Fig. 3: Effective third-order nonlinear electric susceptibility.
From: Mimicking bio-mechanical principles in photonic metamaterials for giant broadband nonlinearity
a Analytical calculation of \(\chi _{{\mathrm{eff}},11}^{(3)}\) as a function of fundamental frequency and aspect ratio. Bright- and dark-dashed lines indicate the material-induced resonance conditions at the third-harmonic, \(a^2/(4h_{\mathrm{m}}h_{\mathrm{d}})\sim |\varepsilon _{\mathrm{m}}^{(3\omega )}/\varepsilon _{\mathrm{d}}^{(3\omega )}|\), and at the fundamental frequency, \(a^2/(4h_{\mathrm{m}}h_{\mathrm{d}})\sim |\varepsilon _{\mathrm{m}}^{(1\omega )}/\varepsilon _{\mathrm{d}}^{(1\omega )}|\), respectively. The gray-shaded region indicates the region where \(a \,> \, \lambda _{\mathrm{o}}^{(3\omega )}/3\) with hd = 10 nm, where the unit-cell size becomes comparable to half a wavelength, and an effective medium description of the crystal is ill-grounded owing to diffraction. b The calculated magnitude and phase of \(\chi _{{\mathrm{eff}},11}^{(3)}\) enhancement of the proposed staggered-array metamaterial (SAMM) are presented at terahertz frequencies. The values from the analytical model and the numerical simulations are compared. The aspect ratio (a/hd) is 600 for green, and 90 for blue dots and lines, respectively. c The calculated \(\chi _{{\mathrm{eff}},11}^{(3)}\) of a SAMM with a/hd = 15 is presented at near-infrared frequencies.
