The optical theorem is a fundamental result that describes the energy budget of wave scattering phenomena. Most past formulations have been derived in the frequency domain and thus apply only to linear time-invariant (LTI) scatterers and background media. In this paper we develop a new theory of the electromagnetic form of the optical theorem directly in the time domain. The derived formulation covers not only the ordinary optical theorem but also the most general form of this result, known as the generalized optical theorem. The developed formulation provides a very general description of the optical theorem for arbitrary probing fields and general scatterers that can be electromagnetically nonlinear, time-varying, and lossy. In the derived formalism, both the scatterer and the background medium can be nonhomogeneous and anisotropic, but the background is assumed to be LTI and lossless. The derived results are illustrated with a computer simulation study of scattering in the presence of a corner reflector which acts as the background. Connections to prior work on the time-domain optical theorem under plane wave excitation in free space are also discussed.
Edwin A. Marengo,
"Generalized Optical Theorem in the Time Domain," Progress In Electromagnetics Research B,
Vol. 65, 1-18, 2016. doi:10.2528/PIERB15110506
3. Carney, P. S., J. C. Schotland, and E. Wolf, "Generalized optical theorem for reflection, transmission, and extinction of power for scalar fields," Phys. Rev. E, Vol. 70, 036611, 2004. doi:10.1103/PhysRevE.70.036611
4. Lytle II, D. R., P. S. Carney, J. C. Schotland, and E. Wolf, "Generalized optical theorem for reflection, transmission, and extinction of power for electromagnetic fields," Phys. Rev. E, Vol. 71, 056610, 2005. doi:10.1103/PhysRevE.71.056610
5. Marengo, E. A., "A new theory of the generalized optical theorem in anisotropic media," IEEE Trans. Antennas Propagat., Vol. 61, 2164-2179, Apr. 2013. doi:10.1109/TAP.2012.2233702
6. Dacol, D. K. and D. G. Roy, "Generalized optical theorem for scattering in inhomogeneous media," Phys. Rev. E, Vol. 72, 036609, 2005. doi:10.1103/PhysRevE.72.036609
7. Halliday, D. and A. Curtis, "Generalized optical theorem for surface waves and layered media," Phys. Rev. E, Vol. 79, 056603, 2008. doi:10.1103/PhysRevE.79.056603
8. Lu, L., Z. Ding, R. S. Zeng, and Z. He, "Retrieval of Green's function and generalized optical theorem for the scattering of complete dyadic fields," J. Acoust. Soc. Am., Vol. 129, 1935-1944, 2011. doi:10.1121/1.3553224
9. Douma, H., I. Vasconcelos, and R. Snieder, "The reciprocity theorem for the scattered field is the progenitor of the generalized optical theorem," J. Acoust. Soc. Am., Vol. 129, 2765-2771, 2011. doi:10.1121/1.3569728
10. Wapenaar, K. and H. Douma, "A unified optical theorem for scalar and vectorial wave fields," J. Acoust. Soc. Am., Vol. 131, 3611-3626, 2012. doi:10.1121/1.3701880
11. Small, A., J. Fung, and V. N. Manoharan, "Generalization of the optical theorem for light scattering from a particle at a planar interface," J. Opt. Soc. Am. A, Vol. 30, 2519-2525, 2013. doi:10.1364/JOSAA.30.002519
12. Mitri, F. G., "Optical theorem for two-dimensional (2D) scalar monochromatic acoustical beams in cylindrical coordinates," Ultrasonics, Vol. 62, 20-26, 2015. doi:10.1016/j.ultras.2015.02.019
13. Mitri, F. G. and G. T. Silva, "Generalization of the extended optical theorem for scalar arbitrary-shape acoustical beams in spherical coordinates," Phys. Rev. E, Vol. 90, 053204, 2014. doi:10.1103/PhysRevE.90.053204
14. Marengo, E. A. and J. Tu, "Optical theorem detectors for active scatterers," Waves in Random and Complex Media, Vol. 25, 682-707, 2015. doi:10.1080/17455030.2015.1080390
15. Gustafsson, M., I. Vakili, S. E. B. Keskin, D. Sjöberg, and C. Larsson, "Optical theorem and forward scattering sum rule for periodic structures," IEEE Trans. Antennas Propagat., Vol. 60, 3818-3826, 2012. doi:10.1109/TAP.2012.2201113
16. Zhang, L. and P. L. Marston, "Optical theorem for acoustic non-diffracting beams and application to radiation force and torque," Biomedical Optics Express, Vol. 4, 1610-1617, 2013. doi:10.1364/BOE.4.001610
17. Smotrova, E. I., V. O. Byelobrov, T. M. Benson, J. Ctyroky, R. Sauleau, and A. I. Nosich, "Optical theorem helps understand thresholds of lasing in microcavities with active region," IEEE J. Quantum Electronics, Vol. 47, 20-30, 2011. doi:10.1109/JQE.2010.2055836
18. Tsai, C.-H., S.-H. Chang, and S. H. Tseng, "Applying the optical theorem in a finite-difference time-domain simulation of light scattering," IEEE Trans. Antennas Propag., Vol. 58, 3091-3094, 2010. doi:10.1109/TAP.2010.2052556
19. De Hoop, A. T., "A time domain energy theorem for scattering of plane electromagnetic waves," Radio Science, Vol. 19, 1179-1184, 1984. doi:10.1029/RS019i005p01179
20. Karlsson, A., "On the time domain version of the optical theorem," Am. J. Phys., Vol. 68, 344-349, 2000. doi:10.1119/1.19437
21. Karlsson, A., "Some results extracted from the time domain version of the optical theorem," Radio Science, Vol. 38, No. 2, article 8008, 10 pages, 2003.
22. Štumpf, M. and I. E. Lager, "The time-domain optical theorem in antenna theory," IEEE Antennas and Wireless Propagation Letters, Vol. 14, 895-897, Apr. 2015. doi:10.1109/LAWP.2014.2384008
23. Marengo, E. A. and F. K. Gruber, "Optical-theorem-based coherent scatterer detection in complex environments," International Journal of Antennas and Propagation, Vol. 2013, article 231729, 12 pages, 2013.
24. Manson, G., K. Worden, and M. Wood, "Analysis of reciprocity breakdown in nonlinear systems," Modern Practice in Stress & Vibration Analysis, J. Physics, conf. series 382, paper 012031, IOP Publishing, 2012.
25. De Hoop, A. T., "Time-domain reciprocity theorems for electromagnetic fields in dispersive media," Radio Science, Vol. 22, 1171-1178, Dec. 1987. doi:10.1029/RS022i007p01171
26. Kong, J. A. and D. K. Cheng, "Modified reciprocity theorem for bianisotropic media," Proc. IEEE, Vol. 117, 349-350, Feb. 1970.
27. Jackson, J. D., Classical Electrodynamics, 3rd Ed., John Wiley & Sons, New York, NY, USA, 1999.
28. Marengo, E. A., "Nonuniqueness of optical theorem detectors," J. Opt. Soc. Am. A, Vol. 32, 1936-1942, 2015. doi:10.1364/JOSAA.32.001936
29. Marengo, E. A. and A. J. Devaney, "Time-dependent plane wave and multipole expansions of the electromagnetic field," J. Math. Phys., Vol. 39, 3643-3660, 1998. doi:10.1063/1.532457