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An Alternate Method for the Determination of the Raman Cross Sections of Optical Phonons in Uniaxial Crystals: Application to LiNbO3

Received: 10 August 2015     Accepted: 13 September 2015     Published: 7 December 2015
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Abstract

The present paper is devoted to the derivation of an alternate and simple method based on the rotation of the crystal in view of the determination of the Raman cross-sections of optical phonon in uniaxial and biaxial crystals. The Raman polarisability tensor whose trace remains invariant under an orthogonal transformation is established as function of the crystal rotation position. The resulting angle dependent Raman scattered intensity is finally used to accurately describe the area under the peak which is measured from the polarised Raman spectra of the lithium niobate single crystal recorded under the backscattering scheme; The extracted parameters from the fit such as integrated areas are then plotted as functions of the crystal rotation angles. This allows to quantitatively determinate the relative phase and the relative values of the Raman tensor elements.

Published in International Journal of Materials Science and Applications (Volume 4, Issue 6)
DOI 10.11648/j.ijmsa.20150406.11
Page(s) 371-378
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Raman Polarisability, Raman Cross-Section, Rotating Crystal, Lithium Niobate

References
[1] T. Strach, J. Brunen, B. Lederle, J. Zegenhagen, and M. Cardona, “Determination of the phase difference between the Raman tensor elements of the A1g, – like phonons in SmBa2Cu3O7-δ”, Phy. Rev. B, vol.57, 1292 (1998).
[2] R. Loudon “The Raman effect in crystals”, ADV. Phys. 13 [52], 423-482 (1964).
[3] N. Biswas and S. Umpathy “Simple Approach to Determine Absolute Raman Cross Section Using an Optical Parametric Oscillator”, Applied Spectroscopy, Vol 52, Issue 4 pp 496 – 499 (1998).
[4] K. T. Schomacker, J. K. Delaney, and P. M Champion, “Measurements of the absolute Raman cross sections of benzene”, J. Chem. Phys. 85 (8), 4240 (1986).
[5] I. P. Kaminow and E. H. Turner, “Temperature Dependence of Raman Scattering and the Electro-optic Properties of CuCl”, Phys. Rev. Bl5, 1564 (1972).
[6] V. S. Gorelik, O. G. Zolotukhin and M. M. Sushchinskiy, “Effective Raman Scattering Cross-Section and Its Coupling With Nonlinear Coefficients in Single Crystals of Gap”, ZhPS 28 [3], 495-498 (1978).
[7] I. Loa, S. Gronemeyer, C. Thomsen, O. Ambacher, D. Shikora and D. J. As, “Comparative Determination of Absolute Raman Scattering Efficiencies and Application to GaN”, Journal of Raman spectroscopyVol.29, 291-295 (1998).
[8] I. P. Kaminow and W. D Johnston, Jr., “Quantitative Determination of Sources of the Electro-Optic Effect in LiNbO3 and LiTaO3”, Phys. Rev. 160, 519 (1967) and 178, 1528 (Errata) (1969).
[9] P. Knoll and H. Kuzmany, “Nonlinear Optical Properties and Signs of the Raman Tensor for LiGaO2” Phys. Rev. B29, N°4, 2221 (1984).
[10] A. F. Penna, A. Chaves, P. da R. Andrade, and S. P. S. Porto, “Light scattering by lithium tantalate at room temperature”, Phys. Rev. B13, 4907 (1976).
[11] W. D Johnston, Jr., “Nonlinear Optical coefficients and the Raman scattering Efficiencies from LO and TO Phonons in Acentric crystals” Phys. Rev. B1, 3494 (1970).
[12] U. Fano, Phys. Rev. 124, 1866 (1961).
[13] M. Nippus, “relative Raman-intensitâten der Phononen von LiNbO3’ Z. Naturfoch, 31a, 231 (1976).
[14] R. Loudon, Advan. Phys. 13, 423 (1964).
[15] N. Djiedeu, B. Mohamadou, P. Bourson and M. Aillerie, J.Phys. Condens. Matter, 21 (2009) 015905.
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  • APA Style

    B. Mohamadou, E. Bouhari, R. Erasmus. (2015). An Alternate Method for the Determination of the Raman Cross Sections of Optical Phonons in Uniaxial Crystals: Application to LiNbO3. International Journal of Materials Science and Applications, 4(6), 371-378. https://doi.org/10.11648/j.ijmsa.20150406.11

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    ACS Style

    B. Mohamadou; E. Bouhari; R. Erasmus. An Alternate Method for the Determination of the Raman Cross Sections of Optical Phonons in Uniaxial Crystals: Application to LiNbO3. Int. J. Mater. Sci. Appl. 2015, 4(6), 371-378. doi: 10.11648/j.ijmsa.20150406.11

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    AMA Style

    B. Mohamadou, E. Bouhari, R. Erasmus. An Alternate Method for the Determination of the Raman Cross Sections of Optical Phonons in Uniaxial Crystals: Application to LiNbO3. Int J Mater Sci Appl. 2015;4(6):371-378. doi: 10.11648/j.ijmsa.20150406.11

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  • @article{10.11648/j.ijmsa.20150406.11,
      author = {B. Mohamadou and E. Bouhari and R. Erasmus},
      title = {An Alternate Method for the Determination of the Raman Cross Sections of Optical Phonons in Uniaxial Crystals: Application to LiNbO3},
      journal = {International Journal of Materials Science and Applications},
      volume = {4},
      number = {6},
      pages = {371-378},
      doi = {10.11648/j.ijmsa.20150406.11},
      url = {https://doi.org/10.11648/j.ijmsa.20150406.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmsa.20150406.11},
      abstract = {The present paper is devoted to the derivation of an alternate and simple method based on the rotation of the crystal in view of the determination of the Raman cross-sections of optical phonon in uniaxial and biaxial crystals. The Raman polarisability tensor whose trace remains invariant under an orthogonal transformation is established as function of the crystal rotation position. The resulting angle dependent Raman scattered intensity is finally used to accurately describe the area under the peak which is measured from the polarised Raman spectra of the lithium niobate single crystal recorded under the backscattering scheme; The extracted parameters from the fit such as integrated areas are then plotted as functions of the crystal rotation angles. This allows to quantitatively determinate the relative phase and the relative values of the Raman tensor elements.},
     year = {2015}
    }
    

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    AB  - The present paper is devoted to the derivation of an alternate and simple method based on the rotation of the crystal in view of the determination of the Raman cross-sections of optical phonon in uniaxial and biaxial crystals. The Raman polarisability tensor whose trace remains invariant under an orthogonal transformation is established as function of the crystal rotation position. The resulting angle dependent Raman scattered intensity is finally used to accurately describe the area under the peak which is measured from the polarised Raman spectra of the lithium niobate single crystal recorded under the backscattering scheme; The extracted parameters from the fit such as integrated areas are then plotted as functions of the crystal rotation angles. This allows to quantitatively determinate the relative phase and the relative values of the Raman tensor elements.
    VL  - 4
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Author Information
  • Center for Atomic Molecular Physics and Quantum Optics, University of Douala, Douala, Cameroon

  • Department of Physics, Higher Teacher’s Training College, The University of Maroua, Maroua, Cameroon

  • School of Physics, University of the Witwatersrand, Johannesburg, South Africa

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