Miniaturized spectrometers have been widely researched in recent years, but few studies are conducted with on-chip multimode schemes for mode-division multiplexing (MDM) systems. Here we propose an ultracompact mode-division demultiplexing spectrometer that includes branched waveguide structures and graphene-based photodetectors, which realizes simultaneously spectral dispersing and light fields detecting. In the bandwidth of 1500–1600 nm, the designed spectrometer achieves the single-mode spectral resolution of 7 nm for each mode of TE₁–TE₄ by Tikhonov regularization optimization. Empowered by deep learning algorithms, the 15-nm resolution of parallel reconstruction for TE₁–TE₄ is achieved by a single-shot measurement. Moreover, by stacking the multimode response in TE₁–TE₄ to the single spectra, the 3-nm spectral resolution is realized. This design reveals an effective solution for on-chip MDM spectroscopy, and may find applications in multimode sensing, interconnecting and processing.Miniaturized spectrometers have been widely researched in recent years, but few studies are conducted with on-chip multimode schemes for mode-division multiplexing (MDM) systems. Here we propose an ultracompact mode-division demultiplexing spectrometer that includes branched waveguide structures and graphene-based photodetectors, which realizes simultaneously spectral dispersing and light fields detecting. In the bandwidth of 1500–1600 nm, the designed spectrometer achieves the single-mode spectral resolution of 7 nm for each mode of TE₁–TE₄ by Tikhonov regularization optimization. Empowered by deep learning algorithms, the 15-nm resolution of parallel reconstruction for TE₁–TE₄ is achieved by a single-shot measurement. Moreover, by stacking the multimode response in TE₁–TE₄ to the single spectra, the 3-nm spectral resolution is realized. This design reveals an effective solution for on-chip MDM spectroscopy, and may find applications in multimode sensing, interconnecting and processing.

涡旋光场因其具有光学轨道角动量（Orbital angular momentum, OAM）而倍受关注。OAM这一独特物理特征赋予了涡旋光场一个无限高维的空间自由度，同时也引发了光场奇特的干涉、衍射、传输等性质。OAM识别和探测技术的发展是涡旋光从基础研究走向应用的关键。文中聚焦于OAM探测领域的一个重点研究方向——涡旋光几何坐标变换技术。详细介绍了该技术的基本原理、优势特点、研究进展和应用情况。涡旋光几何坐标变换是指通过特殊的调制相位设计，使涡旋光束的空间几何结构发生特殊的变化，从而可通过简单透镜聚焦等方法实现OAM模式的识别、分选等。相较于传统的涡旋光识别和探测技术，涡旋光的几何坐标变换这一新兴技术具有器件无源、无能量损耗、结构紧凑、价格低廉等突出优势，成为涡旋光的空间分离和解复用的高效有力工具，为涡旋光束在经典/量子态密度测量、OAM乘除法器、经典光通信和量子纠缠等前沿应用提供了全新的研究平台，蕴含巨大的发展潜力，具有广阔的发展空间。