Optical meta-atoms: Going nonlinear

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Science  27 Nov 2015:
Vol. 350, Issue 6264, pp. 1033-1034
DOI: 10.1126/science.aad7212

Nonlinear optics investigates the light-matter interactions in media, in which the dielectric polarization of the medium responds nonlinearly to the electric and/or magnetic field of the light. Materials with the potential for a large, fast, and broadband nonlinear response have been explored for decades; if realized, these would revolutionize nonlinear optics, leading to low-power, compact, and ultrafast applications. However, the materials now available are limited, either by relatively low nonlinear susceptibilities for ultrafast nonlinear processes or by slow response times attributable to photorefractive effect and thermal nonlinear phenomena. Moreover, growing demand for integration of multiple optoelectronic functionalities on a chip calls for nonlinear materials that are compatible with standard fabrication approaches, such as complementary metal-oxide semiconductor technology. Metamaterials have been predicted to enable a plethora of novel light-matter interactions, including magnetic nonlinear response, backward phase-matching, and the nonlinear mirror (13). Linear optical properties such as dielectric permittivity, magnetic permeability, and refractive index can be designed to be positive, negative, or even zero by properly tailoring various properties of meta-atoms (the unit cells of metamaterials). Engineering nonlinear properties of metamaterials beyond those available in nature may be feasible by judiciously designing their quantum, geometric, and topological properties (4).

A question of fundamental and practical importance that arises with these metamaterials is whether there is a limit to the nonlinear response characterized by macroscopic nonlinear susceptibilities or microscopic hyperpolarizabilities. Indeed, it has been shown that there are fundamental limits to the off-resonant, electronic, nonlinear optical response (5). However, the largest hyperpolarizabilities of the best molecules fall short of the fundamental limit by a factor of 103/2 (see the figure, panel A). Understanding of this discrepancy is still a subject of extensive research.

In parallel with the development of fundamental quantum models, a semi-empirical relationship (Miller's rule) has been proposed to estimate the nonlinear response from its linear counterpart (6). Because metamaterials gain their unique linear properties from their structural design, it is not obvious whether any generalized rules relating linear and nonlinear properties can be established. The initial studies of the second-order susceptibility of a plasmonic metasurface (see the figure, panel B) suggest that although Miller's rule may not provide accurate estimates, the nonlinear scattering theory approach does agree well with experimental results (7).

Nonlinearity at the limit.

(A) Normalized values from the literature (points), maximum limit (solid line), and apparent limit (dashed line). (B) Top: Schematic of the metamaterial array with unit cell gradually changing from a symmetric bar to an asymmetric U-shape. Bottom: Second-harmonic intensity as a function of the asymmetry ratio. (C) The ABC-sample cross section. (D) Left: Conduction band diagram of one period of an In0.53Ga0.47As/Al0.48In0.52As coupled quantum well structure designed for giant nonlinear response for second-harmonic generation. Right: Schematic of the unit cell of a semiconductor metasurface for second-harmonic generation.


To date, appreciable efforts have been devoted to enhancing the nonlinear optical response using various plasmonic metamaterials (8). However, a majority of these studies exploited local field enhancements rather than the actual design of the nonlinear optical response of meta-atoms. The local field enhancement inside each meta-atom leads to increased effective nonlinearity, but this comes at the expense of increased loss or decreased coherence length (9). Consequently, this approach might be useful for applications such as sensing, but not for ultrafast, low-power switching or wavelength conversion.

One of the first designs relying on the unique capabilities of metamaterials to enable effective nonlinear properties surpassing those of its ingredients was demonstrated by structuring three centrosymmetric dielectrics to realize nanolaminates exhibiting second-order nonlinearity not seen in any of the three components. Thin layers of A = Al2O3, B = TiO2, and C = HfO2 were arranged into a noncentrosymmetric ABC-stack such that the individual surface nonlinearities originating at the boundary of neighboring materials do not sum to zero (see the figure, panel C) (10). Following this approach, artificial unidimensional crystals with the main component of their nonlinear susceptibility tensor of about 5 pm/V, comparable to well-established materials, were reported (11). These dielectric nonlinear metamaterials were grown by atomic layer deposition, making them compatible with standard fabrication technologies.

A different approach to realizing strongly nonlinear metamaterials is based on quantum engineering of electronic intersubband transitions in electron-doped multi–quantum-well semiconductor heterostructures (12). By controlling the widths of wells and barriers in these structures, the transition energy and dipole moments between electron subbands can be tailored in order to maximize the quantum mechanical expression for a particular nonlinear process. By combining quantum electronic engineering of intersubband nonlinearities with electromagnetic engineering of plasmonic nanoresonators, an ultrathin, planarized, highly nonlinear, optical 400-nm-thick metasurface with nonlinear susceptibility greater than 5 × 104 pm/V for second-harmonic generation at 8 µm has been demonstrated (see the figure, panel D).

Meta-atoms are poised to empower new strategies for optimizing the nonlinear response. Breakthroughs in the field of fast and strongly nonlinear materials are likely to be achieved by combining the current advances in both classical and quantum theory of artificial nanostructures, pattern optimization, and understanding how topology and geometry affect the nonlinearities. If realized, such materials would revolutionize nonlinear optics, leading to low-power, compact, and ultrafast applications of nonlinear effects in optical communications, optical computing, image processing, and quantum optical devices.

References and Notes

  1. Acknowledgments: We appreciate discussions with the participants of the 2015 OSA Incubator workshop on Nonlinear Metamaterials and the support of the U.S. Army Research Office under award W911NF-15-1-0146 and Multidisciplinary University Research Initiative grant W911NF-11-0297.

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