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Determining the optimal communication channels of arbitrary optical systems using integrated photonic processors

Nature Photonics volume 18, pages 149–155 (2024)Cite this article

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A Publisher Correction to this article was published on 05 December 2023

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Abstract

Modes of propagation through an optical system are generally defined as the eigensolutions of the wave equation in the system. When propagation occurs through complicated or highly scattering media, however, modes are better identified as the best orthogonal communication channels to send information between sets of input and output apertures. Here we determine the optimal bidirectional orthogonal communication channels through arbitrary and scattering optical systems using photonic processors. The processors consist of meshes of electrically tuneable Mach–Zehnder interferometers in silicon photonics. The meshes can configure themselves based on simple power maximization or minimization algorithms, without external calculations or calibration or any prior knowledge of the optical system. The identification of the communication mode channels corresponds to a singular value decomposition of the entire optical system, autonomously performed by the photonic processors. We observe crosstalk below –30 dB between the optimized channels even in the presence of distorting masks or partial obstructions. In these cases, although the beams bear little resemblance to conventional mode families, they still show orthogonality. These findings offer potential for applications in multimode optical communication systems, promising efficient channel identification, adaptability to dynamic media and robustness against environmental challenges.

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Fig. 1: Automatically finding the best orthogonal communication modes with a pair of photonic integrated processors.
Fig. 2: Orthogonal modes between arbitrary sets of optical apertures.
Fig. 3: Orthogonal modes through obstacles and scattering media.
Fig. 4: Orthogonality between data communication channels.

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Data availability

All the data supporting the findings of this study are available within this Article and its Supplementary Information. Any additional data are available from the corresponding author on reasonable request.

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The computer codes that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

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References

  1. Cox, M. A. et al. Structured light in turbulence. IEEE J. Sel. Topics Quantum Electron. 27, 1–21 (2021).

    Article  Google Scholar 

  2. Hill, R. J. Optical propagation in turbulent water. J. Opt. Soc. Am. 68, 1067–1072 (1978).

    Article  ADS  Google Scholar 

  3. Matthès, M. W., Bromberg, Y., de Rosny, J. & Popoff, S. M. Learning and avoiding disorder in multimode fibers. Phys. Rev. X 11, 021060 (2021).

    Google Scholar 

  4. Vellekoop, I. M. & Mosk, A. P. Focusing coherent light through opaque strongly scattering media. Opt. Lett. 32, 2309–2311 (2007).

    Article  CAS  PubMed  ADS  Google Scholar 

  5. Yoon, S. et al. Deep optical imaging within complex scattering media. Nat. Rev. Phys. 2, 141–158 (2020).

    Article  Google Scholar 

  6. Biton, N., Kupferman, J. & Arnon, S. OAM light propagation through tissue. Sci. Rep. 11, 2407 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  7. Ishimaru, A. The beam wave case and remote sensing. in Laser Beam Propagation in the Atmosphere. Topics in Applied Physics (ed Strohbehn, J. W.) 129–170 (Springer, 1978).

  8. Heck, M. J. R. Highly integrated optical phased arrays: photonic integrated circuits for optical beam shaping and beam steering. Nanophotonics 6, 93–107 (2017).

    Article  CAS  Google Scholar 

  9. Nape, I. et al. Revealing the invariance of vectorial structured light in complex media. Nat. Photon. 16, 538–546 (2022).

    Article  CAS  ADS  Google Scholar 

  10. Churnside, J. H. & Lataitis, R. J. Wander of an optical beam in the turbulent atmosphere. Appl. Opt. 29, 926–930 (1990).

    Article  CAS  PubMed  ADS  Google Scholar 

  11. Gong, L. et al. Optical orbital-angular-momentum-multiplexed data transmission under high scattering. Light Sci. Appl. 8, 27 (2019).

    Article  PubMed  PubMed Central  ADS  Google Scholar 

  12. Miller, D. A. B. Waves, modes, communications, and optics: a tutorial. Adv. Opt. Photon. 11, 679–825 (2019).

    Article  Google Scholar 

  13. Miller, D. A. B. Communicating with waves between volumes: evaluating orthogonal spatial channels and limits on coupling strengths. Appl. Opt. 39, 1681–1699 (2000).

    Article  CAS  PubMed  ADS  Google Scholar 

  14. Miller, D. A. B. Establishing optimal wave communication channels automatically. J. Lightwave Technol. 31, 3987–3994 (2013).

    Article  ADS  Google Scholar 

  15. Miller, D. A. B. Self-configuring universal linear optical component. Photon. Res. 1, 1–15 (2013).

    Article  ADS  Google Scholar 

  16. Harris, N. C. et al. Linear programmable nanophotonic processors. Optica 5, 1623–1631 (2018).

    Article  CAS  ADS  Google Scholar 

  17. Zhou, H. et al. Chip-scale optical matrix computation for PageRank algorithm. IEEE J. Sel. Topics Quantum Electron. 26, 8300910 (2020).

    Article  CAS  Google Scholar 

  18. Bogaerts, W. et al. Programmable photonic circuits. Nature 586, 207–216 (2020).

    Article  CAS  PubMed  ADS  Google Scholar 

  19. Zhou, H. et al. Photonic matrix multiplication lights up photonic accelerator and beyond. Light Sci. Appl. 11, 30 (2022).

    Article  PubMed  PubMed Central  ADS  Google Scholar 

  20. Pai, S. et al. Experimental evaluation of digitally verifiable photonic computing for blockchain and cryptocurrency. Optica 10, 552–560 (2023).

    Article  CAS  ADS  Google Scholar 

  21. Shen, Y. et al. Deep learning with coherent nanophotonic circuits. Nat. Photon. 11, 441–446 (2017).

    Article  CAS  ADS  Google Scholar 

  22. Shokraneh, F., Geoffroy-gagnon, S. & Liboiron-Ladouceur, O. The diamond mesh, a phase-error- and loss-tolerant field-programmable MZI-based optical processor for optical neural networks. Opt. Express 28, 23495–23508 (2020).

    Article  CAS  PubMed  ADS  Google Scholar 

  23. Tian, Y. et al. Scalable and compact photonic neural chip with low learning-capability-loss. Nanophotonics 11, 329–344 (2022).

    Article  CAS  Google Scholar 

  24. Pai, S. et al. Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380, 398–404 (2023).

    Article  CAS  PubMed  ADS  Google Scholar 

  25. Tzarouchis, D. C., Mencagli, M. J., Edwards, B. & Engheta, N. Mathematical operations and equation solving with reconfigurable metadevices. Light Sci. Appl. 11, 263 (2022).

    Article  CAS  PubMed  PubMed Central  ADS  Google Scholar 

  26. Harris, N. C. et al. Quantum transport simulations in a programmable nanophotonic processor. Nat. Photon. 11, 447–452 (2017).

    Article  CAS  ADS  Google Scholar 

  27. Milanizadeh, M. et al. Coherent self-control of free-space optical beams with integrated silicon photonic meshes. Photon. Res. 9, 2196–2204 (2021).

    Article  Google Scholar 

  28. Miller, D. A. B. Analyzing and generating multimode optical fields using self-configuring networks. Optica 7, 794–801 (2020).

    Article  ADS  Google Scholar 

  29. Milanizadeh, M. et al. Separating arbitrary free-space beams with an integrated photonic processor. Light Sci. Appl. 11, 197 (2022).

    Article  CAS  PubMed  PubMed Central  ADS  Google Scholar 

  30. Bütow, J. et al. Spatially resolving amplitude and phase of light with a reconfigurable photonic integrated circuit. Optica 9, 939–946 (2022).

    Article  ADS  Google Scholar 

  31. Miller, D. A. B. Self-aligning universal beam coupler. Opt. Express 21, 6360–6370 (2013).

    Article  PubMed  ADS  Google Scholar 

  32. Annoni, A. et al. Unscrambling light-automatically undoing strong mixing between modes. Light Sci. Appl. 6, 17110–17110 (2017).

    Article  Google Scholar 

  33. Fontaine, N. K. et al. Space-division multiplexing and all-optical MIMO demultiplexing using a photonic integrated circuit. In National Fiber Optic Engineers Conference PDP5B.1 (Optica Publishing Group, 2012).

  34. Harris, N. C. et al. Efficient, compact and low loss thermo-optic phase shifter in silicon. Opt. Express 22, 10487–10493 (2014).

    Article  PubMed  ADS  Google Scholar 

  35. Rahim, A. et al. Taking silicon photonics modulators to a higher performance level: state-of-the-art and a review of new technologies. Adv. Photon. 3, 024003 (2021).

    Article  CAS  ADS  Google Scholar 

  36. Choutagunta, K., Roberts, I., Miller, D. A. B. & Kahn, J. M. Adapting Mach-Zehnder mesh equalizers in direct-detection mode-division-multiplexed links. J. Lightwave Technol. 38, 723–735 (2020).

    Article  ADS  Google Scholar 

  37. Tzang, O. et al. Wavefront shaping in complex media with a 350 kHz modulator via a 1D-to-2D transform. Nat. Photon. 13, 788–793 (2019).

    Article  CAS  ADS  Google Scholar 

  38. Zanetto, F. et al. Dithering-based real-time control of cascaded silicon photonic devices by means of non-invasive detectors. IET Optoelectronics 15, 111–120 (2021).

    Article  Google Scholar 

  39. Xue, Y. et al. High-speed and low dark current silicon-waveguide-coupled III-V photodetectors selectively grown on SoI. Optica 9, 1219–1226 (2022).

    Article  CAS  ADS  Google Scholar 

  40. Fatemi, R., Khial, P. P., Khachaturian, A. & Hajimiri, A. Breaking FOV-aperture trade-off with multi-mode nano-photonic antennas. IEEE J. Sel. Topics Quantum Electron. 27, 6100614 (2021).

    Article  Google Scholar 

  41. Sacher, W. D., Huang, Y., Lo, G.-Q. & Poon, J. K. S. Multilayer silicon nitride-on-silicon integrated photonic platforms and devices. J. Lightwave Technol. 33, 901–910 (2015).

    Article  CAS  ADS  Google Scholar 

  42. Milanizadeh, M., Aguiar, D., Melloni, A. & Morichetti, F. Canceling thermal cross-talk effects in photonic integrated circuits. J. Lightwave Technol. 37, 1325–1332 (2019).

    Article  CAS  ADS  Google Scholar 

  43. Zemtsov, D. S. et al. Broadband silicon grating couplers with high efficiency and a robust design. Opt. Lett. 47, 3339–3342 (2022).

    Article  CAS  PubMed  ADS  Google Scholar 

  44. Lu, Z. et al. Broadband silicon photonic directional coupler using asymmetric-waveguide based phase control. Opt. Express 23, 3795–3808 (2015).

    Article  CAS  PubMed  ADS  Google Scholar 

  45. Poulton, C. V. et al. Long-range LiDAR and free-space data communication with high-performance optical phased arrays. IEEE J. Sel. Topics Quantum Electron. 25, 7700108 (2019).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

S.S., G.F., M. Sampietro, M. Sorel, A.M. and F.M. acknowledge support from the European Commission under the Horizon 2020 Programme (SuperPixels, grant no. 829116). S.S., M. Sorel, A.M. and F.M. acknowledge support from the Italian National Recovery and Resilience Plan (NRRP) of NextGenerationEU, partnership on ‘Telecommunications of the Future’ (PE00000001—program ‘RESTART’, Structural Project ‘Rigoletto’ and Focused Project ‘HePIC’). D.A.B.M. acknowledges support by the Air Force Office of Scientific Research (AFOSR, grants FA9550-17-1-0002 and FA9550-21-1-0312). Part of this work was carried out at Polifab, the micro- and nanofabrication facility of Politecnico di Milano (https://www.polifab.polimi.it/). We thank C. De Vita for his support in the realization of the phase masks used in the experiments and V. Grimaldi for his support in the development of the control electronics.

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Author notes

  1. Maziyar Milanizadeh

    Present address: Advanced Electronics and Photonics Research Centre, National Research Council Canada, Ottawa, Ontario, Canada

Authors and Affiliations

  1. Department of Electronics, Information and Bioengineering, Politecnico di Milano, Milan, Italy

    SeyedMohammad SeyedinNavadeh, Maziyar Milanizadeh, Francesco Zanetto, Marco Sampietro, Andrea Melloni & Francesco Morichetti

  2. Department of Physics, Politecnico di Milano, Milan, Italy

    Giorgio Ferrari

  3. School of Engineering, University of Glasgow, Glasgow, UK

    Marc Sorel

  4. TeCIP Institute, Scuola Superiore Sant’Anna, Pisa, Italy

    Marc Sorel

  5. Ginzton Laboratory, Stanford University, Stanford, CA, USA

    David A. B. Miller

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Contributions

M.M. and S.S. designed the photonic chips and performed the optical measurements. F.Z., G.F. and M. Sampietro developed the electronic control systems. M. Sorel contributed to the design of the photonic chip. S.S., M.M., A.M., D.A.B.M. and F.M. conceived the experiments and analysed the experimental data. S.S., D.A.B.M. and F.M. wrote the manuscript. All the authors contributed to the revision of the manuscript. F.M. supervised the project.

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Correspondence to Francesco Morichetti.

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Extended data

Extended Data Fig. 1 Beam shapes of orthogonal modes between arbitrary sets of optical apertures.

Complete set of beam pairs (far fields \({{{\Psi }}}_{{\hat{{{{\bf{u}}}}}}_{1,2}}\) and \({{{\Phi }}}_{{\hat{{{{\bf{v}}}}}}_{1,2}}\)) measured when the number of input M / output N apertures in the source/receiving volumes are progressively reduced, a in a non-symmetric configuration (M = 9, 8, . . . , 5; N = 9), and b in a (point-)symmetric configuration (M = N = 9, 8, . . . , 5).

Extended Data Fig. 2 Coupling strength of mode pairs established between arbitrary sets of optical apertures.

Simulated coupling strengths of modes established between the source/receiving volumes when the number of input M and output N apertures are progressively reduced a in a non-symmetric configuration (M = 9, 8, . . . , 5; N = 9), and b in a (point-)symmetric configuration (M = N = 9, 8, . . . , 5). Coupling strengths are normalized to that of the first mode when M = N = 9. Experimental data are shown in Fig. 2b,c, while measured beam shapes are reported in Extended Data Fig. 1.

Extended Data Fig. 3 Orthogonal modes through obstacles and scattering media.

The full set of obstacles used in the experiments include metal obstructions arranged as a periodic pattern of a circles (and laterally shifted in b), c donuts, d crosses, and e a microscale reproduction of the Politecnico di Milano logo. The far-field beam shapes of the first two modes \({{{\Psi }}}_{{\hat{{{{\bf{u}}}}}}_{1,2}}\) providing the maximum coupling strengths and the minimum mutual cross-talk through these obstacles are shown. For each case, bar charts show the coupling strength (σij, i = j) and the mutual cross-talk (σij, i ≠ j), which are both deteriorated with the insertion of the obstacle (dashed bars, before configuration), and can be mostly recovered by optimizing the two photonic processors (solid bars, after configuration). In the experiments reported in panel f the obstacle is a phase aberrator emulated by using an SLM; the recovery of the coupling strength (σij, i = j) and the mutual cross-talk (σij, i ≠ j) is shown for 11 different example configurations of the SLM. The peak-to-peak phase shift introduced by the phase-only aberrator is 2π.

Supplementary information

Supplementary Information

Supplementary Sections 1–3, Figs. 1–4 and caption for Video 1.

Supplementary Video 1

Camera view of the measured far field of the first (mode 1; left) and second (mode 2; right) modes during the automated setting performed by the two-processor system. The experimental conditions are the ones considered in Fig. 1e. ‘Reset’ operations correspond to random settings of all the phase actuators of the two meshes, which are scrambled at each trial. To better appreciate the mode evolution, the control algorithm is intentionally slowed down and is paused at each reset. Two modes are sequentially established (search for mode 2 starts after the convergence of mode 1); however, for a better comparison, the evolution of the two modes is shown together in the video.

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SeyedinNavadeh, S., Milanizadeh, M., Zanetto, F. et al. Determining the optimal communication channels of arbitrary optical systems using integrated photonic processors. Nat. Photon. 18, 149–155 (2024). https://doi.org/10.1038/s41566-023-01330-w

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