Analogue of rayleigh-sommerfeld integral for anisotropic and gyrotropic media
S.N. Khonina, S.I. Kharitonov

Full text of article: Russian language.

Abstract:
Integral representations of the solution of Maxwell’s equations for anisotropic and gyrotropic media with factorization of longitudinal and transverse components are written in a closed analytical form. In special cases, the integral expressions received are reduced to an analogue of the Rayleigh-Sommerfeld integral.

Key words:
anisotropic and gyrotropic media, diffraction, Maxwell’s equations, plane wave expansion, analogue of the Rayleigh-Sommerfeld integral, Faraday effect.

References:

  1. Ciattoni, A. Circularly polarized beams and vortex generation in uniaxial media / A. Ciattoni, G. Cincotti, C. Palma // J. Opt. Soc. Am. A. - 2003. - Vol. 20(1). - P. 163-171.
  2. Marrucci, L. Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media / L. Mar­rucci, C. Manzo and D. Paparo // Phys. Rev. Lett. - 2006. - Vol. 96. - P. 163905-4.
  3. Spatially engineered polarization states and optical vortices in uniaxial crystals / T.A. Fadeyeva, V.G. Shvedov, Y.V. Izdebskaya, A.V. Volyar, E. Brasselet, D.N. Neshev, A.S. Desyatnikov, W. Krolikowski and Y.S. Kivshar // Opt. Expr. - 2010. - Vol. 18(10). - P. 10848-10863.
  4. Picon, A. Spin and orbital angular momentum propagation in anisotropic media: theory / A. Picon, A. Benseny, J. Mompart and G.F. Calvo // J. Opt. - 2011. - Vol. 13. - P. 064019-064015.
  5. Fleck, J.A. Jr. Beam propagation  in uniaxial  anisotropic media / J.A. Fleck, Jr. and M.D. Feit // J. Opt. Soc. Am. - 1983. - Vol. 73(7). - P. 920-926.
  6. Ciattoni, A. Vectorial theory of propagation in uniaxially anisotropic media / A. Ciattoni, B. Crosignani and P. Di Porto // J. Opt. Soc. Am. A. - 2001. - Vol. 18(7). - P. 1656-1661.
  7. Zhao, Y. Spin-to-orbital angular momentum conversion in a strongly focused optical beam / Y. Zhao, J.S. Edgar, G.D.M. Jeffries, D. McGloin and D.T. Chiu // Phys. Rev. Lett. - 2007. - Vol. 99. - P. 073901.
  8. Chen, L. Electro-optically forbidden or enhanced spin-to-orbital angular momentum conversion in a focused light beam / L. Chen and W. She // Opt. Lett. - 2008. - Vol. 33. - P. 696-698.
  9. Khonina, S.N. Controlling the contribution of the electric ?eld components to the focus of a high-aperture lens using binary phase structures / S.N. Khonina, S.G. Volotovsky // J. Opt. Soc. Am. A. - 2010. - Vol. 27, N 10. - P. 2188-2197.
  10. Stallinga, S. Axial birefringence in high-numerical-aper­ture optical systems and the light distribution close to focus / S. Stallinga // J. Opt. Soc. Am. A. - 2001. - Vol. 18(11). - P. 2846-2859.
  11. Seshadri, S.R. Beam dynamics of two modes propagating along the optic axis in a uniaxial crystal / S.R. Seshadri // J. Opt. Soc. Am. A. - 2005. - Vol. 22(2). - P. 361-369.
  12. Liu, D. Various dark hollow beams propagating in uniaxial crystals orthogonal to the optical axis / D. Liu and Z. Zhou // J. Opt. A: Pure Appl. Opt. - 2008. - Vol. 10. - P. 095005-095013.
  13. Bessel beam transformation by anisotropic crystals / D.H. Zusin, R. Maksimenka, V.V. Filippov, R.V. Chul­kov, M. Perdrix, O. Gobert and A.S. Grabtchikov // J. Opt. Soc. Am. A. - 2010. - Vol. 27(8). - P. 1828-1833.
  14. Yariv, A. Optical Waves in Crystals / A. Yariv and P. Yeh. - New York: Wiley, 1984.
  15. Potehin, A.I. Radiation and distribution of electromagnetic waves in the anisotropic environment / A.I. Potehin. - Moscow: “Nauka” Publisher, 1979. - 76 p.
  16. Stamnes, J.J. Radiation of electromagnetic fields in uniaxially anisotropic media / J.J. Stamnes and G.C. Sher­man // J. Opt. Soc. Am. - 1976. - Vol. 66(8). - P. 780-788.
  17. Bleistein, N. Asymptotic Expansions of Integrals / N. Bleistein and R.A. Handelsman. - New York: Holt, Rinehart and Winston, 1975. - P. 340-359.
  18. Stamnes, J.J. Double refraction of a Gaussian beam into a uniaxial crystal / J.J. Stamnes, V. Dhayalan // J. Opt. Soc. Am. A. - 2012. - Vol. 29(4). - P. 486-497.
  19. Qiu, C.-W. Eigenfunctional representation of dyadic Green’s functions in multilayered gyrotropic chiral media / C.-W. Qiu, H.-Y. Yao, L.-W. Li, S. Zouhdi, T.-S. Yeo // J. Phys. A: Math. Theor. - 2007. - Vol. 40. - P. 5751-5766.
  20. Doskolovich, L.L. Integral representations for solutions of Maxwell’s equations for anisotropic media / L.L. Do­skolovich, N.L. Kazanskiy, S.I. Kharitonov // Computer Optics. - 2010. - Vol. 34, N 1. - P. 52-57.
  21. Nye, J.F. Physical proprities of crystals. Their representation by tensors and matrices / J.F. Nye. - Oxford, 1964.
  22. Ciattoni, A. Optical propagation in uniaxial crystals orthogonal to the optical axis: paraxial theory and beyond / A. Ciattoni, C. Palma // J. Opt. Soc. Am. A. - 2003. - Vol. 20(11). - P. 2163-2171.
  23. Fadeyeva, T. Non-canonical propagation of high-order elliptic vortex beams in a uniaxially anisotropic medium / T. Fadeyeva, C. Alexeyev, B. Sokolenko, M. Kudryav­tseva and A. Volyar // Ukr. J. Phys. Opt. - 2011. - Vol. 12(2). - P. 62-82.
© 2009, IPSI RAS
Institution of Russian Academy of Sciences, Image Processing Systems Institute of RAS, Russia, 443001, Samara, Molodogvardeyskaya Street 151; E-mail: ko@smr.ru; Phones: +7 (846 2) 332-56-22, Fax: +7 (846 2) 332-56-20