Significant amplification of electromagnetic waves in disordered dispersive temporal multilayered structures with randomness in plasma frequency or dielectric permittivity

In this paper, two disordered temporal multilayered structures are proposed based on dispersive Lorentzian materials for amplification of electromagnetic waves in the frequency range of [25 GHz, 38 GHz] without using gain media. The first structure is composed of nondispersive dielectric and dispersive Lorentzian slabs alternatively. The electric permittivity of dispersive slabs is the same while the electric permittivity of nondispersive slabs changes randomly after the same time intervals. The averages of transmission and reflection coefficients of this structure are calculated versus the frequency of incident wave by employing the 4 × 4 temporal transfer matrix. This structure demonstrates the significant amplification of electromagnetic waves incident onto the structure for both forward and backward waves in the final medium at two different generated frequencies. It is shown that the increase of disorder level in the designed temporal structure leads to the enhancement of wave amplification. To indicate the effect of dispersion on the amount of amplification, the transmission and reflection coefficients are calculated for a disordered multilayered temporal structure composed of only nondispersive slabs. Our results confirm that the wave amplification in this nondispersive structure is so weaker compared to the structure containing dispersive materials. The effects of average of electric permittivity of nondispersive slabs are also investigated on the amount of wave amplification in the first proposed temporal disordered multilayered structure. The second disordered temporal structure proposed in this paper consists of spatially homogeneous dispersive Lorentzian materials whose plasma frequency changes abruptly and randomly after equal time intervals. This structure is also able to amplify the electromagnetic propagating through it efficiently. With increasing the disorder level and number of slabs existing in this structure, stronger amplification of incident wave can be observed. However, the temporal width of slabs should be selected suitably in order to achieve significant amplification.