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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 20, Iss. 11 — Nov. 1, 2003
  • pp: 2163–2171

Optical propagation in uniaxial crystals orthogonal to the optical axis: paraxial theory and beyond

Alessandro Ciattoni and Claudio Palma  »View Author Affiliations


JOSA A, Vol. 20, Issue 11, pp. 2163-2171 (2003)
http://dx.doi.org/10.1364/JOSAA.20.002163


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Abstract

We describe monochromatic light propagation in uniaxial crystals by means of an exact solution of Maxwell’s equations. We subsequently develop a paraxial scheme for describing a beam traveling orthogonal to the optical axis. We show that the Cartesian field components parallel and orthogonal to the optical axis are extraordinary and ordinary, respectively, and hence uncoupled. The ordinary component exhibits a standard Fresnel behavior, whereas the extraordinary one exhibits interesting anisotropic diffraction dynamics. We interpret the anisotropic diffraction as a composition of two spatial geometrical affinities and a single Fresnel propagation step. As an application, we obtain the analytical expression of the extraordinary Gaussian beam. We then derive the first nonparaxial correction to the paraxial beam, thus giving a scheme for describing slightly nonparaxial fields. We find that nonparaxiality couples the Cartesian components of the field and that the resultant longitudinal component is greater than the correction to the transverse component orthogonal to the optical axis. Finally, we derive the analytical expression for the nonparaxial correction to the paraxial Gaussian beam.

© 2003 Optical Society of America

OCIS Codes
(260.1180) Physical optics : Crystal optics
(260.1960) Physical optics : Diffraction theory

History
Original Manuscript: May 6, 2003
Revised Manuscript: July 11, 2003
Manuscript Accepted: July 21, 2003
Published: November 1, 2003

Citation
Alessandro Ciattoni and Claudio Palma, "Optical propagation in uniaxial crystals orthogonal to the optical axis: paraxial theory and beyond," J. Opt. Soc. Am. A 20, 2163-2171 (2003)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-11-2163


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References

  1. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
  2. H. C. Chen, Theory of Electromagnetic Waves (McGraw-Hill, New York, 1983).
  3. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1999).
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  6. A. Ciattoni, B. Crosignani, P. Di Porto, “Paraxial vector theory of propagation in uniaxially anisotropic media,” J. Opt. Soc. Am. A 18, 1656–1661 (2001). [CrossRef]
  7. A. Ciattoni, B. Crosignani, P. Di Porto, “Vectorial free-space optical propagation: a simple approach for generating all-order nonparaxial corrections,” Opt. Commun. 177, 9–13 (2000). [CrossRef]
  8. M. Lax, W. H. Luoisell, W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975). [CrossRef]
  9. A. Ciattoni, G. Cincotti, C. Palma, “Ordinary and extraordinary beams characterization in uniaxially anisotropic crystals,” Opt. Commun. 195, 55–61 (2001). [CrossRef]
  10. A. Ciattoni, G. Cincotti, C. Palma, H. Weber, “Energy exchange between the Cartesian components of a paraxial beam in a uniaxial crystal,” J. Opt. Soc. Am. A 19, 1894–1900 (2002). [CrossRef]
  11. A. Ciattoni, G. Cincotti, D. Provenziani, C. Palma, “Paraxial propagation along the optical axis of a uniaxial medium,” Phys. Rev. E 66, 036614 (2002). [CrossRef]
  12. To be more precise, Eq. (23) describes an harmonic oscillator only if k02ne2-(ne2/no2)kx2-ky2>0 and the corresponding plane waves are homogeneous. For k02ne2-(ne2/no2)kx2-ky2<0, Eq. (A3) permits exponential but not sinusoidal solutions, and the corresponding plane waves are the well-known evanescent ones.
  13. Analogously to the case of Eq. (A3), Eq. (A5) is the case of a forced harmonic oscillator only if k02no2-k⊥2>0(homogeneous waves); for k02no2-k⊥2<0 its solutions exhibit exponential behavior (evanescent waves).

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