NONLINEAR RESONANT OPTICAL PHENOMENA AND SOLITONS IN POLARITONIC PHOTONIC CRYSTALS

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This project aims to provide a detailed theoretical understanding of the individual and collective nonlinear dynamics of solitary waves in a special class of artificial materials, namely Polaritonic Photonic Crystals (PPCs). With this generic term we refer to those structures that combine the Bragg periodicity typical of Photonic Crystals and the material resonances due to the existence of quasi-particles existing in semiconductors, namely phonon- or exciton-polaritons. These quasi-particles are the result of the avoided crossing between the photon dispersion and the phonon or exciton dispersion, and due to their phonon/exciton components, they exhibit strong nonlinear interactions of various kinds. The hybridization of the photonic modes with the material polarization leads to qualitative changes in the optical response of the whole system, and the periodicity adds an extra degree of freedom in the manipulation and engineering of the dynamics of optical solitons of novel conception. The first type of PPC considered in the proposal is a Photonic Crystal made of materials which exhibit phonon-polaritons, in which flat optical dispersion characteristics can arise, for certain polarizations of light, due to the coexistence of the Photonic Bandgap (PBG) with the Polariton Bandgap, which can be used to reduce the speed of light in the material or to excite nonlinear waves and solitons with small optical powers, a circumstance that would be beneficial for a variety of commercial applications. Another example of PPC that this project wants to analyze in detail is a structure consisting of multiple Quantum Wells spaced with Bragg periodicity. In this case, no direct photonic Bandgap can arise, because the refractive index is not periodically modulated, but the exciton resonance will acquire a large radiative width, proportional to the number of Quantum Wells. In the limit of a large number of Bragg-spaced Quantum Wells, the exciton linewidth assumes a square profile and turns into an Photonic Bandgap. Contrarily to a conventional PBG, this stop band is active, i.e. can be controlled nonlinearly: the nonlinear interaction between light and exciton-polaritons translates into a nonlinear bandgap response, which can be used to engineer, for instance, ultrafast active Bragg mirrors, trasmittive for low powers and reflective for higher powers. The third and last example of PPC that we consider in this proposal consists of coupled semiconductor microcavities, spaced with a multiple of the Bragg wavelength. Coupling of microcavities provides and extra degree of freedom in the engineering of photonic modes and of their interaction with excitons. New surprising linear physics has been demonstrated in these structures recently, such as a giant Rabi splitting and nonlocal interaction of excitons located in different Quantum Wells; while the nonlinear physics, and especially the dynamics of solitons that are inevitably present in the system due to strong nonlinear interactions between exciton-polaritons, is much less explored and constitutes one of the main themes of this proposal.