FLASH: Ultrafast beam quality characterization via spatial-to-temporal mapping

Abstract: Accurate and real-time monitoring of spatial beam quality has emerged as the absolute prerequisite for intelligent optical field regulation and advanced laser applications. However, modern high-power and multimode optical systems exhibit highly complex, nonlinear, and transient behaviors. In these systems, the spatial beam profile undergoes dramatic reorganizations within extremely short timeframes. Phenomena such as spatio-temporal mode-locking, transient beam self-cleaning, and plasma-induced aberrations demand nanosecond-level dynamic characterization. Yet, capturing these ultrafast dynamics is fundamentally bottlenecked by the kilohertz frame rates of conventional two-dimensional image sensors. To break this dimensional and temporal barrier, we propose an ultrafast non-imaging beam quality monitoring technique, termed Fiber-based Laser Assessment via Spatial-to-temporal High-speed-mapping (FLASH). By utilizing a multimode fiber to encode spatial beam variations into high-dimensional speckle fingerprints and a multicore fiber delay line array to serialize these features, we transform two-dimensional spatial information into high-speed one-dimensional temporal pulse sequences. Empowered by a deep learning model to decipher the serialized signals, the FLASH system achieves an unprecedented 100 MHz measurement rate with a minimal mean relative error of 0.32%. Realizing a five-order-of-magnitude speed improvement over standard camera-based methods, this spatial-to-temporal mapping paradigm provides a transformative spatial oscilloscope. It unlocks new possibilities for real-time intelligent adaptive control and the exploration of complex multimode nonlinear physics.

• The paper introduces FLASH, a system that boosts beam quality measurement speed by five orders of magnitude via spatial-to-temporal mapping.
• It employs a three-stage method involving multimode fiber encoding, multicore fiber serialization, and deep neural regression to deliver accurate M² measurements.
• Experimental results demonstrate MHz measurement rates with sub-percent errors, enabling real-time adaptive optics and ultrafast laser diagnostics.

Ultrafast Beam Quality Assessment via Spatial-to-Temporal Mapping: The FLASH Paradigm

Introduction

FLASH ("Fiber-based Laser Assessment via Spatial-to-temporal High-speed-mapping") introduces a paradigm shift in ultrafast optical diagnostics, directly addressing the persistent limitations of beam quality characterization in high-power and multimode laser systems. Modern laser applications—including adaptive optics, spatial beam shaping, and the study of multimode nonlinear dynamics—demand real-time, high-fidelity spatial diagnostics. However, spatio-temporal laser phenomena often manifest on nanosecond timescales, whereas traditional 2D imaging methods (e.g., camera-based M² metrics) are fundamentally rate-limited by physical sensor constraints, creating a mismatch with the requirements of advanced photonic systems.

Methodology

FLASH achieves a five-order-of-magnitude enhancement over conventional M² metrology by transducing high-dimensional spatial beam features into temporally serialized, high-bandwidth electrical signals. The technique's core involves three stages:

1. Spatial Encoding via Multimode Fiber (MMF): A highly structured speckle pattern is generated as the input optical pulse excites and interferes among many mode channels within a large-core MMF. This transformation deterministically encodes the full 2D amplitude and phase information into spatial speckle fingerprints extremely sensitive to beam quality variations.
2. Spatial-to-Temporal Serialization: A 7-core multicore fiber (MCF) samples the speckle field at discrete locations, and a fiber delay line array temporally separates each channel. The combined output, captured by a single high-speed photodetector, manifests as a serialized temporal pulse train—drastically reducing information dimensionality while preserving high-information-content features.
3. Deep Neural Regression: A densely connected Multilayer Perceptron (MLP) with eleven hidden layers is trained to map these seven-dimensional intensity vectors to the continuous M² factor associated with each input beam. The neural network is robustly trained using data incorporating realistic environmental and system noise, producing highly generalizable predictions.

The FLASH system supports a 100 MHz effective measurement rate with a pulse duration of 0.5 ns, leveraging both advanced fiber photonics and AI-powered regression to achieve state-of-the-art optical diagnostic performance.

Experimental Results

Data Synthesis and Training

Comprehensive ground-truth datasets are generated in silico by stochastically superposing up to twenty LP modes. Each near-field spatial profile is labeled using Yoda's rigorous second-moment formalism, ensuring high-fidelity M² values across the range from 1.0 to 5.0. The training corpus comprises over one million labeled data samples.

System Performance

• Measurement Rate and Precision: FLASH achieves a 100 MHz measurement throughput with a mean relative error (MRE) of 0.32% in M², exceeding conventional imaging-based approaches by five orders of magnitude in speed and offering 3–10x lower error rates. Predictive linearity (Pearson’s r > 0.99) is sustained across the entire M² range.
• Sampling Core Analysis: Increasing the number of MCF cores reduces predictive error monotonically, with seven cores delivering an optimal compromise between fidelity and throughput. Marginal accuracy gains diminish beyond six cores due to the intrinsic dimensionality reduction limit.
• Modal Complexity Robustness: Prediction error exhibits non-monotonic dependence on the number of mixed modes; the minimal MRE (0.16%) is observed at intermediate modal complexity, attributed to symmetry breaking and feature richness. Aliasing effects due to high-frequency speckle structure become apparent above ten mixed modes, but the system remains robust (MRE < 0.5%) due to the network's adaptability.

System Robustness

Stochastic experimental noise and environmental fluctuations are integrated into both the training process and real-world testing, ensuring that the MLP develops invariant internal representations of beam quality. Uncertainty envelopes in error analysis remain tight, underscoring both the denoising and decoding power of the neural model.

Implications and Future Perspectives

FLASH fundamentally reconceptualizes beam quality monitoring as a temporal single-pixel regression problem, rather than a spatial imaging task, allowing for the deployment of ultrafast feedback and adaptive control in a breadth of optical scenarios:

• Intelligent Adaptive Optics: Real-time M² telemetry at MHz rates enables closed-loop suppression of Transverse Mode Instability in LMA fibers and immediate compensation for laser-induced aberrations in precision manufacturing.
• Ultrafast Laser Physics: The temporal bandwidth is sufficient to directly observe evolving phenomena such as spatio-temporal mode-locking and nonlinear beam self-cleaning.
• Atmospheric Free-space Transmission: FLASH’s MHz feedback capability provides a technical basis for turbulence compensation and atmospheric channel stabilization.

The reuse and extension of the architecture to additional optical observables (e.g., higher-order modal content, polarization-resolved speckle analysis) is straightforward, supporting scalable upgrades. Moreover, the modularity of the serialization hardware and the transferability of the AI model suggest practical deployment in both laboratory and industrial environments.

Conclusion

FLASH represents a significant advance in ultrafast photonic diagnostics, replacing inherently slow 2D-imaging-based spatial analysis with a physically and algorithmically efficient spatial-to-temporal mapping framework. By uniting deterministic MMF speckle encoding, MCF serialization, and deep learning regression, the system achieves MHz-order measurement rates with sub-percent errors, without sacrificing diagnostic interpretability. The paradigm supports a range of next-generation applications in ultrafast laser science and high-power photonic system control, and its methodological framework is poised for broad adoption as spatio-temporal complexity escalates in applied optics and photonics.