A new publication from Opto-Electronic Sciences; DOI 10.29026/oes.2025.240020, discusses direct detection with an optimal transfer function.

Driven by bandwidth-hungry Internet services, such as artificial intelligence (AI) applications, video streaming, e-commerce, and social networks, traffic demands for data center interconnections and metro networks have experienced exponential growth. Coherent detection is a promising candidate owing to its superior performance. However, an expensive narrow-linewidth local oscillator (LO) laser is required at the receiver, which inevitably increases the system cost. Consequently, intensity modulation-direct detection (IM-DD) is still widely implemented as a low-cost solution for short-reach applications. However, the conventional IM-DD system sacrifices approximately half of the electrical spectral efficiency (ESE=Data rate/Receiver electrical bandwidth), because only the amplitude is used as the modulation dimension. ESE is the dictating factor that determines the cost of short-reach transmission systems. Additionally, various impairments, such as chromatic dispersion, cannot be digitally compensated owing to the lack of field recovery capability, which significantly limits the attainable ESE. Consequently, it is worthwhile to investigate the complex-valued double-sideband (CV-DSB) DD schemes with capability of field recovery and high ESE.

Recently, various CV-DSB DD schemes have been proposed, such as carrier-assisted differential detection (CADD), carrier-less phase retrieval receiver based on a modified Gerchberg-Saxton (GS) algorithm, asymmetric self-coherent detection (ASCD), and deep-learning-enabled DD (DLEDD). However, a fundamental issue to explore is: what is the optimal DD receiver structure to approach the ESE of the coherent homodyne detection with the simplest design?

Starting from the receiver structure of conventional phase-diversity coherent homodyne detection, a research team including Dr. Xingfeng Li, Prof. Yikai Su, and associate Prof. Qunbi Zhuge from Shanghai Jiao Tong University, Prof. William Shieh from Westlake University, and Dr. Haoshuo Chen from Nokia Bell Labs derived an optimal DD receiver architecture comprising a coupler, two single-ended photodiodes (PDs), two analog-to-digital converters (ADCs), and a frequency-selective phase shifter with an optimal transfer function, as shown in Fig. 1. By considering the impact of both noise and signal-to-signal beat interference (SSBI) on system performance, the optimal transfer function exhibits an all-pass amplitude response accompanied by a phase response that introduces an adjustable phase shift on either the carrier or the information-bearing signal. In practice, the operators need to judiciously select an appropriate phase shift according to the operating conditions. At the receiver-side digital signal processing (DSP), the authors used a convolutional neural network to seamlessly achieve signal reconstruction and SSBI mitigation in a unified step, thus enabling optimal system performance.

By invoking Shannon’s formula, the authors derived the theoretical ESE limit, which is dependent on the net rate and optical signal-to-noise ratio (OSNR), as shown in Fig. 2(a). Subsequently, the ESE limit of the proposed scheme is normalized to the coherent-homodyne case, as illustrated in Fig. 2(b). To provide a clearer visual representation, the authors considered three different data rates. Fig. 2(c) depicts the normalized theoretical ESE limit of the proposed scheme versus the OSNR for 200 Gb/s, 300 Gb/s and 400 Gb/s. As the OSNR increases, the theoretical ESE limit of the proposed scheme gradually approaches that of coherent homodyne detection. The normalized ESE limit is expected to approach 100% if the OSNR is sufficiently high.

Furthermore, the authors performed a proof-of-concept experiment by leveraging the WaveShaper to construct an optimal transfer function. Using a 110°-phase shift, we have achieved a 228.85-Gb/s net rate and 8.76-b/s/Hz net ESE by transmitting a 46-GBaud 64-QAM signal in an 80-km single-mode fiber (SMF) without probabilistic constellation shaping. To the best of the knowledge, the authors report a record net ESE for single-polarization and single-wavelength DD transmission beyond a 40-km SMF. For a comprehensive metric denoted as 2^ESE×Reach, the authors achieve the highest 2^ESE×Reach for single-polarization and single-wavelength DD transmission. The authors believe that the proposed DD receiver with an optimal transfer function may pave the way for new applications in large-capacity and cost-effective data center interconnections, metro networks, and mobile backhauls.

Keywords: optical communication / direct detection / optical field recovery / electrical spectral efficiency

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This work was performed by a team of including Prof. Yikai Su, and associate Prof. Qunbi Zhuge from Shanghai Jiao Tong University, Prof. William Shieh from Westlake University, and Dr. Haoshuo Chen from Nokia Bell Labs. The collaboration between Prof. Su and Prof. Shieh traced back to 2020. In 2020, Prof. Shieh proposed the CADD receiver at the University of Melbourne, and subsequently Prof. Su’s group experimentally demonstrated a prototype. In 2022, Prof. Shieh joined Westlake University, as the Chair Professor of optical communication and sensing. Then, the collaboration was further developed. Some representative collaboration results include silicon photonics integrated CADD receiver (OFC, 2022, Th4B.6, PDP), four-dimensional silicon-photonics integrated direct-detection receiver (ECOC, 2023, Th.C.1.9, PDP), chip-to-chip multimode transmission through rectangular core fibe r (Laser & Photonics Reviews, vol. 17, no. 11, 2023), etc.

Home page of Prof. Su’s research group: https://otip.sjtu.edu.cn/en
Home page of Prof. Shieh’s research group: https://ocs.lab.westlake.edu.cn/index.htm

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Li XF, Li JC, Ni X et al. Direct detection with an optimal transfer function: toward the electrical spectral efficiency of coherent homodyne detection. Opto-Electron Sci 4, 240020 (2025). doi: 10.29026/oes.2025.240020