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

Nature Materials volume 14, pages 807–811 (2015)Cite this article

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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 ∼780 nm 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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Figure 1: Phase-matching conditions for second-harmonic generation in nonlinear optical media.
Figure 2: Operating point for backward phase-matching in a plasmonic waveguide.
Figure 3: Experimental design for backward phase-matching in a waveguide with a dual-layered dielectric core.
Figure 4: Frequency-doubled signals emerging from the plasmonic waveguide.
Figure 5: Backward phase-matched second-harmonic generation.

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Acknowledgements

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.

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Authors and Affiliations

  1. School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA

    Shoufeng Lan, Sean P. Rodrigues & Wenshan Cai

  2. School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA

    Lei Kang, Sean P. Rodrigues, Yonghao Cui & Wenshan Cai

  3. Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA

    David T. Schoen & Mark L. Brongersma

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  1. Shoufeng Lan
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Contributions

W.C. and M.L.B. conceived the idea and designed the experiment. S.L., D.T.S. and Y.C. fabricated the sample. S.L., L.K. and S.P.R. carried out measurements. All authors contributed to the interpretation of results and participated in the preparation of manuscript.

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Correspondence to Wenshan Cai.

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The authors declare no competing financial interests.

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Lan, S., Kang, L., Schoen, D. et al. Backward phase-matching for nonlinear optical generation in negative-index materials. Nature Mater 14, 807–811 (2015). https://doi.org/10.1038/nmat4324

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