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

doi:10.1038/nmat4324

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

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81 Scopus citations

Abstract

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_2ω=2k_ω and n_2ω=-n_ω, where the coherent harmonic wave emerges along a direction opposite to that of the incoming fundamental light.

Original language	English (US)
Pages (from-to)	807-811
Number of pages	5
Journal	Nature Materials
Volume	14
Issue number	8
DOIs	https://doi.org/10.1038/nmat4324
State	Published - 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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title = "Backward phase-matching for nonlinear optical generation in negative-index materials",

abstract = "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 k2ω=2kω and n2ω=-nω, where the coherent harmonic wave emerges along a direction opposite to that of the incoming fundamental light.",

author = "Shoufeng Lan and Lei Kang and Schoen, {David T.} and Rodrigues, {Sean P.} and Yonghao Cui and Brongersma, {Mark L.} and Wenshan Cai",

note = "Funding Information: This work was performed in part at the Georgia Tech Institute for Electronics and Nanotechnology, a member of the National Nanotechnology Infrastructure Network, which is supported by the National Science Foundation. W.C. acknowledges the start-up fund from the Georgia Institute of Technology and the generous gift by OPE LLC in support of the scientific research in the Cai Lab. S.P.R. acknowledges the support of the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1148903. M.L.B. acknowledges support from the AFOSR MURI on Integrated Hybrid Nanophotonic Circuits, Grant FA9550-12-1-0024. Publisher Copyright: {\textcopyright} 2015 Macmillan Publishers Limited.",

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AU - Kang, Lei

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AU - Rodrigues, Sean P.

AU - Cui, Yonghao

AU - Brongersma, Mark L.

AU - Cai, Wenshan

N1 - Funding Information: This work was performed in part at the Georgia Tech Institute for Electronics and Nanotechnology, a member of the National Nanotechnology Infrastructure Network, which is supported by the National Science Foundation. W.C. acknowledges the start-up fund from the Georgia Institute of Technology and the generous gift by OPE LLC in support of the scientific research in the Cai Lab. S.P.R. acknowledges the support of the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1148903. M.L.B. acknowledges support from the AFOSR MURI on Integrated Hybrid Nanophotonic Circuits, Grant FA9550-12-1-0024. Publisher Copyright: © 2015 Macmillan Publishers Limited.

PY - 2015/8/28

Y1 - 2015/8/28

N2 - 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 k2ω=2kω and n2ω=-nω, where the coherent harmonic wave emerges along a direction opposite to that of the incoming fundamental light.

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

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