Photonic-crystal waveguides and patterned materials: new modelling applications for Helmholtz soliton theory

空间孤子是局域的、自稳定的光束，可以成为介质平面波导的主要电磁模式。当材料效应(非线性引起的折射率变化)与衍射展宽相反，导致光束具有传输不变的强度分布时，它们就会出现。自从20世纪60年代中期非线性光子学文献问世以来，这种光的稳定状态--空间孤子--已经成为了它们的普遍特征。空间孤子对微扰的固有健壮性使得空间孤子非常适合在各种拟议的器件应用中使用，直到今天，它们仍然是理论和实验研究中不可或缺的一部分。角度考虑是光学的核心。例如，即使是最简单的实验布置--两束光束的重叠，或者一束光束倾斜地撞击材料界面--也具有固有的角度相关(离轴)特性。这些系统不能用传统的(近轴)建模方法来充分描述，其中角度(相对于参考轴定义的)被约束为可以忽略或几乎可以忽略的小。此外，交互和单接口场景是基本的构建块几何结构，许多最奇特和复杂的配置(例如，感应波导、光交换、光信息的处理和存储、光计算)都是从这些构建块几何结构中构建出来的。因此，在理解斜传播效应方面的智力投入是整个光学科学的基础，也是未来光子器件和结构有效设计和实现的关键。当前光子学研究的一个非常活跃的分支研究光在周期性图案化介质中的演化。传统上，周期结构主要有两类：耦合波导阵(CWA)和光子晶体(PC)。参照图1，CWA(PC)配置倾向于涉及主要垂直(平行)于光束轴的折射率分布中的调制。虽然这两种配置都等同于多层接口问题，但它们之间的关系要微妙得多。通过牢牢记住角度因素来处理这些系统，CWA和PC显然是几何上相同的结构--它们通过旋转联系在一起。这种联系在近轴模拟中被掩盖了，在近轴模拟中，旋转效应受到固有近似的严格限制。由于这一见解，很明显，亥姆霍兹模型对于研究光在图案结构中的斜向传播是必不可少的。尽管角度效应在非线性光子学中扮演着关键角色，但这一领域在很大程度上仍然是未知的。亥姆霍兹孤子理论是解决斜入射问题的独特之处，它在数学上是优雅的，在计算上也是可行的。它为设计工作依赖于固有角度特性的新型器件提供了理想的平台。拟议的研究项目是科学出版物和新设备应用的潜在金矿，其优势是理论预测立即可以在实验室中得到验证。

Spatial solitons are localized, self-stabilizing beams of light that can become the dominant electromagnetic modes of a dielectric planar waveguide . They can arise when material effects (nonlinearly-induced refractive-index changes) oppose diffractive broadening, resulting in beams with propagation-invariant intensity profiles. Such stationary states of light - spatial solitons - have become a universal feature of the nonlinear photonics literature since their inception in the mid 1960s. Intrinsic robustness against perturbations makes spatial solitons ideal candidates for use in a diverse range of proposed device applications and, to this day, they remain an integral part of both theoretical and experimental research.Angular considerations lie at the heart of optics. For instance, even the simplest experimental arrangements - the overlapping of two beams , or a single beam impinging obliquely on a material interface - have intrinsic angle-dependent (off-axis) characteristics. These systems cannot be adequately described by conventional (paraxial) modelling approaches, where angles (defined with respect to a reference axis) are constrained to be negligibly or near-negligibly small. Moreover, interaction and single-interface scenarios are elementary building block geometries from which many of the most exotic and sophisticated configurations (e.g., induced waveguiding, optical switching, processing and storing of optical information, optical computing) are constructed. Intellectual investment in the understanding of oblique-propagation effects is thus fundamental to optical science in general, and essential for the effective design and realization of future photonic devices and architectures.A highly active branch of current photonics research considers light evolving in periodically-patterned media. Conventionally, there are two main classes of periodic structure: coupled-waveguide arrays (CWAs) and photonic crystals (PCs). Referring to Fig. 1, CWA (PC) configurations tend to involve modulations in the refractive-index profile that are predominantly perpendicular (parallel) to the beam axis. While both configurations are equivalent to a multi-layer interface problem, their relationship is much more subtle. By approaching these systems with angular considerations firmly in mind, it becomes apparent that CWAs and PCs are geometrically identical structures - they are related by a rotation. Such a connection is masked in paraxial modelling, where rotational effects are strictly limited by inherent approximations. As a result of this insight alone, it is clear that Helmholtz modelling becomes essential for studying oblique propagation of light across patterned structures.Despite the pivotal role played by angular effects in nonlinear photonics, this territory remains largely uncharted. Helmholtz soliton theory is uniquely placed to address oblique-incidence problems within a mathematically elegant and computationally accessible framework. It provides the ideal platform for designing novel devices whose operation relies on intrinsic angular characteristics. The proposed research project is a potential gold mine for scientific publications and new device applications, with the advantage that theoretical predictions are immediately testable in the laboratory.