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Schematic representation of α-MoO3 and graphene heterostructure on silicon substrate exhibiting the hybrid plasmon-phonon polariton modes propagation at the surface. Inset: crystallographic direction of α-MoO3 and φ-angle between plane of incidence of light and x-axis of the α-MoO3.

Schematic representation of α-MoO3 and graphene heterostructure on silicon substrate exhibiting the hybrid plasmon-phonon polariton modes propagation at the surface. Inset: crystallographic direction of α-MoO3 and φ-angle between plane of incidence of light and x-axis of the α-MoO3.

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The recent discovery of natural biaxial hyperbolicity in van der Waals crystals, such as $\alpha$-MoO\textsubscript{3}, has opened up new avenues for nanophotonics due to their deep subwavelength phonon-polaritons. However, a significant challenge is the lack of active tunability of these hyperbolic phonon polaritons. In this work, we investigate h...

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... this work, we present a platform for tunable HPPPs over a broad spectral region (from 545 cm −1 to 1100 cm −1 ) via integration of graphene with biaxial hyperbolic vdW thin film, i.e. α-MoO 3 , shown in Fig. 1. We investigate optical properties of air/graphene/α-MoO 3 /Si heterostructure using the well-known transfer matrix method (TMM) [30] as a function of chemical potential of graphene. Furthermore, we develop a framework by combining TMM with Green's dyadic function [31][32][33] to investigate anisotropic SERs from an electric dipole in ...
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... α-MoO 3 unit cell has lattice constants of around 0.396 nm, 0.369 nm, and 1.385 nm in the x, y, and z crystallographic directions [4] as shown in Fig. 1. The orthorhombic nature of the unit cell results in different sets of longitudinal optical (LO) and transverse optical (TO) phonons in the three crystallographic directions. The three sets of LO and TO phonons constitute three RBs in the mid-infrared spectral region, where α-MoO 3 exhibits natural biaxial hyperbolicity. Spectral ...
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... spectral region, where α-MoO 3 exhibits natural biaxial hyperbolicity. Spectral region for RB-1, RB-2, and RB-3 of α-MoO 3 lies in the range of 545 cm -1 -850 cm -1 , 820 cm -1 -972 cm -1 , and 958 cm -1 -1006 cm -1 respectively, where real part of dielectric permittivity is negative along y, x and z crystallographic directions, respectively (Fig. S1 of supplementary information) [34]. Since α-MoO 3 is a biaxial hyperbolic material, the dispersion of PhPs strongly depends on angle between plane of propagation of the polaritons and x− crystallographic direction as shown in Fig. 1 and represented by φ. We investigate the dispersion of PhPs of α-MoO 3 at φ = 0 • , 45 • and 90 • as ...
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... where real part of dielectric permittivity is negative along y, x and z crystallographic directions, respectively (Fig. S1 of supplementary information) [34]. Since α-MoO 3 is a biaxial hyperbolic material, the dispersion of PhPs strongly depends on angle between plane of propagation of the polaritons and x− crystallographic direction as shown in Fig. 1 and represented by φ. We investigate the dispersion of PhPs of α-MoO 3 at φ = 0 • , 45 • and 90 • as shown in Fig. 2(a)-(c). Here, the thickness of α-MoO 3 is chosen to be 50 nm, and the imaginary part of the Fresnel reflection coefficient for p− polarized light is plotted in frequency-momentum space. Fig. 2(a) reveals discrete modes ...
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... examine the hybridization of SPPs of graphene with hyperbolic PhPs of α-MoO 3 via modulation of chemical potential (µ) of graphene. We consider a heterostructure having the configuration: air/graphene/α-MoO 3 /silicon as shown in Fig. 1 and explore the dispersion of polaritons, shown in the Fig. 2. For µ = 0.025 eV and 0.05 eV, we observe smearing of hyperbolic PhP modes in all the RBs of α-MoO 3 (Figs. 2(d)-(i)), however, there are no significant changes in the dispersion of hyperbolic PhPs in the plotted range of wave-vectors. This is due to interband transition in ...
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... we explore the anisotropic SER enhancement from an electric dipole placed in the vicinity of graphene/α-MoO 3 /Si heterostructure, as shown in Fig. 1. To the best of our knowledge, anisotropic SERs for natural biaxial hyperbolic material have not been reported in the literature so far. Since α-MoO 3 exhibits in-plane hyperbolicity, we examine the anisotropic SERs by considering the polarization of the electric dipole along x−, y−, and z− directions. Distance of the electric dipole ...
Context 7
... this work, we present a platform for tunable HPPPs over a broad spectral region (from 545 cm −1 to 1100 cm −1 ) via integration of graphene with biaxial hyperbolic vdW thin film, i.e. α-MoO 3 , shown in Fig. 1. We investigate optical properties of air/graphene/α-MoO 3 /Si heterostructure using the well-known transfer matrix method (TMM) [30] as a function of chemical potential of graphene. Furthermore, we develop a framework by combining TMM with Green's dyadic function [31][32][33] to investigate anisotropic SERs from an electric dipole in ...
Context 8
... α-MoO 3 unit cell has lattice constants of around 0.396 nm, 0.369 nm, and 1.385 nm in the x, y, and z crystallographic directions [4] as shown in Fig. 1. The orthorhombic nature of the unit cell results in different sets of longitudinal optical (LO) and transverse optical (TO) phonons in the three crystallographic directions. The three sets of LO and TO phonons constitute three RBs in the mid-infrared spectral region, where α-MoO 3 exhibits natural biaxial hyperbolicity. Spectral ...
Context 9
... spectral region, where α-MoO 3 exhibits natural biaxial hyperbolicity. Spectral region for RB-1, RB-2, and RB-3 of α-MoO 3 lies in the range of 545 cm -1 -850 cm -1 , 820 cm -1 -972 cm -1 , and 958 cm -1 -1006 cm -1 respectively, where real part of dielectric permittivity is negative along y, x and z crystallographic directions, respectively (Fig. S1 of supplementary information) [34]. Since α-MoO 3 is a biaxial hyperbolic material, the dispersion of PhPs strongly depends on angle between plane of propagation of the polaritons and x− crystallographic direction as shown in Fig. 1 and represented by φ. We investigate the dispersion of PhPs of α-MoO 3 at φ = 0 • , 45 • and 90 • as ...
Context 10
... where real part of dielectric permittivity is negative along y, x and z crystallographic directions, respectively (Fig. S1 of supplementary information) [34]. Since α-MoO 3 is a biaxial hyperbolic material, the dispersion of PhPs strongly depends on angle between plane of propagation of the polaritons and x− crystallographic direction as shown in Fig. 1 and represented by φ. We investigate the dispersion of PhPs of α-MoO 3 at φ = 0 • , 45 • and 90 • as shown in Fig. 2(a)-(c). Here, the thickness of α-MoO 3 is chosen to be 50 nm, and the imaginary part of the Fresnel reflection coefficient for p− polarized light is plotted in frequency-momentum space. Fig. 2(a) reveals discrete modes ...
Context 11
... examine the hybridization of SPPs of graphene with hyperbolic PhPs of α-MoO 3 via modulation of chemical potential (µ) of graphene. We consider a heterostructure having the configuration: air/graphene/α-MoO 3 /silicon as shown in Fig. 1 and explore the dispersion of polaritons, shown in the Fig. 2. For µ = 0.025 eV and 0.05 eV, we observe smearing of hyperbolic PhP modes in all the RBs of α-MoO 3 (Figs. 2(d)-(i)), however, there are no significant changes in the dispersion of hyperbolic PhPs in the plotted range of wave-vectors. This is due to interband transition in ...
Context 12
... we explore the anisotropic SER enhancement from an electric dipole placed in the vicinity of graphene/α-MoO 3 /Si heterostructure, as shown in Fig. 1. To the best of our knowledge, anisotropic SERs for natural biaxial hyperbolic material have not been reported in the literature so far. Since α-MoO 3 exhibits in-plane hyperbolicity, we examine the anisotropic SERs by considering the polarization of the electric dipole along x−, y−, and z− directions. Distance of the electric dipole ...

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