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Abstract
We present a theoretical framework for nonlinear optics of graphene and other 2D materials in layered structures. We derive a key equation to find the effective electric field and the sheet current density in the 2D material for given incident light beams. Our approach takes into account the effect of the surrounding environment and characterizes its contribution as a structure factor. We apply our approach to two experimental setups, and discuss the structure factors for several nonlinear optical processes including second harmonic generation, third harmonic generation, and parametric frequency conversion. Our systematic study gives a strict extraction method for the nonlinear coefficients, and provides new insights in how layered structures influence the nonlinear signal observed from 2D materials.
Highlights
Graphene possesses extraordinary optical properties,[1] including broadband absorption,[2] the existence of tightly confined plasmon modes,[3,4,5] and extremely strong optical nonlinearities.[6,7,8] Most of these properties strongly depend on the chemical potential, which can be controlled chemically,[9,10] optically,[11] or with the use of an external gate voltage.[12]
We present a theoretical framework for nonlinear optics of graphene and other 2D materials in layered structures
We apply our approach to two experimental setups, and discuss the structure factors for several nonlinear optical processes including second harmonic generation, third harmonic generation, and parametric frequency conversion
Summary
Graphene possesses extraordinary optical properties,[1] including broadband absorption,[2] the existence of tightly confined plasmon modes,[3,4,5] and extremely strong optical nonlinearities.[6,7,8] Most of these properties strongly depend on the chemical potential, which can be controlled chemically,[9,10] optically,[11] or with the use of an external gate voltage.[12]. With the integration of graphene onto photonic chips becoming a mature technology,[1,14,15] graphene is recognized as a potential resource for many photonic devices that exploit optical nonlinearities, including saturable absorbers,[16] broadband optical modulators,[17,18,19] optical switches,[20] and wavelength converters.[15] For these applications to be developed, a full understanding of the nonlinear radiation of graphene is necessary This is determined by both the intrinsic optical nonlinearity of graphene, and the effects of the surrounding environment. We model the current density in graphene as a “current sheet” described by a Dirac δ-function, and derive a key equation for graphene nonlinear optics, from which the effective electric fields and current density inside 2D materials can be determined as a response to incident laser beams These results are combined with the transfer matrix formalism, and are used to analyze the nonlinear fields generated by a graphene sheet on multilayered structures.
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