Spatiotemporal Topological Combs for Robust High-Dimensional Information Transmission

Abstract

Sculpting light across its independent degrees of freedom-from orbital angular momentum to the discrete wavelengths of optical frequency combs-has unlocked vast communication bandwidth by enabling massively parallel information channels. However, the Shannon-Hartley theorem sets a hard limit by tying channel capacity to the trade-off between SNR and rate, a central challenge in communication. Inspired by lock-in amplification in electronics, we encode data on THz optical burst carriers so the signal resides beyond the conventional noise band, yielding exceptional robustness. By leveraging a programmable all-degree-of-freedom (All-DoF) modulator, we generate a spatiotemporal topological comb (ST-Comb) that structures light into a vast, highentropy state space for high-dimensional information encoding. Crucially, we find that the associated topological winding number is preserved under diverse perturbations, ensuring stable information encoding and retrieval. This paradigm illustrates how structured light can simultaneously expand channel dimensionality and maintain robustness, charting a pathway to chip-scale, reconfigurable photonic platforms for the PHz era, while also opening previously inaccessible regimes of light-matter interaction.

Figures (4)

• Figure 1: Generation of the ST-Comb and spatiotemporal optical lock-in.a, Formation and encoding. An ultrafast pulse is shaped by a spatiotemporal modulator into a sequence of spatiotemporal-topological sub-pulses. The fs–ps inter-pulse spacing corresponds to a THz-rate carrier. The topological modes (including radial index $\mathit{p}$ and azimuthal index $\ell$), temporal separation $\tau$, and relative phase difference $\boldsymbol{\varphi}_{ST-CEP}$ of each sub-pulse can all be utilized for information encoding. b, Spatiotemporal lock-in encoding. All spatiotemporal information is loaded onto a THz-burst carrier via the modulator, achieving spatiotemporal phase lock-in, heterodyning with an information-free Gaussian THz gating pulse retrieves the encoded spatiotemporal content. c, Self-reference “Guide-Star” Detection. The first sub-pulse is set as a Gaussian guide-star and temporally separated from the information-bearing sub-pulses, subtracting the two-Gaussian reference ST-Comb isolates the spatiotemporal topological information.
• Figure 2: Temporal and Spectral properties of ST-CEP and ST-Comb.a, Time- and frequency-domain waveforms under two ST-CEP settings. Tuning the ST-CEP enables THz-scale spectral sweeping. b, ST-Comb in the time domain. The comb forms a pulse train with $100$ fs–$10$ ps inter-pulse spacing and a total burst duration of $5$–$50$ ps, adjusting ST-CEP translates the electromagnetic-field envelope within the burst. c, ST-Comb in the frequency domain. The inter-pulse spacing $\tau$ sets the comb-line spacing in the sub-THz–THz band, yielding a dense comb, long-period modulation of the pulse train introduces an additional low-frequency spacing of $20$–$200$ GHz.
• Figure 3: Degrees of freedom for high-dimensional manipulation of the ST-Comb and mapping relation from time–frequency resources.a, Schematic of the high-dimensional information space of the ST-Comb. b, Spatiotemporal topological encoding (information-space $\mathit{z}$-axis). Examples showing ST-Combs with linear and nonlinear mappings between time and topological charge $\ell$. c, ST-CEP control (parameter-space $\theta$-axis). Varying the spatiotemporal carrier-envelope phase $\boldsymbol{\varphi}_{ST-CEP}$ preserves the time-domain waveform while inducing pronounced spectral differences. d, Radial topological $\mathit{p}$ control. ST-Combs combining $\ell$ with the radial index $\mathit{p}$. e, Mapping Relation from frequency to time across three modes frequency multiplexing, spatiotemporal multiplexing, and hybrid frequency–spatiotemporal multiplexing.
• Figure 4: Multiplexing-Demultiplexing Mechanism of ST-Comb.a, Multiplexing process, femtosecond pulses undergo time multiplexing and spatiotemporal topological multiplexing to form hybrid-state ST-Comb. b, Time demultiplexing process, after coherent decoding hybrid-state ST-Combs undergo time demultiplexing to isolate individual sub-pulses. c, Topological demultiplexing process, time-demultiplexed sub-pulses are fed into machine learning for topological demultiplexing to recover original topological information. d, Repeatability demonstration, intensity stability results from $100$ repetitions of identical ST-Comb configurations e, Experimental measurement of $1000$ distinct ST-Combs achieves $100\%$ recognition accuracy.