New Horizons in Near-Zero Refractive Index Photonics and Hyperbolic Metamaterials

Abstract

The engineering of the spatial and temporal properties of both the electric permittivity and the refractive index of materials is at the core of photonics. When vanishing to zero, those two variables provide efficient knobs to control light-matter interactions. This Perspective aims at providing an overview of the state of the art and the challenges in emerging research areas where the use of near-zero refractive index and hyperbolic metamaterials is pivotal, in particular, light and thermal emission, nonlinear optics, sensing applications, and time-varying photonics.

Figure 1

(a) Classification of photonic materials according to their relative electric permittivity ε_r and relative magnetic permeability μ_r, exhibiting three NZI classes: ENZ class, MNZ class, and EMNZ class, inspired by refs ( and 25). (b) Uniform phase distribution and electrodynamical quantities reaching extremes values in NZI media. (c) Isofrequency surfaces in HMMs. Reproduced with permission from ref (11). Copyright 2013 Nature.

Figure 2

(a) Schematic depiction of a two-level system {|e⟩,|g⟩} with transition frequency ω₀ coupled to a continuum of photonic modes in a virtual cavity model both in (left) vacuum and in (right) a near-zero-index (NZI) medium that suppresses the spatial density of modes. (b) Purcell factor, PF = Γ_s/Γ₀, in one-dimensional (1D, left), two-dimensional (2D, center), and three-dimensional (3D, right) systems, mimicking NZI media with ENZ, MNZ, and EMNZ material properties. ω_NZI refers to the near-zero refractive index frequency crossing. Reproduced with permission from ref (20). Copyright 2020 ACS. (c) (Left) SEM image of a rectangular metallic waveguide effectively implementing a 1D ENZ medium at optical frequencies. (Center) Cathodoluminiscence (CL) intensity as a function of wavelength and emission point demonstrating position-independent properties at the effective ENZ wavelength. (Right) CL intensity for different waveguide widths confirming the emission enhancement at the ENZ wavelength. Reproduced with permission from ref (36). Copyright 2013 APS.

Figure 3

(a) Real part of the refractive index of a Drude-based material (blue) with ε_∞ = 4, τ = 6 fs, N = 8 × 10²⁰ cm^–3, whose effective mass m* is modulated via intraband nonlinear processes, resulting in a shift of the index curve (red), giving rise to a (b) change in refractive index. (c) Group index of the unmodulated Drude-based film, as shown in (a). The ENZ region is shaded blue, with the crossover wavelength indicated as a vertical line. (d) Strong index tuning in Al:ZnO films with ENZ near 1300 nm. Reproduced with permission from ref (94). Copyright 2016 APS. (e) Strong modulation of transmission in effective ENZ materials with crossover at 509 nm. Reproduced with permission from ref (96). Copyright 2020 APS. (f) Modulation of cavity reflection for the guided plasmonic mode, with a mode index near zero. Reproduced with permission from ref (97). Copyright 2020 Nature.

Figure 4

(a) Schematic of a conventional Kretschmann-like setup for plasmonic nanorod HMM biosensors and (b) their corresponding reflectance curves for different incident angles. Reproduced with permission from ref (144). Copyright 2009 Nature. The inset in (a) shows the electromagnetic field confinement in the volume of the nanorod array. Reproduced with permission from ref (145). Copyright 2022 OPG. (c) Illustration of a grating-coupler-based multilayer HMM biosensor with a fully integrated fluid flow channel. The inset shows a scanning electron microscopy image of the subwavelength gold diffraction grating on top of the HMM. (d) The reflectance spectra for the grating-coupler-HMM at different angles of incidence. Reproduced with permission from ref (146). Copyright 2016 Nature. The blue shift of resonance angles in (b) and (d) with increasing angle of incidence demonstrate that the VPP modes are guided modes. (e) Pictorial view of a MO-HMM comprising dielectric MO layers of bismuth–iron garnet (BIG) and Ag. (f) Fano-like TMOKE curves for the magnetoplasmonic structure in (e) when varying the superstrate refractive index from 1.333 to 1.337. Reproduced with permission from ref (149). Copyright 2022 ACS.

Figure 5

(a, b) All-optical switching of an ENZ plasmon resonance in ITO, showing subpicosecond amplitude modulation of a reflected signal produced by an ultrafast shift in its plasma frequency. Reproduced with permission from ref (192). Copyright 2021 Nature. (c, d) Illustration of a broadband frequency translation through time refraction in an ENZ material, and (e) its measurement in ITO for increasing pump intensities. (f) Experimental measurement (red) and theoretical prediction (blue) of double-slit time diffraction, produced by shining two pump pulses separated by a delay of (left) 800 fs and (right) 500 fs, resulting in different diffraction fringes. Reproduced with permission from ref (178). Copyright 2023 Nature. (g) Experimental (left) and theoretical (right) field intensities from a double-slit time diffraction as a function of frequency and slit separation, quantitatively compared in panel (h). (i) Time-dependence of (left) the electron temperature, (middle) real and (right) imaginary parts of the ITO permittivity under optical pumping via (purple) a 220 fs pulse at an intensity of 22 GW/cm², (orange) a 20 fs pulse at 161 GW/cm² and (magenta) 30 fs at 22 GW/cm², clearly predicting femtosecond-scale responses in ITO. Reproduced with permission from ref (190). Copyright 2023 APS.