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Abstract
We solve the nonlinear Maxwell equations in an InP-based dielectric metamaterial, considering both two-photon absorption and photo-induced free-carrier absorption. We obtain the intensity-dependent reflection, absorption, and effective permittivity and permeability of the metamaterial. Our results show that nonlinear absorption dampens both the electric and magnetic Mie resonance, although the magnetic resonance is more affected because it occurs at longer wavelengths where the free-carrier absorption cross section is larger. Owing to field concentration in the metamaterial at resonance, the threshold intensity for nonlinear absorption is reduced by a factor of about 30 compared to a homogeneous layer of the same thickness. Our results have implications on the use of dielectric metamaterials for nonlinear applications such as higher harmonic generation, optical limiting, and ultrafast modulation.
Highlights
Materials with strong nonlinear response are desired for applications such as optical limiting[1,2,3], ultrafast modulation[4,5,6], frequency conversion[7,8], and optical isolation[9,10]
We find that nonlinear absorption leads to damping of the electric and magnetic Mie resonances at high intensities
We developed a self-consistent full-wave model to study the effects of two-photon absorption and photo-induced free-carrier absorption on the effective parameters and optical properties of a dielectric metamaterial operating in the near infrared spectral band
Summary
Materials with strong nonlinear response are desired for applications such as optical limiting[1,2,3], ultrafast modulation[4,5,6], frequency conversion[7,8], and optical isolation[9,10]. Field enhancement in dielectric metamaterials has been demonstrated[27] and applied to achieve third-harmonic generation[26,28,29,30,31,32], optical limiting[33], and ultrafast optical modulation[34,35,36]. A few examples employ the recently-developed generalized source method for nonlinear materials[37,38,39], which calculates the diffraction by periodic structures containing linear and nonlinear media These models provide important insights, they decouple the linear and nonlinear responses, and do not represent self-consistent solutions of the nonlinear Maxwell equations. Owing to the enhancement of the electric field at resonance, we find that the intensity threshold of nonlinear absorption in the metamaterial is nearly 30 times lower compared to a homogeneous material of the same thickness
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