Guided Modes of Anisotropic van der Waals Materials Investigated by near-Field Scanning Optical Microscopy

Abstract

Guided modes in anisotropic two-dimensional van der Waals materials are experimentally investigated and their refractive indices in visible wavelengths are extracted. Our method involves near-field scanning optical microscopy of waveguide (transverse electric) and surface plasmon polariton (transverse magnetic) modes in h-BN/SiO2/Si and Ag/h-BN stacks, respectively. We determine the dispersion of these modes and use this relationship to extract anisotropic refractive indices of h-BN flakes. In the wavelength interval 550-700 nm, the in-plane and out-of-plane refractive indices are in the range 1.98-2.12 and 1.45-2.12, respectively. Our approach of using near-field scanning optical microscopy allows for direct study of interaction between light and two-dimensional van der Waals materials and heterostructures. KEYWORDS: 2D materials, near-field scanning optical microscopy, optical constants, hexagonal boron nitride Two-dimensional (2D) materials have recently garnered significant interest due to their high electrical mobility, atomic-level flatness, and large exciton binding energies which enable versatile nanophotonics and optoelectronics applications [1-23]. However, the understanding of the interaction of visible light surface plasmon polaritons with 2D materials and more complex van der Waals (vdW) heterostructures [5-7] is still in its infancy [9, 23]. In this work, we report a nearfield scanning optical microscopy (NSOM) [25-28] study of highly crystalline hexagonal boron nitride (h-BN) [21] mechanically-exfoliated flakes at visible wavelengths, demonstrating the direct observation of (i) transverse electric (TE) waveguide modes supported by h-BN on SiO2 and (ii) the interaction of transverse magnetic (TM) surface plasmon polariton (SPP) modes supported by silver (Ag) with a thin h-BN flake. From NSOM scans, we estimate the intrinsically anisotropic optical dielectric constants ( = ≠ ) of h-BN, which is an arduous task by conventionalmethods such as ellipsometry [24]. Our technique can be extended to other vdW solids and heterostructures, where we anticipate the study of guided modes coupled to 2D materials to be a useful tool in exploring rich physics of surface polaritons [9-14], plexcitons (SPPs-excitons) [29], gate-tunable [17, 30, 31], layer number dependent optical properties [13], in-plane anisotropy [15, 23], and selective circular dichroism [18, 19].

Infrared Permittivity of the Biaxial van der Waals Semiconductor α‐MoO3 from Near‐ and Far‐Field Correlative Studies

“…Additionally, we employ DFT to give insights into the vibrational modes dictating the oscillators on which this dielectric function model is based and into the intriguing optical properties of the material. Our work therefore reports an accurate and predictive model for the IR dielectric function of α‐MoO 3 , an emerging vdW material for nanophotonics, [ 22,23 ] while also offering an innovative approach to extracting dielectric functions of nanomaterials, where the use of traditional methods is challenging [ 24–26 ] or even not possible.…”

Layer-dependent dielectric and optical properties of centimeter-scale 2D WSe2: evolution from a single layer to few layers

“…So far, experimental studies on the layer-dependent dielectric and optical parameters of 2D WSe 2 have scarcely been reported. Commonly used techniques to determine the dielectric function and complex refractive index of 2D WSe 2 include the reflection (or absorption) spectrum method, 15 differential reflection (or transmission) spectrum method, 16 scattering-type scanning near-field optical microscopy (s-SNOM), [17][18][19][20] and ellipsometry. [21][22][23][24] With the reflection (or absorption) spectrum method, Li et al obtained the dielectric function of the monolayer WSe 2 over an energy range of 1.5-3.0 eV by combining a Kramers-Kronig (K-K) constrained variational analysis.…”

“…s-SNOM is sensitive to the optical anisotropy in 2D materials, and can be used to determine the dielectric tensor of a thin film. 18 It has been recently developed to probe the optical anisotropy in 2D van der Waals materials, 18,19 and to investigate the plasmonic and polaritonic properties in 2D materials, metamaterials, quantum materials, etc. 20 Compared with the techniques discussed above, ellipsometry detects the polarization state changes of polarized light before and after reaction (reflection or transmission) with the samples, and the dielectric and optical parameters of 2D materials can be accurately extracted from the ellipsometric spectra without any additional functions.…”

Engineering terahertz surface magnon-polaritons in hyperbolic antiferromagnets

“…This has led to the design of new types of metamaterials which not only support but also guide such waves [3][4][5][6]. For example, van der Waals heterostructures [7][8][9][10] that have hyperbolic dispersion [6,11] display interesting features in their surface polaritons. Similar phenomena are also observed in man-made structures, often referred to as hyperbolic metamaterials.…”