Fig. 1. (a) Illustration of the proposed mode-division demultiplexing (MDD) spectrometer. The multimode spectral signal (mode₁–mode_k) dispersed in the branched waveguide structures and detected by graphene-photodetector units. The generated photocurrents I₁–I_m at unit₁–unit_m from the input multimode spectral signals are fed into a deep neural network (DNN) to extract the desired spectral profiles F₁ (λ)–F_k(λ). (b) Structural parameters of a designed branched waveguide and graphene photodetector. Inset: the cross-section view of a silicon waveguide and graphene photodetector.

Fig. 2. Simulated characterizations of the proposed device for the single-mode (TE₁–TE₄) spectrometer by Tikhonov regularization optimization. (a) Normalized photoresponses of two typical spectral detecting units. (b) Correlation functions of the spectral responses for different TE modes. (c, d) Recovered spectral profiles of dual peaks separated by 7 nm (c) and the same random spectra (d) for TE₁–TE₄.

Fig. 3. Principle of the single-shot multimode reconstruction (SMR) algorithm. The unknown multimode spectra are imported to the proposed MDD spectrometer at the same time. The response photocurrents I₁-I_mare captured at unit₁-unit_m, and then are fed into the trained SMR-DNN as a pixel image to implement simultaneous reconstruction of different mode spectra in single shot.

Fig. 4. Single-shot simultaneous multimode reconstructions from the trained SMR-DNN for TE₁–TE₄. (a) Dual spectral peaks resolution with light wavelength separated by 15 nm, (b) single peaks with FWHM-15 nm uniformly distributed in the bandwidth of 1500-1600 nm. (c–f) The construction of multimode spectra in different modes: (c) TE₁, (d) TE₂, (e) TE₃, and (f) TE₄.

Fig. 5. Principle and performance of the designed multi-shot resolution-enhanced (MRE) architecture. (a) Principle of the MRE algorithm. The various single-mode photocurrent (T₁–T_k) images are generated by the spectral responses of photodetecting arrays and are fed into MRE-DNN to obtain resolution-improved results. (b–d) Recovered results of dual spectral peaks with light wavelength separated by 3 nm (b), single peaks with FWHM-3 nm uniformly distributed in the bandwidth (c), and the constructed random spectra (d).