## Journal of the European Optical Society - Rapid publications, Vol 6 (2011)

### Focusing of electromagnetic waves into a dielectric slab. II. Numerical results

#### Abstract

field inside a dielectric slab is observed, especially at observation points near to one of the interfaces. This difference is believed to be due to contributions from surface waves, which are not accounted for in the asymptotic Kirchhoff solutions. At low Fresnel numbers focal shift phenomena are observed in all three cases.

© The Authors. All rights reserved. [DOI: 10.2971/jeos.2011.11036]

#### Citation Details

Cite this article

#### References

M. Mansuripur, "Distribution of light at and near the focus of high-numerical-aperture objectives", J. Opt. Soc. Am. A 3, 2086- 2093 (1995).

D. G. Flagello, T. Milster, and A. E. Rosenbluth, "Theory of high-NA imaging in homogeneous thin films", J. Opt. Soc. Am. A 13, 53-64 (1996).

H. Ling, and S. W. Lee, "Focusing of electromagnetic waves through a dielectric interface", J. Opt. Soc. Am. A 1, 965-973 (1984).

H. Ling, S. W. Lee, and W. Gee, "Frequency optimization of focused microwave hyperthermia applications", Proc. IEEE 72, 224- 225 (1984).

P. Török, 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).

P. Török, P. Varga, and G. R. Booker, "Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices. I. Structure of the electromagnetic field", J. Opt. Soc. Am. A 12, 2136-2144 (1995).

P. Török, P. Varga, and G. Nemeth, "Analytical solution of the diffraction integrals and interpretation of wave-front distortion when light is focused through a planar interface between materials of mismatched refractive indices", J. Opt. Soc. Am. A 12, 2660-2671 (1995).

P. Török, "Focusing of electromagnetic waves through a dielectric interface by leses of finite fresnel number", J. Opt. Soc. Am. A 3, 2086-2093 (1998).

J. H. Erkkila, and M. E. Rogers, "Diffracted fields in the focal volume of a converging wave", J. Opt. Soc. Am. 71, 904-905 (1981).

J. J. Stamnes, and B. Spjelkavik, "Focusing at small angular apertures in the Debye and Kirchhoff approximations", Opt. Commun. 40, 81-85 (1981).

E. Wolf, and Y. Li, "Conditions for the validity of the Debye integral representation of focused fields", Opt. Commun. 39, 205-210 (1981).

Y. Li, "Encircled energy for systems of different Fresnel numbers", Optik 64, 207-218 (1983).

Y. Li, and H. Platzer, "An experimental investigation of diffraction patterns in low-Fresnel-number focusing systems", Opt. Acta 30, 1621-1643 (1983).

Y. Li, "Dependence of the focal shift on Fresnel number and f_number", J. Opt. Soc. Am. A 72, 770-4 (1982).

V. Dhayalan, and J. J. Stamnes, "Focusing of electric-dipole waves in the Debye and Kirchhoff approximations", Pure Appl. Opt. 6, 347-372 (1997).

G. W. Farnell, "Measured phase distribution in the image space of a microwave lens", Can. J. Phys. 36, 935-943 (1958).

C. A. Taylor, and B. J. Thompson, "Attempt to investigate experimentally the intensity distribution near the focus in the error-free diffraction patterns of circular and annular apertures", J. Opt. Soc. Am. 48, 844-50 (1958).

J. J. Stamnes, and V. Dhayalan, "Focusing of electric-dipole waves", Pure Appl. Opt. 5, 195-226 (1996).

Q. W. Zhan, "Trapping metallic Rayleigh particles with radial polarization", Opt. Express 12, 3377-3382 (2004).

L. E. Helseth, "Focusing of atoms with strongly confined light potentials", Opt. Commun. 212, 343-352 (2002).

M. Meier, V. Romano, and T. Feurer, "Material processing with pulsed radially and azimuthally polrized laser radiation", Appl. Phys. A-Matter 86, 21965-21972, (2010).

R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam", Phys. Rev. Lett. 91, 233901-233904 (2003).

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "Focusing light to tighter spot", Opt. Commun. 179, 1-7 (2000).

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "The focus of light - theoretical calculation and experimental tomographic reconstruction", Appl. Phys. B-Lasers O72, 109-113 (2001).

H. P. Urbach, and S. F. Pereira, "The field in focus with maximum electric field components", Phys. Rev. A 79, 013825 (2009).

V. Dhayalan, and J. J. Stamnes, "Focusing of electromagnetic waves into a dielectric slab I. Exact and asymptotic results", Pure Appl. Opt. 7, 33-52 (1998).

J. J. Stamnes, and H. A. Eide, "Exact and approximate solutions for focusing of two-dimensional waves. I. Theory", J. Opt. Soc. Am. A 15, 1285-1291 (1998).

H. A. Eide, and J. J. Stamnes, "Exact and approximate solutions for focusing of two-dimensional waves. II. Numerical comparisons between exact, Debye, and Kirchhoff theories", J. Opt. Soc. Am. A 15, 1308-1319 (1998).

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, 1292-1307 (1998).

D. Jiang and J. J. Stamnes, "Theoretical and experimental results for two-dimensional electromagnetic waves focused through an interface", Pure Appl. Opt. 7, 627-641 (1998).

J. J. Stamnes, and D. Jiang, "Focusing of two-dimensional electromagnetic waves through a plane interface", Pure Appl. Opt, 7, 603-625 (1998).

J. J. Stamnes, Waves in Focal Regions, (Adam Hilger, Bristol and Boston, 1986).

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes, (Cambridge Univ. Press, 1989. [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).

V. Dhayalan, and J. J. Stamnes, "Comparison of exact asymptotic results for the focusing of electromagnetic waves through a plane interface", Appl. Opt. 39, 6332-6340 (2000).

M. Abramowitz, and I. A. Stegun, Handbook of Mathematical Functions, (Dover, New York, 5th edition (1968)).

Y. Li, and E. Wolf, "Three-dimensional intensity distribution near the focus in systems of different Fresnel numbers", J. Opt. Soc. Am. A 1, 801-808 (1984).

Y. Li, "Focal shifts in small-fresnel-number focusing systems of different relative aperture", J. Opt. Soc. Am. A 20, 234-239 (2003).

Y. Li, "Focal shifts in diffracted converging electromagnetic waves. I. Kirchhoff theory", J. Opt. Soc. Am. A 22, 68-76 (2005).

Y. Li, "Focal shifts in diffracted converging electromagnetic waves. II. Rayleigh theory", J. Opt. Soc. Am. A 22, 77-83 (2005).

J. J. Stamnes, and V. Dhayalan, "Focal shifts on focusing through a plane interface", Opt. Commun. 282, 2286-2291 (2009).

M. Mansuripur, "Certain computational aspects of vector diffraction problems", J. Opt. Soc. Am. A 6, 786-805 (1989).