volume | PIER Journals

Abstract

The aim of this work is to study the parameter estimation of a nonlinear medium in terms of scattered electromagnetic fields.The surface parameters are defined in terms of linear and nonlinear components of susceptibility and permeability. A set of Maxwell's equations are derived for an inhomogeneous medium using Green's function and the scattered Electromagnetic fields solving integrodifferential equations. Mathematical formulas are simplified using wavelet based method. Susceptibility and permeability is assumed as a function of wavelet basis. For parameter estimation, least square method and inner product methods are used with wavelets as a basis function, which gives solutions for nonlinear integrodifferential equation. Both time and spatial domain analysis is done using wavelets, and parameter coefficients are obtained. It is found that in both the parameter estimation methods, least square estimation gives better results. At the end of the paper statistical analysis of the scattered signals is included by calculating the mean and covariance of the signals.

1. Seema, N., A. Sabouni, T. Desell, and A. Ashtari, Microwave Tomography, Global Optimization Parallelization and Performance, Springer, 2014.

2. Gao, J. K., Y. L. Qin, B. Deng, H. Q. Wang, J. Li, and X. Li, "Terahertz wide angle imaging and analysis on plane wave criteria based on inverse synthetic aperture techniques," J. Infrared Milli. Terahertz Waves, Vol. 31, 373-393, 2016.
doi:10.1007/s10762-016-0249-x

3. Shea, J. D., B. D. Van Veen, and S. C. Hagness, "A TSVD analysis of microwave inverse scattering for breast imaging," IEEE Transactions on Biomedical Engineering, Vol. 59, No. 4, 936-945, Apr. 2012.
doi:10.1109/TBME.2011.2176727

4. Nahata, A., J. T. Yardley, and T. F. Heinz, "A two dimensional imaging of CW THz radiation using electro-optic detection," Applied Physics Letters, Vol. 81, No. 6, 963-965, Aug. 2002.
doi:10.1063/1.1497190

5. Khulbe, M., H. Parthasarathy, and M. R. Tripathy, "Mathematical analysis and design of RF imaging techniques and signal processing using wavelets," International Journal of Signal and Imaging System Engineering, Inderscience Journal, Vol. 10, No. 6, 2017.

6. Chattopadhyay, G., C. Dengler, T. E. Bryllert, E. Schlecht, A. Skalare, I. Mehdi, and P. H. Siegel, "A 600 GHz imaging radar for contraband detection," 19th International Symposium on Space Terahertz Technology, 300-300, Groningen, Apr. 28-30, 2008.

7. Brasselel, S., "Polarization resolved nonlinear microscopy Applications to structure molecular and biological imaging," Advances in Optics and Photonics, Vol. 3, 205-271, 2011.
doi:10.1364/AOP.3.000205

8. Kumar, A., A. Basu, and S. K. Kaul, "Circuits and active antennas for ultrawide band pulse generation and transmission," Progress In Electromagnetic Research B, Vol. 23, 251-272, 2010.
doi:10.2528/PIERB10052103

9. William, W. H., W. C. Chew, and C. A. Ruwe, "A step frequency radar system for broadband microwave inverse scattering and imaging," Review of Progress in Quantitative Nondestructive Evaluation, 643-649, Springer, 1995.

10. Balanis, C. A., Antenna Theory Analysis and Design, 2nd Ed., Wiley, 1997.

11. Robert, B. W., Nonlinear Optics, 3rd Ed., Elsevier, 2008.

12. Derili, H. A., S. Schrabi, and A. Arzhang, "Two dimensional wavelets for numerical solution of integral equations," Mathematical Sciences, 2, 5, 6, 2012.

13. Khulbe, M., H. Parthasarathy, and M. R. Tripathy, "THz generation using nonlinear optics: Mathematical analysis and design of THz antennas," Advanced Electromagnetics Journal, Vol. 7, No. 1, Feb. 2018.

14. Khulbe, M., M. R. Triparty, and H. Parthasarathy, "Wavelet-based method for nonlinear inverse scattering problem using least mean square estimation," 2017 Progress In Electromagnetics Research Symposium --- Spring (PIERS), 496-501, St Petersburg, Russia, May 22-25, 2017.

Ms. Manisha Khulbe

Professor Harish Parthasarathy

Dr. Malay Ranjan Tripathy