Radiation of a charge flying from vacuum into anisotropic dispersive medium

1. Sergey N. Galyamin, Andrey V. Tyukhtin Radiophysics Department, Physical faculty, Saint Petersburg State University Radiation of a charge flying from vacuum into anisotropic dispersive medium

2. Formulation of the problem Detailed investigation of the structure of the electromagnetic field Taking into account the specific frequency dispersion and losses Goals: Vacuum – аnisotropic plasma-like medium interface vacuum R q 0

3. Motivation Vacuum – “left-handed medium” (LHM) interface Reversed Cherenkov-transition radiation (RCTR) occurs in both vacuum and medium vacuum Isotropic LHM: reversed VCR: Left-handed frequency band

4. Spatial distribution of the Fourier harmonic Motivation Vacuum – “left-handed medium” (LHM) interface – lines parallel to the Poyting vector of VCR – lines parallel to the Poyting vector of RCTR in medium – lines parallel toi Poyting vector of RCTR in vacuum

5. сm nC (Vm–1s) Motivation Field spectrum in vacuum

6. Solution of the problem Vacuum – аnisotropic plasma-like medium interface V.L. Ginzburg, V.N. Tsytovich. “Transition radiation and transition scattering» Self-field of the charge Scattered field Vavilov-Cherenkov radiation (VCR): Reversed Cherenkov – transition radiation (RCTR) Transitionradiation (TR)

7. Anisotropic plasma-like medium guasistatic (“quasiqulomb”) field wave field (VCR) Self-field of the charge – cuts – branchpoints

8. Anisotropic plasma-like medium Self-field of the charge backward radiation forward radiation in units of

9. Numerical approach Fourier harmonics of the scattered field Fourier harmonics of the scattered field Analytical investigation of the integrands behavior, choosing the appropriate integration step and integration interval Asymptotic representation in the far field zone (with respect to the incident point) Total scattered field Numerical investigation of the integrands behavior, choosing the appropriate integration step and interval Impact of losses in medium on the radiation field Scattered field Vacuum – anisotropic plasma-like medium interface Analytical approach “Half-shadow” regions estimation

10. Scattered field Vacuum – anisotropic plasma-like medium interface Field in vacuum, the case of backward VCR: Analytical approach RCTR

11. Spherical wave of TR: Cylindrical wave of RCTR: Results Vacuum – anisotropic plasma-like medium interface Conditions of the RCTR existence in vacuum Field asymptoticin vacuum, “half-shadow” regions

12. Spatial distribution of the Fourier harmonic Results – lines parallel to the Poyting vector of VCR – lines parallel to the Poyting vector of RCTR in medium – lines parallel toi Poyting vector of RCTR in vacuum

13. Spatial distribution of the Fourier harmonic Results

14. nC cm Field spectrum in vacuum Results (Am–1s)

15. сm nC (Am–1s) Vacuum – “left-handed medium” (LHM) interface

16. nC Time evolution of the total field Results

17. Conclusion Investigation of the electromagnetic field generated at a charge flight from vacuum into anisotropic plasma-like medium Reversed Cherenkov-Transition Radiation (RCTR) • Analytical approach: • Rigorous condition of the RCTR presence • Spatial structure of the far-field Fourier harmonics • “Half-shadow” areas • Impact of losses • Numerical approach: • Field spectrum results • Time evolution of the total field • Possibility of the RCTR dominance in the total field

18. Thank you for your attention!