Beyond the Fresnel approximation for focused waves

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 16, Issue 8, 1999, Pages 1958-1969

  Alonso, M A ^a   Asatryan, A A ^a   Forbes, G W ^a  

^a MACQUARIE UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038718199     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.16.001958     Document Type: Article

References (12)

1. A. Wunsche, “Transition from the paraxial approximation to exact solutions of the wave equation and application to Gaussian beams,” J. Opt. Soc. Am. A 9, 765–774 (1992).
2. G. W. Forbes, D. J. Butler, R. L. Gordon, and A. A. Asatryan, “Algebraic corrections for paraxial wave fields,” J. Opt. Soc. Am. A 14, 3300–3315 (1997).
3. M. Lax, W. H. Louisell, and W. B. McBright, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
4. G. P. Agrawal and M. Lax, “Free-space wave propagation beyond the paraxial approximation,” Phys. Rev. A 27, 1693–1695 (1983).
5. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, 1st ed. (Cambridge U. Press, New York, 1995), Sec. 3.2, pp. 109–127.
6. See Ref. 5, Sec. 3.2.4, pp. 120–124.
7. See Ref. 5, Sec. 3.2.5, pp. 125–127.
8. W. H. Southwell, “Validity of the Fresnel approximation in the near field,” J. Opt. Soc. Am. 71, 7–14 (1981).
9. G. W. Forbes, “Scaling properties in the diffraction of focused waves and an application to scanning beams,” Am. J. Phys. 62, 434–443 (1994).
10. H. Osterberg and L. Smith, “Closed solutions of Rayleigh’s diffraction integral for axial points,” J. Opt. Soc. Am. 51, 1050–1054 (1961).
11. The required expressions can be found either by returning to Eq. (5.2c) and taking the derivatives before evaluating at focus or by using Eqs. (4.8) and (4.11). Equivalently, since Eq. (5.5) is evaluated at z 5 f, we can take the partial f derivatives as ]ŪF /]f 5 d ŪF /df 2] ŪF /]z, whereEq.(4.8) is then used for taking the partial z derivative. As an example, the first correction term given in Eq. (4.2a) can be found in this way to be 13. G. W. Forbes and A. A. Asatryan, “Reducing canonical diffraction problems to singularity-free one-dimensional integrals,” J. Opt. Soc. Am. A 15, 1320–1328 (1998).
12. Such contour plots have been given recently, for example, in Ref. 2 and in G. W. Forbes, “Validity of the Fresnel approximation in the diffraction of collimated beams,” J. Opt. Soc. Am. A 13, 1816–1826 (1996).