Maximized Frequency Doubling through the Inverse Design of Nonlinear Metamaterials.

The conventional process for developing an optimal design for nonlinear optical responses is based on a trial-and-error approach that is largely inefficient and does not necessarily lead to an ideal result. Deep learning can automate this process and widen the realm of nonlinear geometries and devices. This research illustrates a deep learning framework used to create an optimal plasmonic design for a nonlinear metamaterial. The algorithm produces a plasmonic pattern that can maximize the second-order nonlinear effect of a nonlinear metamaterial. A nanolaminate metamaterial is used as a nonlinear material, and plasmonic patterns are fabricated on the prepared nanolaminate to demonstrate the validity and efficacy of the deep learning algorithm. The optimal pattern produced yielded second-harmonic generation from the nanolaminate with normal incident fundamental light. The deep learning architecture applied in this research can be expanded to other optical responses and light-matter interaction processes.

Waveguide coupling via magnetic gratings with effective strips.

Gratings with complex multilayer strips are studied under inclined incident light. Great interest in these gratings is due to applications as input/output tools for waveguides and as subwavelength metafilms. The structured strips introduce anisotropy in the effective parameters, providing additional flexibility in polarization and angular dependences of optical responses. Their characterization is challenging in the intermediate regime between subwavelength and diffractive modes. The transition between modes occurs at the Wood's anomaly wavelength, which is different at different angle of incidence. The usual characterization with an effective film using permittivity ε and permeability µ has limited effectiveness at normal incidence but does not apply at inclined illumination, due to the effect of periodicity. The optical properties are better characterized with effective medium strips instead of an effective medium layer to account for the multilayer strips and the underlying periodic nature of the grating. This approach is convenient for describing such intermediate gratings for two types of applications: both metafilms and the coupling of incident waves to waveguide modes or diffraction orders. The parameters of the effective strips are retrieved by matching the spectral-angular map at different incident angles.

Self-Organized Freestanding One-Dimensional Au Nanoparticle Arrays.

One-dimensional Au nanoparticle arrays encapsulated within freestanding SiO2 nanowires are fabricated by thermal oxidation of Au-coated Si nanowires with controlled diameter and surface modulation. The nanoparticle diameter is determined by the Si nanowire diameter and Au film thickness, while the interparticle spacing is independently controlled by the Si nanowire modulation. The optical absorption of randomly oriented Au nanoparticle arrays exhibits a strong plasmonic response at 550 nm. Scanning transmission electron microscopy (STEM)-electron energy loss spectrum (EELS) of nanoparticle arrays confirmed the same plasmonic response and demonstrated uniform optical properties of the Au nanoparticles. The plasmonic response in the STEM-EELS maps is primarily confined around the vicinity of the nanoparticles. On the other hand, examination of the same nanowires by energy-filtered transmission electron microscopy also revealed significant enhancement in the plasmonic excitation in the regions in between the nanoparticles. This versatile route to synthesize one-dimensional Au nanoparticle arrays with independently tailorable nanoparticle diameter and interparticle spacing opens up opportunities to exploit enhanced design flexibility and cost-effectiveness for future plasmonic devices.

Multipolar interference for non-reciprocal nonlinear generation.

We show that nonlinear multipolar interference allows achieving not only unidirectional, but also non-reciprocal nonlinear generation from a nanoelement, with the direction of the produced light decoupled from the direction of at least one of the excitation beams. Alternatively, it may allow inhibiting the specified nonlinear response in a nanoelement or in its periodic arrangement by reversing the direction of one of the pumps. These general phenomena exploit the fact that, contrary to the linear response case, nonlinear magneto-electric interference stems from a combination of additive and multiplicative processes and includes an interference between various terms within the electric and magnetic partial waves themselves. We demonstrate the introduced concept numerically using an example of a plasmonic dimer geometry with realistic material parameters.

Deterministic Construction of Plasmonic Heterostructures in Well-Organized Arrays for Nanophotonic Materials.

Plasmonic heterostructures are deterministically constructed in organized arrays through chemical pattern directed assembly, a combination of top-down lithography and bottom-up assembly, and by the sequential immobilization of gold nanoparticles of three different sizes onto chemically patterned surfaces using tailored interaction potentials. These spatially addressable plasmonic chain nanostructures demonstrate localization of linear and nonlinear optical fields as well as nonlinear circular dichroism.

Forward and backward unidirectional scattering from plasmonic coupled wires.

We analyze the resonant electromagnetic response of sub-wavelength plasmonic dimers formed by two silver strips separated by a thin dielectric spacer and embedded in a uniform dielectric media. We demonstrate that the off-resonant electric and resonant, geometric shape-leveraged, magnetic polarizabilities of the dimer element can be designed to have close absolute values in a certain spectral range, resulting in a predominantly unidirectional scattering of the incident field due to pronounced magneto-electric interference. Switching between forward and backward directionality can be achieved with a single element by changing the excitation wavelength, with the scattering direction defined by the relative phases of the polarizabilities. We extend the analysis to some periodic configurations, including the specific case of a perforated metal film, and discuss the differences between the observed unidirectional scattering and the extraordinary transmission effect. The unidirectional response can be preserved and enhanced with periodic arrays of dimers and can find applications in nanoantenna devices, integrated optic circuits, sensors with nanoparticles, photovoltaic systems, or perfect absorbers; while the option of switching between forward and backward unidirectional scattering may create interesting possibilities for manipulating optical pressure forces.

Enhancing four-wave-mixing processes by nanowire arrays coupled to a gold film.

We consider the process of four-wave mixing in an array of gold nanowires strongly coupled to a gold film. Using full-wave simulations, we perform a quantitative comparison of the four-wave mixing efficiency associated with a bare film and films with nanowire arrays. We find that the strongly localized surface plasmon resonances of the coupled nanowires provide an additional local field enhancement that, along with the delocalized surface plasmon of the film, produces an overall four-wave mixing efficiency enhancement of up to six orders of magnitude over that of the bare film. The enhancement occurs over a wide range of excitation angles. The film-coupled nanowire array is easily amenable to nanofabrication, and could find application as an ultra-compact component for integrated photonic and quantum optic systems.

Nonlinear parameter retrieval from three- and four-wave mixing in metamaterials.

We present a generalized nonlinear susceptibility retrieval method for metamaterials based on transfer matrices and valid in the nondepleted pump approximation. We construct a general formalism to describe the transfer matrix method for nonlinear media and apply it to the processes of three- and four-wave mixing. The accuracy of this approach is verified via finite element simulations. The method is then reversed to give a set of equations for retrieving the nonlinear susceptibility. Finally, we apply the proposed retrieval operation to a three-wave mixing transmission experiment performed on a varactor loaded split ring resonator metamaterial sample and find quantitative agreement with an analytical effective medium theory model.