The paper is focused on reliable modeling and analysis of the effects connected with the resonant transformation of the field of a plane and density-modulated electron beam flying over the periodic rough boundary of a natural or artificial medium. In the paper such a medium occupies a part of the half-space, limited in thickness. Therefore, the numerous effects appeared due to transverse (in the thickness of the periodic structure) resonances, and the coupling of eigen regimes of two different periodic interfaces also contributes to the anomalies appearing due to excitation of the surface eigen waves of the periodic boundary interface that had been discussed in previous papers of this series.
2. Sirenko, Y., S. Sautbekov, N. Yashina, and K. Sirenko, "Diffraction radiation generated by a density-modulated electron beam flying over the periodic boundary of the medium section. II. Impact of true eigen waves," Progress In Electromagnetics Research B, Vol. 91, 9-17, 2021.
3. Sirenko, Y., S. Sautbekov, N. Yashina, and K. Sirenko, "Diffraction radiation generated by a density-modulated electron beam flying over the periodic boundary of the medium section. III. Anomalous and resonant phenomena," Progress In Electromagnetics Research B, Vol. 91, 143-155, 2021.
4. Cherenkov, P., "Visible radiation produced by electrons moving in a medium with velocities exceeding that of light," Physical Review, Vol. 52, 378-379, 1937.
5. Smith, S. and E. Purcell, "Visible light from localized surface charges moving across a grating," Physical Review, Vol. 92, No. 4, 1069-1073, 1953.
6. Jelley, J., Cherenkov Radiation and Its Applications, Pergamon Press, London, 1958.
7. Bolotovskiy, B. and G. Voskresenskiy, "Radiation of charged particles in periodic structures," Uspehi Fizicheskih Nauk, Vol. 94, No. 3, 378-416, 1968 (in Russian).
8. Frank, I., Vavilov-Cherenkov Radiation, Nauka, Moscow, 1988 (in Russian).
9. Shestopalov, V., The Smith-Purcell Effect, Nova Science Publishes, New York, 1998.
10. Sirenko, Y., P. Melezhik, A. Poyedinchuk, S. Sautbekov, A. Shmat’ko, K. Sirenko, A. Vertiy, and N. Yashina, "Radiation of electromagnetic waves induced by electron beam passage over artificial material periodic interfaces," An Essential Guide to Electrodynamics, Vol. Chapter 5, 169-206, N. Brewer (ed), Nova Science Publishers, New York, 2019.
11. Shestopalov, V., L. Litvinenko, S. Masalov, and V. Sologub, Wave Diffraction by Gratings, Kharkov State Univ, Press, Kharkov, 1973 (in Russian).
12. Shestopalov, V., A. Kirilenko, S. Masalov, and Y. Sirenko, Resonance Wave Scattering. Vol. 1. Diffraction Gratings, Naukova Dumka, Kiev, 1986 (in Russian).
13. Shestopalov, V. and Y. Sirenko, Dynamic Theory of Gratings, Naukova Dumka, Kiev, 1989 (in Russian).
14. Sirenko, Y., S. Strom, and (eds), Modern Theory of Gratings. Resonant Scattering: Analysis Techniques and Phenomena, Springer, New York, 2010.
15. Tretyakov, O., S. Tretyakova, and V. Shestopalov, "Electromagnetic wave radiation by electron beam mowing over diffraction grating," Radiotehnika I Elektronika, Vol. 10, No. 7, 1233-1243, 1965 (in Russian).
16. Shestopalov, V., A. Kirilenko, and S. Masalov, Matrix Convolution-Type Equations in the Diffraction Theory, Naukova Dumka, Kiev, 1984 (in Russian).
17. Shestopalov, V., Y. Tuchkin, A. Poyedinchuk, and Y. Sirenko, New Solution Methods for Direct and Inverse Problems of the Diffraction Theory. Analytical Regularization of the Boundary Value Problems in Electromagnetic Theory, Osnova, Kharkov, 1997 (in Russian).
18. Sirenko, Y., "On the validation of the method of semi-inversion of matrix operators in the problems of wave diffraction," Zhurnal Vychislitelnoy Matematiki I Matematicheskoy Fiziki, Vol. 23, No. 6, 1381-1391, 1983 (in Russian).
19. Shestopalov, V. and V. Shcherbak, "Matrix operators in diffraction problems," Izvestiya Vuzov. Radiofizika, Vol. 11, No. 2, 285-305, 1968 (in Russian).
20. Mittra, R. and S. Lee, Analytical Techniques in the Theory of Guided Waves, Macmillan, New York, 1971.
21. Kantorovich, L. and G. Akilov, Functional Analysis in Normed Spaces, Pergamon Press, New Work, 1982.
22. Shestopalov, V. and Y. Shestopalov, Spectral Theory and Excitation of Open Structures, The Institution of Electrical Engineers, London, 1996.
23. Sanchez-Palencia, E., Nonhomogeneous Media and Vibration Theory, Springer-Verlag, New York, 1980.
24. Kirilenko, A. and N. Yashina, "Relationship between the trapped-mode resonances and the excitation of quasimodes of open volumes," Soviet Technical Physics Letters, Vol. 6, No. 12, 652-653, 1980.