Resonant modes in metamaterials have been widely utilized to amplify the optical response of 2D materials for practical device applications. However, the high loss at the resonant mode severely hinders metamaterial applications. Here, we introduce a field-enhancement gain (FEG) factor to find the FEG mode for significantly improving light-matter interaction. As a demonstration, we experimentally compared the second harmonic generation enhancement of monolayer MoS2 induced by the optimal FEG and resonant modes in hyperbolic meta-structures. With the optimal FEG mode, we obtained an enhancement of 22145-fold and a conversion efficiency of 1.1*10-6 W-1, which are respectively one and two orders of magnitude higher than that previously reported of monolayer MoS2. A broadband high-FEG region over ~80 nm where the nonlinear enhancement is larger than that induced by the resonant mode is achieved. The concept of FEG factor is general to metamaterials, opening a new way for advancing their applications.
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