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Register a new userLimits to the Optical Response of Graphene and 2D Materials
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2D materials provide a platform for strong light--matter interactions, creating wide-ranging design opportunities via new-material discoveries and new methods for geometrical structuring. We derive general upper bounds to the strength of such light--matter interactions, given only the optical conductivity of the material, including spatial nonlocality, and otherwise independent of shape and configuration. Our material figure of merit shows that highly doped graphene is an optimal material at infrared frequencies, whereas single-atomic-layer silver is optimal in the visible. For quantities ranging from absorption and scattering to near-field spontaneous-emission enhancements and radiative heat transfer, we consider canonical geometrical structures and show that in certain cases the bounds can be approached, while in others there may be significant opportunity for design improvement. The bounds can encourage systematic improvements in the design of ultrathin broadband absorbers, 2D antennas, and near-field energy harvesters.
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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, higher index directly leads to better devices with greater functionality. Although standard transparent materials have been limited to refractive indices smaller than 3 in the visible, recent metamaterials designs have achieved refractive indices above 5, accompanied by high losses, and near the phase transition of a ferroelectric perovskite a broadband index above 26 has been claimed. In this work, we derive fundamental limits to the refractive index of any material, given only the underlying electron density and either the maximum allowable dispersion or the minimum bandwidth of interest. The Kramers--Kronig relations provide a representation for any passive (and thereby causal) material, and a well-known sum rule constrains the possible distribution of oscillator strengths. In the realm of small to modest dispersion, our 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. Surprisingly, our bound shows a cube-root dependence on electron density, meaning that a refractive index of 26 over all visible frequencies is likely impossible. Conversely, for narrow-bandwidth applications, nature does not provide the highly dispersive, high-index materials that our bounds suggest should be possible. We use 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.
At visible and infrared frequencies, metals show tantalizing promise for strong subwavelength resonances, but material loss typically dampens the response. We derive fundamental limits to the optical response of absorptive systems, bounding the largest enhancements possible given intrinsic material losses. Through basic conservation-of-energy principles, we derive geometry-independent limits to per-volume absorption and scattering rates, and to local-density-of-states enhancements that represent the power radiated or expended by a dipole near a material body. We provide examples of structures that approach our absorption and scattering limits at any frequency, by contrast, we find that common antenna structures fall far short of our radiative LDOS bounds, suggesting the possibility for significant further improvement. Underlying the limits is a simple metric, $|chi|^2 / operatorname{Im} chi$ for a material with susceptibility $chi$, that enables broad technological evaluation of lossy materials across optical frequencies.
We show that standard approximations in nonlinear optics are violated for situations involving a small value of the linear refractive index. Consequently, the conventional equation for the intensity-dependent refractive index, $n(I) = n_0 + n_2 I$, becomes inapplicable in epsilon-near-zero and low-index media, even in the presence of only third-order effects. For the particular case of indium tin oxide, we find that the $chi^{(3)}$, $chi^{(5)}$ and $chi^{(7)}$ contributions to refraction eclipse the linear term; thus, the nonlinear response can no longer be interpreted as a perturbation in these materials. Although the response is non-perturbative, we find no evidence that the power series expansion of the material polarization diverges.
Photonic devices play an increasingly important role in advancing physics and engineering, and while improvements in nanofabrication and computational methods have driven dramatic progress in expanding the range of achievable optical characteristics, they have also greatly increased design complexity. These developments have led to heightened relevance for the study of fundamental limits on optical response. Here, we review recent progress in our understanding of these limits with special focus on an emerging theoretical framework that combines computational optimization with conservation laws to yield physical limits capturing all relevant wave effects. Results pertaining to canonical electromagnetic problems such as thermal emission, scattering cross sections, Purcell enhancement, and power routing are presented. Finally, we identify areas for additional research, including conceptual extensions and efficient numerical schemes for handling large-scale problems.
Resonant modes in metamaterials have been widely utilized to amplify the optical response of 2D materials for practical device applications. However, the high loss at the resonant mode severely hinders metamaterial applications. Here, we introduce a field-enhancement gain (FEG) factor to find the FEG mode for significantly improving light-matter interaction. As a demonstration, we experimentally compared the second harmonic generation enhancement of monolayer MoS2 induced by the optimal FEG and resonant modes in hyperbolic meta-structures. With the optimal FEG mode, we obtained an enhancement of 22145-fold and a conversion efficiency of 1.1*10-6 W-1, which are respectively one and two orders of magnitude higher than that previously reported of monolayer MoS2. A broadband high-FEG region over ~80 nm where the nonlinear enhancement is larger than that induced by the resonant mode is achieved. The concept of FEG factor is general to metamaterials, opening a new way for advancing their applications.
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