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

空间孤子是一种局域化的自稳定光束，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）与衍射展宽相反时，它们就会出现，从而导致光束具有传播不变的强度分布。这种光的定态-空间孤子-自20世纪60年代中期问世以来，已经成为非线性光子学文献的普遍特征。空间孤子具有抗扰动的内在鲁棒性，因此成为各种器件应用的理想候选者，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。例如，即使是最简单的实验安排-重叠的两个光束，或一个单一的光束斜撞击在材料界面-有内在的角度依赖（离轴）的特点。这些系统不能通过传统的（近轴）建模方法充分描述，其中角度（相对于参考轴定义）被约束为可忽略或接近可忽略的小。此外，相互作用和单界面场景是基本的构建块几何形状，许多最奇特和复杂的配置（例如，诱导波导、光开关、光信息的处理和存储、光计算）。因此，对光子传播效应的理解是光学科学的基础，也是有效设计和实现未来光子器件和结构的关键。光子学研究的一个高度活跃的分支是光在图案化介质中的演化。传统上，周期性结构主要有两类：耦合波导阵列（CWA）和光子晶体（PC）。参考图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的调制。虽然这两种配置都等效于多层界面问题，但它们的关系要微妙得多。通过对这些系统的角度考虑，很明显，CWAs和PC是几何上相同的结构-它们通过旋转而相关。这种联系在傍轴模型中被掩盖了，其中旋转效应受到固有近似的严格限制。仅仅因为这一点，亥姆霍兹模型就成为研究光在图案化结构中斜传播的关键。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。亥姆霍兹孤立子理论是唯一的放置在一个数学优雅和计算可访问的框架内，以解决入射问题。它提供了一个理想的平台，设计新的设备，其操作依赖于内在的角度特性。拟议的研究项目是科学出版物和新设备应用的潜在金矿，其优点是理论预测可立即在实验室中进行测试。

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.