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Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves


The arbitrary control of electromagnetic waves is a key aim of photonic research. Although, for example, the control of freely propagating waves (PWs; refs 1, 2, 3, 4, 5, 6) and surface waves (SWs; refs 7, 8, 9, 10) has separately become possible using transformation optics and metamaterials, a bridge linking both propagation types has not yet been found. Such a device has particular relevance given the many schemes of controlling electromagnetic waves at surfaces and interfaces, leading to trapped rainbows11,12, lensing13,14,15,16, beam bending17, deflection18,19,20, and even anomalous reflection/refraction21,22. Here, we demonstrate theoretically and experimentally that a specific gradient-index meta-surface can convert a PW to a SW with nearly 100% efficiency. Distinct from conventional devices such as prism23 or grating24,25,26 couplers, the momentum mismatch between PW and SW is compensated by the reflection-phase gradient of the meta-surface, and a nearly perfect PW–SW conversion can happen for any incidence angle larger than a critical value. Experiments in the microwave region, including both far-field and near-field characterizations, are in excellent agreement with full-wave simulations. Our findings may pave the way for many applications, including high-efficiency surface plasmon couplers, anti-reflection surfaces, light absorbers, and so on.

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Figure 1: Physical concept of the PW–SW conversion and mode-expansion calculations on model systems.
Figure 2: Sample design, fabrication, and far-field characterization.
Figure 3: Near-field characterizations on the meta-surfaces.
Figure 4: Verifications of the dispersion relation = ξ+k0sinθi.
Figure 5: Guiding the driven SWs outside the meta-surface.


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This work was supported by the National Natural Science Foundation of China (60990321, 11174055, 60725417) and the Ministry of Education of China (B06011). S.S. was supported by the National Science Council and National Center for Theoretical Sciences of Taiwan. We thank Y. R. Shen and C. T. Chan for helpful discussions.

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S.S. did the theoretical calculations and designed the samples. Q.H. and S.X. made the samples and did the measurements. Q.X. helped in theoretical calculations. X.L. helped in experimental measurements. L.Z. conceived the idea, developed the mode-expansion theory and wrote the manuscript.

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Correspondence to Lei Zhou.

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Sun, S., He, Q., Xiao, S. et al. Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves. Nature Mater 11, 426–431 (2012).

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