation measurements; G. Zhang and B. Li at Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences for their help with 266 nm light generation and NLO coefficients test.

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M. Mutailipu proposed the idea and performed the data analysis and paper writing. J. Han grew the single crystals. Z. Li developed the theoretical calculations. F. Li and Z. Yang performed data analysis of theoretical results. J. Li and F. Zhang assisted with the optical performance characterization. X. Long supervised the crystal growth and the laser output experiments. S. Pan conceived the idea and supervised the project. All of the authors discussed the results and commented on the manuscript.

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Correspondence to Shilie Pan.

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Nature Photonics thanks Gerard Aka and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Experimental, Figs. 1–21 and Tables 1–6.

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Mutailipu, M., Han, J., Li, Z. et al. Achieving the full-wavelength phase-matching for efficient nonlinear optical frequency conversion in C(NH2)3BF4. Nat. Photon. 17, 694–701 (2023). https://doi.org/10.1038/s41566-023-01228-7

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