Spatiotemporal flat optics for terabit-per-second single-channel data transmission

Abstract: Exponential growth in global data traffic demands ever-increasing transmission rates--a pursuit fundamentally constrained by the physical limitations of digital-to-analog converters (DACs). Existing strategies to overcome this bottleneck, such as multi-DAC arrays and optical time-division multiplexing, inevitably introduce system complexity and coordination overhead. Here we demonstrate an all-optical spatiotemporal transmitter that generates controllable high-repetition information-carrying femtosecond pulses at the focus of a phase-modulated planar diffractive lens (PDL) through optical-path-induced spatial-to-temporal conversion. Each pulse serves as an information bit, encoding binary data via on-axis focal intensity states corresponding to '0' and '1', achieved by switching between topological and constant phase modulations. High experimental orthogonality between arbitrary bits enables nearly error-free transmission of 15X15-pixel grayscale (8-bit coding) and colour (9-bit coding) images at a record-high single-channel rate of approximately 3 terabits per second (Tbit/s). Free from electronic and coordination bottlenecks, this all-optical transmitter establishes a scalable high-speed single-channel pathway toward ultrahigh-capacity optical communication.

• The paper introduces a novel spatiotemporal encoding scheme using a planar diffractive lens that bypasses conventional electronic DAC bottlenecks.
• It demonstrates robust image transmission via femtosecond pulse shaping, achieving near-zero error rates with precise intensity discrimination.
• Simulations project scalability up to 10 Tbit/s by increasing encoding zones, highlighting a transformative approach to single-channel optical communications.

Spatiotemporal Flat Optics for Terabit-Per-Second Single-Channel Optical Data Transmission

Introduction and Motivation

The surge in global data traffic, accelerated by AI, cloud, and IoT, necessitates innovative approaches to high-speed optical communications that can overcome the intrinsic electronic bottlenecks of current transmitters. Notably, the fundamental limitations of digital-to-analog converters (DACs) restrict both bandwidth and spectral efficiency in single-channel transmission by IMDD, confining practical systems to sub-terabit capacities. Electronic workarounds such as multi-DAC arrays and OTDM introduce detrimental complexity and synchronization issues, preventing scalable single-channel rates at the multi-terabit level.

All-optical paradigms hold transformational potential, particularly where spatiotemporal modulation can bypass electronic constraints. Recent advances in precise optical field synthesis suggest that compact spatially patterned optics, if used as dynamic encoders, may unlock radically increased throughput while maintaining compatibility with existing IMDD architectures. Yet, practical scalable, flexible implementations—particularly for single-shot, ultrafast, high-bit-rate image/data transmission—remain elusive.

Methodology: Spatiotemporal Encoding via Planar Diffractive Lenses

The architecture replaces traditional electronic data encoding with all-optical space-to-time conversion using a planar diffractive lens (PDL) integrated with programmable phase modulation. Binary data are mapped to on-axis intensity states (focal hotspot for "^^^^^^^^1 null for "^^^^1^^^^") of femtosecond pulses at the focus of a phase-engineered PDL. Encoding is performed via concentric annular zones, each introducing controlled phase delays that yield precise, temporally ordered pulse trains. Switching between constant and vortex (topological charge PRESERVED_PLACEHOLDER_^^^^1^^^^) phase masks directly toggles the focal intensity state per bit.

For an N-bit binary sequence, each bit is assigned to a unique zone, leveraging the radial position–induced optical pathlength difference to impart sub-picosecond, programmable temporal separation among bits. The on-axis intensity evolution at the focal plane thus reveals the transmitted sequence, detected by time-gated intensity sampling with a discrimination threshold. The core advantages are the bypassing of DAC bandwidth limits, the elimination of inter-channel synchronization, and programmable bit durations scalable by zone count and temporal path engineering.

Experimental Demonstration and Data Integrity

The authors implement an SLM-driven optical setup: femtosecond pulses are shaped by the SLM, then relayed through a high-NA, electron-beam-fabricated PDL, with spatiotemporal focus field characterization via Mach-Zehnder interferometry and chirped pulse referencing for femtosecond time resolution. Two principal data stream types are transmitted:

• 8-bit grayscale image (^^^^^^^^1 pixels; 225 bytes): Each pixel's 8-bit code is radially mapped; after transmission and discrete sampling (8×35^^^^1^^^^ fs windows), the image is reconstructed with zero errors (BER = ^^^^1^^^^). Separation between "^^^^^^^^1 states is robust (PRESERVED_PLACEHOLDER_^^^^^^^^1 $I_{0,\max}<0.3$), and RMSE for all gray levels is tightly bounded ($0.1$–$0.3$).
• 9-bit color image (^^^^^^^^1 pixels; 9 bits/pixel via 3 bits/channel): The zone count increases to 9; sampling windows contract to 3^^^^1^^^^^^^^1 fs. Five trials yield BER $=0$–$0.148\%$, with all errors localized to the 8th bit due to increased crosstalk and timing jitter; even in worst cases, artifact pixels remain visually negligible, and intensity-based discrimination stays robust over all other bits.

Bit orthogonality is maintained up to $3.33$ Tbit/s with 9-bit encoding, and simulations validate the scalability of the architecture (see below).

Scalability and Theoretical Limits

The principal scaling bottleneck—zone count and temporal resolution—is addressed via simulation of a ^^^^^^^^1 phase modulator with $\Delta t = 100$ fs per bit (^^^^^^^^1 GHz input pulse repetition). By temporally concatenating pulse streams from dynamically refreshed SLM masks, continuous data transmission at ^^^^^^^^1 Tbit/s single-channel is projected. The temporal refresh of the phase modulator is synchronized with the pulsed source, and programmable tuning of sub-pulse durations allows for further capacity expansion. The only practical limitation is the speed and pixel count of SLMs; emerging platforms (LiNbO$_3$ on insulator, barium titanate, gigahertz-response plasmonic SLMs) have demonstrated phase-only modulation at the required update rates, indicating feasibility for next-generation high-density optical links.

Implications and Future Directions

This approach establishes a fundamentally all-optical, single-channel transmission paradigm that overtakes the canonical electronic bottlenecks. The implications are profound:

• Practical deployments: The transmitter design is compatible with IMDD systems and could be deployed in data centers, upgrading backbone links to few-terabit capacities per fiber without OFDM or complex multiplexing.
• Theoretical communication limit: By directly scaling the number of encoding zones and shrinking window durations, the architecture approaches the physical limit set by pulse overlap, SNR, and focal spot discrimination, effectively decoupling electronic bandwidth and resolution from system level throughput.
• Ultrafast optical field engineering: The programmable control of spatial and temporal DOFs can drive applications in high-dimensional optical communications, ultrafast field synthesis, and rapid optical signal processing for AI, real-time imaging, and adaptive photonic hardware.

Continued advances in high-speed SLM technology and low-loss, high-NA flat optics will further push single-channel rates. Moreover, adaptive feedback mechanisms, noise reduction via advanced detection, and hybrid architectures (e.g., dynamic multiplexing) may elevate capacity and robustness, with direct consequences for next-generation optical networks.

Conclusion

The work presents a rigorous experimental and theoretical foundation for spatiotemporal flat optics as a practical, scalable means of achieving terabit-per-second single-channel data transmission without electronic bottlenecks (26^^^^1^^^^4.^^^^1 By encoding binary data as phase-engineered femtosecond pulse trains at the focus of a planar diffractive lens, and demonstrating robust image transmission with femtosecond time resolution, the authors map a viable path toward all-optical network infrastructures capable of order-of-magnitude advances in throughput, field control, and system simplicity. The architecture's intrinsic scalability, high-fidelity, and integration compatibility signal a step change in the field of flat optics and optical communications.