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. 2022 Jun 6;13:3170. doi: 10.1038/s41467-022-30451-z

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© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 4 — a Picture of a fabricated chip shows Mie modulators that are integrated with GHz coplanar waveguides (CPW). Also visible are test CPW. b Electronic scattering parameters S₂₁ of Mie modulators are compared to test CPW. The S₂₁ are measured using a vector network analyzer (VNA) connected to the sample by high-frequency cables and high-speed microwave GSG (ground-source-ground) probes (one ground floating) and exhibits a cut-off of f_−6dB = 4.2 GHz owing to the intrinsic RC bandwidth. RF cable losses are deducted from the S₂₁ response. Beyond 4.2 GHz, only the Mie modulators exhibit a decay of –20 dB/decade (much less steep roll-over for the test CPW). c Optoelectronic experimental setup. The electronic characteristics are measured in a transmission configuration using the VNA, and the wavelength-resolved electro-optical (EO) modulation is measured using a lock-in amplifier. A double modulation scheme combined with a local oscillator (LO) is used, where the laser emission is modulated at the source and the Mie modulators (details in the methods) are actuated electronically by the RF source. d Resonance of sample (h_SiO2 = 200 nm, θ = 25°). e Peak electro-optic modulation amplitude for frequencies f_RF up to 5 GHz. We find a 3-dB electro-optic bandwidth of f_EO,−3dB = 3 GHz. Insets: wavelength-resolved modulation strength for several values of f_RF, the peak values have been utilized to plot the data in e. f Peak electro-optic modulation amplitude for different modulation voltages (reported as power in dBm), at 1.5 and 5 GHz, the latter well beyond the electro-optic bandwidth.