Multiple Tunable Hyperbolic Resonances in Broadband Infrared Carbon-Nanotube Metamaterials

John Andris Roberts, Po-Hsun Ho, Shang-Jie Yu, Xiangjin Wu, Yue Luo, William L. Wilson, Abram L. Falk, and Jonathan A. Fan

Phys. Rev. Applied 14, 044006 – Published 5 October 2020

Abstract

Aligned densely packed carbon-nanotube metamaterials prepared using vacuum filtration are an emerging infrared nanophotonic material. We report multiple hyperbolic plasmon resonances, together spanning the mid-infrared, in individual resonators made from aligned and densely packed carbon nanotubes. In a near-field scanning optical microscopy (NSOM) imaging study of nanotube metamaterial resonators, we observe distinct deeply subwavelength field profiles at the fundamental and higher-order resonant frequencies. The wafer-scale area of the nanotube metamaterials allows us to combine this near-field imaging with a systematic far-field spectroscopic study of the scaling properties of many resonator arrays. Thorough theoretical modeling agrees with these measurements and identifies the resonances as higher-order Fabry-Perot (FP) resonances of hyperbolic waveguide modes. Nanotube resonator arrays show broadband extinction from 1.5–10 µm and reversibly switchable extinction in the 3–5 µm atmospheric transparency window through the coexistence of multiple modes in individual ribbons. Broadband carbon-nanotube metamaterials supporting multiple resonant modes are a promising candidate for ultracompact absorbers, tunable thermal emitters, and broadband sensors in the mid-infrared.

Received 6 May 2020
Revised 3 July 2020
Accepted 30 July 2020

DOI:https://doi.org/10.1103/PhysRevApplied.14.044006

Physics Subject Headings (PhySH)

Metamaterials Nanoantennas Optoelectronics Plasmonics

Carbon-based materials Nanotubes Thin films

Resonance techniques

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

John Andris Roberts ^1,*,§, Po-Hsun Ho^2,§, Shang-Jie Yu ^2,§, Xiangjin Wu², Yue Luo ³, William L. Wilson ³, Abram L. Falk ^4,†, and Jonathan A. Fan ^2,‡

¹Department of Applied Physics, Stanford University, Stanford, California 94305, USA
²Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA
³Center for Nanoscale Systems, Harvard University, Cambridge, Massachusetts 02138, USA
⁴IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA

^*johnr3@stanford.edu
^†alfalk@us.ibm.com
^‡jonfan@stanford.edu
^§These authors contributed equally to this work.

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Vol. 14, Iss. 4 — October 2020

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Images

Figure 1
(a) SEM image of ribbon resonators patterned in a thick (approximately 80 nm) film of aligned unsorted single-walled carbon nanotubes overlaid with a schematic depicting the FP resonant condition for hyperbolic waveguide modes and cartoons of the field profiles for FP resonances of different orders. (b) Experimental far-field extinction spectra of highly doped nanotube resonator arrays patterned in the film shown in (a), with varying ribbon widths, measured using FTIR spectroscopy immediately after doping with nitric acid vapor. In wider ribbons, higher-order resonances appear. Dashed lines are guides to the eye. Spectra are offset vertically for clarity. (c) Simulated extinction spectra corresponding to the measurement in (b) using effective dielectric functions for a moderately doped nanotube film in a FDTD model. Green shaded area represents the wavelength range where the moderately doped nanotube film has hyperbolic dispersion.
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Figure 2
(a) Cartoons of NSOM measurement of resonant modes in a nanotube ribbon resonator, showing the incident light with wavevector k perpendicular to the ribbon and the tip used to measure the near-field signal (top), and cartoons showing the symmetric round-trip and antisymmetric direct-coupling signals. (b) Far-field extinction spectra of two resonator arrays with ribbon widths of 1 and 2.5 µm and thickness of 85 nm (vertically offset for clarity), showing the wavelengths used for the near-field imaging experiment. For the 2.5 µm ribbon, the laser is chosen to coincide with the higher-order peak, and for the 1 µm ribbon the laser wavelength is chosen to measure only the fundamental resonance. Right, NSOM phase images of the two ribbons at the chosen wavelengths. Asymmetry is a sign of the presence of a localized resonance. Scale bars, 500 nm. (c) Real component of the antisymmetric part of the NSOM signals (experiment), corresponding to the signal from the localized modes, compared with the simulated field Re(E_y) of the ribbon resonators, showing qualitative agreement. Center part of the NSOM signal for the 2.5 µm ribbon is shown in more detail in the red-outlined inset. Simulated fields are normalized to the amplitude of an excitation plane wave.
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Figure 3
(a) SEM image of a nanotube film (thickness approximately 80 nm) overlaid with a cartoon showing the cut angle θ between the ribbon direction and the nanotube alignment and indicating the direction of the resonant wavevector and its magnitude. Bottom cartoon shows the resonant wavevector on the nanotube hyperbolic isofrequency surface. (b) Experimental FTIR extinction spectra of ribbon arrays with width of 1 µm, thickness of approximately 80 nm, and a range of cut angles (vertical offset for clarity). As the cut angle is decreased, the m = 3 peak redshifts because the resonant wavevector samples high-k points on the hyperbolic isofrequency surface. (c) Experimental dispersion plot of the hyperbolic waveguide modes constructed using the FP relation and the extinction spectra of many resonator arrays. When the mode orders m = 1, 3, and 5 are used for the fundamental and higher-order peaks, the dispersion relation for a given direction follows a single line, confirming that these are the correct FP mode orders. For smaller cut angles, the hyperbolic waveguide mode becomes more highly confined as expected from the in-plane hyperbolic dispersion. Reflection phase is estimated as ϕ ≈ π/4 based on simulations [61, 69, 70].
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Figure 4
(a) FTIR extinction spectra of a nanotube resonator array with ribbon width of 1.5 µm and thickness of approximately 195 nm before (blue) and immediately after (yellow) vapor doping for incident light polarized along the nanotubes, showing broadband reversible extinction enabled by multiple resonances. Spectra at moderate (one day after vapor doping) and ambient doping (five days after vapor doping) are shown in orange and purple, respectively. Wavelengths of the three resonances (λ₁, λ₂, and λ₃) are marked with arrows. (b) Simulated field profiles at the three wavelengths labeled in (a) in a moderately doped ribbon with width 1.5 µm and thickness 200 nm. Top, m = 1 resonance in the region where the nanotube films are similar to an anisotropic metal; middle: m = 3 hyperbolic resonance; bottom, m = 5 hyperbolic resonance. Fields are normalized to the amplitude of an excitation plane wave.
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