NONLINEAR RESONANT OPTICAL PHENOMENA AND SOLITONS IN POLARITONIC PHOTONIC CRYSTALS

本项目旨在对一类特殊的人工材料，即极化光子晶体(PPC)中的孤立波的个体和集体的非线性动力学提供详细的理论理解。在这个通用术语中，我们指的是那些结合了光子晶体典型的布拉格周期性和由于半导体中存在的准粒子，即声子-或激子-极化子的存在而产生的材料共振的结构。这些准粒子是光子色散和声子或激子色散避免交叉的结果，由于它们的声子/激子成分，它们表现出各种强烈的非线性相互作用。光子模与材料偏振的杂化使整个系统的光学响应发生了质的变化，这种周期性为新概念的光孤子动力学的操纵和工程增加了额外的自由度。建议中考虑的第一种类型的PPC是由具有声子-偏振子的材料制成的光子晶体，其中由于光子带隙(PBG)和偏振子带隙的共存，对于某些光的偏振，可以产生平坦的光学色散特性，可以用来降低材料中的光速或激发具有小光功率的非线性波和孤子，这种情况将有利于各种商业应用。这个项目想要详细分析的另一个PPC的例子是一个由多个布喇格周期间隔的量子阱组成的结构。在这种情况下，不会产生直接的光子带隙，因为折射率不是周期性调制的，但激子共振将获得较大的辐射宽度，与量子阱的数量成正比。在大量Bragg间隔量子阱的限制下，激子线宽呈正方形，并转变为光子带隙。与传统的PBG相反，这种阻带是有效的，即可以非线性控制：光和激子-偏振子之间的非线性相互作用转化为非线性带隙响应，该响应可用于设计例如超快有源布拉格反射镜，在低功率时传输，在更高功率时反射。我们在本方案中考虑的第三个也是最后一个PPC示例由耦合的半导体微腔组成，这些微腔之间的间隔是布拉格波长的倍数。微腔的耦合在光子模式及其与激子相互作用的工程中提供了额外的自由度。最近在这些结构中展示了新的令人惊讶的线性物理，例如位于不同量子阱中的激子的巨大拉比分裂和非局域相互作用；而非线性物理，特别是由于激子-极化子之间强烈的非线性相互作用而不可避免地存在于系统中的孤子的动力学，被较少地研究，并构成了本提议的主要主题之一。

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.