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.
Robert J. Burkholder,
"Electromagnetic Scattering from One Dimensional Random Rough Surfaces of Dielectric Layered Media with Waveguide Modes Using Second Order Small Perturbation Method," Progress In Electromagnetics Research B,
Vol. 80, 1-17, 2018. doi:10.2528/PIERB17101005
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
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
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
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
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
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
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
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
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
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
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
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.
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
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.
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
16. Piegari, A. and F. Flory, Optical Thin Films and Coatings: From Materials to Applications, Woodhead Publishing Elsevier, Cambridge, 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
18. Tsang, L. and J. A. Kong, Scattering of Electromagnetic Waves, Vol. 3: Advanced Topics, Wiley Interscience, 2001. doi:10.1002/0471224278