The wavelength scale confinement of light offered by photonic crystal (PhC) cavities is one of the fundamental features on which many important on-chip photonic components are based, opening silicon photonics to a wide range of applications from telecommunications to sensing. This trapping of light in a small space also greatly enhances optical nonlinearities and many potential applications build on these enhanced light-matter interactions. In order to use PhCs effectively for this purpose it is necessary to fully understand the nonlinear dynamics underlying PhC resonators. In this work, we derive a first principles thermal model outlining the nonlinear dynamics of optically pumped silicon two-dimensional (2D) PhC cavities by calculating the temperature distribution in the system in both time and space. We demonstrate that our model matches experimental results well and use it to describe the behavior of different types of PhC cavity designs. Thus, we demonstrate the model's capability to predict thermal nonlinearities of arbitrary 2D PhC microcavities in any material, only by substituting the appropriate physical constants. This renders the model critical for the development of nonlinear optical devices prior to fabrication and characterization.

中文翻译：

---

光子晶体腔的热光非线性动力学模型

光子晶体（PhC）腔提供的光的波长范围限制是许多重要的片上光子组件所基于的基本特征之一，从而使硅光子学在从电信到传感的广泛应用中得到了广泛应用。在很小的空间中捕获光也大大增强了光学非线性，并且在这些增强的光-质相互作用上建立了许多潜在的应用。为了有效地将PhC用于此目的，有必要充分了解PhC谐振器的非线性动力学。在这项工作中，我们通过计算系统在时间和空间上的温度分布，导出了第一原理热模型，该模型概述了光泵浦硅二维（2D）PhC腔的非线性动力学。我们证明了我们的模型与实验结果吻合得很好，并用它来描述不同类型的PhC腔设计的行为。因此，我们证明了该模型仅通过替换适当的物理常数即可预测任何材料中任意2D PhC微腔的热非线性的能力。这使得该模型对于在制造和表征之前开发非线性光学器件至关重要。