Theoretical Studies of Sub-THz Active Split-Ring Resonators for Near-Field Imaging

TL;DR

The paper develops a comprehensive theoretical framework for Active Split-Ring Resonators (ASRRs) as switchable, high-Q imaging pixels for sub-THz near-field imaging on silicon. By formulating equivalent LC models, optimal coupling conditions, and detailed noise analyses (white, flicker, supply, and input phase noise), it derives design guidelines to maximize SNR while minimizing power in dense 2D arrays. It demonstrates that negative-resistance boosting can substantially enhance sensitivity to dielectric losses while outlining nonlinear and saturation considerations. The findings enable scalable, real-time near-field imaging of biological tissues with improved resolution and reduced cost. Overall, the work provides actionable methodologies for engineering ASRR-based imagers with solid theoretical backing and validated simulations.

Abstract

This paper develops a theoretical framework for the design of Active Split-Ring Resonators (ASRRs). An ASRR is a Split-Ring Resonator (SRR) equipped with a tunable negative resistor, enabling both switchability and quality factor boosting and tuning. These properties make ASRRs well-suited for integration into dense arrays on silicon chips, where pixelated near-fields are generated and leveraged for high-resolution 2D imaging of samples. Such imagers pave the way for real-time, non-invasive, and low-cost imaging of human body tissue. The paper investigates ASRR coupling to host transmission lines, nonlinear effects, signal flow, and the influence of various noise sources on detection performance. Verified through simulations, these studies provide design guidelines for optimizing the Signal-to-Noise Ratio (SNR) and power consumption of a single pixel, while adhering to the constraints of a scalable array.

Figures (15)

• Figure 1: Resonator-based near-field imaging approaches. (\ref{['fig:imgr_topol_1']}) One detector and one source per pixel.(\ref{['fig:imgr_topol_2']}) One detector per pixel and one source per multiple pixels. (\ref{['fig:imgr_topol_3']}) One detector and one source per multiple pixels.
• Figure 2: Different SRR coupling configurations: (a) Edge-coupled, (b) Broadside-coupled. (c) HFSS EM simulated resonance frequencies of the resonators as a function $\theta$.
• Figure 3: (\ref{['fig:srr_cpl_tl']}) An SRR coupled to a transmission line. (\ref{['fig:srr_cpl_tl_lc_1']}) The LC equivalent circuit of an SRR coupled to a transmission line. (\ref{['fig:srr_cpl_tl_lc_2']}) The equivalent SRR, modeled as a parallel resonator inserted in the transmission line at the point of coupling. (\ref{['fig:srr_at_res']}) The equivalent SRR at resonance.
• Figure 4: (\ref{['fig:srr_em']}) The HFSS EM model of an SRR. (\ref{['fig:s21_lc_vs_em']}) Simulated $S_{21}$ for the SRR LC, equivalent LC, and EM models.
• Figure 5: The magnitude and phase of $S_{21}$ while changing $k$ for when (\ref{['fig:s21_q_const']}) $Q$ is kept constant, and (\ref{['fig:s21_q_calc']}) $Q$ is calculated from (\ref{['eq_kq_srr']}). (\ref{['fig:s11_cntrs']}) The contours of $S_{11}$ for various $(k,Q_{ON})$ pairs and the boundary where $S_{11}<-10dB$. (\ref{['fig:sp_q_calc_sim']}) $S_{11}$, $S_{21}$, and $Q_{ON}$ of EM simulated SRR compared to the calculated values as a function of SRR spacing to the host transmission line, and therefore $k$.