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We describe some of the properties of light propagation through a material for which the dielectric permittivity and hence the refractive index are nearly vanishing. Among other unusual optical properties, we find that such epsilon-near-zero (ENZ) materials display an extremely large nonlinear optical response, with important implications for the field of photonics.


The propagation of light is profoundly modified for a material for which the dielectric permittivity epsilon is nearly vanishing. In such a situation, the refractive index also nearly vanishes, and thus both the wavelength of light and the phase velocity of light become nearly infinite. Radiative processes also are strongly modified, with both the Einstein A and B coefficients being dependent on the refractive index of the material. We have recently found that nonlinear optical properties tend to be strongly enhanced in epsilon-near-zero (ENZ) materials [1]. For the case of indium-tin-oxide (ITO), we measured a huge value (10^6 times larger than that of fused silica) of the nonlinear coefficient n_2 with an ultrafast (sub picosecond) response time.  Moreover, the overall nonlinear change in refractive index can be as large as 0.8. In subsequent work, we fabricated a metasurface consisting of gold nanorods on an ITO substrate, and we have found that the nonlinear coefficient is further enhanced and can be controlled in both magnitude and sign [2].

The ultrastrong nonlinear response of ITO [3] and other transparent conducting oxides, such as aluminum-doped zinc oxide [4], suggests that ENZ materials will play a key role as a material platform for applications in the field of nanophotonics.  In this talk, we report on one of these applications, adiabatic wavelength conversion, enabled by the process of time refraction. Specifically, we have shown experimentally that the effect of time refraction is significantly enhanced in an ENZ material as a result of the rapidly varying, unit-order change in refractive index. We are able to impress a large and controllable translation of the frequency of a laser pulse by as much as 15 THz in passing through a thin sub-wavelength thick layer of ITO.  The effect is broadband in nature, that is, the central wavelength of the pump and degenerate probe can be tuned over a 500 nm range centered at 1240 nm. Various applications enabled by these results include octave-spanning frequency conversion, on-chip nonreciprocity, photonic time crystals, and topological physics in the time domain.


  1. Z. Alam, I. D. Leon, and R. W. Boyd, Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region, Science 352, 795 (2016).
  2. Z. Alam, S. A. Schulz, J. Upham, I. De Leon and R. W. Boyd, Large optical nonlinearity of nanoantennas coupled to an epsilon-near-zero material, Nature Photonics,12 79-83 (2018).
  3. Reshef, E. Giese, M. Z. Alam, I. D. Leon, J. Upham, and R. W. Boyd, Beyond the Perturbative Description of the Nonlinear Optical Response of low-Index Materials, Opt. Lett. 42, 3225 (2017
  4. Caspani, R. P. M. Kaipurath, M. Clerici, M. Ferrera, T. Roger, J. Kim, N. Kinsey, M. Pietrzyk, A. Di Falco, V. M. Shalaev, A. Boltasseva, and D. Faccio, Enhanced Nonlinear Refractive Index in ε-Near-Zero Materials, Phys. Rev. Lett. 116, 233901 
  5. Zhou, M. Z. Alam, M. Karimi, J. Upham, O. Reshef, C. Liu, A. E. Willner, and R. W. Boyd, Broadband frequency translation through time refraction in an epsilon-near-zero material, to appear in Nature Communications.


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How Light Behaves When the Refractive Index Vanishes - Robert Boyd (UOttawa)