Tapering the Incident Field When Solving Problems of Electromagnetic Wave Scattering Over Finite-Size Random Surfaces

Introduction. An analysis of radio wave scattering over random surfaces frequently involves integral equations, which are solved by numerical methods. These methods are feasible only provided limited dimensions of the surface. The requirement of surface limitation leads to the appearance of edge currents, resulting in significant errors when calculating the radar cross section (RCS), particularly for grazing incident angles. The influence of edge currents is reduced by a function tapering the incident field amplitude. This function should satisfy the following requirements: to provide a low suppression of the field along the entire finite-size surface between its edges at the same time as decreasing the incident field amplitude to negligible values when approaching the edges. The incident field under the application of the tampering function should satisfy the wave equation with a minimum error. Although various tapering functions are applied for incident field amplitude (i.e. Gaussian, Thorsos, integral), none of them satisfies the aforementioned requirements.
Aim. To suggest a novel function for tapering the amplitude of an electromagnetic wave incident on a perturbed finite-size surface when calculating RCS. In comparison with the known functions, the proposed function must satisfy the entire set of requirements.
Materials and methods. A comparison of the proposed tapering function for incident field amplitude with the known tapering functions was performed, including the estimation of the error of satisfying the wave equation. To prove the applicability of the proposed tapering function, a mathematical modeling of the bistatic scatter diagram of a two-dimensional sea-like finite surface with a spatial Elfouhaily spectrum was carried out using Monte Carlo calculations in the Matlab environment.
Results. Compared to the known tapering functions, the proposed tapering function satisfies the entire set of requirements. The results of mathematical modeling showed that the proposed function for tapering the incident field amplitude provides acceptable accuracy of estimating the RCS of finite-size random surfaces.
Conclusion. A novel function for tapering the incident field amplitude was derived. This function reduces the influence of edge currents on the accuracy of RCS estimation of two-dimensional finite-size random surfaces, thus being instrumental for solving scattering problems.

1. Toporkov J. V., Awadallah R. S., Brown G. S. Issues related to the Use of a Gaussian-like Incident Field for Low-grazing-angle Scattering. J. Optical Society of America A. 1999, vol. 16, no. 1, pp. 176-187. doi: 10.1364/JOSAA.16.000176

2. Thorsos E. The validity of the Kirchhhoff Approximation for Rough Surface Scattering using Gaussian Roughness Spectrum. J. Acoustical Society of America. 1988, vol. 83, no. 1, pp. 78-92. doi: 10.1121/1.396188

3. Pan G., Zhang L. Closed Form Solution to the Incident Power of Gaussian-Like Beam for Scattering Problems. IEEE Trans. on antennas and propagation. 2019, vol. 67, no. 2, pp. 1364-1367. doi: 10.1109/TAP.2018.2884851

4. Zhang Y., Wang Y., Zheng H. EM Scattering from a Simple Water Surface composed of Two Time-varying Sinusoidal Waves. Proc. of IEEE Intern. Conf. on Computational Electromagnetics (ICCEM). 2020, vol. 8, pp. 200684-200694. doi: 10.1109/COMPEM.2019.8779021

5. Tsang L., Kong J. A., Ding K.-H., Ao C. O. Scattering of Electromagnetic Waves: Numerical Simulations. New York, John Wiley & Sons, 2001, 736 p. doi: 10.1002/0471224278

6. Ye H., Jin Y.-Q. Parameterization of the Tapered Incident Wave for Numerical Simulation of Electromagnetic Scattering from Rough Surface. IEEE Trans. on Antennas and Propagation. 2005, vol. 53, no. 3, pp. 1234-1237. doi: 10.1109/TAP.2004.842586

7. Borodin M. A., Leont'ev V. V. Analysis of the Accuracy of an Iterative Algorithm for Calculating the Field Scattered by a Rough Surface. J. of Communications Technology and Electronics. 2009, vol. 54, no. 9, pp. 989-994. doi: 10.1134/S1064226909090034

8. Xu X., Brekke C., Doulgeris A. P., Melandso F. Numerical Analysis of Microwave Scattering from Layered Sea Ice Based on the Finite Element Method. Remote sensing. 2018, vol. 10, no. 9, pp. 1-16. doi: 10.3390/rs10091332

9. Jun M., Guo L-X., Zeng H. Study on 1D Large-scale Rough Surface EM scattering at Low Grazing Incident Angle by Parallel MOM based on PC Clusters. Wave in Random and Complex Media. 2009, vol. 19, no. 4, pp. 585-599. doi: 10.1080/17455030903033190

10. Leont’ev V. V., Borodin M. A., Ignatieva O. A. Bistatic scattering diagrams of the sea surface covered with a monomolecular film of oil. Radio Engineering. 2012, no. 7, pp. 39-44. (In Russ.)

11. Toporkov J. V., Brown G. S. Numerical Simulations of Scattering from Time-varing Randomly Rough Surfaces. IEEE Trans. on Geoscience and Remote Sensing. 2000, vol. 38, no. 4, pp. 1616-1624. doi: 10.1109/36.851961

12. Johnson J. T., Toporkov J., Brown G. A Numerical Study of Backscattering from Time-evolving Sea Surfaces: Comparison of Hydrodynamic Models. IEEE Trans. on Geoscience and Remote Sensing. 2001, vol. 39, no. 11, pp. 2411-2420. doi: 10.1109/36.964977

13. Rino C. L., Crystal T. L., Koide A. K., Ngo H. D., Guthart H. Numerical Simulation of Backscatter from Linear and Nonlinear Ocean Surface Realization. Radio Science. 1991, vol. 26, no. 1, pp. 51-71. doi: 10.1029/90RS01687

14. Elfouhaily T., Chapron B., Katsaros K., Vandemark D. A Unified Directional Spectrum for Long and Shot Wind-driven Waves. J. of Geophysical Research. Oceans. 1997, vol. 102, no. C7, pp. 15781-15796. doi: 10.1029/97JC00467

15. Bourlier C., Saillard J., Berginc G. Intrinsic Infrared Radiation of the Sea Surface. Progress in Electromagnetics Research. 2000, vol. 27, pp. 185-335. doi: 10.2528/PIER99080103