Near-zero refractive index photonics

Journal name:
Nature Photonics
Year published:
Published online
Corrected online


Structures with near-zero parameters (for example, media with near-zero relative permittivity and/or relative permeability, and thus a near-zero refractive index) exhibit a number of unique features, such as the decoupling of spatial and temporal field variations, which enable the exploration of qualitatively different wave dynamics. This Review summarizes the underlying principles and salient features, physical realizations and technological potential of these structures. In doing so, we revisit their distinctive impact on multiple optical processes, including scattering, guiding, trapping and emission of light. Their role in emphasizing secondary responses of matter such as nonlinear, non-reciprocal and non-local effects is also discussed.

At a glance


  1. Tunnelling through distorted channels.
    Figure 1: Tunnelling through distorted channels.

    a, Conceptual sketch of stretching the wavelength (left) and power flow concentration (right) in waveguide channels filled with media with near-zero parameters. b,c, Power flow (real part of the Poynting vector field (b) normalized to its maximal value Smax) and snapshot of the magnetic field Hz obtained via numerical simulations (c; see Methods) for ENZ (ε 0, narrow channel, left), MNZ (μ 0, wide channel, centre) and EMNZ (ε 0 and μ 0, arbitrarily shaped channel, right) supercoupling/tunnelling effects. d, Experimental demonstrations of tunnelling, near-unity transmission coefficient T with zero phase advance, in waveguide set-ups. Left: ENZ tunnelling implemented by using a microwave metallic waveguide supporting the TE10 mode with cut-off frequency f10 = 1.47 GHz for relative permittivity εr = 1 (see Box I), and revealing full transmission independently of the length of the channel L; centre: MNZ coupling implemented by using a waveguide filled with split-ring resonators; right: sketch of the possible set-up for EMNZ coupling implemented by using a waveguide at cut-off filled with a dielectric rod (experimental results to be reported in a future publication). Figure adapted with permission from: d (left), ref. 16, APS; d (centre), ref. 19, APS.

  2. Highly directive emission and geometry-invariant phenomena.
    Figure 2: Highly directive emission and geometry-invariant phenomena.

    a, Numerical simulations (see Methods) of the 2D electric field magnitude, |Ez|, and normalized radiation intensity, Wrad(ϕ) = ½Re{E × H*}, excited by an insulated 2D current line source immersed in 2D EMNZ cylinders of rectangular and triangular cross-sections. The current line is insulated from the EMNZ medium by a vacuum circular cylinder. Highly directive beams are generated perpendicular to the sides of the EMNZ body. b, Experimental realization and measured radiation pattern based on a wire mesh fed by a monopole antenna at GHz frequencies. c, ENZ metallic lens (implemented as waveguides at cut-off) and measured electric field distribution, evidencing high directivity (centred case, top) and beamforming (displaced case, bottom). d, Sketch and numerical prediction (see Methods) of the electric and magnetic field distributions for 3D 'open' ENZ cavities containing a dielectric particle of relative permittivity εp and supporting a bound (non-radiating or embedded) eigenmode, independently of the geometry of the external boundary, which is touching the vacuum. Figure adapted with permission from: b, ref. 7, APS; c, ref. 30, IEEE.

  3. Nonlinear phenomena in structures with near-zero parameters.
    Figure 3: Nonlinear phenomena in structures with near-zero parameters.

    a, Phase matching in zero-index media leading to efficient four-wave mixing (FWM) in both the forward and backward directions. DFWM, degenerate four-wave mixing. Sketch (left), geometry (centre) and measured data (right) of the experimental realization with a fishnet metamaterial at near-infrared frequencies. The measured FWM signal in the forward (purple) and backward (blue) directions are shown (right). b, Strong nonlinear response in ENZ thin films. Measured nonlinear effective refractive index, n2(eff), and effective nonlinear attenuation constant, β(eff), of an ITO film of 310 nm thickness. The ENZ point ε(λp) 0 occurs at λp 1,240 nm, centre of the shaded region). c, Frozen light. Self-sustained 3D confinement of light in an ENZ medium with Kerr nonlinearity. Electric field iso-surface (left) and intensity distribution (centre) as well as dielectric permittivity profile (right) are shown. Blue plane (right) corresponds to the zero-permittivity points. All positions normalized with respect to the inverse of the wavevector at the plasma frequency kp−1. Figure adapted with permission from: a, ref. 64, AAAS; b, ref. 71, AAAS; c, ref. 85, under a Creative Commons licence (

  4. Different realizations of structures with near-zero parameters.
    Figure 4: Different realizations of structures with near-zero parameters.

    a, Continuous media including polaritonic materials such as SiC at mid-infrared frequencies (left), doped semiconductors such as transparent conducting oxides (TCOs) at near-infrared frequencies (centre) and topological insulators such as Bi1.5Sb0.5Te1.8Se1.2 (BSTS) at ultraviolet frequencies (right). b, Synthetic implementations including waveguides at cut-off (i), wire media (ii), multilayered structures (iii), arrays of dielectric rods (iv) and/or photonic crystals (v). c, Hybrid implementation of continuous and synthetic media such as dielectric particles immersed in a continuous ENZ medium. Figure adapted with permission from: a (left and centre), ref. 113, OSA; a (right), ref. 117, Macmillan Publishers Ltd.; b (i, SEM inset), ref. 36, APS; b (ii, SEM inset), ref. 95, APS; b (iii, SEM inset), ref. 128, Macmillan Publishers Ltd.; b (iv), ref. 22, Macmillan Publishers Ltd.; b (v), ref. 131, Macmillan Publishers Ltd.

Change history

Corrected online 06 March 2017
Owing to technical problems, this Review Article was published online later than the date given in the print version. The published date should read '1 March 2017', and is correct in the online versions.


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  1. Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

    • Iñigo Liberal &
    • Nader Engheta

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