Spatiotemporal Topological Combs Enable Robust High-Dimensional Information Transmission Beyond the Shannon-Hartley Limit

Leveraging the principles of lock-in amplification, Dawei Liu, Daijun Luo, Huiming Wang, Xingyuan Zhang, Zhirong Tao, Dana JiaShaner, Zhensheng Tao, Qian Cao, Xiaoshi Zhang, Guangyu Fan, and Qiwen Zhan demonstrate a novel method for encoding information onto spatiotemporal topological combs (ST-Combs), sequences of ultrafast pulses carrying topological degrees of freedom. This research overcomes limitations imposed by the Shannon-Hartley theorem by shifting signals to a frequency band beyond conventional noise, achieving exceptional robustness and expanding communication bandwidth. By generating ST-Combs with an all-degree-of-freedom modulator, the team achieves high-dimensional information encoding while maintaining signal stability through the preservation of a key topological property, the winding number, even under various perturbations. This work charts a pathway toward chip-scale photonic platforms capable of operating in the PHz era and establishes a new paradigm for optical communication with unprecedented bandwidth and noise resilience.

Spatiotemporal Comb Encoding for High-Dimensional Data

This research details a novel approach to information encoding and retrieval using controlled bursts of sub-THz to THz radiation, known as a Spatiotemporal Comb, or ST-Comb. The core idea is to manipulate the properties of this comb to encode and retrieve high-dimensional information, offering a significant advancement in data transmission. The team demonstrates the ability to encode data across multiple characteristics of the light itself, including its shape in space and time, and the phase of its carrier wave. The technology centers on generating and precisely controlling the ST-Comb. Ultrafast pulses are shaped using a specialized modulator, creating a sequence of sub-pulses with tailored properties.

Researchers meticulously control the comb’s topology, the spacing between sub-pulses, and the phase of the carrier wave, allowing for complex data encoding. This approach operates in the sub-THz to THz range, providing a large bandwidth for transmitting information. The researchers utilize a technique inspired by lock-in amplification, commonly used in electronics, to embed information within the phase of the ST-Comb. This “optical lock-in” enhances robustness, allowing for reliable data retrieval even in noisy environments. A self-reference technique, employing a Gaussian pulse, isolates and retrieves the encoded spatiotemporal information, further improving signal clarity.

The team also demonstrated a hybrid multiplexing scheme, combining time and spatial multiplexing to increase data capacity. Experimental results demonstrate the potential for extremely high data transmission rates due to the multiple degrees of freedom available for encoding. The system achieves 100% recognition accuracy for a large number of distinct ST-Comb configurations, demonstrating its reliability and stability. This research presents a promising new approach to high-dimensional information encoding and retrieval, offering increased data capacity, robustness, and accuracy compared to traditional methods. Potential applications include high-speed wireless communication, advanced imaging systems, secure data transmission, optical computing, and spectroscopy.

Spatiotemporal Light Encoding Boosts Bandwidth and Robustness

Scientists have developed a new method for encoding data onto light by structuring it into a spatiotemporal topological comb, or ST-Comb, dramatically expanding communication bandwidth and enhancing signal robustness. Inspired by lock-in amplification techniques, the research team encodes data on THz optical carriers, effectively shifting the signal beyond the conventional noise band and isolating it from environmental fluctuations. This approach leverages a modulator to generate the ST-Comb, creating a vast state space capable of high-dimensional information encoding, and crucially, preserves topological characteristics under diverse perturbations, ensuring stable information encoding and retrieval. The breakthrough lies in a systematic approach to encoding wavepackets using an all-degree-of-freedom modulator, transforming an input pulse into a programmable sequence of ultrafast pulses with tailored spatiotemporal properties.

The electric field distribution of the generated comb is mathematically formulated to account for peak amplitude, amplitude distribution, and topological characteristics. By precisely modulating the phase of the carrier wave, scientists control the spectral shift and generate complex spatiotemporal structures without computationally intensive reconstruction algorithms. This method achieves exceptional noise suppression by combining the information-bearing ST-Comb with a co-propagating reference carrier, enabling phase-sensitive detection and significant signal-to-noise ratio improvement. Beyond noise reduction, the ST-Comb exhibits topological protection; while waveform details may distort during propagation, the global topological charge remains invariant, ensuring encoded information remains secure.

Researchers extended the concept of phase control to a spatiotemporal topological phase within the ST-Comb framework, modulating a single wavepacket into a picosecond-spaced pulse train where each sub-pulse carries the same phase. To demonstrate the potential for high-dimensional information encoding, scientists constructed a parameter space using the ST-Comb, encoding information along the spatiotemporal degree of freedom, inter-pulse spacing, and phase. Experimental and simulated control of each degree of freedom was achieved, demonstrating the ability to encode information along an additional dimension. This paves the way for chip-scale, reconfigurable photonic platforms for the PHz era.

Spatiotemporal Light Structuring Enables Robust Communication

Scientists have achieved a breakthrough in optical communication by sculpting light across multiple degrees of freedom, creating a system capable of vastly expanded bandwidth. This work demonstrates a new paradigm for encoding data on terahertz optical carriers, effectively isolating the signal from conventional noise and yielding exceptional robustness. The team generated a spatiotemporal topological comb (ST-Comb), structuring light into a high-entropy state space for high-dimensional information encoding. Crucially, experiments reveal that the associated topological characteristics remain preserved even under diverse perturbations, ensuring stable encoding and retrieval.

The research establishes a concept termed “optical lock-in,” analogous to lock-in amplification in electronics, by shifting the signal to a frequency band beyond the typical noise floor. By utilizing an all-degrees-of-freedom modulator, the team created ST-Combs consisting of sequences of ultrafast pulses, each carrying individually addressable topological degrees of freedom. The electric field distribution of the generated comb is defined by a specific formulation, allowing precise control over the spatiotemporal spectral structure. This approach enables the generation of complex spatiotemporal structures, including both orthogonal and non-orthogonal configurations, without computationally intensive reconstruction.

Measurements confirm that the ST-Comb exhibits topological protection; while waveform details may distort during propagation, the global topological charge remains invariant. This invariance ensures that local perturbations do not compromise the encoded information. By modulating the carrier-envelope phase (CEP) and extending it to a spatiotemporal topological phase, scientists achieved sub-cycle waveform control, pushing light-matter interaction to its temporal limit. The ST-Comb displays a unique spatiotemporal structure in both the time and frequency domains, with a two-scale temporal structure defined by inter-pulse delay and total train duration.

For an ST-Comb with a specific topological number, the field can be modeled as the convolution of a Gaussian pulse train with a spatiotemporal wavepacket. The resulting spectrum spans orders of magnitude, demonstrating the system’s potential for petahertz-rate information processing. This work demonstrates a parameter-space encoding scheme for high-dimensional information, highlighting the potential of this new degree of freedom for next-generation optical communication with unprecedented bandwidth and noise resilience.

Topological Combs Enable Stable High-Density Encoding

This research demonstrates a new framework for high-dimensional information encoding using spatiotemporal topological optical frequency combs, termed ST-Combs. By encoding data on terahertz optical carriers and employing all-degree-of-freedom modulation, the team achieved robust signal transmission, effectively reducing the impact of low-frequency noise. The method structures light into a high-entropy state space, enabling dense encoding strategies and simplifying the decoding process. Near-unity classification accuracy in machine learning tests confirms this simplification.