Space-Time Modulation in Lossy Dispersive Media and the Implications for Amplification and Shielding

We investigate the dispersion, attenuation, amplification, and the area of solutions of electromagnetic (EM) waves in a lossy progressively disturbed medium. Approximate, rigorous, and numerical methods are fully developed for a lossy environment, and the differences, merits, and drawbacks are discussed. A new representation of the Floquet theorem accounts for the loss exposed to both the pumped wave and the signal wave. The second-order small perturbation approximation is employed to yield closed-form solutions for transverse EM waves' dispersion relation. It is proven to be valid in small-perturbed lossy space-time-modulated (STM) media with nonsuperluminal modulation. Analyzing the dispersion relation, an elaborated sufficiency condition is proposed. Moreover, the nonunique solutions and abnormal effects created by the loss factor are analyzed thoroughly. The special harmonic amplification and shielding properties experienced in a lossy STM media are brought to attention throughout the process. The developed approximate and rigorous analytical results are finally compared to finite-difference time-domain (FDTD) simulations in a realistic test, where a signal is going through upconversion/downconversion in an STM medium. Finally, a set of useful conclusions, implications, and applications has been raised to give more insight into how amplification and shielding might be affected in a lossy STM environment.