Conclusion and Future Scopes

Abstract

The objective of this book was to present computational and analytical frameworks to critically analyse EM wave interaction with time-varying media, a problem that is gaining significant attention among physicists and engineers these days. In Chap. 1 (Introduction), we presented the various exotic properties of such time-periodic media, which are distinctly different from the conventional space-periodic media (metamaterials, photonic crystals, etc.). The motivation for exploring generic time-periodic modulation of medium properties (like medium permittivity) is further emphasized upon in Chap. 4. In Chap. 2, we developed the 1D-FDTD codes starting from the basic electromagnetic theory (Maxwell’s equations and boundary equations). In Chap. 3, we described the process of incorporating time-varying permittivity in the FDTD update equations. Applying these modified FDTD equations, we demonstrated the interaction between a single-frequency carrier EM wave and a dielectric slab having sinusoidally (Chap. 3) as well as step-periodically (Chap. 4) modulated permittivity. The phenomena like non-linear modulation, carrier wave suppression and parametric amplification are demonstrated with several numerical 1D-FDTD examples, which involve different slab-width, modulation index (or permittivity contrast) and modulating frequency values. Besides the computational EM technique (1D-FDTD), we formulated a quasi-analytical approach relying on the numerical solution of ODEs using MATLAB, to study EM wave propagation in infinitely extended space-invariant media, having time-modulated permittivity. Essentially this ODE approach applies variable-separable method on the electric flux density (or electric displacement) vector, generating coupled space-time ODEs, where the time-varying permittivity is embedded.