[1] D. Dai, J. E. Bowers. Silicon-based on-chip multiplexing technologies and devices for peta-bit optical interconnects. Nanophotonics, 3, 283-311(2014).

[2] S. Berdagu, P. Facq. Mode division multiplexing in optical fibers. Appl. Opt., 21, 1950-1955(1982).

[3] S. Bagheri, W. M. Green. Silicon-on-insulator mode-selective add-drop unit for on-chip mode-division multiplexing. Proceedings of IEEE Conference on Group IV Photonics(2009).

[4] L. W. Luo, N. Ophir, C. P. Chen, L. Gabrielli, C. B. Poitras, K. Bergmen, M. Lipson. WDM-compatible mode-division multiplexing on a silicon chip. Nat. Commun., 5, 3069(2014).

[5] Y. Ding, J. Xu, H. Ou, C. Peuchere. Mode-selective wavelength conversion based on four-wave mixing in a multimode silicon waveguide. Opt. Express, 22, 127-135(2014).

[6] M. Ma, L. Chen. On-chip silicon mode-selective broadband wavelength conversion based on cross-phase modulation. Conference on Lasers and Electro-Optics, STh3E.3(2016).

[7] Y. Qiu, X. Li, M. Luo, D. Chen, J. Wang, J. Xu, Q. Yang, S. Yu. Mode-selective wavelength conversion of OFDM-QPSK signals in a multimode silicon waveguide. Opt. Express, 25, 4493-4499(2017).

[8] R. W. Boyd. Nonlinear Optics(2003).

[9] M. Borghi, C. Castellan, S. Signorini, A. Trenti, L. Pavesi. Nonlinear silicon photonics. J. Opt., 19, 093002(2017).

[10] M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, A. L. Gaeta. Broad-band optical parametric gain on a silicon photonic chip. Nature, 441, 960-963(2006).

[11] K. Guo, L. Lin, J. Christensen, E. Christensen, X. Shi, Y. Ding, K. Rottwitt, H. Ou. Broadband wavelength conversion in a silicon vertical-dual-slot waveguide. Opt. Express, 25, 32964-32971(2017).

[12] R. J. Essiambre, M. A. Mestre, R. Ryf, A. H. Gnauck, R. W. Tkach, A. R. Chraplyvy, Y. Sun, X. Jiang, R. Lingle. Experimental investigation of inter-modal four-wave mixing in few-mode fibers. IEEE Photon. Technol. Lett., 25, 539-542(2013).

[13] H. Pourbeyram, E. Nazemosadat, A. Mafi. Detailed investigation of intermodal four-wave mixing in SMF-28: blue-red generation from green. Opt. Express, 23, 14487-14500(2015).

[14] W. Pan, Q. Jin, X. Li, S. Gao. All-optical wavelength conversion for mode-division multiplexing signals using four-wave mixing in a dual-mode fiber. J. Opt. Soc. Am. B, 32, 2417-2424(2015).

[15] S. Friis, I. Begleris, Y. Jung, K. Rottwitt, P. Petropoulos, D. Richardson, P. Horak, F. Parmigiani. Inter-modal four-wave mixing study in a two-mode fiber. Opt. Express, 24, 30338-30349(2016).

[16] J. Yuan, Z. Kang, F. Li, X. Zhang, X. Sang, G. Zhou, Q. Wu, B. Yan, K. Wang, C. Yu, H. Tam, P. Wai. Demonstration of intermodal four-wave mixing by femtosecond pulses centered at 1550 nm in an air-silica photonic crystal fiber. J. Lightwave Technol., 35, 2385-2390(2017).

[17] R. Dupiol, A. Bendahmane, K. Krupa, J. Fatome, A. Tonello, M. Fabert, V. Couderc, S. Wabnitz, G. Millot. Intermodal modulational instability in graded-index multimode optical fibers. Opt. Lett., 42, 3419-3422(2017).

[18] F. Parmigiani, Y. Jung, S. M. M. Friis, Q. Kang, I. Begleris, P. Horak, K. Rottwitt, P. Petropoulos, D. J. Richardson. Study of inter-modal four wave mixing in two few-mode fibres with different phase matching properties. Proceedings of 42nd European Conference on Optical Communication(2016).

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

[20] J. Cheng, M. E. Pedersen, K. Charan, K. Wang, C. Xu, L. Grner-Nielsen, D. Jakobsen. Intermodal four-wave mixing in a higher-order-mode fiber. Appl. Phys. Lett., 101, 161106(2012).

[21] H. Tu, Z. Jiang, D. L. Marks, S. A. Boppart. Intermodal four-wave mixing from femtosecond pulse-pumped photonic crystal fiber. Appl. Phys. Lett., 94, 101109(2009).

[22] S. Signorini, M. Mancinelli, M. Bernard, M. Ghulinyan, G. Pucker, L. Pavesi. Broad wavelength generation and conversion with multi modal four wave mixing in silicon waveguides. Proceedings of IEEE Conference on Group IV Photonics, 59-60(2017).

[23] E. A. Kittlaus, N. T. Otterstrom, P. T. Rakich. On-chip inter-modal Brillouin scattering. Nat. Commun., 8, 15819(2017).

[24] J. G. Crowder, S. D. Smith, A. Vass, J. Keddie. Infrared methods for gas detection. Mid-Infrared Semiconductor Optoelectronics, 595-613(2006).

[25] M. Mancinelli, A. Trenti, S. Piccione, G. Fontana, J. S. Dam, P. Tidemand-Lichtenberg, C. Pedersen, L. Pavesi. Mid-infrared coincidence measurements on twin photons at room temperature. Nat. Commun., 8, 15184(2017).

[26] B. Kuyken, P. Verheyen, P. Tannouri, X. Liu, J. Van Campenhout, R. Baets, W. Green, G. Roelkens. Generation of 3.6  µm radiation and telecom-band amplification by four-wave mixing in a silicon waveguide with normal group velocity dispersion. Opt. Lett., 39, 1349-1352(2014).

[27] S. K. Liao, H. L. Yong, C. Liu, G. L. Shentu, D. D. Li, J. Lin, H. Dai, S. Q. Zhao, B. Li, J. Y. Guan, W. Chen, Y. H. Gong, Y. Li, Z. H. Lin, G. S. Pan, J. S. Pelc, M. M. Fejer, W. Z. Zhang, W. Y. Liu, J. Yin, J. G. Ren, X. B. Wang, Q. Zhang, C. Z. Peng, J. W. Pan. Long-distance free-space quantum key distribution in daylight towards inter-satellite communication. Nat. Photonics, 11, 509-513(2017).

[28] A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, A. L. Gaeta. Tailored anomalous group-velocity dispersion in silicon channel waveguides. Opt. Express, 14, 4357-4362(2006).

[29] C. Lin, M. A. Bsch. Large-Stokes-shift stimulated four-photon mixing in optical fibers. Appl. Phys. Lett., 38, 479-481(1981).

[30] Y. Xiao, R. J. Essiambre, M. Desgroseilliers, A. M. Tulino, R. Ryf, S. Mumtaz, G. P. Agrawal. Theory of intermodal four-wave mixing with random linear mode coupling in few-mode fibers. Opt. Express, 22, 32039-32059(2014).

[31] X. Liu, B. Kuyken, G. Roelkens, R. Baets, R. M. Osgood, W. M. Green. Bridging the mid-infrared-to-telecom gap with silicon nanophotonic spectral translation. Nat. Photonics, 6, 667-671(2012).

[32] Q. Lin, J. Zhang, P. M. Fauchet, G. P. Agrawal. Ultrabroadband parametric generation and wavelength conversion in silicon waveguides. Opt. Express, 14, 4786-4799(2006).

[33] M. A. Foster, A. C. Turner, R. Salem, M. Lipson, A. L. Gaeta. Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides. Opt. Express, 15, 12949-12958(2007).

[34] W. S. Chang. Fundamentals of Guided-Wave Optoelectronic Devices(2009).

[35] S. Signorini, M. Borghi, M. Mancinelli, M. Bernard, M. Ghulinyan, G. Pucker, L. Pavesi. Oblique beams interference for mode selection in multimode silicon waveguides. J. Appl. Phys., 122, 113106(2017).

[36] G. P. Agrawal. Nonlinear Fiber Optics(2013).

[37] R. M. Osgood, N. C. Panoiu, J. I. Dadap, X. Liu, X. Chen, I.-W. Hsieh, E. Dulkeith, W. M. J. Green, Y. A. Vlasov. Engineering nonlinearities in nanoscale optical systems: physics and applications in dispersion-engineered silicon nanophotonic wires. Adv. Opt. Photon., 1, 162-235(2009).

[38] [38] The conversion efficiency is calculated as the ratio between the on-chip idler peak power and the on-chip signal power, both evaluated at the end of the waveguide. The input on-chip signal power was about 47 µW (= −13.3 dB) at 1640 nm on the second-order mode. At the end of the waveguide, considering 4.6 dB·cm−1 of propagation losses and 1.5 cm waveguide length, the signal power on the second-order mode is −20.2 dBm. The off-chip generated average idler power is about −74.2 dBm, as shown in Fig. 8(a). Considering the coupling losses for the first-order mode, 5.3 dB, the on-chip average idler power is −68.9 dBm. Considering that the pump laser has 10 MHz repetition rate and 40 ps pulse width, the on-chip idler peak power, at the end of the waveguide, is −34.9 dBm. Therefore, the conversion between the signal power, −20.2 dBm, and the idler peak power, −34.9 dBm, is −14.7 dB.