Abstract

Imaging systems are typically partitioned into three components: focusing of incident light, scattering of incident light by an object and imaging of scattered light. We present a model of high Numerical Aperture (NA) imaging systems which differs from prior models as it treats each of the three components of the imaging system rigorously. It is well known that when high NA lenses are used the imaging system must be treated with vectorial analysis. This in turn requires that the scattering of light by the object be calculated rigorously according to Maxwell’s equations. Maxwell’s equations are solvable analytically for only a small class of scattering objects necessitating the use of rigorous numerical methods for the general case. Finally, rigorous vectorial diffraction theory and focusing theory are combined to calculate the image of the scattered light. We demonstrate the usefulness of the model through examples.

© 2008 Optical Society of America

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    [CrossRef]

2007 (3)

A.S. van de Nes, P. Török, "Rigorous analysis of spheres in Gauss-Laguerre beams," Opt. Express 15, 13360-13374 (2007)
[CrossRef] [PubMed]

P. R. T. Munro and P. Török, "Calculation of the image of an arbitrary vectorial electromagnetic field," Opt. Express 15, 9293-9307 (2007).
[CrossRef] [PubMed]

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. Baida, B. Guizal and D. van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 207022 (2007).
[CrossRef]

2006 (1)

2005 (1)

2004 (2)

P. R. T. Munro and P. Török, "Vectorial, high-numerical-aperture study of phase-contrast microscopes," J. Opt. Soc. Am. A. 21, 1714-1723 (2004).
[CrossRef]

L. Liu, Z. Shi, and S. He, "Analysis of the polarization-dependent diffraction from a metallic grating by use of a three-dimensional combined vectorial method," J. Opt. Soc. Am. A 21, 1545-1552 (2004).
[CrossRef]

2002 (1)

2000 (2)

P. Török, "Propagation of electromagnetic dipole waves through dielectric interfaces," Opt. Lett. 25, 1463-1465 (2000).
[CrossRef]

J. Liu, B. Xu, and T. Chong, "Three-Dimensional Finite-Difference Time-Domain Analysis of Optical Disk Storage System," Jpn. J. App. Phys. 39, 687-692 (2000).
[CrossRef]

1998 (2)

P. Török, P. Higdon, R. Juskaitis, and T. Wilson, "Optimising the image contrast of conventional and confocal optical microscopes imaging finite sized spherical gold scatterers," Opt. Commun. 155, 335-341 (1998).
[CrossRef]

P. Török, P. Higdon, and T. Wilson, "Theory for confocal and conventional microscopes imaging small dielectric scatterers," J. Mod. Opt. 45, 1681-1698 (1998).
[CrossRef]

1997 (1)

1995 (2)

1994 (2)

1990 (1)

R. Luebbers, F. Hunsberger, K. Kunz, R. Standler, and M. Schneider, "A frequency-dependent finite-difference time-domain formulation for dispersive materials," IEEE Trans. Electromag. Compat. 32, 222-227 (1990).
[CrossRef]

1982 (1)

C. J. R. Sheppard and T. Wilson, "The image of a single point in microscopes of large numerical aperture," Proc. R. Soc. London, Ser. A 379, 145-58 (1982).
[CrossRef]

1981 (2)

G. Mur, "Absorbing boundary conditions for finite-difference approximation of the time-domain electromagnetic-field equations," IEEE Trans. Electromag. Compat. 23, 377-382 (1981).
[CrossRef]

M. G. Moharam and T. K. Gaylord, "Rigorous coupled-wave analysis of planar-grating di_raction," J. Opt. Soc. Am. 71, 811-818 (1981).
[CrossRef]

1980 (1)

A. Bayliss and E. Turkel, "Radiation boundary conditions for wave-like equations," Commun. Pure App. Math. 23, 707-725 (1980).
[CrossRef]

1977 (1)

B. Engquist, "Absorbing boundary conditions for the numerical simulation of waves," Math. Comput. 31, 629-651 (1977).
[CrossRef]

1972 (1)

P. Johnson and R. Christy, "Optical constants for noble metals," Phys. Rev. Lett. 6, 4370-4379 (1972).

1966 (3)

K. Yee, "Numerical solution of inital boundary value problems involving maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

B. Karczewski and E. Wolf, "Comparison of three theories of electromagnetic diffraction at an aperture Part I: coherence matrices, Part II The far field," J. Opt. Soc. Am. 56, 1207-19 (1966).
[CrossRef]

1959 (1)

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).
[CrossRef]

1919 (1)

V. S. Ignatowsky, "Diffraction by a lens of arbitrary aperture," Trans. Opt. Inst. Petr. 1, 1-36 (1919).

1897 (1)

H. Pocklington, "Electrical oscillations in wires," Proc. Cam. Phil. Soc. 9, 324-332 (1897).

Baida, F.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. Baida, B. Guizal and D. van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 207022 (2007).
[CrossRef]

Bayliss, A.

A. Bayliss and E. Turkel, "Radiation boundary conditions for wave-like equations," Commun. Pure App. Math. 23, 707-725 (1980).
[CrossRef]

Berenger, J.-P.

J.-P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

Besbes, M.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. Baida, B. Guizal and D. van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 207022 (2007).
[CrossRef]

Bienstman, P.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. Baida, B. Guizal and D. van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 207022 (2007).
[CrossRef]

Booker, G. R.

Chong, T.

J. Liu, B. Xu, and T. Chong, "Three-Dimensional Finite-Difference Time-Domain Analysis of Optical Disk Storage System," Jpn. J. App. Phys. 39, 687-692 (2000).
[CrossRef]

Christy, R.

P. Johnson and R. Christy, "Optical constants for noble metals," Phys. Rev. Lett. 6, 4370-4379 (1972).

Dereux, A.

Engquist, B.

B. Engquist, "Absorbing boundary conditions for the numerical simulation of waves," Math. Comput. 31, 629-651 (1977).
[CrossRef]

Erni, D.

Gaylord, T. K.

Girard, C.

Granet, G.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. Baida, B. Guizal and D. van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 207022 (2007).
[CrossRef]

Guizal, B.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. Baida, B. Guizal and D. van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 207022 (2007).
[CrossRef]

Hafner, C.

He, S.

Helfert, S.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. Baida, B. Guizal and D. van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 207022 (2007).
[CrossRef]

Higdon, P.

P. Török, P. Higdon, and T. Wilson, "Theory for confocal and conventional microscopes imaging small dielectric scatterers," J. Mod. Opt. 45, 1681-1698 (1998).
[CrossRef]

P. Török, P. Higdon, R. Juskaitis, and T. Wilson, "Optimising the image contrast of conventional and confocal optical microscopes imaging finite sized spherical gold scatterers," Opt. Commun. 155, 335-341 (1998).
[CrossRef]

Hugonin, J. P.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. Baida, B. Guizal and D. van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 207022 (2007).
[CrossRef]

Hunsberger, F.

R. Luebbers, F. Hunsberger, K. Kunz, R. Standler, and M. Schneider, "A frequency-dependent finite-difference time-domain formulation for dispersive materials," IEEE Trans. Electromag. Compat. 32, 222-227 (1990).
[CrossRef]

Ignatowsky, V. S.

V. S. Ignatowsky, "Diffraction by a lens of arbitrary aperture," Trans. Opt. Inst. Petr. 1, 1-36 (1919).

Janssen, O. T. A.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. Baida, B. Guizal and D. van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 207022 (2007).
[CrossRef]

Johnson, P.

P. Johnson and R. Christy, "Optical constants for noble metals," Phys. Rev. Lett. 6, 4370-4379 (1972).

Judkins, J.

J. Judkins and R. Ziolkowski, "Finite-difference time-domain modeling of nonperfectly conducting metallic thin-film gratings," J. Opt. Soc. Am. A. 12(9), 1974-1983 (1995).
[CrossRef]

Juskaitis, R.

P. Török, P. Higdon, R. Juskaitis, and T. Wilson, "Optimising the image contrast of conventional and confocal optical microscopes imaging finite sized spherical gold scatterers," Opt. Commun. 155, 335-341 (1998).
[CrossRef]

Karczewski, B.

Kriezis, E.

Kunz, K.

R. Luebbers, F. Hunsberger, K. Kunz, R. Standler, and M. Schneider, "A frequency-dependent finite-difference time-domain formulation for dispersive materials," IEEE Trans. Electromag. Compat. 32, 222-227 (1990).
[CrossRef]

Laczik, Z.

Lalanne, P.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. Baida, B. Guizal and D. van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 207022 (2007).
[CrossRef]

Liu, J.

J. Liu, B. Xu, and T. Chong, "Three-Dimensional Finite-Difference Time-Domain Analysis of Optical Disk Storage System," Jpn. J. App. Phys. 39, 687-692 (2000).
[CrossRef]

Liu, L.

Luebbers, R.

R. Luebbers, F. Hunsberger, K. Kunz, R. Standler, and M. Schneider, "A frequency-dependent finite-difference time-domain formulation for dispersive materials," IEEE Trans. Electromag. Compat. 32, 222-227 (1990).
[CrossRef]

Martin, O.

Moharam, M. G.

Moreau, A.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. Baida, B. Guizal and D. van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 207022 (2007).
[CrossRef]

Moreno, E.

Munro, P. R. T.

Mur, G.

G. Mur, "Absorbing boundary conditions for finite-difference approximation of the time-domain electromagnetic-field equations," IEEE Trans. Electromag. Compat. 23, 377-382 (1981).
[CrossRef]

Nugrowati, A. M.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. Baida, B. Guizal and D. van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 207022 (2007).
[CrossRef]

Pereira, S. F.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. Baida, B. Guizal and D. van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 207022 (2007).
[CrossRef]

Pocklington, H.

H. Pocklington, "Electrical oscillations in wires," Proc. Cam. Phil. Soc. 9, 324-332 (1897).

Richards, B.

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).
[CrossRef]

Schneider, M.

R. Luebbers, F. Hunsberger, K. Kunz, R. Standler, and M. Schneider, "A frequency-dependent finite-difference time-domain formulation for dispersive materials," IEEE Trans. Electromag. Compat. 32, 222-227 (1990).
[CrossRef]

Schulz, L. G.

Seideman, T.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. Baida, B. Guizal and D. van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 207022 (2007).
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard and T. Wilson, "The image of a single point in microscopes of large numerical aperture," Proc. R. Soc. London, Ser. A 379, 145-58 (1982).
[CrossRef]

Shi, Z.

Standler, R.

R. Luebbers, F. Hunsberger, K. Kunz, R. Standler, and M. Schneider, "A frequency-dependent finite-difference time-domain formulation for dispersive materials," IEEE Trans. Electromag. Compat. 32, 222-227 (1990).
[CrossRef]

Sukharev, M.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. Baida, B. Guizal and D. van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 207022 (2007).
[CrossRef]

Tangherlini, F. R.

Török, P.

P. R. T. Munro and P. Török, "Calculation of the image of an arbitrary vectorial electromagnetic field," Opt. Express 15, 9293-9307 (2007).
[CrossRef] [PubMed]

A.S. van de Nes, P. Török, "Rigorous analysis of spheres in Gauss-Laguerre beams," Opt. Express 15, 13360-13374 (2007)
[CrossRef] [PubMed]

P. Török, P. R. T. Munro, and E. Kriezis, "A rigorous near to farfield transformation for vectorial diffraction calculations and its numerical implementation," J. Opt. Soc. Am. A 23, 713-722 (2006).
[CrossRef]

P. R. T. Munro and P. Török, "Vectorial, high numerical aperture study of Nomarski’s differential interference contrast microscope," Opt. Express 13, 6833-6847 (2005).
[CrossRef] [PubMed]

P. R. T. Munro and P. Török, "Vectorial, high-numerical-aperture study of phase-contrast microscopes," J. Opt. Soc. Am. A. 21, 1714-1723 (2004).
[CrossRef]

P. Török, "Propagation of electromagnetic dipole waves through dielectric interfaces," Opt. Lett. 25, 1463-1465 (2000).
[CrossRef]

P. Török, P. Higdon, R. Juskaitis, and T. Wilson, "Optimising the image contrast of conventional and confocal optical microscopes imaging finite sized spherical gold scatterers," Opt. Commun. 155, 335-341 (1998).
[CrossRef]

P. Török, P. Higdon, and T. Wilson, "Theory for confocal and conventional microscopes imaging small dielectric scatterers," J. Mod. Opt. 45, 1681-1698 (1998).
[CrossRef]

P. Török and P. Varga, "Electromagnetic diffraction of light focused through a stratified medium," Appl. Opt. 36(11), 2305-2312 (1997).
[CrossRef] [PubMed]

P. Török, P. Varga, Z. Laczik, 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).
[CrossRef]

Turkel, E.

A. Bayliss and E. Turkel, "Radiation boundary conditions for wave-like equations," Commun. Pure App. Math. 23, 707-725 (1980).
[CrossRef]

Urbach, H. P.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. Baida, B. Guizal and D. van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 207022 (2007).
[CrossRef]

Vahldieck, R.

van de Nes, A. S.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. Baida, B. Guizal and D. van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 207022 (2007).
[CrossRef]

van de Nes, A.S.

van Haver, S.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. Baida, B. Guizal and D. van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 207022 (2007).
[CrossRef]

van Labeke, D.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. Baida, B. Guizal and D. van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 207022 (2007).
[CrossRef]

Varga, P.

Wilson, T.

P. Török, P. Higdon, and T. Wilson, "Theory for confocal and conventional microscopes imaging small dielectric scatterers," J. Mod. Opt. 45, 1681-1698 (1998).
[CrossRef]

P. Török, P. Higdon, R. Juskaitis, and T. Wilson, "Optimising the image contrast of conventional and confocal optical microscopes imaging finite sized spherical gold scatterers," Opt. Commun. 155, 335-341 (1998).
[CrossRef]

C. J. R. Sheppard and T. Wilson, "The image of a single point in microscopes of large numerical aperture," Proc. R. Soc. London, Ser. A 379, 145-58 (1982).
[CrossRef]

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[CrossRef]

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).
[CrossRef]

Xu, B.

J. Liu, B. Xu, and T. Chong, "Three-Dimensional Finite-Difference Time-Domain Analysis of Optical Disk Storage System," Jpn. J. App. Phys. 39, 687-692 (2000).
[CrossRef]

Xu, M.

M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. Baida, B. Guizal and D. van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 207022 (2007).
[CrossRef]

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K. Yee, "Numerical solution of inital boundary value problems involving maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

Yee, S.

S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

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J. Judkins and R. Ziolkowski, "Finite-difference time-domain modeling of nonperfectly conducting metallic thin-film gratings," J. Opt. Soc. Am. A. 12(9), 1974-1983 (1995).
[CrossRef]

Appl. Opt. (1)

Commun. Pure App. Math. (1)

A. Bayliss and E. Turkel, "Radiation boundary conditions for wave-like equations," Commun. Pure App. Math. 23, 707-725 (1980).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

K. Yee, "Numerical solution of inital boundary value problems involving maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

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R. Luebbers, F. Hunsberger, K. Kunz, R. Standler, and M. Schneider, "A frequency-dependent finite-difference time-domain formulation for dispersive materials," IEEE Trans. Electromag. Compat. 32, 222-227 (1990).
[CrossRef]

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[CrossRef]

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[CrossRef]

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M. Besbes, J. P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. Baida, B. Guizal and D. van Labeke, "Numerical analysis of a slit-groove diffraction problem," J. Eur. Opt. Soc. 207022 (2007).
[CrossRef]

J. Mod. Opt. (1)

P. Török, P. Higdon, and T. Wilson, "Theory for confocal and conventional microscopes imaging small dielectric scatterers," J. Mod. Opt. 45, 1681-1698 (1998).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (4)

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J. Judkins and R. Ziolkowski, "Finite-difference time-domain modeling of nonperfectly conducting metallic thin-film gratings," J. Opt. Soc. Am. A. 12(9), 1974-1983 (1995).
[CrossRef]

P. R. T. Munro and P. Török, "Vectorial, high-numerical-aperture study of phase-contrast microscopes," J. Opt. Soc. Am. A. 21, 1714-1723 (2004).
[CrossRef]

Jpn. J. App. Phys. (1)

J. Liu, B. Xu, and T. Chong, "Three-Dimensional Finite-Difference Time-Domain Analysis of Optical Disk Storage System," Jpn. J. App. Phys. 39, 687-692 (2000).
[CrossRef]

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B. Engquist, "Absorbing boundary conditions for the numerical simulation of waves," Math. Comput. 31, 629-651 (1977).
[CrossRef]

Opt. Commun. (1)

P. Török, P. Higdon, R. Juskaitis, and T. Wilson, "Optimising the image contrast of conventional and confocal optical microscopes imaging finite sized spherical gold scatterers," Opt. Commun. 155, 335-341 (1998).
[CrossRef]

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[CrossRef]

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Supplementary Material (4)

» Media 1: AVI (360 KB)     
» Media 2: AVI (199 KB)     
» Media 3: AVI (74 KB)     
» Media 4: AVI (225 KB)     

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Figures (11)

Fig. 1.
Fig. 1.

Diagrammatic description of general imaging model. Each colour represents one of the four components of the model.

Fig. 2.
Fig. 2.

Diagram showing discrepancy between polar angle in the first and second principal focal planes.

Fig. 3.
Fig. 3.

Labelling scheme for calculating the image of an equivalent magnetic dipole embedded in a stratified medium in reflection (a - left) and transmission (b - right).

Fig. 4.
Fig. 4.

Line scan of a single sphere for both a confocal scanning and conventional scanning microscopes. Focused x-polarised light was employed and the line scan is along the x-axis.

Fig. 5.
Fig. 5.

Two-point resolution of two gold spheres positioned on the x-axis for linearly polarised light of various angles under a wide-field (a - left) and scanning microscope (b - right).

Fig. 6.
Fig. 6.

Plot of saddle-to-peak ratio against particle spacing for a range of angles of linear polarised incident light θ.

Fig. 7.
Fig. 7.

Magnitudes of the x-, y- and z-field components for focused x- and y- polarised illumination.

Fig. 8.
Fig. 8.

First frame of an animation showing the scattered electric field intensity on a plane tangential to the spheres and perpendicular to the optical axis. Each frame of the animation corresponds to a different angle orientation of focused linearly polarised incident light. The angle of incident light is indicated by the white arrow in the top left hand corner of the frame. [Media 1]

Fig. 9.
Fig. 9.

Plot showing how the two-point resolution varies with detector size for three angles of linear polarisation The convetional limit for each case is shown by a broken line. The dash-dot plot shows the FWMH of the point spread function along the x scan direction for x polarised incident light. This is given for the sake of comparison.

Fig. 10.
Fig. 10.

First frame of animation showing the image obtained as the angle of linearly polarised incident illumination is rotated from horizontal to vertical. The angle of orientation is indicated by a rotating line. Inset shows pattern etched into a slab of gold. The width of the central region of the “I” is λ/2. [Media 2]

Fig. 11.
Fig. 11.

First frame of animation showing the image obtained as the angle of linearly polarised incident illumination (solid line) is rotated from horizontal to vertical. An analyzer which is crossed relative to the incident polarisation of light is placed in front of the detector (broken line) (a - left) and Animation as the the focus of the objective lens moves from 2 wavelengths below the surface of the gold slab to 2 wavelengths above it. The position of the focus is indicated by the bar in the animation (b - right).[Media 3][Media 4]

Equations (38)

Equations on this page are rendered with MathJax. Learn more.

{ E , H } ( r p ) = ikf 2 π Ω { E a , H a } ( s x , s y ) s z e ik s · r p d s x d s y
{ E N , H N } ( r p ) = i k 1 2 π Ω 1 { ε N , 𝓗 N } exp ( i ρ κ ) exp ( i k 0 Ψ i ) exp ( i k N z p cos θ N ) sin θ 1 d θ 1 d ϕ
ε N ( s ( ϕ , θ ) ) = cos θ 1 1 ( ϕ + π ) 𝕃 ( θ N ) 𝕀 E ( N 1 ) ( ϕ + π ) 𝔹 𝕊 E ( 1 , 0 , 0 ) T
𝓗 N ( s ( ϕ , θ ) ) = 0 μ 0 cos θ 1 1 ( ϕ + π ) 𝕃 ( θ N ) 𝕀 H ( N 1 ) ( ϕ + π ) 𝔹 𝕊 H ( 0 , 1 , 0 ) T
= [ cos ϕ sin ϕ 0 sin ϕ cos ϕ 0 0 0 1 ] , 𝕃 = [ cos θ 0 sin θ 0 1 0 sin θ 0 cos θ ]
𝔹 𝕊 E = [ A + i B 0 i B A 0 0 0 1 ] , 𝔹 𝕊 H = [ A i B 0 i B A + 0 0 0 1 ]
𝕀 E ( N 1 ) = [ T p ( N 1 ) 0 0 0 T s ( N 1 ) 0 0 0 T p ( N 1 ) ] , 𝕀 E ( N 1 ) = n N n 1 [ T s ( N 1 ) 0 0 0 T p ( N 1 ) 0 0 0 T s ( N 1 ) ]
s= -1 (φ)L(θ)(φ) (0,0,1) T =(cos(φ+π)sinθ,sin(φ+π)sinθ,cosθ)
ε Nx = 1 2 cos θ 1 [ A + C + + C ( A + cos ( 2 ϕ ) + i B sin ( 2 ϕ ) ]
ε Ny = 1 2 cos θ 1 [ i B C + + C ( i B cos ( 2 ϕ ) A + sin ( 2 ϕ ) ]
ε Nz = cos θ 1 T p ( N 1 ) sin θ N ( A + cos φ + i B sin φ )
𝓗 Nx = 1 2 n N n 1 cos θ 1 [ i B D + + D ( i B cos ( 2 ϕ ) + A + sin ( 2 ϕ ) ]
𝓗 Ny = 1 2 n N n 1 cos θ 1 [ A + D + + D ( A + cos ( 2 ϕ ) + i B sin ( 2 ϕ ) ]
𝓗 Nz = n N n 1 cos θ 1 T s ( N 1 ) sin θ N ( i B cos φ + A + sin φ ) )
E x N = i k 1 f 2 [ A + I 0 E + A + I 2 E cos ( 2 φ ) + i B I 2 E sin ( 2 φ ) ] E y N = i k 1 f 2 [ i B I 0 E i B I 2 E cos ( 2 φ ) + A + I 2 E sin ( 2 φ ) ] E zN = i k 1 f [ i A + I 1 E cos φ B I 1 E sin φ ] H x N = i k N f 2 η 0 [ i B I 0 H + i B I 2 H cos ( 2 φ ) A + I 2 H sin ( 2 φ ) ] H y N = i k N f 2 η 0 [ A + I 0 H A + I 2 H cos ( 2 φ ) i B I 2 H sin ( 2 φ ) ] H zN = i k N f η 0 [ B I 1 H cos φ + A + i I 2 H sin φ ]
I 0 E = 0 α 1 cos θ 1 sin θ 1 ( T s ( N 1 ) + T p ( N 1 ) cos θ N ) J 0 ( k 1 ρ sin θ 1 ) exp ( i k 0 Ψ i ) exp ( i Ψ d ) d θ 1
I 1 E = 0 α 1 cos θ 1 sin θ 1 T p ( N 1 ) sin θ N J 1 ( k 1 ρ sin θ 1 ) exp ( i k 0 Ψ i ) exp ( i Ψ d ) d θ 1
I 2 E = 0 α 1 cos θ 1 sin θ 1 ( T s ( N 1 ) T p ( N 1 ) cos θ N ) J 2 ( k 1 ρ sin θ 1 ) exp ( i k 0 Ψ i ) exp ( i Ψ d ) d θ 1
I 0 H = 0 α 1 cos θ 1 sin θ 1 ( T p ( N 1 ) + T s ( N 1 ) cos θ N ) J 0 ( k 1 ρ sin θ 1 ) exp ( i k 0 Ψ i ) exp ( i Ψ d ) d θ 1
I 1 H = 0 α 1 cos θ 1 sin θ 1 T s ( N 1 ) sin θ N J 1 ( k 1 ρ sin θ 1 ) exp ( i k 0 Ψ i ) exp ( i Ψ d ) d θ 1
I 2 H = 0 α 1 cos θ 1 sin θ 1 ( T p ( N 1 ) T s ( N 1 ) cos θ N ) J 2 ( k 1 ρ sin θ 1 ) exp ( i k 0 Ψ i ) exp ( i Ψ d ) d θ 1
E x t = 1 [ H z y H y z σ E x ]
E x i , j + 1 2 , k + 1 2 n + 1 2 = α i , j + 1 2 , k + 1 2 E x i , j + 1 2 , k + 1 2 n 1 2 + β i , j + 1 2 , k + 1 2 ( H z i , j + 1 , k + 1 2 n H z i , j , k + 1 2 n Δ y
H y i , j + 1 2 , k + 1 n H y i , j + 1 2 , k n Δ z )
E ( x p , y p , z p ) = 1 4 π S 0 [ i ω μ ( m ̂ × H ) G + ( m ̂ × E ) × G + ( m ̂ · E ) G ] d S
H ( x p , y p , z p ) = 1 4 π S 0 [ i ω ε ( m ̂ × E ) G ( m ̂ × H ) × G ( m ̂ · H ) G ] d S
U ( r p ) = i = 1 N facets ( 1 3 j = 1 3 I ( r p , m ̂ i , r s , ν i j , E ν i j , H ν i j ) ) Δ i
E ( P ) = 1 2 π S 0 ( r × ( n × E ( Q ) ) exp ( i k 0 r ) r 2 i k 0 d S
E x = p x ( I 0 , r eq , s + I 2 , r eq , s cos 2 φ d ) + p y I 2 , r eq , s sin 2 φ d
E y = p y ( I 0 , r eq , s I 2 , r eq , s cos 2 φ d ) + p x I 2 , r eq , s sin 2 φ d
E z = 2 i ( p x I 1 , r eq , s cos φ d + p y I 1 , r eq , s sin φ d )
I 0 , r eq , s = π α d π cos θ d cos θ 1 sin θ d ( T s cos θ N + T p cos θ d ) J 0 ( k d r dt sin θ d ) exp [ i k 0 ( Ψ i + κ ) ] d θ d
I 1 , r eq , s = π α d π cos θ d cos θ 1 T p sin 2 θ d J 1 ( k d r dt sin θ d ) exp [ i k 0 ( Ψ i + κ ) ] d θ d
I 2 , r eq , s = π α d π cos θ d cos θ 1 sin θ d ( T s cos θ N T p cos θ d ) J 2 ( k d r dt sin θ d ) exp [ i k 0 ( Ψ i + κ ) ] d θ d
I 0 , t eq , s = 0 α d cos θ d cos θ 1 sin θ d ( T s cos θ N + T p cos θ d ) J 0 ( k d r dt sin θ d ) exp [ i k 0 ( Ψ i + κ ) ] d θ d
I 1 , t eq , s = 0 α d cos θ d cos θ 1 T p sin 2 θ d J 1 ( k d r dt sin θ d ) exp [ i k 0 ( Ψ i + κ ) ] d θ d
I 2 , t eq , s = 0 α d cos θ d cos θ 1 sin θ d ( T s cos θ N T p cos θ d ) J 2 ( k d r dt sin θ d ) exp [ i k 0 ( Ψ i + κ ) ] d θ d
E t r ( r d ) = i k 0 2 π s 0 E oa , t r ( n × E i ( Q ) , r d + β q ) d S

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