Dispersion of optical constants of Si:PbGeO crystal in the terahertz range

Objectives. Advances in laser physics over the last decade have led to the creation of sources of single-period electromagnetic pulses having a duration of about 1 ps, corresponding to the terahertz (THz) frequency range and a field amplitude of several tens of MV/cm. This allows the electrode-free application of an electric field to a ferroelectric for observing not only the excitation of coherent phonons, but also ultrafast (at the sub-picosecond timescale) dynamic polarization switching. To detect polarization switching, a pump-probe technique is used in which a THz pulse is used with an optical probe. Since its intensity is proportional to the square of the polarization, the signal of the optical second harmonic is used to measure polarization switching under the action of a THz pulse. To evaluate switching efficiency, both linear (refractive index and absorption coefficient) and non-linear optical characteristics (quadratic and cubic susceptibilities) are required. For any application of ferroelectric crystals in the THz range, knowledge of the relevant linear optical characteristics is also necessary.

Methods. The technique of THz spectroscopy in the time domain was used; here, a picosecond THz pulse transmitted through the crystal is recorded by strobing the detector with a femtosecond optical pulse. The THz-induced dynamics of the order parameter in a ferroelectric was studied by detecting the intensity of a nonlinear optical signal at the frequency of the second optical harmonic.

Results. The transmission of a THz wave and the intensity of second harmonic generation on a lead germanate crystal doped with silicon in the time and spectral domains were measured. On this basis, the absorption coefficient dispersion and cubic nonlinear susceptibility were calculated in the range of 0.5-2.0 THz. The presence of a region of fundamental absorption near the phonon modes was confirmed along with a resonant enhancement of the cubic nonlinear susceptibility for two phonon modes Ω₁ = 1.3 THz and Ω₂ = 2.0 THz.

Conclusions. The proposed technique is effective for analyzing the dispersion of the optical characteristics of ferroelectric crystals. The significantly improved spectral resolution (0.1 THz) increases the accuracy of determining nonlinear susceptibility due to the detailed analysis of the linear and nonlinear contributions to the second harmonic intensity.

1. Iwasaki H., Sugii K., Yamada T., Niizeki N. 5PbO·3GeO2 Crystal; a new ferroelectric. Appl. Phys. Lett. 1971;18(10):444-445. http://aip.scitation.org/doi/10.1063/1.1653487

2. Bush A.A., Kamentsev K.E., Mamin R.F. Transformation of dielectric properties and appearance of relaxation behavior in Pb5(Ge1-xSix)3O11 crystals. J. Exp. Theor Phys. 2005;100(1):139-151. http://link.springer.com/10.1134/1.1866206

3. Hosea T.J.C. Raman scattering from soft modes in barium-doped lead germanate. J. Raman Spectrosc. 1990;21(11): 717-724. https://doi.org/10.1002/jrs.1250211104

4. Gorelik V.S., Pyatyshev A.Y. Raman scattering from the effective soft mode in lead germanate crystal. J. Raman Spectrosc. 2020;51(6):969-977. https://doi.org/10.1002/jrs.5854

5. Udina M., Cea T., Benfatto L. Theory of coherent- oscillations generation in terahertz pump-probe spectroscopy: From phonons to electronic collective modes. Phys. Rev. B. 2019;100(16):165131. https://doi.org/10.1103/PhysRevB.97.214304

6. Melnikov A.A., Boldyrev K.N., Selivanov Y.G., Martovitskii V.P., Chekalin S.V., Ryabov E.A. Coherent phonons in a Bi2Se3 film generated by an intense single-cycle THz puls2e. 3Phys. Rev. B. 2018;97(21):214304. https://doi.org/10.1103/PhysRevB.97.214304

7. Kozina M., Fechner M., Marsik P., van Driel T., Glownia J.M., Bernhard C., Radovic M., Zhu D., Bonetti S., Staub U., Hoffmann M.C. Terahertz-driven phonon upconversion in SrTiO3. Nat. Phys. 2019;15(4):387-392. https://doi.org/10.1038/3s41567-018-0408-1

8. Salen P., Basini M., Bonetti S., Hebling J., Krasilnikov M., Nikitin A.Y., Shamuilov G., Tibaid Z., Zhaunerchyk V., Goryashko V. Matter manipulation with extreme terahertz light: Progress in the enabling THz technology. Phys. Rep. 2019;836-837:1-74. https://doi.org/10.1016/j.physrep.2019.09.002

9. Bawuah P., Zeitler J.A. Advances in terahertz time-domain spectroscopy of pharmaceutical solids: A review. TrAC Trends Anal. Chem. 2021;139(40):116272. https://doi.org/10.1016/j.trac.2021.116272

10. Ryu H.-C., Kwak M.-H., Kang S.-B., Jeong S.-Y., Paek M.-C., Kang K.-Y., Lee S.-J., Moon S.E., Park S.-O. A dielectric property analysis of ferroelectric thin film using terahertz time-domain spectroscopy. Integr. Ferroelectr. 2007;95(1):83-91. https://doi.org/10.1080/10584580701756573

11. Bilyk V.R., Grishunin K.A. Complex refractive index of strontium titanate in the terahertz frequency range. Russ. Technol. J. 2019;7(4):71-80 (in Russ.). https://doi.org/10.32362/2500-316X-2019-7-4-71-80

12. Bilyk V., Mishina E., Sherstyuk N., BushA., OvchinnikovA. , Agranat M. Transient polarization reversal using an intense THz pulse in silicon-doped lead germanate. Phys. Status Solidi (RRL)-RapidRes. Lett. 2021;15(1):2000460. https://doi.org/10.1002/pssr.202000460, https://onlinelibrary.wiley.com/doi/10.1002/pssr.202000460

13. Lockwood D.J., Hosea T.J., Taylor W. The complete Raman spectrum of paraelectric and ferroelectric lead germanate. J. Phys. C: Solid State Phys. 1980;13(8): 1539. https://doi.org/10.1088/0022-3719/13/8/023

14. Vicario C., Jazbinsek M., OvchinnikovA.V., Chefonov O.V., Ashitkov S.I., Agranat M.B., Hauri C.P. High efficiency THz generation in DSTMS, DAST and OH1 pumped by Cr:forsterite laser. Opt. Express. 2015;23(4):4573-4580. https://doi.org/10.1364/OE.23.004573

15. Ovchinnikov A.V., Chefonov O.V., Agranat M.B., Fortov V.E., Jazbinsek M., Hauri C.P. Generation of strong-field spectrally tunable terahertz pulses. Opt. Express. 2020;28(23):33921-33936. https://doi.org/10.1364/OE.405545, https://opg.optica.org/abstract.cfm?URI=oe-28-23-33921

16. Bloembergen N. Nonlinear Optics. Harvard University. New-York, Amsterdam: Benjamin W.A.; 1965. 220 p.