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  • Open Access

Upper bounds on focusing light through multimode fibers

Amna Ammar1, Sarp Feykun Şener1,2, Mert Ercan1,2, and Hasan Yılmaz1,*

  • *Contact author: hasan.yilmaz@unam.bilkent.edu.tr
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Phys. Rev. Applied 24, 054006 – Published 4 November, 2025

DOI: https://doi.org/10.1103/64xd-3cbs

Abstract

Wavefront shaping enables precise control of light propagation through multimode fibers (MMFs), facilitating diffraction-limited focusing for applications such as high-resolution single-fiber imaging and high-power fiber amplifiers. While the theoretical intensity enhancement at the focal point is dictated by the number of input degrees of freedom, practical constraints—such as phase-only modulation and experimental noise—impose significant limitations. Despite its importance, the upper bounds of enhancement under these constraints remain largely unexplored. In this work, we establish a theoretical framework to predict the fundamental limits of intensity enhancement with phase-only modulation in the presence of noise-induced phase errors, and we experimentally demonstrate wavefront shaping that approaches these limits. Our experimental results confirm an enhancement factor of 5000 in a large-core MMF, approaching the theoretical upper bound, enabled by noise-tolerant wavefront shaping. These findings provide key insights into the limits of phase-only control in MMFs, with profound implications for single-fiber imaging, optical communication, high-power broad-area fiber amplification, and beyond.

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References (62)

  1. T. Čižmár and K. Dholakia, Exploiting multimode waveguides for pure fibre-based imaging, Nat. Commun. 3, 1027 (2012).
  2. Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber, Phys. Rev. Lett. 109, 203901 (2012).
  3. I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, Focusing and scanning light through a multimode optical fiber using digital phase conjugation, Opt. Express 20, 10583 (2012).
  4. I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, High-resolution, lensless endoscope based on digital scanning through a multimode optical fiber, Biomed. Opt. Express 4, 260 (2013).
  5. D. Loterie, S. Farahi, I. Papadopoulos, A. Goy, D. Psaltis, and C. Moser, Digital confocal microscopy through a multimode fiber, Opt. Express 23, 23845 (2015).
  6. L. V. Amitonova and J. F. De Boer, Compressive imaging through a multimode fiber, Opt. Lett. 43, 5427 (2018).
  7. L. V. Amitonova and J. F. de Boer, Endo-microscopy beyond the Abbe and Nyquist limits, Light Sci. Appl. 9, 81 (2020).
  8. T. Čižmár and K. Dholakia, Shaping the light transmission through a multimode optical fibre: Complex transformation analysis and applications in biophotonics, Opt. Express 19, 18871 (2011).
  9. I. T. Leite, S. Turtaev, X. Jiang, M. Šiler, A. Cuschieri, P. S. J. Russell, and T. Čižmár, Three-dimensional holographic optical manipulation through a high-numerical-aperture soft-glass multimode fibre, Nat. Photonics 12, 33 (2018).
  10. K. Li, X. Chen, A. R. Zakharian, J. E. Hurley, J. S. Stone, and M.-J. Li, Large core multimode fiber with high bandwidth and high connector tolerance for broadband short distance communications, APL Photonics 6, 070802 (2021).
  11. E. Kakkava, M. Romito, D. B. Conkey, D. Loterie, K. M. Stankovic, C. Moser, and D. Psaltis, Selective femtosecond laser ablation via two-photon fluorescence imaging through a multimode fiber, Biomed. Opt. Express 10, 423 (2019).
  12. J. W. Dawson, M. J. Messerly, R. J. Beach, M. Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. P. J. Barty, Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power, Opt. Express 16, 13240 (2008).
  13. D. J. Richardson, J. Nilsson, and W. A. Clarkson, High power fiber lasers: Current status and future perspectives, J. Opt. Soc. Am. B 27, B63 (2010).
  14. M. N. Zervas and C. A. Codemard, High power fiber lasers: A review, IEEE J. Sel. Top. Quantum Electron. 20, 219 (2014).
  15. S. Fu, W. Shi, Y. Feng, L. Zhang, Z. Yang, S. Xu, X. Zhu, R. A. Norwood, and N. Peyghambarian, Review of recent progress on single-frequency fiber lasers, J. Opt. Soc. Am. B 34, A49 (2017).
  16. R. Di Leonardo and S. Bianchi, Hologram transmission through multi-mode optical fibers, Opt. Express 19, 247 (2011).
  17. A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Controlling waves in space and time for imaging and focusing in complex media, Nat. Photonics 6, 283 (2012).
  18. R. Horstmeyer, H. Ruan, and C. Yang, Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue, Nat. Photonics 9, 563 (2015).
  19. I. M. Vellekoop, Feedback-based wavefront shaping, Opt. Express 23, 12189 (2015).
  20. S. Rotter and S. Gigan, Light fields in complex media: Mesoscopic scattering meets wave control, Rev. Mod. Phys. 89, 015005 (2017).
  21. O. Tzang, A. M. Caravaca-Aguirre, K. Wagner, and R. Piestun, Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres, Nat. Photonics 12, 368 (2018).
  22. S. Gigan, O. Katz, H. B. de Aguiar, E. R. Andresen, A. Aubry, J. Bertolotti, E. Bossy, D. Bouchet, J. Brake, S. Brasselet, et al., Roadmap on wavefront shaping and deep imaging in complex media, J. Phys. Photonics 4, 042501 (2022).
  23. H. Cao, A. P. Mosk, and S. Rotter, Shaping the propagation of light in complex media, Nat. Phys. 18, 994 (2022).
  24. H. Cao, T. Čižmár, S. Turtaev, T. Tyc, and S. Rotter, Controlling light propagation in multimode fibers for imaging, spectroscopy, and beyond, Adv. Opt. Photonics 15, 524 (2023).
  25. C.-W. Chen, L. V. Nguyen, K. Wisal, S. Wei, S. C. Warren-Smith, O. Henderson-Sapir, E. P. Schartner, P. Ahmadi, H. Ebendorff-Heidepriem, A. D. Stone, D. J. Ottaway, and H. Cao, Mitigating stimulated brillouin scattering in multimode fibers with focused output via wavefront shaping, Nat. Commun. 14, 7343 (2023).
  26. K. Wisal, C.-W. Chen, Z. Kuang, O. D. Miller, H. Cao, and A. D. Stone, Optimal input excitations for suppressing nonlinear instabilities in multimode fibers, Optica 11, 1663 (2024).
  27. S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media, Phys. Rev. Lett. 104, 100601 (2010).
  28. M. Kim, W. Choi, Y. Choi, C. Yoon, and W. Choi, Transmission matrix of a scattering medium and its applications in biophotonics, Opt. Express 23, 12648 (2015).
  29. S. Li, S. A. R. Horsley, T. Tyc, T. Čižmár, and D. B. Phillips, Memory effect assisted imaging through multimode optical fibres, Nat. Commun. 12, 3751 (2021).
  30. N. Bender, H. Haig, D. N. Christodoulides, and F. W. Wise, Spectral speckle customization, Optica 10, 1260 (2023).
  31. I. M. Vellekoop and A. P. Mosk, Focusing coherent light through opaque strongly scattering media, Opt. Lett. 32, 2309 (2007).
  32. I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, Exploiting disorder for perfect focusing, Nat. Photonics 4, 320 (2010).
  33. A. M. Caravaca-Aguirre, E. Niv, D. B. Conkey, and R. Piestun, Real-time resilient focusing through a bending multimode fiber, Opt. Express 21, 12881 (2013).
  34. A. Drémeau, A. Liutkus, D. Martina, O. Katz, C. Schülke, F. Krzakala, S. Gigan, and L. Daudet, Reference-less measurement of the transmission matrix of a highly scattering material using a DMD and phase retrieval techniques, Opt. Express 23, 11898 (2015).
  35. L. V. Amitonova, A. Descloux, J. Petschulat, M. H. Frosz, G. Ahmed, F. Babic, X. Jiang, A. P. Mosk, P. S. Russell, and P. W. H. Pinkse, High-resolution wavefront shaping with a photonic crystal fiber for multimode fiber imaging, Opt. Lett. 41, 497 (2016).
  36. A. Descloux, L. V. Amitonova, and P. W. H. Pinkse, Aberrations of the point spread function of a multimode fiber due to partial mode excitation, Opt. Express 24, 18501 (2016).
  37. M. N’Gom, T. B. Norris, E. Michielssen, and R. R. Nadakuditi, Mode control in a multimode fiber through acquiring its transmission matrix from a reference-less optical system, Opt. Lett. 43, 419 (2018).
  38. K. Nam and J.-H. Park, Increasing the enhancement factor for DMD-based wavefront shaping, Opt. Lett. 45, 3381 (2020).
  39. Z. Lyu, G. Osnabrugge, P. W. H. Pinkse, and L. V. Amitonova, Focus quality in raster-scan imaging via a multimode fiber, Appl. Opt. 61, 4363 (2022).
  40. A. D. Gomes, S. Turtaev, Y. Du, and T. Čižmár, Near perfect focusing through multimode fibres, Opt. Express 30, 10645 (2022).
  41. Z. Lyu and L. V. Amitonova, Wavefront shaping and imaging through a multimode hollow-core fiber, Opt. Express 32, 37098 (2024).
  42. H. C. Hammer and R. Uppu, Effect of core geometry on frequency correlations and channel capacity of a multimode optical fiber, Adv. Photonics Res. 6, 2400156 (2025).
  43. B. Mastiani, D. Cox, and I. M. Vellekoop, Practical considerations for high-fidelity wavefront shaping experiments, J. Phys. Photonics 6, 033003 (2024).
  44. I. M. Vellekoop and A. P. Mosk, Phase control algorithms for focusing light through turbid media, Opt. Commun. 281, 3071 (2008).
  45. H. Yılmaz, W. L. Vos, and A. P. Mosk, Optimal control of light propagation through multiple-scattering media in the presence of noise, Biomed. Opt. Express 4, 1759 (2013).
  46. B. Mastiani and I. M. Vellekoop, Noise-tolerant wavefront shaping in a Hadamard basis, Opt. Express 29, 17534 (2021).
  47. S. Resisi, Y. Viernik, S. M. Popoff, and Y. Bromberg, Wavefront shaping in multimode fibers by transmission matrix engineering, APL Photonics 5, 036103 (2020).
  48. K. Wisal, C.-W. Chen, H. Cao, and A. D. Stone, Theory of transverse mode instability in fiber amplifiers with multimode excitations, APL Photonics 9, 066114 (2024).
  49. S. Rothe, K. Wisal, C.-W. Chen, M. Ercan, A. Jesacher, A. D. Stone, and H. Cao, Output beam shaping of a multimode fiber amplifier, Opt. Commun. 577, 131405 (2025).
  50. S. Rothe, C.-W. Chen, P. Ahmadi, K. Wisal, M. Ercan, K. Lee, N. Vigne, A. D. Stone, and H. Cao, Wavefront shaping enables high-power multimode fiber amplifier with output control, Science 390, 173 (2025).
  51. F. van Beijnum, Master’s thesis, Department of Science and Technology, University of Twente (2009).
  52. C. W. Hsu, S. F. Liew, A. Goetschy, H. Cao, and A. D. Stone, Correlation-enhanced control of wave focusing in disordered media, Nat. Phys. 13, 497 (2017).
  53. H. Yılmaz, C. W. Hsu, A. Yamilov, and H. Cao, Transverse localization of transmission eigenchannels, Nat. Photonics 13, 352 (2019).
  54. H. Yılmaz, C. W. Hsu, A. Goetschy, S. Bittner, S. Rotter, A. Yamilov, and H. Cao, Angular memory effect of transmission eigenchannels, Phys. Rev. Lett. 123, 203901 (2019).
  55. E. G. van Putten, Ph.D. thesis, Department of Science and Technology, University of Twente (2011).
  56. M. Duan, Y. Zhao, Z. Yang, X. Deng, H. Huangfu, H. Zuo, Z. Li, and D. Wang, Modulate scattered light field with point guard algorithm, Opt. Commun. 548, 129832 (2023).
  57. I. M. Vellekoop and A. P. Mosk, Universal optimal transmission of light through disordered materials, Phys. Rev. Lett. 101, 120601 (2008).
  58. L. Shaughnessy, R. E. McIntosh, A. Goetschy, C. W. Hsu, N. Bender, H. Yılmaz, A. Yamilov, and H. Cao, Multiregion light control in diffusive media via wavefront shaping, Phys. Rev. Lett. 133, 146901 (2024).
  59. S.-Y. Lee, MMF-simulation, 2023, https://github.com/szuyul/MMF-simulation/releases/tag/v1.0
  60. M. Jang, C. Yang, and I. M. Vellekoop, Optical phase conjugation with less than a photon per degree of freedom, Phys. Rev. Lett. 118, 093902 (2017).
  61. K. Wisal, S. C. Warren-Smith, C.-W. Chen, H. Cao, and A. D. Stone, Theory of stimulated Brillouin scattering in fibers for highly multimode excitations, Phys. Rev. X 14, 031053 (2024).
  62. D. E. Boonzajer Flaes, J. Stopka, S. Turtaev, J. F. de Boer, T. Tyc, and T. Čižmár, Robustness of light-transport processes to bending deformations in graded-index multimode waveguides, Phys. Rev. Lett. 120, 233901 (2018).

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Phys. Rev. Applied 24, 054006– Published 4 November, 2025
  • Received 10 April 2025
  • Revised 14 August 2025
  • Accepted 9 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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