## Numerical solutions of the Rayleigh equations for the scattering of light from a two-dimensional randomly rough perfectly conducting surface |

JOSA A, Vol. 31, Issue 5, pp. 1126-1134 (2014)

http://dx.doi.org/10.1364/JOSAA.31.001126

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### Abstract

We present rigorous, nonperturbative, purely numerical solutions of the Rayleigh equations for the scattering of

© 2014 Optical Society of America

**OCIS Codes**

(240.0240) Optics at surfaces : Optics at surfaces

(240.5770) Optics at surfaces : Roughness

(240.6680) Optics at surfaces : Surface plasmons

(290.5880) Scattering : Scattering, rough surfaces

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: January 28, 2014

Revised Manuscript: March 30, 2014

Manuscript Accepted: March 31, 2014

Published: April 30, 2014

**Virtual Issues**

Vol. 9, Iss. 7 *Virtual Journal for Biomedical Optics*

**Citation**

T. Nordam, P. A. Letnes, I. Simonsen, and A. A. Maradudin, "Numerical solutions of the Rayleigh equations for the scattering of light from a two-dimensional randomly rough perfectly conducting surface," J. Opt. Soc. Am. A **31**, 1126-1134 (2014)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-5-1126

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### References

- L. Tsang, C. Chan, and K. Pak, “Monte Carlo simulation of a two-dimensional random rough surface using the sparse-matrix flat-surface iterative approach,” Electron. Lett. 29, 1153–1154 (1993). [CrossRef]
- L. Tsang, C. H. Chan, and K. Pak, “Backscattering enhancement of a two-dimensional random rough surface (three-dimensional scattering) based on Monte Carlo simulations,” J. Opt. Soc. Am. A 11, 711–715 (1994). [CrossRef]
- K. Pak, L. Tsang, C. H. Chan, and J. Johnson, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces based on Monte Carlo simulations,” J. Opt. Soc. Am. A 12, 2491–2499 (1995). [CrossRef]
- J. T. Johnson, L. Tsang, R. T. Shin, K. Pak, C. H. Chan, A. Ishimaru, and Y. Kuga, “Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces: a comparison of Monte Carlo simulations with experimental data,” IEEE Trans. Antennas Propag. 44, 748–756 (1996). [CrossRef]
- D. Torrungrueng, H.-T. Chou, and J. Johnson, “A novel acceleration algorithm for the computation of scattering from two-dimensional large-scale perfectly conducting random rough surfaces with the forward-backward method,” IEEE Trans. Geosci. Remote Sens. 38, 1656–1668 (2000). [CrossRef]
- G. Soriano and M. Saillard, “Scattering of electromagnetic waves from two-dimensional rough surfaces with an impedance approximation,” J. Opt. Soc. Am. A 18, 124–133 (2001). [CrossRef]
- P. Tran, V. Celli, and A. A. Maradudin, “Electromagnetic scattering from a two-dimensional, randomly rough, perfectly conducting surface: iterative methods,” J. Opt. Soc. Am. A 11, 1686–1689 (1994). [CrossRef]
- P. Tran, “Calculation of the scattering of electromagnetic waves from a two-dimensional perfectly conducting surface using the method of ordered multiple interaction,” Waves Random Media 7, 295–302 (1997). [CrossRef]
- R. Wagner, J. Song, and W. Chew, “Monte Carlo simulation of electromagnetic scattering from two-dimensional random rough surfaces,” IEEE Trans. Antennas Propag. 45, 235–245 (1997). [CrossRef]
- I. Simonsen, A. A. Maradudin, and T. A. Leskova, “Scattering of electromagnetic waves from two-dimensional randomly rough perfectly conducting surfaces: the full angular intensity distribution,” Phys. Rev. A 81, 013806 (2010). [CrossRef]
- I. Simonsen, A. A. Maradudin, and T. Leskova, “The scattering of electromagnetic waves from two-dimensional randomly rough penetrable surfaces,” Phys. Rev. Lett. 104, 223904 (2010). [CrossRef]
- A. Madrazo and A. A. Maradudin, “Numerical solutions of the reduced Rayleigh equation for the scattering of electromagnetic waves from rough dielectric films on perfectly conducting substrates,” Opt. Commun. 134, 251–263 (1997). [CrossRef]
- I. Simonsen and A. A. Maradudin, “Numerical simulation of electromagnetic wave scattering from planar dielectric films deposited on rough perfectly conducting substrates,” Opt. Commun. 162, 99–111 (1999). [CrossRef]
- K. A. O’Donnell and E. R. Mendéz, “Enhanced specular peaks in diffuse light scattering from weakly rough metal surfaces,” J. Opt. Soc. Am. A 20, 2338–2346 (2003). [CrossRef]
- I. Simonsen, “Enhanced back and forward scattering in the reflection of light from weakly rough random metal surfaces,” Phys. Status Solidi B 247, 2075–2083 (2010). [CrossRef]
- I. Simonsen, “Optics of surface disordered systems: a random walk through rough surface scattering phenomena,” Eur. J. Phys. Spec. Top. 181, 1–103 (2010). [CrossRef]
- T. M. Elfouhaily and C.-A. Guérin, “A critical survey of approximate scattering wave theories from random rough surfaces,” Waves Random Media 14, R1–R40 (2004). [CrossRef]
- J. A. Kong, Electromagnetic Wave Theory (EMW, 2005).
- T. A. Leskova, P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “The scattering of light from two-dimensional randomly rough surfaces,” Proc. SPIE 8172, 817209 (2011). [CrossRef]
- T. Nordam, P. A. Letnes, I. Simonsen, and A. A. Maradudin, “Satellite peaks in the scattering of light from the two-dimensional randomly rough surface of a dielectric film on a planar metal surface,” Opt. Express 20, 11336–11350 (2012). [CrossRef]
- P. A. Letnes, A. A. Maradudin, T. Nordam, and I. Simonsen, “Calculation of the Mueller matrix for scattering of light from two-dimensional rough surfaces,” Phys. Rev. A 86, 031803 (2012). [CrossRef]
- P. A. Letnes, T. Nordam, and I. Simonsen, “Coherent effects in the scattering of light from two-dimensional rough metal surfaces,” J. Opt. Soc. Am. A 30, 1136–1145 (2013). [CrossRef]
- A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990). [CrossRef]
- I. Simonsen, J. B. Kryvi, A. A. Maradudin, and T. A. Leskova, “Light scattering from anisotropic, randomly rough, perfectly conducting surfaces,” Comput. Phys. Commun. 182, 1904–1908 (2011). [CrossRef]
- T. Nordam, P. Letnes, and I. Simonsen, “Numerical simulations of scattering of light from two-dimensional surfaces using the reduced Rayleigh equation,” Front. Phys. 1, 1–15 (2013). [CrossRef]
- W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd ed. (Cambridge University, 2007).
- “ScaLAPACK: Scalable linear algebra package,” www.netlib.org/scalapack/ (2012).
- Intel Math Kernel Library, http://software.intel.com/en-us/intel-mkl .
- From Fig. 1 it should be observed that the unit vector in the ϕ0 direction, ϕ^0, defines a vector normal to the plane of incidence. This way of defining the plane of incidence has the additional advantage of also being well-defined for normal incidence, and we will here assume this definition. Therefore when we for normal incidence say that the incident electromagnetic field is p polarized, it means that the electric field vector Ep(x|ω)inc lies in the x1x2 plane, but with a direction so that ϕ^0⊥Ep(x|ω)inc. Similarly, for an s-polarized field incident normally onto the surface we have ϕ^0∥Es(x|ω)inc.
- A. R. McGurn, A. A. Maradudin, and V. Celli, “Localization effects in the scattering of light from a randomly rough grating,” Phys. Rev. B 31, 4866–4871 (1985). [CrossRef]
- C. S. West and K. A. O’Donnell, “Observations of backscattering enhancement from polaritons on a rough metal surface,” J. Opt. Soc. Am. A 12, 390–397 (1995). [CrossRef]
- S. Y. Kim and K. Vedam, “Analytic solution of the pseudo-Brewster angle,” J. Opt. Soc. Am. A 3, 1772–1773 (1986). [CrossRef]
- R. M. A. Azzam, “Complex reflection coefficients of p- and s-polarized light at the pseudo-Brewster angle of a dielectric–conductor interface,” J. Opt. Soc. Am. A 30, 1975–1979 (2013). [CrossRef]
- A. G. Voronovich, “Rayleigh hypothesis,” in Light Scattering and Nanoscale Surface Roughness (Springer, 2007), pp. 93–106.
- T. Nordam, P. A. Letnes, and I. Simonsen, “Validity of the Rayleigh hypothesis for two-dimensional randomly rough metal surfaces,” J. Phys.: Conf. Ser. 454, 012033 (2013). [CrossRef]
- A. V. Tishchenko, “Numerical demonstration of the validity of the Rayleigh hypothesis,” Opt. Express 17, 17102–17117 (2009). [CrossRef]

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