Fundamental Limits to the Refractive Index of Transparent Optical Materials

Abstract

Increasing the refractive index available for optical and nanophotonic systems opens new vistas for design, for applications ranging from broadband metalenses to ultrathin photovoltaics to high‐quality‐factor resonators. In this work, fundamental limits to the refractive index of any material are derived, given only the underlying electron density and either the maximum allowable dispersion or the minimum bandwidth of interest. In the realm of small to modest dispersion, the bounds are closely approached and not surpassed by a wide range of natural materials, showing that nature has already nearly reached a Pareto frontier for refractive index and dispersion. Conversely, for narrow‐bandwidth applications, nature does not provide the highly dispersive, high‐index materials that the bounds suggest should be possible. The theory of composites to identify metal‐based metamaterials that can exhibit small losses and sizeable increases in refractive index over the current best materials is used. Moreover, if the “elusive lossless metal” can be synthesized, it is shown that it would enable arbitrarily high refractive index in the high‐dispersion regime, nearly achieving the bounds even at refractive indices of 100 and beyond at optical frequencies.

Expanding the Photonic Palette: Exploring High Index Materials

“…Although relatively primitive, the picture presented so far very well describes the limits on the refractive indexes imposed by Nature. Indeed, the authors of a remarkable recent work 40 have performed an exhaustive search of the data on the refractive index and its dispersion dn/dω that confirmed eq 2. Furthermore, they have shown (based on the oscillator sum rule and the Kramer Kronig relation) that since, in agreement with eq 1, the only feasible way of enhancing the refractive index is to come close to the resonance, a strict constraint is placed on the refractive index and its dispersion, So, the possibility of getting a broadband large refractive index appears to be quite remote, but for many modern applications broadband operation is not necessary.…”

ℏω versus ℏk: dispersion and energy constraints on time-varying photonic materials and time crystals [Invited]

“…Specifically, changing the refractive index in time Δ𝑛(𝑡) always involves prodigious amounts of energy. One can recognize the scale of the effort required to change the refractive index by a large amount by first noting that the range of refractive indices for all materials in the visible-near IR range is rather small, somewhere between 1.4 and 3.4 [73]. Low-index materials, like SiO 2 , have bandgaps of about 10 eV, while high-index materials, such as GaAs or Si, have bandgaps of about 1 eV.…”

Mapping the Binding Energy of Layered Crystals to Macroscopic Observables

“…A passive material is causal and must obey the Kramers-Kronig relations. [29] If dielectric function is approximated as the sum of lossless Drude-Lorentz oscillator, then 𝜖 ∞ can be given as Equation (7): [30]…”