Reconfigurable Linear Optical Transformations in a Single Integrated Multimode Waveguide
Abstract
Wavefront shaping enables control over optical fields for applications ranging from imaging to photonic information processing. While conventional wavefront shaping relies on free-space systems comprising bulk optical components, compact and fully integrated approaches are comparatively unexplored. Here, we introduce a concept based on a single multimode waveguide with distributed thermo-optic perturbations for controlling multimode propagation. We develop a differentiable physical model and numerically demonstrate shaping the outgoing wavefront and programmable linear optical transformations, using gradient-based optimization. We achieve diffraction-limited focusing with 20 spatial modes and show that the theoretical focusing limit can be retained while maintaining more than 99% of the input optical power. We extend this approach to complete input--output transformations and implement Sylvester--Hadamard matrix operations with dimensions up to 32×32 with correlations exceeding 99%. Reducing the number of tunable elements requires stronger individual perturbations, resulting in stronger and broader mode coupling that extends beyond the target modes. To mitigate this effect, we consider ancillary modes and realize a 4×4 transformation that reaches 93.8%±4.8% correlation with only 5N2 tunable elements, where N=4 denotes the number of spatial modes. The best-performing realization reaches 98.3% correlation with the target. Our results demonstrate that thermo-optic control of multimode waveguides offers an approach to fully-integrated wavefront shaping and programmable linear optical transformations, with potential applications in classical and quantum photonic processing
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BibTeX
@misc{worp2026reconfigurable,
title = {{Reconfigurable Linear Optical Transformations in a Single Integrated Multimode Waveguide}},
author = {Manoah van der Worp and Jonas Krimmer and Ivo M. Vellekoop and Pepijn W. H. Pinkse and Stefan Rothe},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32683},
eprint = {2609.32683},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32683},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Reconfigurable Linear Optical Transformations in a Single Integrated Multimode Waveguide
AU - Manoah van der Worp
AU - Jonas Krimmer
AU - Ivo M. Vellekoop
AU - Pepijn W. H. Pinkse
AU - Stefan Rothe
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32683
UR - https://arxiv.org/abs/2609.32683
AB - Wavefront shaping enables control over optical fields for applications ranging from imaging to photonic information processing. While conventional wavefront shaping relies on free-space systems comprising bulk optical components, compact and fully integrated approaches are comparatively unexplored. Here, we introduce a concept based on a single multimode waveguide with distributed thermo-optic perturbations for controlling multimode propagation. We develop a differentiable physical model and numerically demonstrate shaping the outgoing wavefront and programmable linear optical transformations, using gradient-based optimization. We achieve diffraction-limited focusing with 20 spatial modes and show that the theoretical focusing limit can be retained while maintaining more than 99% of the input optical power. We extend this approach to complete input--output transformations and implement Sylvester--Hadamard matrix operations with dimensions up to 32×32 with correlations exceeding 99%. Reducing the number of tunable elements requires stronger individual perturbations, resulting in stronger and broader mode coupling that extends beyond the target modes. To mitigate this effect, we consider ancillary modes and realize a 4×4 transformation that reaches 93.8%±4.8% correlation with only 5N^2 tunable elements, where N=4 denotes the number of spatial modes. The best-performing realization reaches 98.3% correlation with the target. Our results demonstrate that thermo-optic control of multimode waveguides offers an approach to fully-integrated wavefront shaping and programmable linear optical transformations, with potential applications in classical and quantum photonic processing
ER -