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Final Report Summary - PEARL (Pulses in active and nonlinear metamaterials)

Artificial electromagnetic materials with novel functional capabilities have been a subject of active research during the last decade. Metamaterials (MMs) and photonic crystals (PhCs) together with modern nanofabrication technologies have shown enormous potential for diverse applications across the entire electromagnetic spectrum. Recently, nonlinear MMs and PhCs have attracted increasing interest as the prospective media for harmonic generation, waveform control and analogue signal processing.
The main objectives of PEARL project are to establish the fundamental properties of pulsed signals in nonlinear MMs and identify the associated mechanisms of waveform control. In particular, the three-wave mixing processes have been studied in the periodic and quasi-periodic semiconductor and anisotropic dielectric layered structures. The phenomenology of the electromagnetic pulse interactions and resonance enhancement of the combinatorial frequency generation in such structures has been investigated. The effects of external dc electric and magnetic bias, parameters of the constituent layers and the stacked configuration on the properties of pulsed waveforms scattered by the semiconductor and anisotropic dielectric based MM have been examined and assessed.
To elucidate the fundamental mechanisms and phenomenology of the distributed nonlinear mixing and combinatorial frequency generation in the nonlinear MMs and PhCs, the following problems have been addressed in the project:
• Nonlinear scattering and combinatorial frequency generation by three-wave mixing in
- anisotropic dielectric and semiconductor layers;
- periodic and quasi-periodic stacks of anisotropic dielectric and semiconductor layers;
- stacks of semiconductor layers with external dc electric or magnetic bias
• Gaussian pulse mixing and scattering by periodic and quasi-periodic stacks of
- anisotropic dielectric and semiconductor layers;
- semiconductor layers with external dc electric or magnetic bias.
The advanced analytical tools have been developed for modelling of the resonance nonlinear scattering and frequency mixing in the stacked layer with weak distributed nonlinearities and semiconductor layers with mobile carriers. The Transfer Matrix Method (TMM) has been generalised and adapted to the solution of the auxiliary canonical problems of linear and nonlinear scattering by individual semiconductor and anisotropic dielectric layers and their arrangements in finite periodic and quasi-periodic stacks. The analytical solutions have been obtained in the self-consistent problem formulation of the nonlinear scattering in the three-wave mixing process associated with the carrier mobility in the stacked semiconductor layers and nipi structures. The developed formalism has provided the enabling tools for the investigations of the mechanisms of combinatorial frequency generation in nonlinear layered structures and analysis of the stationary process of combinatorial frequencies generation by the nipi layers with drifting charges.

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