International Electronic Journal of Mathematics Education

Calculation of the Laser Beam Path through the Anisotropic Crystalline Lens
  • Article Type: Research Article
  • International Electronic Journal of Mathematics Education, 2016 - Volume 11 Issue 7, pp. 2025-2046
  • Published Online: 01 Sep 2016
  • Article Views: 678 | Article Download: 698
  • Open Access Full Text (PDF)
AMA 10th edition
In-text citation: (1), (2), (3), etc.
Reference: Umbetov AU, Zhumabaeva SB, Zhakenova A, et al. Calculation of the Laser Beam Path through the Anisotropic Crystalline Lens. Int Elect J Math Ed. 2016;11(7), 2025-2046.
APA 6th edition
In-text citation: (Umbetov et al., 2016)
Reference: Umbetov, A. U., Zhumabaeva, S. B., Zhakenova, A., Sadykova, B. S., Tulegenova, A. K., Aubakirova, A. A., & Dzhaketova, S. Z. (2016). Calculation of the Laser Beam Path through the Anisotropic Crystalline Lens. International Electronic Journal of Mathematics Education, 11(7), 2025-2046.
Chicago
In-text citation: (Umbetov et al., 2016)
Reference: Umbetov, Abilhan U., Sania B. Zhumabaeva, Anuza Zhakenova, Bazargul S. Sadykova, Anar K. Tulegenova, Assel A. Aubakirova, and Saule Zh. Dzhaketova. "Calculation of the Laser Beam Path through the Anisotropic Crystalline Lens". International Electronic Journal of Mathematics Education 2016 11 no. 7 (2016): 2025-2046.
Harvard
In-text citation: (Umbetov et al., 2016)
Reference: Umbetov, A. U., Zhumabaeva, S. B., Zhakenova, A., Sadykova, B. S., Tulegenova, A. K., Aubakirova, A. A., and Dzhaketova, S. Z. (2016). Calculation of the Laser Beam Path through the Anisotropic Crystalline Lens. International Electronic Journal of Mathematics Education, 11(7), pp. 2025-2046.
MLA
In-text citation: (Umbetov et al., 2016)
Reference: Umbetov, Abilhan U. et al. "Calculation of the Laser Beam Path through the Anisotropic Crystalline Lens". International Electronic Journal of Mathematics Education, vol. 11, no. 7, 2016, pp. 2025-2046.
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Umbetov AU, Zhumabaeva SB, Zhakenova A, Sadykova BS, Tulegenova AK, Aubakirova AA, et al. Calculation of the Laser Beam Path through the Anisotropic Crystalline Lens. Int Elect J Math Ed. 2016;11(7):2025-46.

Abstract

Pursuant to the well-known theory of electromagnetic waves propagation in isotropic and anisotropic crystals, rigorous calculation of beam propagation in a system consisting of several anisotropic crystals, results in cumbersome expressions that are not suitable for engineering calculations and do not provide the possibility to study general properties of the two-component crystal-optical lenses. The authors developed an effective method of calculating propagation of electromagnetic waves through the two-component crystal-optical lenses based on uniaxial Iceland spar crystals with different orientations of the optical axes of the crystals in the lens components. Using a narrow beam method (paraxial approximation), the authors obtained an expression describing propagation of electromagnetic waves at the output of the two-component crystal-optical lenses. Based on the developed technique, propagation of electromagnetic waves through each section of crystal-optical lenses was calculated; the authors obtained expressions that are suitable for the analysis of properties in these systems as well as for engineering calculations. The paper presents a comprehensive experimental study of crystal-optical lenses in a split mode of electromagnetic waves at the output of crystal-optical lenses. Research results showed significant agreement between the results of calculations by formulas and experimental data.

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