Multiple Gaussian pulse interactions and scattering in the nonlinear layered dielectric structures have been examined. The Gaussian pulses with different centre frequencies and lengths are incident at oblique angles on the finite stack of nonlinear dielectric layers. The properties of the reflected and refracted waveforms and the effects of the structure and the incident pulses' parameters on the mixing process are discussed. It is shown that the efficiency of forward emission at the combinatorial frequency can be considerably increased when the wavelengths of interacting pulses are close to the edges of electromagnetic bandgap. Keywords: Gaussian pulse, nonlinear dielectric susceptibility, small nonlinearity, three-wave interaction, intensity of the scattered wave
INTRODUCTIONElectromagnetic pulses have been extensively studies in various contexts owing to their ubiquitous applications as information carriers. Driven by the practical needs, research in the physical phenomena underlying pulse propagation and scattering always attracted strong interest. While most studies in metamaterials and their prospective applications to date have been focused on the linear effects, nonlinear artificial materials have huge potential not only for controlling the waveforms but also for signal amplification and conversion between different frequency bands through nonlinear parametric processes [1-6]. The periodic and quasi-periodic layered semiconductor structures represent an important class of artificial electromagnetic media possessing natural nonlinearity. Therefore the study of pulsed signals in such structures has not only significant theoretical interest but also offers novel opportunities for the design of innovative nonlinear devices for microwave and THz applications. Nonlinear interactions of pulsed waveforms are usually analysed in the limiting cases of either short or long pulses in unbounded media. Recently, considerable attention has been attracted to pulse interactions in finite nonlinear structures. In order to explore the phenomenology of pulse mixing at the commensurate temporal and spatial scales, nonlinear scattering of two Gaussian pulses in the finite periodic nonlinear layered structures is considered in this paper. We have obtained a rigorous solution of the full-wave problem, which is applicable to both limiting cases of short and long pulses as well as to the case of resonance mixing of the pulses interacting at the scale commensurable with the structure periodicity. The effect of the structure parameters on nonlinear response and shape of the scattered waveform has been examined. It is demonstrated that the efficiency of the pulse mixing is enhanced by matching the central frequencies of both pump pulses with the periodic structure bandgap edges.