On-chip spectrometers with tailored spectral range and compact footprint have been pursued widely in the last decade. Splitting different frequencies typically requires a propagation length that scales inversely with the frequency resolution, which leads to a trade-off between resolution and size. Scattering media in the diffusive regime provide a long light path and multipath interference in a compact area, resulting in strong dispersive properties that can be used for on-chip compressive spectrometry. However, the performance suffers from the low light transmission through the diffusive medium. It has been found that there exist “open channels” such that light with certain wavefronts can pass through the medium with high transmission. Here we show that a scattering structure can be designed so that open channels match target input/output channels in order to maximize transmission while keeping the dispersive properties typical of diffusive media. Specifically, we use inverse design to generate a scattering structure where the open channels match the output waveguides at desired wavelengths. For a proof of concept, we propose a ${{1}} \times {{10}}$ multiplexer covering a band of 500 nm in the mid-infrared spectrum, with a footprint of only ${9.4}\;\unicode{x00B5}{\rm m} \times {14.4}\;\unicode{x00B5}{\rm m}$. We also show that filters with nearly arbitrary spectral response can be designed, enabling a new degree of freedom in on-chip spectrometer design, and we investigate the ultimate resolution limits of these structures. The structures can also be designed based on a simple geometry consisting of circular holes with diameters from 200 to 700 nm etched in a dielectric slab, making them highly suited for fabrication. With the help of compressive sensing, the proposed method represents an important tool in the quest towards integrated lab-on-a-chip spectroscopy.

中文翻译：

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在片上光谱仪的随机散射介质中设计开放通道

在过去的十年中，具有定制光谱范围和紧凑占位面积的片上光谱仪得到了广泛的追求。划分不同的频率通常需要传播长度，该传播长度与频率分辨率成反比，这导致分辨率和尺寸之间的权衡。扩散区中的散射介质在紧凑的区域中提供了较长的光路和多径干涉，从而产生了可用于片上压缩光谱的强大色散特性。然而，该性能受到穿过扩散介质的低透光率的困扰。已经发现存在“开放通道”，使得具有某些波前的光可以以高透射率穿过介质。在这里，我们表明可以设计一种散射结构，以使开放通道与目标输入/输出通道匹配，从而在保持扩散介质典型的分散特性的同时最大化传输率。具体来说，我们使用逆设计来生成散射结构，在该结构中，开放通道与所需波长的输出波导相匹配。为了证明概念，我们建议$ {{1}} \ times {{10}} $多路复用器，覆盖中红外光谱的500 nm频段，占用空间仅为$ {9.4} \; \ unicode {x00B5} {\ rm m} \次{14.4} \; \ unicode {x00B5} {\ rm m} $。我们还表明，可以设计具有几乎任意光谱响应的滤波器，从而在片上光谱仪设计中实现了新的自由度，并且我们研究了这些结构的最终分辨率极限。还可以基于简单的几何形状来设计结构，该几何形状包括在介电平板中蚀刻的直径为200至700 nm的圆形孔，因此非常适合制造。借助于压缩感测，所提出的方法代表了寻求集成芯片实验室光谱学的重要工具。