Numerical results are presented in section \[sec:tests\] to show the effectiveness of high-order HDG methods for solving problems in nanophotonics. We draw conclusions in section \[sec:con\].

Physics problem: nonlocal optical response by nanoparticles {#sec:models}
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The problem considered is shown in Figure \[fig:struct\] where the nanometer-size metal $\Omega_S$ is illuminated by an incident plane wave of light. The infinite scattering domain is truncated as a finite computational domain $\Omega$ by employing an artificial absorbing boundary condition, which is designed to absorb outgoing waves.

![Sketch of the incident electromagnetic wave illuminating the scatterer $\Omega_S$ that has a subwavelength size and is surrounded by free space. $\Omega_S$ is usually filled with metals, such as gold, silver or sodium. An artificial absorbing boundary $\partial\Omega$ is introduced to make a computational domain $\Omega$.[]{data-label="fig:struct"}](./struct.pdf)

Nonlocal hydrodynamic Drude model
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There are a number of theories for the modeling of the light-matter interactions which are used under different settings. In this subsection, we briefly introduce the NHD model. The incoming light is described as a propagating electromagnetic wave that satisfies Maxwell’s equations. Without external charge and current, Maxwell’s equations of macroscopic electromagnetism for non-magnetic materials can be written as $$\label{eq:max}
\left\{
\begin{array}{l}
\nabla\times {\mathbf{H}}=   \varepsilon_0\varepsilon_{\text{loc}}\partial_t{\mathbf{E}}+{\mathbf{J}},\\
\nabla\times{\mathbf{E}}= 