Extracting the infrared permittivity of sio2 substrates locally by near-field imaging of phonon polaritons in a van der waals crystal

P.A.-M. acknowledges financial support through JAE Intro program from the Superior Council of Scientific Investigations and the Spanish Ministry of Science and Innovation (grant number JAEINT_20_00589). G.Á.-P. and J.T.-G. acknowledge financial support through the Severo Ochoa Program from the Government of the Principality of Asturias (grant numbers PA-20-PF-BP19-053 and PA-18-PF-BP17-126, respectively). J.M.-S. acknowledges financial support from the Ramón y Cajal Program of the Government of Spain (RYC2018-026196-I) and the Spanish Ministry of Science and Innovation (State Plan for Scientific and Technical Research and Innovation grant number PID2019-110308GA-I00). P.A.-G. acknowledges support from the European Research Council under starting grant no. 715496, 2DNANOPTICA and the Spanish Ministry of Science and Innovation (State Plan for Scientific and Technical Research and Innovation grant number PID2019-111156GB-I00).