Spatiotemporal Multiplexing in Photonics

• Spatiotemporal multiplexing is a technique that jointly exploits spatial and temporal channels to enhance capacity and efficiency in photonic, quantum, and imaging applications.
• It employs methods such as time-to-space mapping using delay networks, active switching (e.g., EOMs, AODs), and mode-selective coupling to achieve parallel signal processing with minimized cross-talk.
• Demonstrations in fiber-optic nonlinear photonics, quantum memory arrays, and gigapixel imaging validate its scalability, with experimental metrics showing high throughput and stable performance.

Spatiotemporal multiplexing refers to techniques that leverage multiple spatial and temporal degrees of freedom simultaneously to increase channel count, throughput, bandwidth, or functionality in physical, quantum, and optical systems. In modern photonics, quantum information, microscopy, and laser science, spatiotemporal multiplexing enables parallelization and high-dimensional operation by mapping, converting, or pre-compensating signals across independently addressable spatial modes and temporally discrete events. Major experimental platforms include fiber-optic nonlinear optics, quantum memory arrays, large-scale imaging architectures, ultrafast laser cavities, and multi-photon sources. Spatiotemporal multiplexing is distinct from pure spatial or pure temporal multiplexing in that its scaling and performance emerge from the joint exploitation and control of both domains.

1. Principles of Spatiotemporal Multiplexing

Spatiotemporal multiplexing involves mapping signals or particles in one domain (typically time) to multiple outputs or channels in another (typically space), allowing simultaneous, parallel, or highly time-resolved readout. The foundational principle is that each degree of freedom—spatial or temporal—provides a distinct channel. The total capacity for information, throughput, or correlated states grows as the product of spatial and temporal channel numbers, $$N_{\text{total}} = N_{\text{spatial}} \times N_{\text{temporal}}$$ (Teller et al., 16 Jul 2025). Practically, this method can be realized via delay networks and fast routing in photonic schemes (Hansen et al., 2023), mode-selective coupling in fibers or free-space optics (Cruz-Delgado et al., 19 Feb 2024), acousto-optic spatial demultiplexers in quantum memories (Teller et al., 16 Jul 2025), or distributed point-spread engineering in imaging arrays (Zhou et al., 19 Jul 2025).

The distinctiveness of spatiotemporal multiplexing versus pure mode-division multiplexing lies in several areas:

• Joint scaling: Mode number increases multiplicatively rather than additively, dramatically increasing achievable throughput.
• Orthogonality and cross-talk suppression: Careful alignment, delay compensation, or mode engineering is necessary to maintain mode orthogonality as channel numbers scale.
• Resource-sharing: Efficient protocols often use a single active switching element, spatial coupler, or pulse-shaper to address many outputs, reducing hardware requirements (Hansen et al., 2023, Zhou et al., 19 Jul 2025).

2. Quantum Photonic Sources and Demultiplexing Networks

Solid-state single-photon emitters such as quantum dots natively produce pulses in the same spatial mode and successive time bins. To prepare larger multi-photon states or parallel single-photon sources, temporal-to-spatial demultiplexing is employed. A representative architecture uses a single active electro-optic modulator (EOM), a cascade of passive optical delays, and polarizing beam splitters (PBS) (Hansen et al., 2023):

• Loading phase: Photons separated by interval $\tau$ are injected sequentially into a fiber or free-space delay network. Each is routed to a distinct delayed trajectory via repeated passes and reflection.
• Release phase: A $\pi$-phase switch rotates the polarization, turning the network into a set of spatial outputs. All photons are simultaneously routed to separate outputs using a single EOM.
• Mapping: The routing operation can be described by a matrix $M_{s,t}$ acting as a near-permutation on creation operators $a^\dagger(t) \rightarrow b^\dagger_s$.

The total success probability for $N$-photon coincidence events is $P_N \approx \eta_s^N \eta_d^{N(N-1)/2}$, where $\eta_s$ is the switch efficiency and $\eta_d$ the per-delay transmission (Hansen et al., 2023). Proof-of-principle implementations demonstrated up to eight spatially demultiplexed, highly indistinguishable photons with $>1$ kHz four-photon rates. Practical limits arise from passive delay losses, switching speed, and stability, but the scheme permits tens of output channels with only one active element.

3. Spatiotemporal Multiplexing in Fiber-Based Nonlinear Photonics

Multi-mode and few-mode fibers enable spatiotemporal multiplexing for ultrafast pulse generation, nonlinear comb synthesis, and high-capacity communications:

• Parallel nonlinear compression: Each linearly-polarized (LP) mode serves as an isolated nonlinear waveguide. Dual-frequency beat signals at distinct wavelengths are injected into each mode, driving intra-modal multiple four-wave mixing (MFWM) (Zhang et al., 2020). This yields parallel frequency combs and picosecond, high-repetition-rate pulse trains.
• Intermodal cross-phase modulation: By group-velocity-matching CW probes to the compressed pump pulses, intermodal XPM imprints the temporal structure of the pump onto weak probes in higher-order modes (Zhang et al., 2020).
• Governing equations: Scalar and coupled nonlinear Schrödinger equations model the dynamics, with cross-phase and four-wave mixing terms specifying modal interactions and pulse formation.
• Scalability: Demonstrated systems generate 4–10 spatially multiplexed, 40 GHz pulse trains in 1.8 km fibers, each channel independently addressable. Cross-talk ($<$–20 dB) is minimized by careful wavelength selection and mode coupling.

Compression ratios of 5–8 (pulse FWHM of 4.9–9.2 ps) are achieved, with negligible pedestals and high stability over minutes. This approach is extensible to $\sim$10 mode groups and higher repetition rates, limited ultimately by mode count and phase-matching bandwidth (Zhang et al., 2020, Zhang et al., 2020).

4. Ultrafast Spatiotemporal Mode-Locking in Laser Cavities

In multimode fiber lasers, spatiotemporal mode-locking (STML) represents the coherent synchronization of many longitudinal and transverse cavity modes, forming robust 3-D dissipative solitons (Wright et al., 2017):

• Cavity configurations: Graded-index multimode fiber sections support $\sim$100 transverse modes, with intracavity spectral and spatial filtering used to balance temporal and modal dispersion.
• Nonlinear coupling: Strong Kerr (SPM and XPM) and saturable absorption (nonlinear polarization rotation) channels energy and phase among modes, locking their dynamics.
• Governing equations: Generalized multimode NLSE models pulse propagation with modal dispersions, loss, and cross-phase modulation integrals.
• Output characterization: Experimental cavities produce transform-limited pulses of energies 5–150 nJ and peak powers $>$1 MW, with multi-mode phase locking verified via autocorrelation and RF spectrum analysis.

STML realizes volumetric spatiotemporal multiplexing—simultaneous coherent superposition of hundreds of spatial × longitudinal channels—enabling high-energy, diffraction-limited ultrashort pulses and multiplexed output for communications, microscopy, and materials processing.

5. Quantum Memory Arrays and Spatiotemporal Storage

Solid-state quantum memory arrays combine spatial and temporal multiplexing to greatly boost entanglement distribution rates (Teller et al., 16 Jul 2025):

• Architecture: Individual spatial cells in a crystal are addressed by crossed acousto-optic deflectors (AODs), while temporal multiplexing stores trains of weak coherent pulses in atomic frequency combs (AFCs) with on-demand spin-wave transfer.
• Scaling: $$N_{\text{total}} = N_{\text{spatial}} \times N_{\text{temporal}}$$ modes; up to 250 modes demonstrated in a 10-cell array, each with up to 25 time bins.
• Efficiency and SNR: Overall per-mode efficiencies $<$2%, but per-mode SNR up to 80 (mean ~10 for 250 modes). Cross-talk measured at $\sim$3% mean, 0–8.8% range, with noise primarily from fluorescence during control pulses.
• Entanglement and readout: Cumulative detection probability increases with channel number. Memory–telecom cross-correlations and retrieval fidelities well above the classical limit indicate readiness for storing non-classical states.

Design improvements for scaling include use of 2D AOD arrays, longer AFC delays, spectral multiplexing, cavity enhancement, and spin-echo techniques.

6. Spatiotemporal Multiplexed Sensing and Imaging Architectures

Large-scale optical imaging platforms exploit spatiotemporal multiplexing via distributed sensor arrays and point-spread function engineering:

• Super-sensor arrays: 48 sensors deployed in a near-4f optical relay, each capturing $3136 \times 4096$ px at 1.1 μm pitch, with gaps spanning 4.95 cm × 6.64 cm FOV (Zhou et al., 19 Jul 2025).
• Diffractive multiplexing: A custom diffractive optical element (DOE) at the pupil plane creates an engineered PSF, which encodes image information from overlapping regions (including gap areas) onto the sensor array. The forward model is $y = A x + n$, with $A_{mn}$ determined by the masked and distorted PSF.
• Compressive recovery: Assuming object sparsity, total variation and $\ell_1$ regularization are used to recover full-field images from erasure-masked, distributed sensor data.
• Performance: Achieves $\sim$3 μm resolution over $>$5.2 cm$^2$ at 120 fps, producing a throughput of 25.2 billion pixels per second—over 259-fold improvement compared to a single sensor.

Applications include gigapixel real-time imaging of structural and functional biological dynamics, high-throughput cytometry, and wafer-scale inspection. Extension to depth encoding (e.g., double-helix PSF) could enable single-shot 3D+time gigapixel microscopy.

7. Performance Metrics, Scaling Laws, and Practical Constraints

Spatiotemporal multiplexing schemes are characterized by channel count, fidelity, efficiency, cross-talk, and throughput. Scaling is dictated by physical constraints:

• Channel orthogonality: Mode isolation requires spectral, spatial, and group-velocity matching; cross-talk suppression $>$10–20 dB essential for independent operation (Zhang et al., 2020, Cruz-Delgado et al., 19 Feb 2024).
• Efficiency: Cascaded routing (multi-photon demultiplexing) incurs a scaling loss $\eta^{N(N-1)/2}$, while in quantum memories, per-mode efficiency is often $<$2% due to AOD, spin transfer, comb finesse, fiber-coupling (Hansen et al., 2023, Teller et al., 16 Jul 2025).
• Resource optimization: Single active-switch designs (EOM-driven demultiplexers), passive delay networks, or computational DOE-based sensor arrays minimize complexity. Fast switches and short delays are critical for scaling to tens of channels in compact footprint (Hansen et al., 2023).
• Bandwidth and resolution: Achievable data rates (Rydberg-EIT receivers), pulse durations (fiber systems), spatial resolution (DOE imaging), and entanglement fidelities are dependent on mode count, device nonlinearity, and compensation strategy (Knarr et al., 2023, Cruz-Delgado et al., 19 Feb 2024).
• Noise and cross-talk: Fluorescence and control-pulse-induced noise set SNR floors for quantum storage; overlapping PSFs in imaging demand careful regularization. Overall, mean cross-talk in leading experiments is $\sim$3% (Teller et al., 16 Jul 2025, Zhou et al., 19 Jul 2025).

The joint exploitation of spatial and temporal degrees of freedom—via precise engineering, compensation protocols, and advanced multiplexing hardware—continues to extend the feasible performance envelope for photonic communications, quantum networks, ultrafast lasers, and large-scale microscopy.