Research ArticlePHYSICS

A mid-infrared biaxial hyperbolic van der Waals crystal

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Science Advances  24 May 2019:
Vol. 5, no. 5, eaav8690
DOI: 10.1126/sciadv.aav8690
  • Fig. 1 Mid-infrared biaxial hyperbolic electromagnetic responses of a vdW α-MoO3 flake.

    (A) Real parts of the permittivities along the three principal axes. The different Reststrahlen bands are shaded in different colors. Inset: Schematic showing the crystalline unit cell of α-MoO3. The three oxygen sites of the asymmetric Mo─O bonds along the different crystalline axes are labeled as O1, O2, and O3. (B) 3D isofrequency surfaces observed in the three Reststrahlen bands, indicating that biaxial hyperbolic dispersion occurs in natural vdW α-MoO3. (C) Isofrequency curves on the x-y plane at three typical frequencies, 623, 925, and 1000 cm−1. The red and green arrows indicate the propagation directions of the hyperbolic PhPs modes arising at 623 and 925 cm−1, respectively. (D) Schematic showing the launching of the PhPs on an α-MoO3 surface with a z-polarized electric dipole. (E to G) Calculated magnitudes of the electric field distributions, |E|, on a natural α-MoO3 surface at the same three frequencies as shown in (C). (H to J) Calculated real parts of z components of the electric field distributions, Re(Ez), on a natural α-MoO3 surface at the same three frequencies. (H) and (I) show two hyperbolic PhPs with in-plane concave wavefronts, while an elliptical wavefront is shown in (J). (K to M) Fourier transforms of (H) to (J), respectively. The white dashed lines delineate the corresponding isofrequency curves that are shown in (C).

  • Fig. 2 Real-space imaging of the hyperbolic PhPs on the surface of a natural 220nm-thick α-MoO3flake.

    (A) Topography of the α-MoO3 flake with a silver nanoantenna placed on its surface. (B) Schematic showing the process of nano-imaging of the PhP waves propagating on the α-MoO3 surface. The black curves shown in (A) and (B) illustrate the wavefronts of the hyperbolic PhPs. (C and E) Real-space near-field optical images recorded at 944 and 980 cm−1, respectively. The edge of the flake and profile of the nanoantenna are denoted by white and black dashed lines, respectively. (D and F) Absolute values of the FT images corresponding to (C) and (E), respectively. The white dashed lines show the theoretically predicted isofrequency curves. (G and I) Numerical simulations of the Re(Ez) distributions corresponding to the PhPs launched by the silver nanoantenna at 944 and 980 cm−1, respectively. (H and J) Profiles of the s-SNOM amplitudes along the yellow dashed lines in (C) and (E), respectively. a.u., arbitrary units.

  • Fig. 3 In-plane PhP dispersion relations for a 160nm-thick α-MoO3flake.

    (A) Schematic showing real-space s-SNOM imaging of the PhPs reflected by the sample edges. (B) Numerical simulation of the PhP near-field distributions. (C) Schematic of PiFM imaging of the PhPs. Light is modulated at the difference between the frequencies of the two first cantilever modes. (D) s-SNOM images obtained with varied illumination frequencies. (E) PiFM images obtained in Band 1 at 790 and 798 cm−1 (left and right, respectively). (F) Near-field optical-amplitude profiles along the [100] (solid) and [001] (dashed) directions extracted from (D). (G) PiFM profiles along the [001] direction extracted from (E). (H) Dispersion relation for the PhPs in the α-MoO3 flake. The blue and red dots indicate experimental data extracted from s-SNOM and PiFM images, respectively, with different excitation frequencies. The pseudocolored image represents the calculated imaginary part of the complex reflectivity, Imrp(q, ω), of the air/α-MoO3/SiO2 multilayered structure.

  • Fig. 4 Subwavelength steering and focusing of the mid-infrared electromagnetic fields with the biaxial hyperbolic PhPs of the vdW α-MoO3flake.

    (A and B) Near-field optical images of a 1.6-μm-diameter, 160-nm-thick α-MoO3 disk (top) and a 1.5-μm-length, 150-nm-thick α-MoO3 square disk (bottom) at different illumination frequencies. Scale bars, 500 nm. (C and D) Schematics showing the top and side views, respectively, of the setup for subwavelength electromagnetic focusing with hyperbolic PhPs. A 20-nm-thick gold plate is placed under a 300-nm-thick α-MoO3 flake. (E and G) Calculated electric near-field distributions on the top surface of the α-MoO3 at illumination frequencies of 914 and 776 cm−1, respectively. (F and H) Calculated electric near-field distributions in a cross-section perpendicular to the top surface of the α-MoO3 flake at illumination frequencies of 914 and 776 cm−1, respectively.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/5/eaav8690/DC1

    Note S1. Theoretical model for calculating the isofrequency surface of the PhPs

    Note S2. Simulation of the dipole-launched PhP waves on the α-MoO3 surface

    Note S3. Simulation of the nanoantenna launched PhPs on the α-MoO3

    Note S4. Determination of the crystalline direction of a typical α-MoO3 flake

    Note S5. Simulation of the s-SNOM image using the phenomenological cavity model

    Note S6. Calculations on the complex reflectivity of the multilayer structure α-MoO3/SiO2

    Fig. S1. Schematic showing the isofrequency curves of the PhPs in the biaxial α-MoO3 flake.

    Fig. S2. Simulations of the dipole-launched hyperbolic PhPs on the α-MoO3 surface.

    Fig. S3. Propagation directions of the in-plane hyperbolic PhPs.

    Fig. S4. Silver nanoantenna-launched PhPs at various incidence frequencies.

    Fig. S5. Determination of the crystalline directions of the α-MoO3 by Raman spectroscopy.

    Fig. S6. Near-field optical images showing in-plane anisotropic PhPs characteristics of the α-MoO3.

    Fig. S7. Comparison of the experiment and simulation near-field images of the PhPs distributions illuminated by 986 cm−1 (Band 3).

    Fig. S8. Scheme of the multi-layered structure consisted of air/α-MoO3/SiO2.

    Fig. S9. Optical image of the α-MoO3 flake used for conducting the hyperspectral PiFM movies.

    Movie S1. Hyperspectral PiFM movie of the edge perpendicular to the [100] direction, which is adjacent to the corner 1 shown in fig. S9.

    Movie S2. Hyperspectral PiFM movie of the edge perpendicular to the [001] direction, which is in proximity of the corner 1 shown in fig. S9.

    Table S1. Parameters used in calculating the relative permittivities (Eq. S1).

  • Supplementary Materials

    The PDF file includes:

    • Note S1. Theoretical model for calculating the isofrequency surface of the PhPs
    • Note S2. Simulation of the dipole-launched PhP waves on the α-MoO3 surface
    • Note S3. Simulation of the nanoantenna launched PhPs on the α-MoO3
    • Note S4. Determination of the crystalline direction of a typical α-MoO3 flake
    • Note S5. Simulation of the s-SNOM image using the phenomenological cavity model
    • Note S6. Calculations on the complex reflectivity of the multilayer structure α-MoO3/SiO2
    • Fig. S1. Schematic showing the isofrequency curves of the PhPs in the biaxial α-MoO3 flake.
    • Fig. S2. Simulations of the dipole-launched hyperbolic PhPs on the α-MoO3 surface.
    • Fig. S3. Propagation directions of the in-plane hyperbolic PhPs.
    • Fig. S4. Silver nanoantenna-launched PhPs at various incidence frequencies.
    • Fig. S5. Determination of the crystalline directions of the α-MoO3 by Raman spectroscopy.
    • Fig. S6. Near-field optical images showing in-plane anisotropic PhPs characteristics of the α-MoO3.
    • Fig. S7. Comparison of the experiment and simulation near-field images of the PhPs distributions illuminated by 986 cm−1 (Band 3).
    • Fig. S8. Scheme of the multi-layered structure consisted of air/α-MoO3/SiO2.
    • Fig. S9. Optical image of the α-MoO3 flake used for conducting the hyperspectral PiFM movies.
    • Legends for movies S1 and S2.
    • Table S1. Parameters used in calculating the relative permittivities (Eq. S1).

    Download PDF

    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mp4 format). Hyperspectral PiFM movie of the edge perpendicular to the 100 direction, which is adjacent to the corner 1 shown in fig. S9.
    • Movie S2 (.mp4 format). Hyperspectral PiFM movie of the edge perpendicular to the 001 direction, which is in proximity of the corner 1 shown in fig. S9.

    Files in this Data Supplement:

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