Agradecimentos: All the authors thank the Brazilian Synchrotron Light Laboratory (LNLS) for providing the beamtime for the experiments. We are grateful to Yves Petroff for the fruitful discussion and for revising this work. NeaSpec GmbH is thanked for the technical support. Angelo L. Gobbi and Maria...

Agradecimentos: All the authors thank the Brazilian Synchrotron Light Laboratory (LNLS) for providing the beamtime for the experiments. We are grateful to Yves Petroff for the fruitful discussion and for revising this work. NeaSpec GmbH is thanked for the technical support. Angelo L. Gobbi and Maria H. de Oliveira Piazetta, from the Brazilian Nanotechnology National Laboratory, are acknowledged for the assistance in sample construction. F. C. B. M. and F. H. F acknowledge the FAPESP project 2018/05425-3. R. O. F. and R. A. M. acknowledge the FAPESP project 2019/08818-9. R. O. F. acknowledges CNPq for research grant 311564/2018-6. D. A. B. acknowledges support from FAPESP projects 2015/11779-4 and 2018/07276-5, CAPES - PrInt (Grant # 88887.310281/2018-00), the Brazilian Nanocarbon Institute of Science and Technology (INCT/Nanocarbono), the National Council for Scientific and Technological Development -CNPq and MackPesquisa. This work was partially supported by the Brazilian Institute of Science and Technology (INCT) in Carbon Nanomaterials and the Brazilian agencies CAPES and CNPq. M. B. R. acknowledges support from the U.S. Department of Energy, Office of Basic Sciences, Division of Material Sciences and Engineering, under award no. DE-SC0008807

Abstract: The nanophotonics of van der Waals (vdW) materials relies critically on the electromagnetic properties of polaritons defined on sub-diffraction length scales. Here, we use a full electromagnetic Hertzian dipole antenna (HDA) model to describe the hyperbolic phonon polaritons (HP(2)s) in...

Abstract: The nanophotonics of van der Waals (vdW) materials relies critically on the electromagnetic properties of polaritons defined on sub-diffraction length scales. Here, we use a full electromagnetic Hertzian dipole antenna (HDA) model to describe the hyperbolic phonon polaritons (HP(2)s) in vdW crystals of hexagonal boron nitride (hBN) on a gold surface. The HP2 waves are investigated by broadband synchrotron infrared nanospectroscopy (SINS) which covers the type I and type II hyperbolic bands simultaneously. Basically, polariton waves, observed by SINS, are assigned to the resultant electric field from the summation over the irradiated electric fields of dipoles distributed along the crystal edge and at the tip location and a non-propagating field. The values of polariton momenta and damping extracted from the HDA model present excellent agreement with theoretical predictions. Our analysis shows that the confinement factor of type I HP(2)s exceeds that of the type II ones by up to a factor of 3. We extract anti-parallel group velocities (v(g)) for type I (v(g,typeI) = -0.005c, c is the light velocity in a vacuum) in relation to type II (v(g,typeII) = 0.05c) polaritonic pulses, with lifetimes of similar to 0.6 ps and similar to 0.3 ps, respectively. Furthermore, by incorporating consolidated optical-near field theory into the HDA model, we simulate real-space images of polaritonic standing waves for hBN crystals of different shapes. This approach reproduces the experiments with a minimal computational cost. Thus, it is demonstrated that the HDA modelling self-consistently explains the measured complex-valued polariton near-field, while being a general approach applicable to other polariton types, like plasmon- and exciton-polaritons, active in the wide range of vdW materials

COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIOR - CAPES

88887.310281/2018-00

CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQ

311564/2018-6

FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP

2015/11779-4; 2018/05425-3; 2018/07276-5; 2019/08818-9

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