Backward phase-matching for nonlinear optical generation in negative-index materials

Shoufeng Lan, Lei Kang, David T. Schoen, Sean P. Rodrigues, Yonghao Cui, Mark L. Brongersma, Wenshan Cai

    Research output: Contribution to journalArticlepeer-review

    78 Scopus citations


    Metamaterials have enabled the realization of unconventional electromagnetic properties not found in nature, which provokes us to rethink the established rules of optics in both the linear and nonlinear regimes. One of the most intriguing phenomena in nonlinear metamaterials is 'backward phase-matching', which describes counter-propagating fundamental and harmonic waves in a negative-index medium. Predicted nearly a decade ago, this process is still awaiting a definitive experimental confirmation at optical frequencies. Here, we report optical measurements showing backward phase-matching by exploiting two distinct modes in a nonlinear plasmonic waveguide, where the real parts of the mode refractive indices are 3.4 and-3.4 for the fundamental and the harmonic waves respectively. The observed peak conversion efficiency at the excitation wavelength of ∼780nm indicates the fulfilment of the phase-matching condition of k=2kω and n=-nω, where the coherent harmonic wave emerges along a direction opposite to that of the incoming fundamental light.

    Original languageEnglish (US)
    Pages (from-to)807-811
    Number of pages5
    JournalNature Materials
    Issue number8
    StatePublished - Aug 28 2015

    All Science Journal Classification (ASJC) codes

    • General Chemistry
    • General Materials Science
    • Condensed Matter Physics
    • Mechanics of Materials
    • Mechanical Engineering


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