Optical properties of borate family nonlinear crystals and their application in sources of intense terahertz radiation

Nonlinear crystals of the borate family are efficient harmonic generators for intense laser sources because of their high laser-induced damage threshold at near-infrared wavelengths. Recent studies have shown that they exhibit relatively low absorption coefficients at sub-terahertz frequencies, which could enable them to generate terahertz radiation. Based on this assumption, we compare terahertz sources based on the frequency down-conversion of the radiation from a titanium-sapphire amplifier in crystals of barium beta-borate (β-BaB2O4), lithium triborate (LiB3O5), and lithium tetraborate (Li2B4O7). The calculation of collinear three-wave interactions, which provide the generation of the subterahertz difference frequency, is carried out considering the previously studied dispersion of the main components of the terahertz refractive index of these crystals. The phase-matching conditions and the corresponding coherence lengths are determined for each of the crystals. Taking into account the quadratic susceptibility tensors, the coefficients of the effective nonlinearity are calculated, and the terahertz generation efficiency in crystals with different cuts is evaluated and compared. The down-conversion in the β-BaB2O4 crystal is numerically shown to be three and five orders of magnitude more efficient than in the LiB3O5 and Li2B4O7 crystals, respectively. Thus, terahertz generation in a sample of β-BaB2O4 crystal with a cut that provides phase-matching for a frequency of 0.3 THz (θ = 5°) has been studied experimentally using radiation from a titanium-sapphire amplifier. The comparison of the experimental data and the numerical results leads to the conclusion that the main contribution to the generation process is given by the o – e → e, e – e → o, and o – o → o types of interaction. The peak terahertz power reaches 20 kW. The data obtained in this work will be useful for the development of intense sub-terahertz radiation sources based on the energy conversion of high-power laser sources. It is estimated that tens of GW of peak terahertz power can be achieved by increasing the intensity of the optical fields to pre-threshold values for the β-BaB2O4 crystal. A source of this intensity can be used in systems for sounding the atmosphere as well as in charged particle accelerators.

1. Wu X., Carbajo S., Ravi K., Ahr F., Cirmi G., Zhou Y., Mücke O.D., Kärtner F.X. Terahertz generation in lithium niobate driven by Ti:sapphire laser pulses and its limitations. Optics Letters, 2014, vol. 39, no. 18, pp. 5403–5406. https://doi.org/10.1364/ol.39.005403

2. Antsygin V.D., Mamrashev A.A., Nikolaev N.A., Potaturkin O.I., Bekker T.B., Solntsev V.P. Optical properties of borate crystals in terahertz region. Optics Communications, 2013, vol. 309, pp. 333– 337. https://doi.org/10.1016/j.optcom.2013.08.014

3. Bernerd C., Segonds P., Debray J., Roux J.-F., Hérault E., Coutaz J.-L., Shoji I., Minamide H., Ito H., Lupinski D., Zawilski K., Schunemann P., Zhang X., Wang J., Hu Z., Boulanger B. Evaluation of eight nonlinear crystals for phase-matched Terahertz second-order difference-frequency generation at room temperature. Optical Materials Express, 2020, vol. 10, no. 2, pp. 561–576. https://doi.org/10.1364/ome.383548

4. Chen C., Sasaki T., Li R., Wu Y., Lin Z., Mori Y., Hu Z., Wang J., Aka G., Masashi Y., Kaneda Y. Nonlinear Optical Borate Crystals: Principles and Applications. Germany, Wiley-VCH Verlag GmbH & Co. KGaA, 2012, 406 p.

5. Nakatani H., Bosenberg W.R., Cheng L.K., Tang C.L. Laser-induced damage in beta-barium metaborate. Applied Physics Letters, 1988, vol. 53, no. 26, pp. 2587–2589. https://doi.org/10.1063/1.100535

6. Eimerl D., Davis L., Velsko S., Graham E.K., Zalkin A. Optical, mechanical, and thermal properties of barium borate. Journal of Applied Physics, 1987, vol. 62, no. 5, pp. 1968–1983. https://doi.org/10.1063/1.339536

7. Ezhov D.M., Lubenko D.M., Andreev Y.M. Doubling of THz radiation frequency in nonlinear borate crystals. Russian Physics Journal, 2021, vol. 64, no. 7, pp. 1358–1362. https://doi.org/10.1007/s11182-021-02461-9

8. Komatsu R., Sugawara T., Sassa K., Sarukura N., Liu Z., Izumida S., Segawa Y., Uda S., Fukuda T., Yamanouchi K. Growth and ultraviolet application of Li2B4O7 crystals: Generation of the fourth and fifth harmonics of Nd:Y3Al5O12 lasers. Applied Physics Letters, 1997, vol. 70, no. 26, pp. 3492–3494. https://doi.org/10.1063/1.119210

9. Umemura N., Watanabe J., Matsuda D., Kamimura T. Refined Sellmeier and thermo-optic dispersion formulas for Li2B4O7. Japanese Journal of Applied Physics, 2017, vol. 56, no. 3, pp. 032602. https://doi.org/10.7567/jjap.56.032602

10. Ezhov D., Turgeneva S., Nikolaev N., Mamrashev A., Mikerin S., Minakov F., Simanchuk A., Antsygin V., Svetlichnyi V., Losev V., Andreev Y. Potential of sub-THz-wave generation in Li2B4O7 nonlinear crystal at room and cryogenic temperatures. Crystals, 2021, vol. 11, no. 11, pp. 1321. https://doi.org/10.3390/cryst11111321

11. Waasem N., Fieberg S., Hauser J., Gomes G., Haertle D., Kühnemann F., Buse K. Photoacoustic absorption spectrometer for highly transparent dielectrics with parts-per-million sensitivity. Review of Scientific Instruments, 2013, vol. 84, no. 2, pp. 023109. https://doi.org/10.1063/1.4792724

12. Röcker C., Weinert P., Villeval P., Lupinski D., Delaigue M., Hönninger C., Weber R., Graf T., Ahmed M.A. Nonlinear absorption in lithium triborate frequency converters for high-power ultrafast lasers. Optics Express, 2022, vol. 30, no. 4, pp. 5423–5438. https://doi.org/10.1364/oe.447255

13. Kato K. Temperature-tuned 90° phase matching properties of LiB3O5. IEEE Journal of Quantum Electronics, 1994, vol. 30, no. 12, pp. 2950–2952. https://doi.org/10.1109/3.362711

14. Andreev Y.M., Kokh A.E., Kokh K.A., Lanskii G.V., Litvinenko K., Mamrashev A.A., Molloy J.F., Murdin B., Naftaly M., Nikolaev N.A., Svetlichnyi V.A. Observation of a different birefringence order at optical and THz frequencies in LBO crystal. Optical Materials, 2017, vol. 66, pp. 94–97. https://doi.org/10.1016/j.optmat.2017.01.031

15. Yoshida H., Fujita H., Nakatsuka M., Yoshimura M., Sasaki T., Kamimura T., Yoshida K. Dependences of laser-induced bulk damage threshold and crack patterns in several nonlinear crystals on irradiation direction. Japanese Journal of Applied Physics, 2006, vol. 45, no. 2A, pp. 766–769. https://doi.org/10.1143/jjap.45.766

16. Zhang Y., Zheng Y., Xu S., Liu W. Empirical study of nonlinearity tensor dominating THz generation in barium borate crystal through optical rectification. Applied Physics B, 2011, vol. 103, no. 4, pp. 831–835. https://doi.org/10.1007/s00340-011-4415-5

17. Andreev Y.M., Naftaly M., Molloy J.F., Kokh A.E., Lanskii G.V., Svetlichnyi V.A., Losev V.F., Kononova N.G., Kokh K.A. LBO: optical properties and potential for THz application. Laser Physics Letters, 2015, vol. 12, no. 11, pp. 115402. https://doi.org/10.1088/1612-2011/12/11/115402

18. Wang C.-R., Pan Q.-K., Chen F., Lanskii G., Nikolaev N., Mamrashev A., Andreev Y., Meshalkin A. Phase-matching in KTP crystal for THz wave generation at room temperature and 81 K. Infrared Physics & Technology, 2019, vol. 97, pp. 1–5. https://doi.org/10.1016/j.infrared.2018.12.012

19. Midwinter J.E., Warner J. The effects of phase matching method and of uniaxial crystal symmetry on the polar distribution of second-order non-linear optical polarization. British Journal of Applied Physics, 1965, vol. 16, no. 8, pp. 1135–1142. https://doi.org/10.1088/0508-3443/16/8/312

20. Shoji I., Nakamura H., Ohdaira K., Kondo T., Ito R., Okamoto T., Tatsuki K., Kubota S. Absolute measurement of second-order nonlinear-optical coefficients of β-BaB2O4 for visible to ultraviolet second-harmonic wavelengths. Journal of the Optical Society of America B, 1999, vol. 16, no. 4, pp. 620–624. https://doi.org/10.1364/josab.16.000620

21. Roberts D.A. Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions. IEEE Journal of Quantum Electronics, 1992, vol. 28, no. 10, pp. 2057–2074. https://doi.org/10.1109/3.159516

22. Petrov V., Rotermund F., Noack F., Komatsu R., Sugawara T., Uda S. Vacuum ultraviolet application of Li2B4O7 crystals: Generation of 100 fs pulses down to 170 nm. Journal of Applied Physics, 1998, vol. 84, no. 11, pp. 5887–5892. https://doi.org/10.1063/1.368904

23. Sutherland R.L. Handbook of Nonlinear Optics. CRC Press, 2003, 976 p. https://doi.org/10.1201/9780203912539

24. Alekseev S.V., Ivanov N.G., Losev V.F., Mesyats G.A., Mikheev L.D., Ratakhin N.A., Panchenko Y.N. THL-100 multi-terawatt laser system of visible spectrum range. Optics Communications, 2020, vol. 455, pp. 124386. https://doi.org/10.1016/j.optcom.2019.124386