Towards Reliable Characterization of Materials' Plasmonic Properties using Fabry-Perot Resonance

TL;DR

This work introduces an in-situ, angle-insensitive method to map the plasmonic dispersion $E-k$ by exploiting Fabry-Pérot resonances in subwavelength FP cavities embedded in plasmonic gratings. By varying the grating periodicity and employing non-Hermitian QNM-FEM analyses alongside FDTD validation, it decouples geometric effects from material dispersion and reveals FP–SPP hybridization across regimes. A geometric correction factor $oldsymbol{\sigma(r)}$ (and its dispersive extension $oldsymbol{\sigma(r,oldsymbol{ ilde{oldsymbol{oldsymbol{oldsymbol{oldsymbol{ mbox{}}}}})}}}$) links resonance frequencies to intrinsic plasmonic properties, enabling direct extraction of dispersion for PEC and dispersive metals. Demonstrated across multiple materials, the approach yields angle-independent dispersion maps suitable for wafer-scale metrology and real-time process monitoring of plasmonic performance. These results offer a practical framework for characterizing new plasmonic materials where conventional spectroscopy is challenging, by leveraging FP resonances as precise probes of both geometry and dielectric response.

Abstract

Accurate characterization of plasmonic materials' dispersion and efficiency remains a key challenge for next-generation nanophotonic devices. Here, we theoretically demonstrate that the plasmon dispersion relation at a metal-dielectric interface can be reconstructed from the resonance peaks of transmission spectra obtained in a series of extraordinary optical transmission (EOT) experiments on plasmonic gratings. A proof-of-concept of direct E-k dispersion mapping is numerically implemented by systematically varying the grating's unit cell size, with each grating serving as a discrete probe in momentum space. The resulting plasmon dispersion curves are derived from the frequencies of Fabry-Perot (FP) resonances localized within subwavelength apertures, scaled by a correction factor that accounts for the interplay between the resonant mechanisms driving enhanced transmission. This factor highlights the aperture's role in mode confinement and resonance shifting, which we examine in both idealized perfect electric conductor (PEC) and realistic dispersive metal regimes. To elucidate eigenstates of the plasmonic system and quantify the modal hybridization within its apertures, we perform a non-Hermitian modal decomposition using the finite element method (FEM) and corroborate it with finite-difference time-domain (FDTD) simulations. The proposed framework enables an angle-insensitive, real-time, and in-situ characterization platform suitable for wafer-scale evaluation of established and emerging plasmonic materials.

Figures (7)

• Figure 1: a) Three-dimensional rendering and b) schematic representation of the numerical model. The structure consists of a free-standing plasmonic grating slab, where H and L denote the horizontal (periodic) and vertical (thickness) parameters of the unit cell.
• Figure 2: a) and b) Photonic dispersion diagrams evaluated using QNM-FEM (left) and FDTD (right) for two sizes, H=1 µm and H=100 nm, respectively. The color pallets in these analyses represent the PSD for FDTD and $\Theta$ for FEM. c) and d) Eigenvectors depicting the modulus of the electric field |E| at $\lambda_{1/2}$, $\lambda_1$, and $\lambda_{3/2}$ for the two sizes.
• Figure 3: a) and b) Transmission responses evaluated using FEM and FDTD through the PEC slab, with a filling factor of $20\%$, for two sizes: 1$\mu$m, $100$ nm, respectively.
• Figure 4: a) Transmission characteristic of a dielectric FP resonator modeled as a three-layer system $z_1-z_{eff}-z_1$ (see inset). b) Optical transmission map for a perfectly conducting grating as a function of frequency and aperture filling factor, illustrating the evolution of FP resonant bands ($\lambda_{1⁄2},\lambda_1,\lambda_{3/2}$). c) Modulus of the electric field |E| at resonance for two aperture filling factors $20 \%$ and $1 \%$. d) Geometrical correction coefficient as a function of aperture filling factor for the two FP modes.
• Figure 5: a) Classic SPP dispersion characteristic, with the color map reflecting PSD. b) Color map of the transmission outlining the effects of filling factor versus frequency in the case of a dispersive metal with the FP resonant bands $(\lambda_{1⁄2},\lambda_1,\lambda_{3/2})$ being depicted. c) and d) Modulus of the electric field in a logarithmic distribution log(|E|) at resonance for two aperture filling factors $20 \%$ and $1 \%$,