volume | PIER Journals

Abstract

An alternative formulation of the Small Perturbation Method (SPM) in solving electromagnetic scattering from multi-layer random rough surfaces to resolve singularities in spectral integrals is presented. Non-monotonic permittivity changes will allow a multi-layer structure with flat interfaces to support guided modes. The presence of these guided modes translates to poles in the zeroth order Green's function of the media for the surface fields. The poles appear in the first and second order perturbation solutions based on a iterative procedure. Thus, evaluating the spectral integrals to obtain the spatial fields becomes problematic. The Sommerfeld integration path instead of real line integrals is introduced by analytic continuation of the integrand into complex spectral space. It is verified that this alternative spectral integration method is valid for both monotonic and non-monotonic cases.

1. Tabatabaeenejad, A. and M. Moghaddam, "Bistatic scattering from three-dimensional layered rough surfaces," IEEE Transactions on Geoscience and Remote Sensing, Vol. 44, No. 8, 2102-2114, 2006.
doi:10.1109/TGRS.2006.872140 Google Scholar

2. Imperatore, P., A. Iodice, and D. Riccio, "Electromagnetic wave scattering from layered structures with an arbitrary number of rough interfaces," IEEE Transactions on Geoscience and Remote Sensing, Vol. 47, No. 4, 1056-1072, 2009.
doi:10.1109/TGRS.2008.2007804 Google Scholar

3. Zamani, H., A. Tavakoli, and M. Dehmollaian, "Second-order perturbative solution of scattering from two rough surfaces with arbitrary dielectric profiles," IEEE Transactions on Antennas and Propagation, Vol. 63, No. 12, 5767-5776, 2015.
doi:10.1109/TAP.2015.2484387 Google Scholar

4. Zamani, H., A. Tavakoli, and M. Dehmollaian, "Scattering from layered rough surfaces: Analytical and numerical investigations," IEEE Transactions on Geoscience and Remote Sensing, Vol. 54, No. 6, 3685-3696, 2016.
doi:10.1109/TGRS.2016.2524639 Google Scholar

5. Sanamzadeh, M., L. Tsang, J. T. Johnson, R. J. Burkholder, and S. Tan, "Scattering of electromagnetic waves from 3d multilayer random rough surfaces based on the second-order small perturbation method: Energy conservation, reflectivity, and emissivity," JOSA A, Vol. 34, No. 3, 395-409, 2017.
doi:10.1364/JOSAA.34.000395 Google Scholar

6. Burkholder, R. J., J. T. Johnson, M. Sanamzadeh, L. Tsang, and S. Tan, "Microwave thermal emission characteristics of a two-layer medium with rough interfaces using the second-order small perturbation method," IEEE Geoscience and Remote Sensing Letters, Vol. 14, No. 10, 1780-1784, 2017.
doi:10.1109/LGRS.2017.2735421 Google Scholar

7. Wu, C. and X. Zhang, "Second-order perturbative solutions for 3-d electromagnetic radiation and propagation in a layered structure with multilayer rough interfaces," IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Vol. 8, No. 1, 180-194, 2015.
doi:10.1109/JSTARS.2014.2320506 Google Scholar

8. Tabatabaeenejad, A. and M. Moghaddam, "Study of validity region of small perturbation method for two-layer rough surfaces," IEEE Geoscience and Remote Sensing Letter, Vol. 7, No. 2, 319-323, 2010.
doi:10.1109/LGRS.2009.2034543 Google Scholar

9. Johnson, J. T., "Third-order small-perturbation method for scattering from dielectric rough surfaces," Journal of the Optical Society of America A, Vol. 16, No. 11, 2720-2736, 1999.
doi:10.1364/JOSAA.16.002720 Google Scholar

10. Demir, M. A. and J. T. Johnson, "Fourth and higher-order small perturbation solution for scattering from dielectric rough surfaces," Journal of the Optical Society of America A, Vol. 20, No. 12, 2330-2337, 2003.
doi:10.1364/JOSAA.20.002330 Google Scholar

11. Demir, M. A., J. T. Johnson, and T. J. Zajdel, "A study of the fourth-order small perturbation method for scattering from two-layer rough surfaces," IEEE Transactions on Geoscience and Remote Sensing, Vol. 50, No. 9, 3374-3382, 2012.
doi:10.1109/TGRS.2011.2182614 Google Scholar

12. Wang, T., L. Tsang, J. T. Johnson, and S. Tan, "Scattering and transmission of waves in multiple random rough surfaces: Energy conservation studies with the second order small perturbation method," Progress In Electromagnetics Research, Vol. 157, 120, 2016. Google Scholar

13. Tan, S., M. Aksoy, M. Brogioni, G. Macelloni, M. Durand, K. C. Jezek, T. L. Wang, L. Tsang, J. T. Johnson, M. R. Drinkwater, and L. Brucker, "Physical models of layered polar firn brightness temperatures from 0.5 to 2 GHz," IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Vol. 8, No. 7, 3681-3691, 2015.
doi:10.1109/JSTARS.2015.2403286 Google Scholar

14. Sanchez-Gil, J. A., A. A. Maradudin, J. Q. Lu, V. D. Freilikher, M. Pustilnik, and I. Yurkevich, "Scattering of electromagnetic waves from a bounded medium with a random surface," Phys. Rev. B, Vol. 50, 15353-15368, Nov. 1994. Google Scholar

15. Freilikher, V., M. Pustilnik, and I. Yurkevich, "Wave scattering from a bounded medium with disorder," Physics Letters A, Vol. 193, No. 5, 467-470, 1994.
doi:10.1016/0375-9601(94)90541-X Google Scholar

16. Piegari, A. and F. Flory, Optical Thin Films and Coatings: From Materials to Applications, Woodhead Publishing Elsevier, 2013.

17. Duan, X. and M. Moghaddam, "3-d vector electromagnetic scattering from arbitrary random rough surfaces using stabilized extended boundary condition method for remote sensing of soil moisture," IEEE Transactions on Geoscience and Remote Sensing, Vol. 50, No. 1, 87-103, 2011.
doi:10.1109/TGRS.2011.2160549 Google Scholar

18. Tsang, L. and J. A. Kong, Scattering of Electromagnetic Waves, Vol. 3: Advanced Topics, Wiley Interscience, 2001.
doi:10.1002/0471224278

Dr. Mohammadreza Sanamzadeh

Professor Leung Tsang

Professor Joel Tidmore Johnson

Prof. Robert J. Burkholder

Professor Shurun Tan