PIER B
 
Progress In Electromagnetics Research B
ISSN: 1937-6472
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 62 > pp. 29-47

SCATTERED FIELD IN RANDOM DIELECTRIC INHOMOGENEOUS MEDIA: A RANDOM RESOLVENT APPROACH

By E. Barzegar, S. J. L. van Eijndhoven, and M. C. van Beurden

Full Article PDF (315 KB)

Abstract:
In modeling electromagnetic phenomena randomness of the propagation medium and of the dielectric object should be taken up in the model. The usually applied Monte-Carlo based methods reveal true characteristics of the random electromagnetic field at the expense of large computation time and computer memory. Use of expansion based methods and their resulting algorithm is an efficient alternative. In this paper the focus is on characteristics of electromagnetic fields that satisfy integral equations where the integral kernel has a random component, typically, electromagnetic fields that describe scattering due to dielectric objects with an inhomogeneous random contrast field. The assumption is that the contrast is affinely related to a random variable. The integral equation is of second kind Fredholm type so that its solutions are determined by the resolvent, a random operator field. The key idea is to expand that operator field with respect to orthogonal polynomials defined by the probability measure on the underlying sample space and to derive the properties of the solution from that expansion. Two types of illustration are presented: an inhomogeneous dielectric slab and a 2D dielectric grating with 1D periodicity.

Citation:
E. Barzegar, S. J. L. van Eijndhoven, and M. C. van Beurden, "Scattered Field in Random Dielectric Inhomogeneous Media: a Random Resolvent Approach," Progress In Electromagnetics Research B, Vol. 62, 29-47, 2015.
doi:10.2528/PIERB14111304

References:
1. Hislop, G., "Measuring the thickness, permittivity and conductivity of layered earth," 8th European Conference on Antennas and Propagation (EuCAP), 3578-3581, The Hague, The Netherlands, 2014.

2. Van Rossum, W., F. Nennie, D. Deiana, A. J. van der Veen, and S. Monni, "Dielectric characterisation of human tissue samples," 8th European Conference on Antennas and Propagation (EuCAP), 524-528, The Hague, The Netherlands, 2014.

3. Garnier, J., "Wave propagation in one-dimensional random media," Panoramas et Synth’eses, Vol. 12, 101-138, 2001.

4. Klyatskin, V. I. and V. I. Tatarskii, "Statistical theory of wave propagation through random layered media,", Institute of Atmospheric Physics, Academy of Sciences of the USSR, (Translated from Izvestiya Vysshikha Uchebnykh Zavedenii, Radiofizika), Vol. 20, No. 7, 1040-1053, 1977 (original document sumitted 1976).

5. Ishimaru, A., "Wave propagation and scattering in random media and rough surfaces," Proceedings of the IEEE, Vol. 79, No. 10, 1359-1366, Oct. 1991.
doi:10.1109/5.104210

6. Metropolis, N. and S. Ulam, "The Monte Carlo method," Journal of the American Statistical Association, Vol. 44, No. 247, 335-341, 1949.
doi:10.1080/01621459.1949.10483310

7. Eckhardt, R., "Stan Ulam, John Neumann, and the Monte Carlo method," Los Alamos Science, Special Issue, Vol. 15, 131-137, 1987.

8. Tatarski, V. I., Wave Propagation in a Turbulent Medium, McGraw-Hill Book Company, INC, New York, 1961.

9. Blaunstein, N., "Theoretical aspects of wave propagation in random media based on quanty and statistical field theory," Progress In Electromagnetics Research, Vol. 47, 135-191, 2004.
doi:10.2528/PIER03111702

10. Jaynes, E. T., "Information theory and statistical mechanics," Physical Review, Vol. 106, No. 4, 620-630, 1957.
doi:10.1103/PhysRev.106.620

11. Einbu, J. M., "On the existence of a class of maximum-entropy probability density function," IEEE Transactions on Information Theory, Vol. 23, No. 6, 772-775, 1977.
doi:10.1109/TIT.1977.1055784

12. Wiener, N., "The homogeneous chaos," American Journal of Mathematics, Vol. 60, No. 4, 897-936, 1938.
doi:10.2307/2371268

13. D’Atona, G., A. Monti, F. Ponci, and L. Rocca, "Maximum entropy multivariate analysis of uncertain dynamical systems based on the Wiener-Askey polynomial chaos," IEEE Transactions on Instrumentation and Measurement, Vol. 56, No. 3, 689-965, 2007.
doi:10.1109/TIM.2007.894920

14. Smith, S. M., "Stochastic finite-difference time-domain,", Department of Electrical and Computer Engineering, University of Utah, 2011.

15. Alabaster, C. M., "The microwave properties of tissue and other lossy dielectrics,", Department of Aerospace, Power and Sensors, College of Defence Technology, Carnfield University, 2004.

16. Comite, D., A. Galli, E. Pettinelli, and G. Valerio, "Numerical analysis of the detection performance of ground coupled radars for different antenna systems and signal features," 8th European Conference on Antennas and Propagation (EuCAP), 3584-3586, The Hague, The Netherlands, 2014.

17. Petit, J., P. Boher, T. Leroux, P. Barritault, J. Hazart, and P. Chaton, "Improved CD and overlay metrology using an optical Fourier transform instrument," SPIE Metrology, Inspection, and Process Control for Microlithography XIX, Vol. 5752, 420-428, 2005.
doi:10.1117/12.599464

18. Ku, Y., H. Pang, W. Hsu, and D. Shyu, "Accuracy of diffraction-based overlay metrology using single array target," Optical Engineering, Vol. 48, No. 12, 123601-1-123601-7, 2009.
doi:10.1117/1.3275449

19. Lan, H., "Approximation solvability of nonlinear random (A, η)-resolvent operator equations with random relaxed cocoercive operators," Computers & Mathematics with Applications, Vol. 57, No. 4, 624-632, 2009.
doi:10.1016/j.camwa.2008.09.036

20. Gautschi, W., Orthogonal Polynomials Computation and Approximation, Oxford Science Publications, New York, 2004.

21. Capinski, M. and P. E. Kopp, Measure, Integral and Probability, 2nd Edition, Springer Undergraduate Mathematics Series , 2013.

22. Conway, J. B., A Course in Functional Analysis, Springer-Verlag, New York, 1985.
doi:10.1007/978-1-4757-3828-5

23. Szego, G., Orthogonal Polynomials, American Mathematical Society, New York, 1939.

24. Van Beurden, M. C., "Fast convergence with spectral volume integral equation for crossed block-shaped gratings with improved material interface conditions," Journal of the Optical Society of America A, Optics, Image Science and Vision, Vol. 28, No. 11, 2269-2278, 2011.
doi:10.1364/JOSAA.28.002269

25. Tijhuis, A. G., A. R. Bretones, P. D. Smith, and S. R. Cloude, Ultra-wideband, Short-pulse Electromagnetics, Vol. 5, 159–166, Kluwer Academic/Plenum Publishers, New York, United States of America , 2002.

26. Barzegar, E., M. C. van Beurden, S. J. L. van Eijndhoven, and A. G. Tijhuis, "Polynomial chaos for wave propagation in a one dimensional inhomogeneous slab," 8th European Conference on Antennas and Propagation (EuCAP), 1720-1723, The Hague, The Netherlands, 2014.

27. Coenen, T. J. and M. C. van Beurden, "A spectral volume integral method using geometrically conforming normal-vector fields," Progress In Electromagnetics Research, Vol. 142, 15-30, 2013.
doi:10.2528/PIER13060706

28. Li, L., "Use of fourier series in the analysis," Journal of the Optical Society of America A, 1870-1876, 1996.
doi:10.1364/JOSAA.13.001870

29. Koekoek, R. and R. F. Swarttouw, The Askey-scheme of Hypergeometric Orthogonal Polynomials and Its q-analogue, TU Delft, Faculty of Technical Mathematics and Informatics, Delf, Netherlands, 1998.


© Copyright 2010 EMW Publishing. All Rights Reserved