Abstract

We present a new technique for computing the electromagnetic field that propagates and is scattered in three-dimensional structures formed by bodies embedded in a stratified background. This fully vectorial technique is based on the Green’s tensor associated with the stratified background. Its advantage lies in the fact that only the scatterers must be discretized, the stratified background being accounted for in the Green’s tensor. Further, the boundary conditions at the different material interfaces as well as at the edges of the computation window are perfectly and automatically fulfilled. Several examples illustrate the utilization of the technique for the modeling of photonic circuits (integrated optical waveguides), the study of the optics of metal (surface plasmons), and the development of new optical lithography techniques.

© 2001 Optical Society of America

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  49. H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, N. B. Piller, “Light-coupling masks: an alternative, lensless approach to high-resolution optical contact lithography,” J. Vac. Sci. Technol. B 16, 3422–3425 (1998).
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2000 (3)

R. Scarmozzino, A. Gopinath, R. Pregla, S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

H. El-Refaei, D. Yevick, I. Betty, “Stable and nonitera-tive bidirectional beam propagation method,” IEEE Photonics Technol. Lett. 12, 389–391 (2000).
[CrossRef]

M. Paulus, P. Gay-Balmaz, O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[CrossRef]

1999 (5)

Y. Hsueh, M. Yang, H. Chang, “Three-dimensional noniterative full-vectorial beam propagation method based on the alternating direction implicit method,” J. Lightwave Technol. 17, 2389–2397 (1999).
[CrossRef]

P. R. Hayes, M. T. O’Keefe, P. R. Woodward, A. Gopinath, “High-order-compact time-domain numerical simulation of optical waveguides,” Opt. Quantum Electron. 31, 813–826 (1999).
[CrossRef]

S. F. Helfert, R. Pregla, “Analysis of thin layers and discontinuities,” Opt. Quantum Electron. 31, 721–732 (1999).
[CrossRef]

W. Huang, R. R. A. Syms, “Analysis of folded erbium-doped planar waveguide amplifiers by the method of lines,” J. Lightwave Technol. 17, 2658–2664 (1999).
[CrossRef]

D. R. Beltrami, J. D. Love, F. Ladouceur, “Multimode planar devices,” Opt. Quantum Electron. 31, 307–326 (1999).
[CrossRef]

1998 (11)

M. J. Noble, J. A. Lott, J. P. Loehr, “Quasi-exact optical analysis of oxide-apertured microcavity VCSEL’s using vector finite elements,” IEEE J. Quantum Electron. 34, 2327–2339 (1998).
[CrossRef]

G. R. Hadley, “Low-truncation-error finite difference equations for photonics simulation. I. Beam propagation,” J. Lightwave Technol. 16, 134–141 (1998).
[CrossRef]

Y. A. Eremin, V. I. Ivakhnenko, “Modeling of light scattering by non-spherical inhomogeneous particles,” J. Quant. Spectrosc. Radiat. Transf. 60, 475–482 (1998).
[CrossRef]

H. Derudder, D. De Zutter, F. Olyslager, “Analysis of waveguide discontinuities using perfectly matched layers,” Electron. Lett. 34, 2138–2140 (1998).
[CrossRef]

G. R. Hadley, “Low-truncation-error finite difference equations for photonics simulation. II. Vertical-cavity surface-emitting lasers,” J. Lightwave Technol. 16, 142–151 (1998).
[CrossRef]

O. J. F. Martin, N. B. Piller, “Electromagnetic scatter-ing in polarizable backgrounds,” Phys. Rev. E 58, 3909–3915 (1998).
[CrossRef]

N. B. Piller, O. J. F. Martin, “Increasing the performances of the coupled-dipole approximation: a spectral approach,” IEEE Trans. Antennas Propag. 46, 1126–1137 (1998).
[CrossRef]

B. M. Nebeker, G. W. Starr, E. D. Hirleman, “Evaluation of iteration methods used when modeling scattering from features on surfaces using the discrete-dipole approximation,” J. Quant. Spectrosc. Radiat. Transf. 60, 493–500 (1998).
[CrossRef]

J.-J. He, B. Lamontagne, A. Delâge, L. Erickson, M. Davies, E. S. Koteles, “Monolithic integrated wavelength demultiplexer based on a waveguide rowland circle grating in InGaAs/InP,” J. Lightwave Technol. 16, 631–638 (1998).
[CrossRef]

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, “Light-coupling masks for lensless, sub-wavelength optical lithography,” Appl. Phys. Lett. 72, 2379–2381 (1998).
[CrossRef]

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, N. B. Piller, “Light-coupling masks: an alternative, lensless approach to high-resolution optical contact lithography,” J. Vac. Sci. Technol. B 16, 3422–3425 (1998).
[CrossRef]

1997 (3)

1996 (1)

1995 (2)

C. Girard, A. Dereux, O. J. F. Martin, M. Devel, “Generation of optical standing waves around mesoscopic surface structures: scattering and light confinement,” Phys. Rev. B 52, 2889–2898 (1995).
[CrossRef]

J. Willems, J. Haes, R. Baets, “The bidirectional mode expansion method for two-dimensional waveguides:  the TM case,” Opt. Quantum Electron. 27, 995–1007 (1995).
[CrossRef]

1994 (2)

1993 (4)

M. A. Taubenblatt, T. K. Tran, “Calculation of light scattering from particles and structures on a surface by the coupled-dipole method,” J. Opt. Soc. Am. A 10, 912–919 (1993).
[CrossRef]

J. B. Davies, “Finite element analysis of waveguides and cavities—a review,” IEEE Trans. Magn. 29, 1578–1583 (1993).
[CrossRef]

C. M. Herzinger, C. C. Lu, T. A. DeTemple, W. C. Chew, “The semiconductor waveguide facet reflectivity problem,” IEEE J. Quantum Electron. 29, 2273–2281 (1993).
[CrossRef]

W. P. Huang, C. L. Xu, “Simulation of three-dimensional optical waveguides by a full-vector beam propagation method,” IEEE J. Quantum Electron. 29, 2639–2646 (1993).
[CrossRef]

1992 (1)

J.-F. Lee, R. Palandech, R. Mittra, “Modeling three-dimensional discontinuities in waveguides using nonorthogonal FDTD algorithm,” IEEE Trans. Microwave Theory Tech. 40, 346–352 (1992).
[CrossRef]

1988 (1)

1984 (1)

G. W. Ford, W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

1980 (1)

A. D. Yaghjian, “Electric dyadic Green’s functions in the source region,” Proc. IEEE 68, 248–263 (1980).
[CrossRef]

Baets, R.

J. Willems, J. Haes, R. Baets, “The bidirectional mode expansion method for two-dimensional waveguides:  the TM case,” Opt. Quantum Electron. 27, 995–1007 (1995).
[CrossRef]

Basterrechea, J.

M. F. Cátedra, R. P. Torres, J. Basterrechea, E. Gago, The CG-FFT Method (Artech House, Boston, Mass., 1995).

Bell, P. M.

J. B. Pendry, P. M. Bell, “Transfer matrix techniques for electromagnetic waves,” in Photonic Band Gap Materials, Vol. 315 of NATO ASI Series, C. M. Soukoulis, ed. (Kluwer, Dordrecht, The Netherlands, 1996), pp. 203–228.

Beltrami, D. R.

D. R. Beltrami, J. D. Love, F. Ladouceur, “Multimode planar devices,” Opt. Quantum Electron. 31, 307–326 (1999).
[CrossRef]

Betty, I.

H. El-Refaei, D. Yevick, I. Betty, “Stable and nonitera-tive bidirectional beam propagation method,” IEEE Photonics Technol. Lett. 12, 389–391 (2000).
[CrossRef]

Biebuyck, H.

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, “Light-coupling masks for lensless, sub-wavelength optical lithography,” Appl. Phys. Lett. 72, 2379–2381 (1998).
[CrossRef]

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, N. B. Piller, “Light-coupling masks: an alternative, lensless approach to high-resolution optical contact lithography,” J. Vac. Sci. Technol. B 16, 3422–3425 (1998).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th. ed. (Pergamon, Oxford, 1987).

Cátedra, M. F.

M. F. Cátedra, R. P. Torres, J. Basterrechea, E. Gago, The CG-FFT Method (Artech House, Boston, Mass., 1995).

Chang, H.

Chew, W. C.

C. M. Herzinger, C. C. Lu, T. A. DeTemple, W. C. Chew, “The semiconductor waveguide facet reflectivity problem,” IEEE J. Quantum Electron. 29, 2273–2281 (1993).
[CrossRef]

W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE Press, Piscataway, N.J., 1995).

Danziger, Y.

E. Hasman, N. Davidson, Y. Danziger, A. A. Friesem, “Diffractive optics:  design, realization, and applications,” Fiber Integr. Opt. 16, 1–25 (1997).
[CrossRef]

Davidson, N.

E. Hasman, N. Davidson, Y. Danziger, A. A. Friesem, “Diffractive optics:  design, realization, and applications,” Fiber Integr. Opt. 16, 1–25 (1997).
[CrossRef]

Davies, J. B.

J. B. Davies, “Finite element analysis of waveguides and cavities—a review,” IEEE Trans. Magn. 29, 1578–1583 (1993).
[CrossRef]

Davies, M.

De Zutter, D.

H. Derudder, D. De Zutter, F. Olyslager, “Analysis of waveguide discontinuities using perfectly matched layers,” Electron. Lett. 34, 2138–2140 (1998).
[CrossRef]

Delâge, A.

Dereux, A.

Derudder, H.

H. Derudder, D. De Zutter, F. Olyslager, “Analysis of waveguide discontinuities using perfectly matched layers,” Electron. Lett. 34, 2138–2140 (1998).
[CrossRef]

DeTemple, T. A.

C. M. Herzinger, C. C. Lu, T. A. DeTemple, W. C. Chew, “The semiconductor waveguide facet reflectivity problem,” IEEE J. Quantum Electron. 29, 2273–2281 (1993).
[CrossRef]

Devel, M.

C. Girard, A. Dereux, O. J. F. Martin, M. Devel, “Generation of optical standing waves around mesoscopic surface structures: scattering and light confinement,” Phys. Rev. B 52, 2889–2898 (1995).
[CrossRef]

Draine, B. T.

El-Refaei, H.

H. El-Refaei, D. Yevick, I. Betty, “Stable and nonitera-tive bidirectional beam propagation method,” IEEE Photonics Technol. Lett. 12, 389–391 (2000).
[CrossRef]

Eremin, Y. A.

Y. A. Eremin, V. I. Ivakhnenko, “Modeling of light scattering by non-spherical inhomogeneous particles,” J. Quant. Spectrosc. Radiat. Transf. 60, 475–482 (1998).
[CrossRef]

Erickson, L.

Felsen, L. B.

L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (IEEE Press, Piscataway, N.J., 1994).

Flatau, P. J.

Ford, G. W.

G. W. Ford, W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

Friesem, A. A.

E. Hasman, N. Davidson, Y. Danziger, A. A. Friesem, “Diffractive optics:  design, realization, and applications,” Fiber Integr. Opt. 16, 1–25 (1997).
[CrossRef]

Gago, E.

M. F. Cátedra, R. P. Torres, J. Basterrechea, E. Gago, The CG-FFT Method (Artech House, Boston, Mass., 1995).

Gay-Balmaz, P.

M. Paulus, P. Gay-Balmaz, O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[CrossRef]

Girard, C.

Goedecke, G. H.

Gopinath, A.

R. Scarmozzino, A. Gopinath, R. Pregla, S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

P. R. Hayes, M. T. O’Keefe, P. R. Woodward, A. Gopinath, “High-order-compact time-domain numerical simulation of optical waveguides,” Opt. Quantum Electron. 31, 813–826 (1999).
[CrossRef]

Hadley, G. R.

Haes, J.

J. Willems, J. Haes, R. Baets, “The bidirectional mode expansion method for two-dimensional waveguides:  the TM case,” Opt. Quantum Electron. 27, 995–1007 (1995).
[CrossRef]

Hafner, C.

C. Hafner, Post-Modern Electromagnetics: Using Intelligent Maxwell Solvers (Wiley, Chichester, UK, 1999).

Hagness, S. C.

A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, Mass., 2000).

Hasman, E.

E. Hasman, N. Davidson, Y. Danziger, A. A. Friesem, “Diffractive optics:  design, realization, and applications,” Fiber Integr. Opt. 16, 1–25 (1997).
[CrossRef]

Hayes, P. R.

P. R. Hayes, M. T. O’Keefe, P. R. Woodward, A. Gopinath, “High-order-compact time-domain numerical simulation of optical waveguides,” Opt. Quantum Electron. 31, 813–826 (1999).
[CrossRef]

He, J.-J.

Helfert, S.

R. Scarmozzino, A. Gopinath, R. Pregla, S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

Helfert, S. F.

S. F. Helfert, R. Pregla, “Analysis of thin layers and discontinuities,” Opt. Quantum Electron. 31, 721–732 (1999).
[CrossRef]

Herzinger, C. M.

C. M. Herzinger, C. C. Lu, T. A. DeTemple, W. C. Chew, “The semiconductor waveguide facet reflectivity problem,” IEEE J. Quantum Electron. 29, 2273–2281 (1993).
[CrossRef]

Hirleman, E. D.

B. M. Nebeker, G. W. Starr, E. D. Hirleman, “Evaluation of iteration methods used when modeling scattering from features on surfaces using the discrete-dipole approximation,” J. Quant. Spectrosc. Radiat. Transf. 60, 493–500 (1998).
[CrossRef]

R. Schmehl, B. M. Nebeker, E. D. Hirleman, “Discrete-dipole approximation for scattering by features on surfaces by means of a two-dimensional fast Fourier transform technique,” J. Opt. Soc. Am. A 14, 3026–3036 (1997).
[CrossRef]

Hsueh, Y.

Huang, W.

Huang, W. P.

W. P. Huang, C. L. Xu, “Simulation of three-dimensional optical waveguides by a full-vector beam propagation method,” IEEE J. Quantum Electron. 29, 2639–2646 (1993).
[CrossRef]

Ivakhnenko, V. I.

Y. A. Eremin, V. I. Ivakhnenko, “Modeling of light scattering by non-spherical inhomogeneous particles,” J. Quant. Spectrosc. Radiat. Transf. 60, 475–482 (1998).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).

Kong, J. A.

J. A. Kong, Electromagnetic Wave Theory (Wiley, New York, 1986).

Koteles, E. S.

Ladouceur, F.

D. R. Beltrami, J. D. Love, F. Ladouceur, “Multimode planar devices,” Opt. Quantum Electron. 31, 307–326 (1999).
[CrossRef]

Lamontagne, B.

Lee, J.-F.

J.-F. Lee, R. Palandech, R. Mittra, “Modeling three-dimensional discontinuities in waveguides using nonorthogonal FDTD algorithm,” IEEE Trans. Microwave Theory Tech. 40, 346–352 (1992).
[CrossRef]

Loehr, J. P.

M. J. Noble, J. A. Lott, J. P. Loehr, “Quasi-exact optical analysis of oxide-apertured microcavity VCSEL’s using vector finite elements,” IEEE J. Quantum Electron. 34, 2327–2339 (1998).
[CrossRef]

Lott, J. A.

M. J. Noble, J. A. Lott, J. P. Loehr, “Quasi-exact optical analysis of oxide-apertured microcavity VCSEL’s using vector finite elements,” IEEE J. Quantum Electron. 34, 2327–2339 (1998).
[CrossRef]

Love, J. D.

D. R. Beltrami, J. D. Love, F. Ladouceur, “Multimode planar devices,” Opt. Quantum Electron. 31, 307–326 (1999).
[CrossRef]

Lu, C. C.

C. M. Herzinger, C. C. Lu, T. A. DeTemple, W. C. Chew, “The semiconductor waveguide facet reflectivity problem,” IEEE J. Quantum Electron. 29, 2273–2281 (1993).
[CrossRef]

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (Adam Hilger, Bristol, UK, 1986).

Marcuvitz, N.

L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (IEEE Press, Piscataway, N.J., 1994).

Martin, O. J. F.

M. Paulus, P. Gay-Balmaz, O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[CrossRef]

N. B. Piller, O. J. F. Martin, “Increasing the performances of the coupled-dipole approximation: a spectral approach,” IEEE Trans. Antennas Propag. 46, 1126–1137 (1998).
[CrossRef]

O. J. F. Martin, N. B. Piller, “Electromagnetic scatter-ing in polarizable backgrounds,” Phys. Rev. E 58, 3909–3915 (1998).
[CrossRef]

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, N. B. Piller, “Light-coupling masks: an alternative, lensless approach to high-resolution optical contact lithography,” J. Vac. Sci. Technol. B 16, 3422–3425 (1998).
[CrossRef]

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, “Light-coupling masks for lensless, sub-wavelength optical lithography,” Appl. Phys. Lett. 72, 2379–2381 (1998).
[CrossRef]

O. J. F. Martin, C. Girard, A. Dereux, “Dielectric vs. topographic contrast in near-field microscopy,” J. Opt. Soc. Am. A 13, 1801–1808 (1996).
[CrossRef]

C. Girard, A. Dereux, O. J. F. Martin, M. Devel, “Generation of optical standing waves around mesoscopic surface structures: scattering and light confinement,” Phys. Rev. B 52, 2889–2898 (1995).
[CrossRef]

O. J. F. Martin, A. Dereux, C. Girard, “Iterative scheme for computing exactly the total field propagating in dielectric structures of arbitrary shape,” J. Opt. Soc. Am. A 11, 1073–1080 (1994).
[CrossRef]

M. Paulus, O. J. F. Martin, “A fully vectorial technique for scattering and propagation in three-dimensional stratified photonic structures,” Opt. Quantum Electron. (to be published).

März, R.

R. März, Integrated Optics Design and Modeling (Artech House, Boston, Mass., 1994).

Michel, B.

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, “Light-coupling masks for lensless, sub-wavelength optical lithography,” Appl. Phys. Lett. 72, 2379–2381 (1998).
[CrossRef]

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, N. B. Piller, “Light-coupling masks: an alternative, lensless approach to high-resolution optical contact lithography,” J. Vac. Sci. Technol. B 16, 3422–3425 (1998).
[CrossRef]

Mittra, R.

J.-F. Lee, R. Palandech, R. Mittra, “Modeling three-dimensional discontinuities in waveguides using nonorthogonal FDTD algorithm,” IEEE Trans. Microwave Theory Tech. 40, 346–352 (1992).
[CrossRef]

Nebeker, B. M.

B. M. Nebeker, G. W. Starr, E. D. Hirleman, “Evaluation of iteration methods used when modeling scattering from features on surfaces using the discrete-dipole approximation,” J. Quant. Spectrosc. Radiat. Transf. 60, 493–500 (1998).
[CrossRef]

R. Schmehl, B. M. Nebeker, E. D. Hirleman, “Discrete-dipole approximation for scattering by features on surfaces by means of a two-dimensional fast Fourier transform technique,” J. Opt. Soc. Am. A 14, 3026–3036 (1997).
[CrossRef]

Noble, M. J.

M. J. Noble, J. A. Lott, J. P. Loehr, “Quasi-exact optical analysis of oxide-apertured microcavity VCSEL’s using vector finite elements,” IEEE J. Quantum Electron. 34, 2327–2339 (1998).
[CrossRef]

O’Brien, S. G.

O’Keefe, M. T.

P. R. Hayes, M. T. O’Keefe, P. R. Woodward, A. Gopinath, “High-order-compact time-domain numerical simulation of optical waveguides,” Opt. Quantum Electron. 31, 813–826 (1999).
[CrossRef]

Olyslager, F.

H. Derudder, D. De Zutter, F. Olyslager, “Analysis of waveguide discontinuities using perfectly matched layers,” Electron. Lett. 34, 2138–2140 (1998).
[CrossRef]

Palandech, R.

J.-F. Lee, R. Palandech, R. Mittra, “Modeling three-dimensional discontinuities in waveguides using nonorthogonal FDTD algorithm,” IEEE Trans. Microwave Theory Tech. 40, 346–352 (1992).
[CrossRef]

Paulus, M.

M. Paulus, P. Gay-Balmaz, O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[CrossRef]

M. Paulus, O. J. F. Martin, “A fully vectorial technique for scattering and propagation in three-dimensional stratified photonic structures,” Opt. Quantum Electron. (to be published).

Pendry, J. B.

J. B. Pendry, P. M. Bell, “Transfer matrix techniques for electromagnetic waves,” in Photonic Band Gap Materials, Vol. 315 of NATO ASI Series, C. M. Soukoulis, ed. (Kluwer, Dordrecht, The Netherlands, 1996), pp. 203–228.

Piller, N. B.

O. J. F. Martin, N. B. Piller, “Electromagnetic scatter-ing in polarizable backgrounds,” Phys. Rev. E 58, 3909–3915 (1998).
[CrossRef]

N. B. Piller, O. J. F. Martin, “Increasing the performances of the coupled-dipole approximation: a spectral approach,” IEEE Trans. Antennas Propag. 46, 1126–1137 (1998).
[CrossRef]

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, N. B. Piller, “Light-coupling masks: an alternative, lensless approach to high-resolution optical contact lithography,” J. Vac. Sci. Technol. B 16, 3422–3425 (1998).
[CrossRef]

Pregla, R.

R. Scarmozzino, A. Gopinath, R. Pregla, S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

S. F. Helfert, R. Pregla, “Analysis of thin layers and discontinuities,” Opt. Quantum Electron. 31, 721–732 (1999).
[CrossRef]

Scarmozzino, R.

R. Scarmozzino, A. Gopinath, R. Pregla, S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

Schmehl, R.

Schmid, H.

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, N. B. Piller, “Light-coupling masks: an alternative, lensless approach to high-resolution optical contact lithography,” J. Vac. Sci. Technol. B 16, 3422–3425 (1998).
[CrossRef]

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, “Light-coupling masks for lensless, sub-wavelength optical lithography,” Appl. Phys. Lett. 72, 2379–2381 (1998).
[CrossRef]

Starr, G. W.

B. M. Nebeker, G. W. Starr, E. D. Hirleman, “Evaluation of iteration methods used when modeling scattering from features on surfaces using the discrete-dipole approximation,” J. Quant. Spectrosc. Radiat. Transf. 60, 493–500 (1998).
[CrossRef]

Syms, R. R. A.

Taflove, A.

A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, Mass., 2000).

Tai, C.-T.

C.-T. Tai, Dyadic Green Function in Electromagnetic Theory (IEEE Press, Piscataway, N.J., 1994).

Taubenblatt, M. A.

Torres, R. P.

M. F. Cátedra, R. P. Torres, J. Basterrechea, E. Gago, The CG-FFT Method (Artech House, Boston, Mass., 1995).

Tran, T. K.

Weber, W. H.

G. W. Ford, W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

Welford, K.

K. Welford, “The method of attenuated total reflections,” in Surface Plasmon-Polaritons (Institute of Physics, Bristol, UK, 1988).

Willems, J.

J. Willems, J. Haes, R. Baets, “The bidirectional mode expansion method for two-dimensional waveguides:  the TM case,” Opt. Quantum Electron. 27, 995–1007 (1995).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th. ed. (Pergamon, Oxford, 1987).

Woodward, P. R.

P. R. Hayes, M. T. O’Keefe, P. R. Woodward, A. Gopinath, “High-order-compact time-domain numerical simulation of optical waveguides,” Opt. Quantum Electron. 31, 813–826 (1999).
[CrossRef]

Xu, C. L.

W. P. Huang, C. L. Xu, “Simulation of three-dimensional optical waveguides by a full-vector beam propagation method,” IEEE J. Quantum Electron. 29, 2639–2646 (1993).
[CrossRef]

Yaghjian, A. D.

A. D. Yaghjian, “Electric dyadic Green’s functions in the source region,” Proc. IEEE 68, 248–263 (1980).
[CrossRef]

Yang, M.

Yevick, D.

H. El-Refaei, D. Yevick, I. Betty, “Stable and nonitera-tive bidirectional beam propagation method,” IEEE Photonics Technol. Lett. 12, 389–391 (2000).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, “Light-coupling masks for lensless, sub-wavelength optical lithography,” Appl. Phys. Lett. 72, 2379–2381 (1998).
[CrossRef]

Electron. Lett. (1)

H. Derudder, D. De Zutter, F. Olyslager, “Analysis of waveguide discontinuities using perfectly matched layers,” Electron. Lett. 34, 2138–2140 (1998).
[CrossRef]

Fiber Integr. Opt. (1)

E. Hasman, N. Davidson, Y. Danziger, A. A. Friesem, “Diffractive optics:  design, realization, and applications,” Fiber Integr. Opt. 16, 1–25 (1997).
[CrossRef]

IEEE J. Quantum Electron. (3)

M. J. Noble, J. A. Lott, J. P. Loehr, “Quasi-exact optical analysis of oxide-apertured microcavity VCSEL’s using vector finite elements,” IEEE J. Quantum Electron. 34, 2327–2339 (1998).
[CrossRef]

C. M. Herzinger, C. C. Lu, T. A. DeTemple, W. C. Chew, “The semiconductor waveguide facet reflectivity problem,” IEEE J. Quantum Electron. 29, 2273–2281 (1993).
[CrossRef]

W. P. Huang, C. L. Xu, “Simulation of three-dimensional optical waveguides by a full-vector beam propagation method,” IEEE J. Quantum Electron. 29, 2639–2646 (1993).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

R. Scarmozzino, A. Gopinath, R. Pregla, S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

H. El-Refaei, D. Yevick, I. Betty, “Stable and nonitera-tive bidirectional beam propagation method,” IEEE Photonics Technol. Lett. 12, 389–391 (2000).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

N. B. Piller, O. J. F. Martin, “Increasing the performances of the coupled-dipole approximation: a spectral approach,” IEEE Trans. Antennas Propag. 46, 1126–1137 (1998).
[CrossRef]

IEEE Trans. Magn. (1)

J. B. Davies, “Finite element analysis of waveguides and cavities—a review,” IEEE Trans. Magn. 29, 1578–1583 (1993).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J.-F. Lee, R. Palandech, R. Mittra, “Modeling three-dimensional discontinuities in waveguides using nonorthogonal FDTD algorithm,” IEEE Trans. Microwave Theory Tech. 40, 346–352 (1992).
[CrossRef]

J. Lightwave Technol. (5)

J. Opt. Soc. Am. A (5)

J. Quant. Spectrosc. Radiat. Transf. (2)

B. M. Nebeker, G. W. Starr, E. D. Hirleman, “Evaluation of iteration methods used when modeling scattering from features on surfaces using the discrete-dipole approximation,” J. Quant. Spectrosc. Radiat. Transf. 60, 493–500 (1998).
[CrossRef]

Y. A. Eremin, V. I. Ivakhnenko, “Modeling of light scattering by non-spherical inhomogeneous particles,” J. Quant. Spectrosc. Radiat. Transf. 60, 475–482 (1998).
[CrossRef]

J. Vac. Sci. Technol. B (1)

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, N. B. Piller, “Light-coupling masks: an alternative, lensless approach to high-resolution optical contact lithography,” J. Vac. Sci. Technol. B 16, 3422–3425 (1998).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (4)

S. F. Helfert, R. Pregla, “Analysis of thin layers and discontinuities,” Opt. Quantum Electron. 31, 721–732 (1999).
[CrossRef]

D. R. Beltrami, J. D. Love, F. Ladouceur, “Multimode planar devices,” Opt. Quantum Electron. 31, 307–326 (1999).
[CrossRef]

J. Willems, J. Haes, R. Baets, “The bidirectional mode expansion method for two-dimensional waveguides:  the TM case,” Opt. Quantum Electron. 27, 995–1007 (1995).
[CrossRef]

P. R. Hayes, M. T. O’Keefe, P. R. Woodward, A. Gopinath, “High-order-compact time-domain numerical simulation of optical waveguides,” Opt. Quantum Electron. 31, 813–826 (1999).
[CrossRef]

Phys. Rep. (1)

G. W. Ford, W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
[CrossRef]

Phys. Rev. B (1)

C. Girard, A. Dereux, O. J. F. Martin, M. Devel, “Generation of optical standing waves around mesoscopic surface structures: scattering and light confinement,” Phys. Rev. B 52, 2889–2898 (1995).
[CrossRef]

Phys. Rev. E (2)

M. Paulus, P. Gay-Balmaz, O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
[CrossRef]

O. J. F. Martin, N. B. Piller, “Electromagnetic scatter-ing in polarizable backgrounds,” Phys. Rev. E 58, 3909–3915 (1998).
[CrossRef]

Proc. IEEE (1)

A. D. Yaghjian, “Electric dyadic Green’s functions in the source region,” Proc. IEEE 68, 248–263 (1980).
[CrossRef]

Other (15)

M. F. Cátedra, R. P. Torres, J. Basterrechea, E. Gago, The CG-FFT Method (Artech House, Boston, Mass., 1995).

C.-T. Tai, Dyadic Green Function in Electromagnetic Theory (IEEE Press, Piscataway, N.J., 1994).

J. B. Pendry, P. M. Bell, “Transfer matrix techniques for electromagnetic waves,” in Photonic Band Gap Materials, Vol. 315 of NATO ASI Series, C. M. Soukoulis, ed. (Kluwer, Dordrecht, The Netherlands, 1996), pp. 203–228.

A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, Mass., 2000).

C. Hafner, Post-Modern Electromagnetics: Using Intelligent Maxwell Solvers (Wiley, Chichester, UK, 1999).

J. A. Kong, Electromagnetic Wave Theory (Wiley, New York, 1986).

M. Born, E. Wolf, Principles of Optics, 6th. ed. (Pergamon, Oxford, 1987).

L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (IEEE Press, Piscataway, N.J., 1994).

W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE Press, Piscataway, N.J., 1995).

R. März, Integrated Optics Design and Modeling (Artech House, Boston, Mass., 1994).

H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (Adam Hilger, Bristol, UK, 1986).

M. Paulus, O. J. F. Martin, “A fully vectorial technique for scattering and propagation in three-dimensional stratified photonic structures,” Opt. Quantum Electron. (to be published).

A. D. Boardman, ed., Electromagnetic Surface Modes (Wiley, New York, 1982).

K. Welford, “The method of attenuated total reflections,” in Surface Plasmon-Polaritons (Institute of Physics, Bristol, UK, 1988).

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).

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Figures (13)

Fig. 1
Fig. 1

Typical geometry under study: Several scatterers with permittivity ε(r) are embedded in a stratified background composed of L layers with respective permittivity εi. Note that the first and last layers are semi-infinite media.

Fig. 2
Fig. 2

The Green’s tensor gives the electric field radiated at r by a dipole located at r, which (a) corresponds in an infinite homogeneous background to only direct radiation from r to r and (b) further includes in a stratified medium all possible reflections at the L1 interfaces.

Fig. 3
Fig. 3

Solving the scattering problem numerically requires that only the scatterers in the structure must be discretized. The sole constraint on the discretization is that a mesh cannot sit astride a boundary between two layers.

Fig. 4
Fig. 4

The incident field must be a solution of the wave equation for the stratified background. It can correspond, for example, (a) to a plane wave impinging on the system or (b) to a waveguide mode propagating in the stratified background.

Fig. 5
Fig. 5

A notch with a depth δ is etched in an InP/InGaAsP planar waveguide (permittivities εInP=10.05 and εInGaAsP=11.42; wavelength λ=1.55 µm). The layer thicknesses are given in the figure. The notch has a finite extension (1 µm) in both the x and the y directions.

Fig. 6
Fig. 6

Field amplitude at y=0 in the structure depicted in Fig. 5 illuminated with a TE0 mode propagating in the x direction. Three notch thicknesses are investigated: (a) δ=200 nm, (b) δ=400 nm, (c) δ=600 nm.

Fig. 7
Fig. 7

Field amplitude in the InGaAsP layer (z=-550 nm) for the geometry depicted in Fig. 6(c) (δ=600-nm notch). The system is illuminated with two different modes, (a) TE0 and (b) TM0, propagating in the x direction. The maximum amplitude of each incident mode is normalized to unity.

Fig. 8
Fig. 8

Attenuated total reflection excitation of a surface plasmon. An incident field propagating in the glass substrate (ε=2.25, λ=633 nm) impinges at a 40.03° angle onto a 100-nm-thick silver film (ε=-18.32+i0.5). This generates a surface plasmon propagating along the metal–vacuum interface. A 100×100×50-nm3 glass protrusion is deposited onto the silver surface. The electric field amplitude is shown. Note the scattering of the surface plasmon by the protrusion.

Fig. 9
Fig. 9

Field amplitude along the two dashed lines in Fig. 8 (y=0). Note the standing wave in the glass substrate and the localized plasmon field at the metal–vacuum, metal–glass, and glass–vacuum interfaces.

Fig. 10
Fig. 10

Field amplitude in a constant-height plane in vacuum (z=-155 nm) below the glass protrusion (Fig. 8). Both the scattering and the confinement of the surface plasmon by the protrusion are visible.

Fig. 11
Fig. 11

LCM for optical nanolithography. (a) The structures to be written in the photoresist are defined as protrusions on a soft polymer substrate. This structure can easily be decomposed into (b) a stratified background with (c) embedded scatterers of various permittivities. A bottom antireflection coating (BARC) is deposited between the substrate and the photoresist.

Fig. 12
Fig. 12

LCM with a 120×480×75 nm3 protrusion. An isosurface of the field intensity distribution transmitted in the photoresist is shown. Such an isosurface corresponds to the profile of the structure that will be developed in the photoresist.

Fig. 13
Fig. 13

(a) In a practical nanolithography experiment, reflections at the photoresist–substrate interface lead to a disturbing interference pattern in the photoresist. (b) To suppress this effect a 60-nm-thick BARC is deposited on the substrate. The electric field intensity is shown.

Equations (9)

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

E(r)=E(0)(r)+VdrG(r, r)·k02Δε(r)E(r),
Δε(r)=ε(r)-εκforrlayerκ.
G(r, r)=GD(r, r)+GI(r, r)r,r insamelayerκGI(r, r)r,r indifferentlayers,
E(r)=E0(r)+VdrGI(r, r)·k02Δε(r)E(r)+limδV0V-δVdrGD(r,r)·k02Δε(r)E(r)-L·Δε(r)εκE(r),
Ei=Ei0+j=1NGi,jI·k02ΔεjEjVj+jlayer κjiGi,jD·k02ΔεjEjVj+Mi·k02ΔεiEi-L·ΔεiεκEi,i=1 ,, N.
Mi=limδV0Vi-δVdrGD(ri, r)=23kκ2[(1-ikκRieff)exp(ikκRieff)-1]1,
Rieff=34πVi1/3.
L=131.
G(r, r)G(r-r).

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