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Joseph Matson1 Lisa Brown2 3 Marcelo Davanco2 Zhiyuan Sun4 Andrey Kretinin5 Yiguo Chen6 7 Igor Vurgraftman8 Nicholas Sharac8 Alexander Giles8 Michael Fogler4 Takashi Taniguchi9 Kenji Watanabe9 Kostya Novoselov5 Stefan Maier6 10 Andrea Centrone2 Joshua Caldwell1 8

1, Vanderbilt University, Nashville, Tennessee, United States
2, National Institute of Standards and Technology, Gaithersburg, Maryland, United States
3, University of Maryland, College Park, Maryland, United States
4, University of California San Diego, La Jolla, California, United States
5, University of Manchester, Manchester, , United Kingdom
6, Imperial College London, London, , United Kingdom
7, National University of Singapore, Singapore, , Singapore
8, U.S. Naval Research Laboratory, Washington, District of Columbia, United States
9, National Institute for Materials Science, Tsukuba, , Japan
10, Ludwig-Maximilians-Universität München, München, , Germany

Surface phonon polaritons (SPhPs) are quasiparticles consisting of a strongly coupled phonon-photon pair resulting from the interaction between light and optic phonons. They occur naturally in polar crystalline solids. SPhPS are an appealing alternative to surface plasmon polaritons due to the longer scattering lifetime of phonons, which subsequently results in substantially lower losses. Hexagonal boron nitride (hBN) is an especially appealing polar crystal due to high crystal and optical anisotropy, making it a naturally hyperbolic material.
A hyperbolic material is one in which the real part of the dielectric function is opposite in sign along orthogonal crystal axes. In the case of hBN, these are the in-plane and out-of-plane axes. This results in two spectral bands where either the in- or out-of-plane permittivity is negative, while the other is positive. Within these spectral bands, hyperbolic phonon polaritons (HPhPs) may be supported, which differ from SPhPs in that they can propagate through the deeply sub-diffractional volume of the material rather than being confined to the surface. Because they are confined in all three dimensions, they must be described using three quantum numbers, resulting in several distinct sets of polaritonic modes appearing in the HPhP dispersion. However, due to optical selection rules, only a subset of these modes has been observed through far-field reflectance and scattering-type scanning near-field optical microscopy (s-SNOM).
Photothermal induced resonance (PTIR) is an emerging technique in which incoming light is scattered off of a metallized AFM tip to excite resonant modes in a sample. Unlike in s-SNOM that measures scattered light, the AFM tip is typically operated in contact mode and is used to directly measure local thermal expansion of the material or nanostructure resulting from resonant optical absorption. Here, PTIR is leveraged for the first time to observe “dark” HPhP modes, which do not radiate to free space, within hBN nanocones. Through careful resonance lineshape analysis and comparison with far-field and nano-FTIR spectra, we have identified ~20 resonant dispersive modes not observed using the more conventional techniques. These resonances were confirmed as HPhP resonances by their dispersion and by comparison with analytical predictions of these modes. Our results show the first clear observation of these predicted, but previously unreported dark HPhP modes. Control of these modes could present a new avenue to novel nanophotonic devices and deeper understanding of nanophotonic materials and devices.

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