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Introduction: Sleep staging is an essential component in the diagnosis of sleep disorders and management of sleep health. It is traditionally measured in a clinical setting and requires a labor-intensive labeling process. We hypothesize that it is possible to perform robust 4-class sleep staging using the raw photoplethysmography (PPG) time series and modern advances in deep learning (DL). Methods: We used two publicly available sleep databases that included raw PPG recordings, totalling 2,374 patients and 23,055 hours. We developed SleepPPG-Net, a DL model for 4-class sleep staging from the raw PPG time series. SleepPPG-Net was trained end-to-end and consists of a residual convolutional network for automatic feature extraction and a temporal convolutional network to capture long-range contextual information. We benchmarked the performance of SleepPPG-Net against models based on the best-reported state-of-the-art (SOTA) algorithms. Results: When benchmarked on a held-out test set, SleepPPG-Net obtained a median Cohen's Kappa ($κ$) score of 0.75 against 0.69 for the best SOTA approach. SleepPPG-Net showed good generalization performance to an external database, obtaining a $κ$ score of 0.74 after transfer learning. Perspective: Overall, SleepPPG-Net provides new SOTA performance. In addition, performance is high enough to open the path to the development of wearables that meet the requirements for usage in clinical applications such as the diagnosis and monitoring of obstructive sleep apnea.