Intermodal group-velocity engineering for broadband nonlinear optics [Cover Paper]
Interest in the nonlinear properties of multi-mode optical waveguides has seen a recent resurgence on account of the large dimensionality afforded by the platform. The large volume of modes in these waveguides provides a new spatial degree of freedom for phase matching nonlinear optical processes. However, this spatial dimension is quantized, which narrows the conversion bandwidths of intermodal processes and constrains spectral and temporal tailoring of the light. Here we show that by engineering the relative group velocity within the spatial dimension, we can tailor the phase-matching bandwidth of intermodal parametric nonlinearities. We demonstrate group-velocity-tailored parametric nonlinear mixing between higher-order modes in a multi-mode fiber with gain bandwidths that are more than an order of magnitude larger than that previously thought possible for intermodal four-wave mixing. As evidence of the technological utility of this methodology, we seed this process to generate the first high-peak-power wavelength-tunable all-fiber quasi-CW laser in the Ti:sapphire wavelength regime. More generally, with the combination of intermodal interactions, which dramatically expand the phase-matching degrees of freedom for nonlinear optics, and intermodal group-velocity engineering, which enables tailoring of the bandwidth of such interactions, we showcase a platform for nonlinear optics that can be broadband while being wavelength agnostic.
基金项目：Air Force Office of Scientific Research (AFOSR)10.13039/100000181 (FA9550-14-1-0165); Office of Naval Research (ONR)10.13039/100000006 (N00014-17-1-2519).
Lars Rish?j：Department of Electrical Engineering, Boston University, Boston, Massachusetts 02115, USA
Xiao Liu：Department of Electrical Engineering, Boston University, Boston, Massachusetts 02115, USA
Gautam Prabhakar：Department of Electrical Engineering, Boston University, Boston, Massachusetts 02115, USA
Siddharth Ramachandran：Department of Electrical Engineering, Boston University, Boston, Massachusetts 02115, USA
【1】T. ?i?már, and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3 , 1027 (2012).
【2】R. J. Essiambre, R. Ryf, N. K. Fontaine, and S. Randel, “Breakthroughs in photonics 2012: space-division multiplexing in multimode and multicore fibers for high-capacity optical communication,” IEEE Photon. J. 5 , 0701307 (2013).
【3】N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340 , 1545–1548 (2013).
【4】J. W. Nicholson, J. M. Fini, A. M. DeSantolo, X. Liu, K. Feder, P. S. Westbrook, V. R. Supradeepa, E. Monberg, F. DiMarcello, R. Ortiz, C. Headley, and D. J. DiGiovanni, “Scaling the effective area of higher-order-mode erbium-doped fiber amplifiers,” Opt. Express 20 , 24575–24584 (2012).
【5】S. Ramachandran, J. M. Fini, M. Mermelstein, J. W. Nicholson, S. Ghalmi, and M. F. Yan, “Ultra-large effective-area, higher-order mode fibers: a new strategy for high-power lasers,” Laser Photon. Rev. 2 , 429–448 (2008).
【6】B. Zwan, S. Legge, J. Holdsworth, and B. King, “Spatio-spectral analysis of supercontinuum generation in higher order electromagnetic modes of photonic crystal fiber,” Opt. Express 21 , 834–839 (2013).
【7】Y. Chen, Z. Chen, W. J. Wadsworth, and T. A. Birks, “Nonlinear optics in the LP02 higher-order mode of a fiber,” Opt. Express 21 , 17786–17799 (2013).
【8】S. O. Konorov, E. E. Serebrannikov, A. M. Zheltikov, P. Zhou, A. Tarasevitch, and D. von der Linde, “Mode-controlled colors from microstructure fibers,” Opt. Express 12 , 730–735 (2004).
【9】L. Rish?j, B. Tai, P. Kristensen, and S. Ramachandran, “Discovery of soliton self-mode conversion in multimode optical fibers,” arXiv:1805.06037.
【10】L. G. Wright, D. N. Christodoulides, and F. W. Wise, “Controllable spatiotemporal nonlinear effects in multimode fibres,” Nat. Photonics 9 , 306–310 (2015).
【11】K. Krupa, A. Tonello, B. M. Shalaby, M. Fabert, A. Barthélémy, G. Millot, S. Wabnitz, and V. Couderc, “Spatial beam self-cleaning in multimode fibres,” Nat. Photonics 11 , 237–241 (2017).
【12】M. Schnack, T. Hellwig, and K. Fallnich, “Ultrafast, all-optical control of modal phases in a few-mode fiber for all-optical switching,” Opt. Lett. 41 , 5588–5591 (2016).
【13】M. Ma, and L. R. Chen, “Harnessing mode-selective nonlinear optics for on-chip multi-channel all-optical signal processing,” APL Photon. 1 , 086104 (2016).
【14】J. Demas, G. Prabhakar, T. He, and S. Ramachandran, “Wavelength-agile high-power sources via four-wave mixing in higher-order modes,” Opt. Express 25 , 7455–7464 (2017).
【15】D. Cruz-Delgado, R. Ramirez-Alarcon, E. Ortiz-Ricardo, J. Monroy-Ruz, F. Dominguez-Serna, H. Cruz-Ramirez, K. Garay-Palmett, and A. B. U’Ren, “Fiber-based photon-pair source capable of hybrid entanglement in frequency and transverse mode, controllably scalable to higher dimensions,” Sci. Rep. 6 , 27377 (2016).
【16】K. Rottwitt, J. G. Koefoed, and E. N. Christensen, “Photon-pair sources based on intermodal four-wave mixing in few-mode fibers,” Fibers 6 , 32–34 (2018).
【17】R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24 , 308–310 (1974).
【18】R. H. Stolen, “Phase-matched-stimulated four-photon mixing in silica-fiber waveguides,” IEEE J. Quantum Electron. 11 , 100–103 (1975).
【19】J. Cheng, M. E. V. Pedersen, K. Charan, K. Wang, C. Xu, L. Grüner-Nielsen, and D. Jakobsen, “Intermodal four-wave mixing in a higher-order-mode fiber,” Appl. Phys. Lett. 101 , 161106 (2012).
【20】R. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, and R. Lingle, “Experimental investigation of inter-modal four-wave mixing in few-mode fibers,” IEEE Photon. Technol. Lett. 25 , 539–542 (2013).
【21】S. M. M. Friis, I. Begleris, Y. Jung, K. Rottwitt, P. Petropoulos, D. J. Richardson, P. Horak, and F. Parmigiani, “Inter-modal four-wave mixing study in a two-mode fiber,” Opt. Express 24 , 30338–30348 (2016).
【22】J. Demas, P. Steinvurzel, B. Tai, L. Rish?j, Y. Chen, and S. Ramachandran, “Intermodal nonlinear mixing with Bessel beams in optical fiber,” Optica 2 , 14–17 (2015).
【23】H. Pourbeyram, E. Nazemosadat, and A. Mafi, “Detailed investigation of intermodal four-wave mixing in SMF-28: blue-red generation from green,” Opt. Express 23 , 14487–14500 (2015).
【24】C.-S. Bres, A. O. J. Wiberg, B. P.-P. Kuo, N. Alic, and S. Radic, “Wavelength multicasting of 320-Gb/s channel in self-seeded parametric amplifier,” IEEE Photon. Technol. Lett. 21 , 1002–1004 (2009).
【25】B. Fang, O. Cohen, M. Liscidini, J. E. Sipe, and V. O. Lorenz, “Fast and highly resolved capture of the joint spectral density of photon pairs,” Optica 1 , 281–284 (2014).
【26】G. P. Agrawal, Nonlinear Fiber Optics (Elsevier, 2005).
【27】J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, “Anomalous dispersion in a photonic crystal fiber,” IEEE Photon. Technol. Lett. 12 , 807–809 (2000).
【28】D. Nodop, C. Jauregui, D. Schimpf, J. Limpert, and A. Tünnermann, “Efficient high-power generation of visible and mid-infrared light by degenerate four-wave-mixing in a large-mode-area photonic-crystal fiber,” Opt. Lett. 34 , 3499–3501 (2009).
【29】J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P. O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8 , 506–520 (2002).
【30】P. Steinvurzel, J. Demas, B. Tai, Y. Chen, L. Yan, and S. Ramachandran, “Broadband parametric wavelength conversion at 1?μm with large mode area fibers,” Opt. Lett. 39 , 743–746 (2014).
【31】J. Demas, L. Rish?j, and S. Ramachandran, “Free-space beam shaping for precise control and conversion of modes in optical fiber,” Opt. Express 23 , 28531–28545 (2015).
【32】J. Demas, G. Prabhakar, T. He, and S. Ramachandran, “Broadband and Wideband parametric gain via intermodal four-wave mixing in optical fiber,” in Conference on Lasers and Electro-Optics (CLEO) (2017), paper?SM3M.1.
【33】J. Demas, L. Rish?j, X. Liu, G. Prabhakar, and S. Ramachandran, “High-power, wavelength-tunable NIR all-fiber lasers via intermodal four-wave mixing,” in Conference on Lasers and Electro-Optics (CLEO) (2017), paper?JTh5A.8.
Jeff Demas, Lars Rish?j, Xiao Liu, Gautam Prabhakar, and Siddharth Ramachandran, "Intermodal group-velocity engineering for broadband nonlinear optics," Photonics Research 7(1), 1-7 (2019)