Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres

Abstract

Recent progress in wavefront shaping has enabled control of light propagation inside linear media to focus and image through scattering objects. In particular, light propagation in multimode fibres comprises complex intermodal interactions and rich spatiotemporal dynamics. Control of physical phenomena in multimode fibres and its applications are in their infancy, opening opportunities to take advantage of complex nonlinear modal dynamics. Here, we demonstrate a wavefront shaping approach for controlling nonlinear phenomena in multimode fibres. Using a spatial light modulator at the fibre input, real-time spectral feedback and a genetic algorithm optimization, we control a highly nonlinear multimode stimulated Raman scattering cascade and its interplay with four-wave mixing via a flexible implicit control on the superposition of modes coupled into the fibre. We show versatile spectrum manipulations including shifts, suppression, and enhancement of Stokes and anti-Stokes peaks. These demonstrations illustrate the power of wavefront shaping to control and optimize nonlinear wave propagation.

This is a preview of subscription content

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: System for WFS in nonlinear multimode fibres.
Fig. 2: WFS of FWM.
Fig. 3: WFS of SRS peaks.
Fig. 4: WFS of spectral shifts.
Fig. 5: SRS cascade suppression through high-mode excitation.

References

  1. 1.

    Mosk, A. P., Lagendijk, A., Lerosey, G. & Fink, M. Controlling waves in space and time for imaging and focusing in complex media. Nat. Photon. 6, 283–292 (2012).

    ADS  Article  Google Scholar 

  2. 2.

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

    ADS  Article  Google Scholar 

  3. 3.

    Katz, O., Small, E. & Silberberg, Y. Looking around corners and through thin turbid layers in real time with scattered incoherent light. Nat. Photon. 6, 549–553 (2012).

    ADS  Article  Google Scholar 

  4. 4.

    Park, J.-H., Sun, W. & Cui, M. High-resolution in vivo imaging of mouse brain through the intact skull. Proc. Natl Acad. Sci. USA 112, 9236–9241 (2015).

    ADS  Article  Google Scholar 

  5. 5.

    Čižmár, T. & Dholakia, K. Exploiting multimode waveguides for pure fibre-based imaging. Nat. Commun. 3, 1027 (2012).

    Article  Google Scholar 

  6. 6.

    Papadopoulos, I. N., Farahi, S., Moser, C. & Psaltis, D. High-resolution, lensless endoscope based on digital scanning through a multimode optical fiber. Biomed. Opt. Express 4, 260–270 (2013).

    Article  Google Scholar 

  7. 7.

    Caravaca-Aguirre, A. M., Niv, E., Conkey, D. B. & Piestun, R. Real-time resilient focusing through a bending multimode fiber. Opt. Express 21, 12881–12887 (2013).

    ADS  Article  Google Scholar 

  8. 8.

    Barsi, C., Wan, W. & Fleischer, J. W. Imaging through nonlinear media using digital holography. Nat. Photon. 3, 211–215 (2009).

    ADS  Article  Google Scholar 

  9. 9.

    Masihzadeh, O., Schlup, P. & Bartels, R. A. Enhanced spatial resolution in third-harmonic microscopy through polarization switching. Opt. Lett. 34, 1240–1242 (2009).

    ADS  Article  Google Scholar 

  10. 10.

    Katz, O., Small, E., Guan, Y. & Silberberg, Y. Noninvasive nonlinear imaging through strongly-scattering turbid layers. Optica. 1, 170–174 (2014).

    Article  Google Scholar 

  11. 11.

    Tzang, O. & Piestun, R. Lock-in detection of photoacoustic feedback signal for focusing through scattering media using wave-front shaping. Opt. Express 24, 28122–28130 (2016).

    ADS  Article  Google Scholar 

  12. 12.

    Frostig, H. et al. Focusing light by wavefront shaping through disorder and nonlinearity. Optica 4, 1073–1079 (2017).

    Article  Google Scholar 

  13. 13.

    Qiao, Y., Peng, Y., Zheng, Y., Ye, F. & Chen, X. Second-harmonic focusing by nonlinear turbid medium via feedback-based wavefront shaping. Opt. Lett. 42, 1895–1898 (2017).

    ADS  Article  Google Scholar 

  14. 14.

    Cohen, O. et al. Observation of random-phase lattice solitons. Nature 433, 500–503 (2005).

    ADS  Article  Google Scholar 

  15. 15.

    Sun, C., Waller, L., Dylov, D. V. & Fleischer, J. W. Spectral dynamics of spatially incoherent modulation instability. Phys. Rev. Lett. 108, 263902 (2012).

    ADS  Article  Google Scholar 

  16. 16.

    Demas, J. et al. Intermodal nonlinear mixing with Bessel beams in optical fiber. Optica 2, 14–17 (2015).

    Article  Google Scholar 

  17. 17.

    Wright, L. G., Christodoulides, D. N. & Wise, F. W. Controllable spatiotemporal nonlinear effects in multimode fibres. Nat. Photon. 9, 306–310 (2015).

    ADS  Article  Google Scholar 

  18. 18.

    Wright, L. G. et al. Self-organized instability in graded-index multimode fibres. Nat. Photon. 10, 771–776 (2016).

    ADS  Article  Google Scholar 

  19. 19.

    Krupa, K. et al. Spatial beam self-cleaning in multimode fiber. Nat. Photon. 11, 237–241 (2017).

    ADS  Article  Google Scholar 

  20. 20.

    Agrawal, G. P. Nonlinear Fiber Optics 4th edn (Academic Press, 2007).

  21. 21.

    Li, G., Bai, N., Zhao, N. & Xia, C. Space-division multiplexing: the next frontier in optical communication. Adv. Opt. Photon. 6, 293–339 (2014).

    Article  Google Scholar 

  22. 22.

    Gong, M. et al. Numerical modeling of transverse mode competition in strongly pumped multimode fiber lasers and amplifiers. Opt. Express 15, 3236–3246 (2007).

    ADS  Article  Google Scholar 

  23. 23.

    Richardson, D. J., Nilsson, J. & Clarkson, W. A. High power fiber lasers: current status and future perspectives. Josa B 27, B63–B92 (2010).

    Article  Google Scholar 

  24. 24.

    Caravaca-Aguirre, A. M. & Piestun, R. Single multimode fiber endoscope. Opt. Express 25, 1656–1665 (2017).

    ADS  Article  Google Scholar 

  25. 25.

    Wright, L. G., Renninger, W. H., Christodoulides, D. N. & Wise, F. W. Spatiotemporal dynamics of multimode optical solitons. Opt. Express 23, 3492–3506 (2015).

    ADS  Article  Google Scholar 

  26. 26.

    Choi, Y. et al. Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber. Phys. Rev. Lett. 109, 203901 (2012).

    ADS  Article  Google Scholar 

  27. 27.

    Florentin, R. et al. Shaping the light amplified in a multimode fiber. Light Sci. Appl. 6, e16208 (2017).

    Article  Google Scholar 

  28. 28.

    Popoff, S. M. et al. 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).

    ADS  Article  Google Scholar 

  29. 29.

    Bowers, M. W., Boyd, R. W. & Hankla, A. K. Brillouin-enhanced four-wave-mixing vector phase-conjugate mirror with beam-combining capability. Opt. Lett. 22, 360–362 (1997).

    ADS  Article  Google Scholar 

  30. 30.

    Stolen, R. H., Ippen, E. P. & Tynes, A. R. Raman oscillation in glass optical waveguide. Appl. Phys. Lett. 20, 62–64 (1972).

    ADS  Article  Google Scholar 

  31. 31.

    Rosman, G. High-order comb spectrum from stimulated Raman scattering in a silica-core fibre. Opt. Quantum Electron. Electron. 14, 92–93 (1982).

    Article  Google Scholar 

  32. 32.

    Pourbeyram, H., Agrawal, G. P. & Mafi, A. Stimulated Raman scattering cascade spanning the wavelength range of 523 to 1750 nm using a graded-index multimode optical fiber. Appl. Phys. Lett. 102, 1–5 (2013).

    Article  Google Scholar 

  33. 33.

    Chiang, K. S. Stimulated Raman scattering in a multimode optical fiber: self-focusing or mode competition? Opt. Commun. 95, 235–238 (1993).

    ADS  Article  Google Scholar 

  34. 34.

    Couny, F., Benabid, F., Roberts, P. J., Light, P. S. & Raymer, M. G. Generation and photonic guidance of multi-octave optical-frequency combs. Science 318, 1118–1121 (2007).

    ADS  Article  Google Scholar 

  35. 35.

    Nazemosadat, E., Pourbeyram, H. & Mafi, A. Phase matching for spontaneous frequency conversion via four-wave mixing in graded-index multimode optical fibers. J. Opt. Soc. Am. B 33, 144–150 (2016).

    ADS  Article  Google Scholar 

  36. 36.

    Conkey, D. B., Brown, A. N., Caravaca-Aguirre, A. M. & Piestun, R. Genetic algorithm optimization for focusing through turbid media in noisy environments. Opt. Express 20, 4840–4849 (2012).

    ADS  Article  Google Scholar 

  37. 37.

    Stolen, R. H., Bjorkholm, J. E. & Ashkin, A. Phase-matched three-wave mixing in silica fiber optical waveguides. Appl. Phys. Lett. 24, 308–310 (1974).

    ADS  Article  Google Scholar 

  38. 38.

    Stolen, R. H. Phase-matched-stimulated four-photon mixing in silica-fiber wave. IEEE J. Quantum Electron. 11, 100–103 (1975).

    ADS  Article  Google Scholar 

  39. 39.

    Pourbeyram, H. & Mafi, A. Photon pair generation in multimode optical fibers via intermodal phase matching. Phys. Rev. A 94, 023815 (2016).

    ADS  Article  Google Scholar 

  40. 40.

    Upiol, R. D. et al. Far-detuned cascaded intermodal four-wave mixing in a multimode fiber. Opt. Lett. 42, 1293–1296 (2017).

    ADS  Article  Google Scholar 

  41. 41.

    Wright, L. G., Wabnitz, S., Christodoulides, D. N. & Wise, F. W. Ultrabroadband dispersive radiation by spatiotemporal oscillation of multimode waves. Phys. Rev. Lett. 115, 223902 (2015).

    ADS  Article  Google Scholar 

  42. 42.

    Krupa, K. et al. Observation of geometric parametric instability induced by the periodic spatial self-imaging of multimode waves. Phys. Rev. Lett. 116, 183901 (2016).

    ADS  Article  Google Scholar 

  43. 43.

    Pourbeyram, H. & Mafi, A. Apparent non-conservation of momentum of light due to strongly coupled nonlinear dynamics in a multimode optical fiber. Preprint at https://arxiv.org/abs/1701.05606 (2017).

  44. 44.

    Dupiol, R. et al. Intermodal modulational instability in graded-index multimode optical fibers. Opt. Lett. 42, 3419–3422 (2017).

    ADS  Article  Google Scholar 

  45. 45.

    Lombard, L., Brignon, A., Huignard, J. P., Lallier, E. & Georges, P. Beam cleanup in a self-aligned gradient-index Brillouin cavity for high-power multimode fiber amplifiers. Opt. Lett. 31, 158–160 (2006).

    ADS  Article  Google Scholar 

  46. 46.

    Sharma, A., Dokhanian, M., Wu, Z., Williams, A. & Venkateswarlu, P. Four-photon-mixing-mediated stimulated Raman scattering in a multimode optical fiber. Opt. Lett. 19, 1122–1124 (1994).

    ADS  Article  Google Scholar 

  47. 47.

    Temprana, E. et al. Overcoming Kerr-induced capacity limit in optical fiber transmission. Science 348, 1445–1448 (2015).

    ADS  Article  Google Scholar 

  48. 48.

    Mitra, P. P. & Stark, J. B. Nonlinear limits to the information capacity of optical fibre communications. Nature 411, 1027–1030 (2001).

    ADS  Article  Google Scholar 

  49. 49.

    Essiambre, R., Kramer, G., Winzer, P. J., Foschini, G. J. & Goebel, B. Capacity limits of optical fiber networks. J. Light. Technol. 28, 662–701 (2010).

    ADS  Article  Google Scholar 

  50. 50.

    Chraplyvy, A. R. Limitations on lightwave communications imposed by optical-fiber nonlinearities. J. Light. Technol. 8, 1548–1557 (1990).

    ADS  Article  Google Scholar 

  51. 51.

    Terry, N. B., Alley, T. G., Russell, T. H. & Engel, K. T. An explanation of SRS beam cleanup in graded-index fibers and the absence of SRS beam cleanup in step-index fibers. Opt. Express 15, 17509–17519 (2007).

    ADS  Article  Google Scholar 

  52. 52.

    Katz, O., Small, E., Bromberg, Y. & Silberberg, Y. Focusing and compression of ultrashort pulses through scattering media. Nat. Photon. 5, 372–377 (2011).

    ADS  Article  Google Scholar 

  53. 53.

    Shen, X., Kahn, J. M. & Horowitz, M. A. Compensation for multimode fiber dispersion by adaptive optics. Opt. Lett. 30, 2985–2987 (2005).

    ADS  Article  Google Scholar 

  54. 54.

    Shibata, N., Shibata, S. & Edahiro, T. Refractive index dispersion of lightguide glasses at high temperature. Electron. Lett. 17, 310–311 (1981).

    ADS  Article  Google Scholar 

  55. 55.

    Tzang, O., Niv, E., Caravaca-Aguirre, A. M. & Piestun, R. Thermal expansion feedback for wave-front shaping. Opt. Express 25, 6122–6131 (2017).

    ADS  Article  Google Scholar 

  56. 56.

    Wright, L. G. et al. Multimode nonlinear fiber optics: massively parallel numerical solver, tutorial and outlook. IEEE J. Sel Top. Quantum Electron. 24, 5100516 (2018).

    Article  Google Scholar 

Download references

Acknowledgements

We thank F. Wise, L. Wright and R. Ulbricht for fruitful discussions. We thank S. Singh for help with the mode simulations. We acknowledge support from the National Science Foundation through awards 1611513 and 1548924, and from the National Institute of Health award REY026436A.

Author information

Affiliations

Authors

Contributions

O.T., A.M.C.-A. and R.P. initiated the project. A.M.C.-A. and O.T. performed the SRS enhancement experiments. O.T. designed and preformed the FWM and suppression experiments. K.W. and O.T. preformed the intermodal phase-matching analysis. O.T. and A.M.C.-A. preformed the numerical simulations. R.P. provided overall supervision. O.T. wrote the first version of the manuscript. All authors were involved in the analysis of the results and revision of the manuscript.

Corresponding author

Correspondence to Omer Tzang.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

This file contains details of modal phase matching, mode analysis for different fibre profile parameters, numerical simulations, fundamental and technological limitations of the approach, wavefront shaping of spectral shifts, fibre length effect on nonlinearity, and SLM damage monitoring procedure for high-power lasers.

Supplementary Video 1

Anti-Stokes enhancement.

Supplementary Video 2

Peak wavelength shift.

Supplementary Video 3

Suppression of stimulated Raman scattering.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Tzang, O., Caravaca-Aguirre, A.M., Wagner, K. et al. Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres. Nature Photon 12, 368–374 (2018). https://doi.org/10.1038/s41566-018-0167-7

Download citation

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing