A simple derivation of the general form of the optical theorem (GOT) is given for the case of a conservative scatterer in a homogeneous lossless medium, suitable for describing point sources and an observation region close to the scatterer. The presentation is based on the use of the operator approach and scalar wave equation in the limit of vanishingly small absorption. This approach does not require asymptotic estimates of rapidly oscillating integrals, does not use the integration of fluxes, which leads to the loss of information about the energy conservation law, and allows a natural generalization to the case of polarized radiation, as well as more complex multi-part fields. Such GOT generalizes the results known in the mathematical literature for models to the case of any conservative (real) scattering potential and arbitrary sources. 1. Bohren C.F., Huffman D.R. Absorption and Scattering of Light by Small Particles. John Wiley, Sons, New York, 1998, 530 p.
2. Jackson J.D. Classical Electrodynamics, 3rd edition, Wiley, New York, 1999, 808 p.
3. Newton R.G. Optical Theorem and Beyond // Am.J. Phys., 1976, Vol. 44, #7, pp. 639–642.
4. Van de Hulst H.C. Light Scattering by Small Particles // New York, Wiley, 1957, Dover, 1981.
5. Mishchenko M.I. The electromagnetic optical theorem revisited // JQSRT, 2006, #101, pp. 404–410.
6. Berg M. J., Sorensen C. M., and Chakrabarti A. Extinction and the optical theorem. Part I Single particles // J. Opt.Soc.Am, A 25, 2008, p. 1504.
7. Markel, V.A. Extinction, scattering and absorption of electromagnetic waves in the coupled- dipole approximation // JQSRT, 2019, #236, p. 106611.
8. Newton R.G. Scattering theory of waves and particles // McGraw-Hill, New York, 1968, 699 p.
9. Lytle D. R., Carney P.S., Schotland J.C., Wolf E. Generalized optical theorem for reflection, transmission, and extinction of power for electromagnetic fields // Phys. Rev. E, 2005, Vol. 71, #5.
10. Dacol D. K., Roy D.G. Generalized optical theorem for scattering in inhomogeneous media // Phys. Rev. E, 2005, Vol. 72, #3.
11. Marengo E.A. A new theory of the generalized optical theorem in anisotropic media // IEEE Trans. Antennas Propagat, 2013, #61, pp. 2164–2179.
12. Zhang L. Generalized optical theorem for an arbitrary incident field // J. Ac. Soc.Am., 2019, Vol. 145, #3, EL185–EL189.
13. Rondon I., Soto-Eguibar F. Generalized optical theorem for propagation invariant beams // Optik –2017, #137, pp. 17–24.
14. Eremin Yu.A., Sveshnikov A.G. Generalized optical theorem to a multipole source excitation in the scattering theory // Russian J. Math. Phys., 2017, #24, pp. 207–215.
15. Carney P.S. The optical cross-section theorem with incident fields containing evanescent components // J. Mod. Opt., 1999, #46, pp. 891–899.
16. Halliday D., Curtis A. Generalized optical theorem for surface waves and layered media // Phys. Rev., 2008, E79, p. 056603.
17. Marengo E. A., Tu J. Generalized optical theorem in the time domain // Prog. Electromagn. Res., 2016, #65, pp. 1–18.
18. Marengo E. A., Tu J. Optical theorem for transmission lines // Prog. Electromagn. Res., 2014, #61, pp. 253–268.
19. Athanasiadis C., Martin P.A., Spyropoulos A. Stratis I.G. Scattering relations for point sources: Acoustic and electromagnetic waves // J. Math. Phys., 2002, Vol. 43, #11, pp. 5683–5697.
20 Apresyan L.A., and Kravtsov Yu.A. Radiation Transfer: Statistical and Wave Aspects (M.: Nauka.-1983, in Russian, Engl. expanded ed.: Gordon and Breach, Amsterdam. – 1996).
21. Vladimirov V.S. Equations of mathematical physics // New York, M. Dekker, 1971.
22. Reed M. C., Simon B. Methods of modern mathematical physics. Analysis of operators. 4 // Academic Press, 1978, 325 p.
23. Margerin L., Sato H. Generalized optical theorems for the reconstruction of Green’s function of an inhomogeneous elastic medium // J. Acoust.Soc.Am., 2011, Vol. 130, #6, pp. 3674–3690.

• Previous article
• Next article

• energy conservation
• generalized optical theorem
• single scatterer
• point sources
• near-and far-field observations