## Near- to far-field transformation in the aperiodic Fourier modal method |

Applied Optics, Vol. 52, Issue 28, pp. 6962-6968 (2013)

http://dx.doi.org/10.1364/AO.52.006962

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### Abstract

This paper addresses the task of obtaining the far-field spectrum for a finite structure given the near-field calculated by the aperiodic Fourier modal method in contrast-field formulation (AFMM-CFF). The AFMM-CFF efficiently calculates the solution to Maxwell’s equations for a finite structure by truncating the computational domain with perfectly matched layers (PMLs). However, this limits the far-field solution to a narrow strip between the PMLs. The Green’s function for layered media is used to extend the solution over the whole super- and substrate. The approach is validated by applying it to the problem of scattering from a cylinder for which the analytical solution is available. Moreover, a numerical study is conducted on the accuracy of the approximate far-field computed with the super-cell Fourier modal method by using the AFMM-CFF with near- to far-field transformation as a reference.

© 2013 Optical Society of America

**OCIS Codes**

(000.4430) General : Numerical approximation and analysis

(050.1755) Diffraction and gratings : Computational electromagnetic methods

(290.2558) Scattering : Forward scattering

**ToC Category:**

Scattering

**History**

Original Manuscript: July 17, 2013

Revised Manuscript: August 22, 2013

Manuscript Accepted: August 29, 2013

Published: October 1, 2013

**Citation**

Ronald Rook, Maxim Pisarenco, and Irwan D. Setija, "Near- to far-field transformation in the aperiodic Fourier modal method," Appl. Opt. **52**, 6962-6968 (2013)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-52-28-6962

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### References

- M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995). [CrossRef]
- M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077–1086 (1995). [CrossRef]
- G. Bao, L. Cowsar, and W. Masters, eds., Mathematical Modeling in Optical Science (Frontiers in Applied Mathematics) (Society for Industrial Mathematics, 2001).
- M. Pisarenco, J. Maubach, I. Setija, and R. Mattheij, “Aperiodic Fourier modal method in contrast-field formulation for simulation of scattering from finite structures,” J. Opt. Soc. Am. A 27, 2423–2431 (2010). [CrossRef]
- M. Pisarenco, J. Maubach, I. Setija, and R. Mattheij, “Modified S-matrix algorithm for the aperiodic Fourier modal method in contrast-field formulation,” J. Opt. Soc. Am. A 28, 1364–1371 (2011). [CrossRef]
- M. Pisarenco, J. M. L. Maubach, I. D. Setija, and R. M. M. Mattheij, “Efficient solution of Maxwell’s equations for geometries with repeating patterns by an exchange of discretization directions in the aperiodic Fourier modal method,” J. Comput. Phys. 231, 8209–8228 (2012). [CrossRef]
- M. Pisarenco, “Scattering from finite structures: an extended Fourier modal method,” Ph.D. thesis (Eindhoven University of Technology, 2011).
- J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994). [CrossRef]
- J. P. Hugonin and P. Lalanne, “Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization,” J. Opt. Soc. Am. A 22, 1844–1849 (2005). [CrossRef]
- O. M. Bucci, C. Gennarelli, and C. Savarese, “Fast and accurate near-field-far-field transformation by sampling interpolation of plane-polar measurements,” IEEE Trans. Antennas Propag. 39, 48–55 (1991). [CrossRef]
- A. Taaghol and T. K. Sarkar, “Near-field to near/far-field transformation for arbitrary near-field geometry, utilizing an equivalent magnetic current,” IEEE Trans. Electromag. Compat. 38, 536–542 (1996).
- T. K. Sarkar and A. Taaghol, “Near-field to near/far-field transformation for arbitrary near-field geometry utilizing an equivalent electric current and MoM,” IEEE Trans. Antennas Propag. 47, 566–573 (1999). [CrossRef]
- P.-W. Zhai, Y.-K. Lee, G. W. Kattawar, and P. Yang, “Implementing the near- to far-field transformation in the finite-difference time-domain method,” Appl. Opt. 43, 3738–3746 (2004). [CrossRef]
- P. Török, P. R. Munro, and E. E. Kriezis, “Rigorous near- to far-field transformation for vectorial diffraction calculations and its numerical implementation,” J. Opt. Soc. Am. A 23, 713–722 (2006). [CrossRef]
- A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
- K. A. Michalski and D. Zheng, “Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media. I—Theory,” IEEE Trans. Antennas Propag. 38, 335–344 (1990). [CrossRef]
- J. R. Wait, Electromagnetic Waves in Stratified Media (IEEE/OUP Series on Electromagnetic Wave Theory) (Oxford University, 1996).
- R. Cools and K. Kim, “A survey of known and new cubature formulas for the unit disk,” J. Appl. Math. Comput. 7, 477–485 (2000).
- A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, 1990).
- R. Courant and D. Hilbert, Methods of Mathematical Physics (Interscience, 1953).
- C. W. Clenshaw and A. R. Curtis, “A method for numerical integration on an automatic computer,” Numer. Math. 2, 197–205 (1960). [CrossRef]
- A. David, H. Benisty, and C. Weisbuch, “Fast factorization rule and plane-wave expansion method for two-dimensional photonic crystals with arbitrary hole-shape,” Phys. Rev. B 73, 075107 (2006). [CrossRef]
- J. Saarinen, E. Noponen, and J. P. Turunen, “Guided-mode resonance filters of finite aperture,” Opt. Eng. 34, 2560–2566 (1995). [CrossRef]

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