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Lattice resonances of lossy transition metal and metalloid antennas

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Abstract

Localized plasmonic resonances in isolated (single) nanoparticles of lossy materials are weak and do not result in resonances or significant field enhancement. In turn, if nanoparticles are arranged in a periodic lattice, collective resonances emerge from the coupling of the localized resonances of each individual nanoparticle. This coupling results in strong lattice resonances even when the nanoparticles are made of material with high optical losses. Here, we study lattice resonances in the arrays of nanoantennas made of lossy materials, such as transition metals, titanium Ti and tungsten W, and metalloid in the carbon group, germanium Ge. We perform both full-wave electromagnetic simulations and proof-of-concept experimental characterization in the near-infrared range, and we study the lattice resonances in lossy nanoantenna arrays and consider various practical scenarios that commonly arise in laboratory measurements and nanofabrication processes. We excite lattice resonance at different wavelengths by changing the refractive index of substrate and superstrate materials. We show lattice resonances in proximity to Rayleigh anomaly wavelength for homogeneous (substrate and superstrate are the same) and inhomogeneous (substrate and superstrate are different) surrounding environments for disk-shaped titanium nanoantennas on top of a substrate. We analyze the case of oblique light incidence with small angles as it often happens in laboratory measurements with a focused light spot. In this work, we observe lattice resonance in different practical conditions, and we show lattice resonances can be tuned for various applications, including sensing, depending on those conditions.

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Acknowledgments

V.E.B. acknowledges the support from the University of New Mexico Research Allocations Committee (Award No. RAC 2023) for the computational resources and WeR1: Investing in Faculty Success Program SURF. This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science by Los Alamos National Laboratory (Contract 89233218CNA000001) and Sandia National Laboratories (Contract DE-NA-0003525). The work is also supported by Contract DE-2375849.

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  1. Department of Electrical and Computer Engineering, University of New Mexico, MSC01 1100, Albuquerque, NM, 87131, USA

    Md. Sakibul Islam & Viktoriia E. Babicheva

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Correspondence to Viktoriia E. Babicheva.

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Appendix

Appendix

Method

Numerical simulations

Full-wave simulations are performed with a frequency-domain solver in the commercial package CST Studio Suite. Electric and magnetic fields of the incident wave are along the x- and y-axes, respectively. Substantial distance \(\sim 5 \lambda\) between the nanoantenna and domain edges is included to account for the decay of near fields around the nanoantenna. The required distance between a nanoparticle array and a detector must be significantly greater when considering diffractive effects compared to a single nanoparticle. The Floquet-Bloch boundary conditions are used in the x- and y-directions, and open boundaries are applied in the z-direction. Open boundaries account for the first 25 modes to ensure complete attenuation of any incoming waves originating from the nanoantenna scattering into different diffraction orders. Titanium, tungsten, and germanium permittivities are taken from Refs. [44,45,46], respectively.

Nanofabrication

Fused silica sample was spin-coated with PMMA 950-A9 (5000 rpm) and baked at 180 °C for 3 min and process was performed twice resulting in \(\sim\)2.5-\(\mu\)m-thick PMMA. E-beam exposure was done with JEOL JBX6300-FS, 60 \(\mu\)m aperture, 100 keV energy, and 1 nA current, and the sample was developed in MIBK-IPA 1:3 solution for 90 sec. Titanium was deposited with an e-beam evaporator with a 0.5 Å/s rate to a total thickness of 500 nm. The sample was immersed in Remover PG and heated to 78 °C for 2 h and 30 min. Afterward, the e-beam resist was lifted off by thoroughly rinsing it with acetone.

Measurements

Reflection was measured using a custom setup connected to Ocean Optics NIRQuest+2.2 spectrometer operating in the range 0.9 - 2.15 \(\mu\)m with a resolution of \(\sim\)5.5 nm. Reflection from the array was normalized to the reflection from the mirror with the same thickness being positioned on the same stage at the sample at the moment of measurement.

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Islam, M.S., Babicheva, V.E. Lattice resonances of lossy transition metal and metalloid antennas. MRS Advances 8, 138–147 (2023). https://doi.org/10.1557/s43580-023-00558-6

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