Exact and approximate solutions for focusing of two-dimensional waves. I. Theory

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

Volumn 15, Issue 5, 1998, Pages 1285-1291

  Stamnes, Jakob J ^a   Eide, Hans A ^a  

^a UNIVERSITY OF BERGEN   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000400371     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.15.001285     Document Type: Article

References (34)

1. P. Debye, “Das Verhalten von Licht Wellen in der Nahe eines Brennpunktes oder eine Brennlinie,” Ann. Phys. (Leipzig) 30, 755–776 (1909).
2. V. S. Ignatowsky, “Diffraction by a lens having arbitrary opening,” Trans. Opt. Inst. Petrograd I (1919)
3. V. S. Ignatowsky, “Diffraction by a parabolic mirror having arbitrary opening” (1920), papers IV and V, respectively (in Russian).
4. E. Wolf, “Electromagnetic diffractions in optical systems. An integral representation of the image field,” Proc. R. Soc. London Ser. A 253, 349–357 (1959).
5. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
6. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1985).
7. J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, UK, 1986).
8. J. J. Stamnes, “Focusing of two-dimensional waves,” J. Opt. Soc. Am. 71, 15–31 (1981).
9. A. Boivin and E. Wolf, “Electromagnetic field in the neighborhood of the focus of a coherent beam,” Phys. Rev. B 138, 1561–1565 (1965).
10. A. Boivin, J. Dow, and E. Wolf, “Energy flow in the neighborhood of the focus of a coherent beam,” J. Opt. Soc. Am. A 57, 1171–1175 (1967).
11. D. J. Innes and A. L. Bloom, “Design of optical systems for use with laser beams,” Spectra-Physics Laser Tech. Bull. 5, 1–10 (1966).
12. A. Yoshida and T. Asakura, “Electromagnetic field in the focal plane of a coherent beam from a wide-angular annular-aperture system,” Optik (Stuttgart) 40, 322–331 (1974).
13. M. Mansuripur, “Certain computational aspects of vector diffraction problems,” J. Opt. Soc. Am. A 6, 786–805 (1989).
14. R. Kant, “An analytical solution of vector diffraction problems for focusing optical systems,” J. Mod. Opt. 40, 337–347 (1993).
15. C. J. R. Sheppard, A. Choudhury, and J. Gannaway, “Electromagnetic field near the focus of wide-angular lens and mirror systems,” IEE J. Microwaves Opt. Acoust. 1, 129–132 (1977).
16. R. Kant, “An analytical solution of vector diffraction for focusing optical systems with Seidel aberrations. I. Spherical aberrations, curvature of field, and distortion,” J. Mod. Opt. 40, 2293–2310 (1993).
17. R. Kant, “An analytical solution of vector diffraction for focusing optical systems with Seidel aberrations. II. Astigmatism and coma,” J. Mod. Opt. 42, 299–320 (1995).
18. P. Torok, P. Varga, Z. Laczic, and G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: an integral representation,” J. Opt. Soc. Am. A 12, 325–332 (1995).
19. C. J. R. Sheppard and K. G. Larkin, “Optimal concentration of electromagnetic radiation,” J. Mod. Opt. 41, 1495–1505 (1994).
20. J. J. Stamnes and V. Dhayalan, “Focusing of electric-dipole waves,” Pure Appl. Opt. 5, 195–226 (1996).
21. W. Hsu and R. Barakat, “Stratton-Chu vectorial diffraction of electromagnetic fields by apertures with application to small Fresnel-number systems,” J. Opt. Soc. Am. A 11, 623–629 (1994).
22. T. D. Visser and S. H. Wiersma, “Spherical aberration and the electromagnetic field in high-aperture systems,” J. Opt. Soc. Am. A 8, 1404–1410 (1991).
23. T. D. Visser and S. H. Wiersma, “Diffraction of converging electromagnetic waves,” J. Opt. Soc. Am. A 9, 2034–2047 (1992).
24. T. D. Visser and S. H. Wiersma, “Electromagnetic description of the image formation in confocal fluorescence microscopy,” J. Opt. Soc. Am. A 11, 599–608 (1994).
25. H. Ling and S. W. Lee, “Focusing of electromagnetic waves through a dielectric interface,” J. Opt. Soc. Am. A 1, 965–973 (1984).
26. V. Dhayalan and J. J. Stamnes, “Focusing of electric-dipole waves in the Debye and Kirchhoff approximations,” Pure Appl. Opt. 6, 347–372 (1997).
27. G. W. Farnell, “Calculated intensity and phase distribution in the image space of a microwave lens,” Can. J. Phys. 35, 777–783 (1957).
28. Y. Li and H. Platzer, “An experimental investigation of diffraction patterns in low-Fresnel-number focusing systems,” Opt. Acta 30, 1621–1643 (1983).
29. J. J. Stamnes, “Exact two-dimensional scattering of an arbitrary wave by perfectly reflecting elliptical cylinders, strips and slits,” Pure Appl. Opt. 4, 841–855 (1995).
30. H. A. Eide and J. J. Stamnes, “Exact and approximate solutions for focusing of two-dimensional waves. II. Numerical comparisons among exact, Debye, and Kirchhoff theories,” J. Opt. Soc. Am. A 15, 1292–1307 (1998).
31. H. A. Eide and J. J. Stamnes, “Exact and approximate solutions for focusing of two-dimensional waves. III. Numerical comparisons between exact and Rayleigh-Sommerfeld theories,” J. Opt. Soc. Am. A 15, 1308–1319 (1998).
32. J. J. Stamnes and B. Spjelkavik, “New method for computing eigenfunctions (Mathieu functions) for scattering by elliptical cylinders,” Pure Appl. Opt. 4, 251–262 (1995).
33. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 5th ed. (Dover, New York, 1968).
34. J. J. Stamnes, B. Spjelkavik, and H. M. Pedersen, “Evaluation of diffraction integrals using local phase and amplitude approximations,” Opt. Acta 30, 207–222 (1983).