Second-Harmonic Generation in Nano-Structured Metamaterials

Abstract

We conduct a theoretical and numerical study on the second-harmonic (SH) optical response of a nano-structured metamaterial composed of a periodic array of inclusions. Both the inclusions and their surrounding matrix are made of centrosymmetrical materials, for which SH is strongly suppressed, but by appropriately choosing the shape of the inclusions, we may produce a geometrically non-centrosymmetric system which does allow efficient SH generation. Variations in the geometrical configuration allows tuning the linear and quadratic spectra of the optical response of the system. We develop an efficient scheme for calculating the nonlinear polarization, extending a formalism for the calculation of the macroscopic dielectric function using Haydock's recursion method. We apply the formalism developed here to an array of holes within an Ag matrix, but it can be readily applied to any metamaterial made of arbitrary materials and for inclusions of any geometry within the long-wavelength regime.

16 pages, 7 figures

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• Negative Index of Refraction in Optical Metamaterials
• Nanofabricated media with negative permeability at visible frequencies
• Nonlinear properties of left-handed metamaterials
• First-Principle Homogenization Theory for Periodic Metamaterials
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• Second-harmonic generation in nonlinear left-handed metamaterials
• Negative Refractive Index in Optics of Metal-Dielectric Composites
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• Effective Dielectric Response of Metamaterials
• Macroscopic optical response and photonic bands
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• Retrieval of all effective susceptibilities in nonlinear metamaterials

Cited by in corpus (6)

• Polaronic Enhancement of Second-Harmonic Generation in Lithium Niobate
• Analytical Theory of Second Harmonic Generation from a Nanoparticle with a Non-Centrosymmetric Geometry
• Recursive Calculation of the Optical Response of Multicomponent Metamaterials
• Mie Scattering in the Macroscopic Response and the Photonic Bands of Metamaterials
• Analytical theory for three wave-mixing processes in a slightly deformed cylinder
• Tangent equations of motion for nonlinear response functions