## Light propagation and scattering in stratified media: a Green’s tensor approach

JOSA A, Vol. 18, Issue 4, pp. 854-861 (2001)

http://dx.doi.org/10.1364/JOSAA.18.000854

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### 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

**OCIS Codes**

(220.3740) Optical design and fabrication : Lithography

(230.0230) Optical devices : Optical devices

(240.0240) Optics at surfaces : Optics at surfaces

(240.6680) Optics at surfaces : Surface plasmons

(290.0290) Scattering : Scattering

(310.0310) Thin films : Thin films

**Citation**

Michael Paulus and Oliver J. F. Martin, "Light propagation and scattering in stratified media: a Green’s tensor approach," J. Opt. Soc. Am. A **18**, 854-861 (2001)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-4-854

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### References

- J. A. Kong, Electromagnetic Wave Theory (Wiley, New York, 1986).
- M. Born and E. Wolf, Principles of Optics, 6th. ed. (Pergamon, Oxford, 1987).
- L. B. Felsen and 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).
- R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
- W. P. Huang and C. L. Xu, “Simulation of three-dimensional optical waveguides by a full-vector beam propagation method,” IEEE J. Quantum Electron. 29, 2639–2646 (1993).
- G. R. Hadley, “Low-truncation-error finite difference equations for photonics simulation. I. Beam propagation,” J. Lightwave Technol. 16, 134–141 (1998).
- Y. Hsueh, M. Yang, and H. Chang, “Three-dimensional noniterative full-vectorial beam propagation method based on the alternating direction implicit method,” J. Lightwave Technol. 17, 2389–2397 (1999).
- H. El-Refaei, D. Yevick, and I. Betty, “Stable and nonitera-tive bidirectional beam propagation method,” IEEE Photonics Technol. Lett. 12, 389–391 (2000).
- Y. A. Eremin and V. I. Ivakhnenko, “Modeling of light scattering by non-spherical inhomogeneous particles,” J. Quant. Spectrosc. Radiat. Transf. 60, 475–482 (1998).
- C. Hafner, Post-Modern Electromagnetics: Using Intelligent Maxwell Solvers (Wiley, Chichester, UK, 1999).
- C. M. Herzinger, C. C. Lu, T. A. DeTemple, and W. C. Chew, “The semiconductor waveguide facet reflectivity problem,” IEEE J. Quantum Electron. 29, 2273–2281 (1993).
- J. Willems, J. Haes, and R. Baets, “The bidirectional mode expansion method for two-dimensional waveguides: the TM case,” Opt. Quantum Electron. 27, 995–1007 (1995).
- H. Derudder, D. De Zutter, and F. Olyslager, “Analysis of waveguide discontinuities using perfectly matched layers,” Electron. Lett. 34, 2138–2140 (1998).
- 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).
- J.-F. Lee, R. Palandech, and R. Mittra, “Modeling three-dimensional discontinuities in waveguides using nonorthogonal FDTD algorithm,” IEEE Trans. Microwave Theory Tech. 40, 346–352 (1992).
- P. R. Hayes, M. T. O’Keefe, P. R. Woodward, and A. Gopinath, “High-order-compact time-domain numerical simulation of optical waveguides,” Opt. Quantum Electron. 31, 813–826 (1999).
- A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, Mass., 2000).
- J. B. Davies, “Finite element analysis of waveguides and cavities—a review,” IEEE Trans. Magn. 29, 1578–1583 (1993).
- M. J. Noble, J. A. Lott, and 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).
- S. F. Helfert and R. Pregla, “Analysis of thin layers and discontinuities,” Opt. Quantum Electron. 31, 721–732 (1999).
- W. Huang and R. R. A. Syms, “Analysis of folded erbium-doped planar waveguide amplifiers by the method of lines,” J. Lightwave Technol. 17, 2658–2664 (1999).
- E. Hasman, N. Davidson, Y. Danziger, and A. A. Friesem, “Diffractive optics: design, realization, and applications,” Fiber Integr. Opt. 16, 1–25 (1997).
- D. R. Beltrami, J. D. Love, and F. Ladouceur, “Multimode planar devices,” Opt. Quantum Electron. 31, 307–326 (1999).
- J. B. Pendry and 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.
- G. H. Goedecke and S. G. O’Brien, “Scattering by irregular inhomogeneous particles via the digitized Green’s function algorithm,” Appl. Opt. 27, 2431–2438 (1988).
- B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
- P. J. Flatau, “Improvements in the discrete-dipole approximation method of computing scattering and absorption,” Opt. Lett. 22, 1205–1207 (1997).
- O. J. F. Martin and N. B. Piller, “Electromagnetic scatter-ing in polarizable backgrounds,” Phys. Rev. E 58, 3909–3915 (1998).
- M. A. Taubenblatt and 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).
- C. Girard, A. Dereux, O. J. F. Martin, and M. Devel, “Generation of optical standing waves around mesoscopic surface structures: scattering and light confinement,” Phys. Rev. B 52, 2889–2898 (1995).
- R. Schmehl, B. M. Nebeker, and 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).
- C.-T. Tai, Dyadic Green Function in Electromagnetic Theory (IEEE Press, Piscataway, N.J., 1994).
- M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E 62, 5797–5807 (2000).
- A. D. Yaghjian, “Electric dyadic Green’s functions in the source region,” Proc. IEEE 68, 248–263 (1980).
- N. B. Piller and O. J. F. Martin, “Increasing the performances of the coupled-dipole approximation: a spectral approach,” IEEE Trans. Antennas Propag. 46, 1126–1137 (1998).
- B. M. Nebeker, G. W. Starr, and 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).
- M. F. Cátedra, R. P. Torres, J. Basterrechea, and E. Gago, The CG-FFT Method (Artech House, Boston, Mass., 1995).
- G. W. Ford and W. H. Weber, “Electromagnetic interactions of molecules with metal surfaces,” Phys. Rep. 113, 195–287 (1984).
- J.-J. He, B. Lamontagne, A. Delâge, L. Erickson, M. Davies, and E. S. Koteles, “Monolithic integrated wavelength demultiplexer based on a waveguide rowland circle grating in InGaAs/InP,” J. Lightwave Technol. 16, 631–638 (1998).
- O. J. F. Martin, A. Dereux, and 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).
- M. Paulus and 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).
- O. J. F. Martin, C. Girard, and A. Dereux, “Dielectric vs. topographic contrast in near-field microscopy,” J. Opt. Soc. Am. A 13, 1801–1808 (1996).
- H. Schmid, H. Biebuyck, B. Michel, and O. J. F. Martin, “Light-coupling masks for lensless, sub-wavelength optical lithography,” Appl. Phys. Lett. 72, 2379–2381 (1998).
- H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, and 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).
- H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (Adam Hilger, Bristol, UK, 1986).

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